these doctorat d’electronique thomas sÄlzer … · frequency domain is a promising candidate for...

Année 2004 N° d’ordre : D4-04

THESE

présentée devant l’Institut National des Sciences Appliquées de Rennes

en vue de l’obtention du

Doctorat d’Electronique

par Thomas SÄLZER

Transmission Strategies Employing Multiple Antennas for the

Downlink of Multi-Carrier CDMA Systems Techniques de transmission utilisant les antennes multiples pour la voie descendante

des systèmes multiporteuses à accès multiple par répartition de codes

Soutenue le 18 juin 2004 devant la commission d’examen:

Président: M. Jacques Citerne (Professeur à l’INSA de Rennes, France) Rapporteurs: M. Atílio Gameiro (Professeur à l’Universidade de Aveiro, Portugal) M. Alain Glavieux (Professeur à l’ENST Brest, France) Examinateurs: M. Joachim Speidel (Professeur à l’Universität Stuttgart, Allemagne) M. Khaled Fazel (Marconi Communications, Backnang, Allemagne) M. Damien Castelain (Mitsubishi Electric ITE-TCL, Rennes, France) M. David Mottier (Mitsubishi Electric ITE-TCL, Rennes, France)

Travail effectué à Mitsubishi Electric ITE-TCL Rennes (France) et à l’Institut für Nachrichtenübertragung, Universität Stuttgart (Allemagne)

Published version 3

Abstract Multi-Carrier CDMA (MC-CDMA) combining multi-carrier modulation and spreading in the frequency domain is a promising candidate for new air interfaces of future mobile radio systems. This scheme is robust to multipath propagation and allows a very flexible management of spectral resources. A further enhancement of this technology may be achieved by exploiting the spatial dimension of the radio channel through multiple antennas. The aim of this thesis is to explore the potential of multiple antenna technologies for a downlink system based on MC-CDMA in typical indoor and outdoor scenarios.

Accounting for the tight implementation constraints at the mobile terminal, we focus on a light receiver design comprising a single antenna and single-user detection schemes. Based on the assumption that the basestation transmitter has some a priori channel knowledge at its disposal, different transmission strategies are developed and compared. Space-frequency transmit filtering is proposed for the case where instantaneous knowledge of the channel fading is available at the basestation, which is typical for time division duplex systems in indoor environments. This approach can optimally exploit the spatial diversity of the channel and efficiently mitigate the multiple access interference. When only covariance knowledge is available, e.g. in outdoor environments, we propose transmit beamforming with direction-based spreading code assignment. This technique benefits from the antenna gain and from an implicit reduction of the interference. The proposed strategies are compared and validated in typical indoor and outdoor scenarios, which account for imperfect channel knowledge at the basestation due to Doppler variations.

Simulation results highlight that the proposed approaches can significantly enhance the system performance in the respective scenarios compared to a conventional single-antenna system. Both transmission strategies employing low-complexity single-user detection at the receiver can outperform the conventional system with optimum linear multi-user detection. In this way, they lead to an increased user capacity and simultaneously allow a transfer of implementation complexity from the mobile terminal to the basestation.

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Résumé La transmission multiporteuse à accès multiple par répartition de codes (MC-CDMA) est un candidat prometteur pour les nouvelles interfaces radio des futurs systèmes radio-mobiles. Cette technique est robuste face à la propagation par trajets multiples et permet une gestion très flexible de la ressource spectrale. Les techniques d’antennes multiples peuvent encore améliorer ce système grâce à l’utilisation de la dimension spatiale du canal radio. L’objectif de cette thèse est d’explorer le potentiel des techniques d’antennes multiples en voie descendante d’un système utilisant le MC-CDMA.

Notre étude tient compte des contraintes de mise en œuvre au niveau du terminal mobile. En conséquence, nous considérons une architecture peu complexe comportant une seule antenne de réception et des techniques de détection mono-utilisateur. Dans l’hypothèse où l’émetteur de la station de base dispose d’une certaine connaissance à priori sur le canal de transmission, nous développons et comparons plusieurs stratégies de transmission. Le pré-filtrage spatio-fréquentiel, est proposé pour le cas où l’émetteur dispose d’une connaissance instantanée des évanouissements du canal. Ce cas de figure est typique pour les systèmes à duplexage temporel dans un environnement intérieur. Dans ce cas, la technique proposée permet de bénéficier de manière optimale de la diversité spatiale du canal et de réduire efficacement l’interférence d’accès multiple. Si seule la connaissance de la covariance spatiale du canal est disponible à l’émission, par exemple dans un environnement extérieur, nous proposons la formation de voies avec répartition directionnelle des codes d’étalement. Cette technique profite du gain d’antennes et d’une réduction implicite de l’interférence d’accès multiple. Les deux approches sont ensuite comparées et validées dans des scénarios typiques en tenant compte d’une connaissance imparfaite du canal à l’émission.

Les résultats de simulations mettent en évidence l’amélioration considérable des performances obtenues avec les techniques proposées par rapport au système conventionnel mono-antenne. Les deux stratégies de transmission utilisant des techniques de détection mono-utilisateur peu complexes à la réception peuvent atteindre des performances supérieures à celles du système conventionnel avec une détection multi-utilisateur linéaire optimale. Ainsi, elles augmentent la capacité en terme de nombre d’utilisateurs tout en permettant un transfert de la complexité algorithmique du terminal vers la station de base.

Published version 7

Acknowledgements

Above all, it’s difficult to overstate my gratitude towards Dr. David Mottier for his continuous support, advice, and encouragement. Without his commitment, this work would not have been possible. Keep calling me whenever your are looking for a beer starting with a “W”.

I would also like to thank all colleagues of Mitsubishi Electric ITE-TCL. There was always an open door whenever I needed technical advice or help with French administration. I’m particularly grateful to Damien Castelain and the whole digital communications team for the enriching technical discussions. Many thanks also to the members of the daily lunch charter for all the things they taught me about French language, culture, and laces.

I am grateful to Prof. Joachim Speidel for his supervision and for giving me the opportunity to work at his department. Many thanks to all colleagues from Stuttgart for their support and the nice atmosphere they made me share. With you it was really fun to transmit the OFDM !

I would like to gratefully acknowledge the supervision and support of Prof. Jacques Citerne. Many thanks to Prof. Atílio Gameiro, Prof. Alain Glavieux and Dr. Khaled Fazel for reviewing my thesis and for their valuable comments.

Table of contents

Published version 9

Table of contents Abstract................................................................................................................................. 3 Résumé................................................................................................................................. 5 Acknowledgements .............................................................................................................. 7 Table of contents.................................................................................................................. 9 1 Introduction..................................................................................................................15

1.1 The future of wireless mobile communications....................................................................... 15 1.2 Multi-Carrier CDMA (MC-CDMA) .......................................................................................... 16 1.3 Multiple antenna techniques and receiver-oriented systems .................................................. 18 1.4 Content and major achievements of this thesis ....................................................................... 19

2 Modelling of mobile radio systems and channels........................................................21 2.1 Transmission chain of cellular communication systems......................................................... 21 2.2 The mobile radio channel............................................................................................................ 24

2.2.1 The fast fading channel model and its characteristic functions..................................... 25 2.2.2 Delay spread and frequency selectivity.............................................................................. 26 2.2.3 Doppler spread and time selectivity................................................................................... 28 2.2.4 Vector channel modelling ................................................................................................... 29 2.2.5 Angle spread and space-selective fading ........................................................................... 30 2.2.6 Channel fading statistics ......................................................................................................32 2.2.7 Propagation environments .................................................................................................. 33

2.3 Practical channel modelling......................................................................................................... 34 2.3.1 The HIPERLAN/2 model and its vector extension....................................................... 35 2.3.2 The 3GPP/3GPP2 Spatial Channel Model...................................................................... 36

2.4 Multiple access techniques .......................................................................................................... 36 2.4.1 Duplexing .............................................................................................................................. 36 2.4.2 Multiple access schemes ...................................................................................................... 38

2.5 Orthogonal Frequency Division Multiplex (OFDM) ............................................................. 39 2.5.1 OFDM basics........................................................................................................................ 39 2.5.2 Frequency domain channel ................................................................................................. 42

3 The Multi-Carrier CDMA system................................................................................ 45 3.1 Transmitter structure ................................................................................................................... 45

3.1.1 Downlink signal .................................................................................................................... 46 3.1.2 Synchronised uplink signal .................................................................................................. 46 3.1.3 Spreading ............................................................................................................................... 47 3.1.4 Chip mapping........................................................................................................................ 48

3.2 Receiver structure and detection algorithms ............................................................................ 49 3.2.1 Single-User Detection.......................................................................................................... 50

3.2.1.1 Maximum Ratio Combining ....................................................................................... 50 3.2.1.2 Equal Gain Combing ................................................................................................... 50 3.2.1.3 Orthogonality Restoring Combining......................................................................... 51 3.2.1.4 Minimum Mean Squared Error Combining ............................................................. 51

3.2.2 Multi-User Detection ........................................................................................................... 52 3.2.2.1 Maximum Likelihood detection ................................................................................. 52 3.2.2.2 Linear multi-user detection ......................................................................................... 52 3.2.2.3 Interference Cancellation ............................................................................................ 53

3.3 Channel estimation....................................................................................................................... 54 3.3.1 Pilot-symbol based channel estimation ............................................................................. 54

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3.3.2 One-dimensional Wiener-filter design .............................................................................. 57 3.3.3 Pilot-based estimation for the synchronous uplink......................................................... 58

3.4 Pre-equalisation for the uplink ................................................................................................... 59 3.5 Performance of the conventional single-antenna system....................................................... 61

3.5.1 Simulation scenarios ............................................................................................................ 61 3.5.2 Single-user performance and theoretical bounds ............................................................ 62 3.5.3 Multi-user performance in the downlink .......................................................................... 63 3.5.4 Multi-user performance in the synchronised uplink ....................................................... 65 3.5.5 Impact of channel estimation in the downlink ................................................................ 65

3.6 Multiple antenna concepts .......................................................................................................... 68 3.6.1 Spatial multiplexing.............................................................................................................. 69 3.6.2 Diversity schemes and space-time coding ........................................................................ 69 3.6.3 Spatial filtering ...................................................................................................................... 71 3.6.4 Channel estimation with multiple transmit antennas...................................................... 72

3.7 Conclusion and choices for this work....................................................................................... 73 4 Space-Frequency Transmit Filtering .......................................................................... 75

4.1 Principles of multi-user pre-filtering ......................................................................................... 75 4.2 System model ................................................................................................................................ 76 4.3 Single-user criteria ........................................................................................................................ 78

4.3.1 Optimum single-user bound............................................................................................... 78 4.3.1.1 Optimisation of transmit and receive weights in frequency .................................. 79 4.3.1.2 Optimisation of transmit weights in space............................................................... 80 4.3.1.3 Optimisation of transmit and receive weights in space and frequency................ 81

4.3.2 Joint Maximum Ratio Transmission (J-MRT) ................................................................. 81 4.3.3 Per-Carrier Maximum Ratio Transmission (PC-MRT) .................................................. 82

4.4 Multi-user criteria ......................................................................................................................... 82 4.4.1 Joint Zero Forcing (J-ZF) ................................................................................................... 82 4.4.2 Joint Maximisation of the SINR (J-MSINR).................................................................... 84 4.4.3 Per-carrier multi-user criteria.............................................................................................. 85

4.5 Comparison of SFTF approaches.............................................................................................. 86 4.5.1 Analysis of the transmit filter responses in space and frequency.................................. 86 4.5.2 Simulation scenarios ............................................................................................................ 88 4.5.3 Single-user performance and diversity .............................................................................. 89 4.5.4 Multi-user performance with chip interleaving................................................................ 91 4.5.5 Multi-user performance with adjacent chip mapping ..................................................... 94 4.5.6 System overloading by code reallocation.......................................................................... 95

4.6 Conclusion on Space-Frequency Transmit Filtering............................................................... 97 5 Transmit beamforming ............................................................................................... 99

5.1 Beamforming in wireless multi-user communications............................................................ 99 5.2 System Model.............................................................................................................................. 100 5.3 Beamforming principles ............................................................................................................ 102

5.3.1 Spatial sampling theorem .................................................................................................. 102 5.3.2 Classical beamforming approaches.................................................................................. 103

5.3.2.1 Criteria for small angle spreads ................................................................................ 103 5.3.2.2 Criteria for large angle spreads ................................................................................. 104 5.3.2.3 Assessment of spatial responses .............................................................................. 105

5.3.3 Wideband beamforming aspects ...................................................................................... 106 5.3.3.1 Coherent wideband array processing ...................................................................... 107 5.3.3.2 Evaluation of the performance loss with frequency compensation ................... 109

5.4 Transmit beamforming criteria for the MC-CDMA downlink ........................................... 111 5.4.1 Spatial covariance matrices in multi-carrier systems ..................................................... 111

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5.4.2 Single-user criterion............................................................................................................113 5.4.3 Multi-user criterion.............................................................................................................114

5.5 Direction-based spreading code assignment ..........................................................................116 5.5.1 Code assignment in the conventional single-antenna system ......................................116 5.5.2 Direction-based code allocation with transmit beamforming .....................................117

5.6 Comparison of beamforming approaches ..............................................................................119 5.6.1 Simulation scenarios...........................................................................................................119 5.6.2 Single-user performance....................................................................................................120 5.6.3 Multi-user performance .....................................................................................................121 5.6.4 Direction-based spreading code assignment ..................................................................123 5.6.5 Comparison of robust beamforming approaches..........................................................125

5.7 Conclusion on transmit beamforming ....................................................................................126 6 System comparison.....................................................................................................129

6.1 Channel coding and decoding ..................................................................................................129 6.1.1 Convolutional coding.........................................................................................................129 6.1.2 Soft de-mapping and Log-Likelihood Ratio...................................................................131

6.2 Impact of imperfect channel knowledge due to mobility.....................................................132 6.3 Performance analysis..................................................................................................................133

6.3.1 Simulation scenarios...........................................................................................................133 6.3.2 Coded performance with perfect channel knowledge ..................................................134 6.3.3 Uncoded performance with imperfect channel knowledge at the basestation..........137 6.3.4 Coded performance with imperfect channel knowledge at the basestation ..............139

6.4 Open issues .................................................................................................................................142 6.4.1 Uplink channel estimation.................................................................................................142 6.4.2 Channel reciprocity ............................................................................................................143 6.4.3 Downlink channel estimation...........................................................................................143

6.5 Conclusions .................................................................................................................................143 7 Conclusions and prospects.........................................................................................145 A Appendix.....................................................................................................................149

A.1 Some channel correlation functions ........................................................................................149 A.1.1 Time correlation and Doppler spectrum ........................................................................149 A.1.2 Spatial correlation and coherence distance .....................................................................150

A.2 Power delay profiles of HIPERLAN/2 models [Med98b] ..................................................151 A.2.1 Channel model A................................................................................................................151 A.2.2 Channel model E................................................................................................................152

A.3 Existence and generation of Hadamard matrices ..................................................................152 A.4 Simplification of the J-MSINR expression .............................................................................153 A.5 Numerical results with the MATRICE simulation chain .....................................................155

A.5.1 Simulation scenarios...........................................................................................................155 A.5.2 Spatial channel properties and parameters .....................................................................155 A.5.3 Results ..................................................................................................................................156

Symbols .............................................................................................................................159 Acronyms...........................................................................................................................163 References .........................................................................................................................165 Publications of the author .................................................................................................172 Patents of the author .........................................................................................................172

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Figures Fig. 1.1: Complement-type vision adopted in MC-CDMA research [MATRICE]. .........................................18 Fig. 1.2: Approaches for exploiting the spatial dimension. ..................................................................................18 Fig. 2.1: Overview of the physical layer. ..................................................................................................................21 Fig. 2.2: Complex symbol constellations. ................................................................................................................22 Fig. 2.3: Example of an outdoor propagation environment. ...............................................................................25 Fig. 2.4: Channel impulse response and transfer function. ..................................................................................26 Fig. 2.5: Uniform array geometries. ..........................................................................................................................29 Fig. 2.6: Spatial correlation.........................................................................................................................................32 Fig. 2.7: Power delay spectrum of HIPERLAN/2 channel model E [Med98b]. .............................................35 Fig. 2.8: Duplex modes...............................................................................................................................................37 Fig. 2.9: Multiple access schemes..............................................................................................................................38 Fig. 2.10: Principle of SDMA....................................................................................................................................39 Fig. 2.11: Power density spectrum of OFDM. .......................................................................................................40 Fig. 2.12: Insertion of a guard interval. ....................................................................................................................41 Fig. 2.13: Frequency domain channel representation. ...........................................................................................42 Fig. 2.14: OFDM time-frequency frame representation. ......................................................................................43 Fig. 3.1: General structure of the MC-CDMA transmitter at the basestation...................................................45 Fig. 3.2: Chip mapping schemes. ..............................................................................................................................48 Fig. 3.3: MC-CDMA receiver structure with linear detection..............................................................................49 Fig. 3.4: Parallel interference cancellation with hard decision..............................................................................54 Fig. 3.5: Pilot symbol grids.........................................................................................................................................55 Fig. 3.6: Example of a 5-tap Wiener filter. ..............................................................................................................57 Fig. 3.7: Example for an uplink pilot grid. ..............................................................................................................59 Fig. 3.8: Terminal transmitter with pre-equalisation..............................................................................................59 Fig. 3.9: Single-user performance bounds (MRC, K=1). ......................................................................................63 Fig. 3.10: Downlink performance of the fully-loaded system (K=L=32, interl., channel E). ........................64 Fig. 3.11: Downlink performance as a function of system load (adjac./interl., channel E)............................64 Fig. 3.12: Uplink performance for half load (K=16, adjac./interl., channel E). ...............................................65 Fig. 3.13: MSE performance of fixed Wiener filter design (channel E, NPF=4). ..............................................66 Fig. 3.14: Downlink performance with channel estimation errors (K=16, interl., channel E).......................67 Fig. 3.15: MIMO system structure............................................................................................................................68 Fig. 3.16: OFDM system with delay diversity.........................................................................................................70 Fig. 3.17: Transmitter structure with space-time coding.......................................................................................71 Fig. 3.18: Receiver structure with space-time decoding. .......................................................................................71 Fig. 3.19: Spatial filtering approaches applied to OFDM. ....................................................................................72 Fig. 4.1: MC-CDMA downlink system with Space Frequency Transmit Filtering (SFTF).............................76 Fig. 4.2: Pre-filtering in frequency or space for a single user. ..............................................................................79 Fig. 4.3: Transmit filter responses in space and frequency...................................................................................87 Fig. 4.4: Single-user performance of SFTF and theoretical bounds (K=1, L=16, interl.)...............................90 Fig. 4.5: Single-user performance of SFTF with different chip mapping (K=1, L=16)..................................90 Fig. 4.6: Multi-user perf. with pre-equalisation in frequency only (K=16, M=1, L=16, interl.).....................91 Fig. 4.7: Multi-user perf. of joint SFTF approaches (K=16, L=16, interl.). ......................................................92 Fig. 4.8: Multi-user perf. of per-carrier SFTF approaches (1) (K=16, M=4, L=16, interl.)............................93 Fig. 4.9: Multi-user perf. of per-carrier SFTF approaches (2) (K=8, M=8, L=8, interl.). ...............................93 Fig. 4.10: Multi-user perf. of joint SFTF approaches (K=16, L=16, adjac.). ....................................................94 Fig. 4.11: Influence of antenna spacing on SFTF perf. (K=16, M=4, L=16, adjac., channel E, AS 30°). ...95 Fig. 4.12: Tolerable system load with code reallocation (L=16, interl.). ............................................................96 Fig. 5.1: MC-CDMA downlink system with transmit beamforming. .............................................................. 101 Fig. 5.2: Spatial resp. for a small angle spread (UCA, M=12, 1 desired DOA, 5 interfering DOAs)......... 105 Fig. 5.3: Spatial resp. for a large angle spread (UCA, M=12, 2 desired DOAs, 4 interfering DOAs)........ 106 Fig. 5.4: Spatial re-sampling. ................................................................................................................................... 108 Fig. 5.5: Example of spatial responses with frequency compensation. ........................................................... 109 Fig. 5.6: Performance loss with frequency compensation. ................................................................................ 110 Fig. 5.7: MAI with transmit beamforming. .......................................................................................................... 116

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Fig. 5.8: Direction-based assignment of Walsh-Hadamard codes. ................................................................... 118 Fig. 5.9: Single-user perf. of beamforming with chip interleaving (K=1, M=4, L=16)................................ 120 Fig. 5.10: Single-user perf. of beamforming with adjacent chip mapping (K=1, M=4, L=16). .................. 121 Fig. 5.11: Multi-user perf. of beamforming with chip interleaving (K=16, M=4, L=16)............................. 121 Fig. 5.12: Multi-user perf. of beamforming with adjacent chip mapping (K=16, M=4, L=16). ................. 122 Fig. 5.13: Comparison of SU-BF and MU-BF (K=8, M=8, L=16, interl., AS 10°). ..................................... 123 Fig. 5.14: Perf. of SU-BF-inst with direction-based code assignment (K=16, M=4, L=32, adjac.). .......... 124 Fig. 5.15: Perf. of SU-BF-inst with direct.-based code assignm. as a function of load (L=32, adjac.). ...... 124 Fig. 5.16: Perf. of SU-BF-inst with code reallocation (L=16, adjac.)............................................................... 125 Fig. 5.17: Perf. comparison of robust SU-BF approaches (K=16, M=4, L=16, adjac.).............................. 126 Fig. 6.1: Convolutional encoder, RC=1/2............................................................................................................. 130 Fig. 6.2: Punctured convolutional coding and decoding.................................................................................... 130 Fig. 6.3: Delay between estimation and usage of CSI in TDD systems. ......................................................... 132 Fig. 6.4: Relation between correlation and velocity for Τu =1 ms. .................................................................... 133 Fig. 6.5: Perf. of SFTF with channel coding and adjacent chip mapping (M=4, channel E, AS 120°)...... 135 Fig. 6.6: Perf. of SFTF with channel coding and chip interleaving (M=4, channel E, AS 120°). ............... 135 Fig. 6.7: Perf. of SU-BF with channel coding for AS 10° (M=4, adjac., channel E, opt. assignment)....... 136 Fig. 6.8: Perf. of SU-BF with channel coding for AS 30° (M=4, adjac., channel E, opt. assignment)....... 137 Fig. 6.9: Perf. of SFTF with imperfect CSI (M=4, adjac., channel E, AS 120°). ........................................... 138 Fig. 6.10: Perf. of SU-BF with imperfect CSI (M=4, adjac., channel E, AS 30°, rand. assignment). ......... 138 Fig. 6.11: Perf. of SFTF and SU-BF-inst (opt. assignment) in the indoor scenario

(M=4, adjac., channel A, AS 120°). ............................................................................................................. 140 Fig. 6.12: Perf. of SFTF and SU-BF-inst (opt. assignment) in the indoor scenario

(M=4, K=16, interl., channel E, AS 120°). ................................................................................................ 140 Fig. 6.13: Perf. of SFTF and SU-BF-inst (opt. assignment) in the outdoor scenario

(M=4, K=16, adjac., channel E, AS 30°).................................................................................................... 141 Fig. 6.14: Perf. of SU-BF in the outdoor scenario

(M=4, K=16, adjac., channel E, AS 30°, opt. assignment)...................................................................... 142 Fig. A.1: Single-user perf. of J-MSINR with MATRICE chain (K=1)............................................................ 157 Fig. A.2: Perf. of J-MSINR with MATRICE chain (K=8). ............................................................................... 158 Fig. A.3: Perf. of J-MSINR with MATRICE chain (K=16).............................................................................. 158

Tables Tab. 1.1: Selected references on MC-CDMA. ...................................................................................... 17 Tab. 2.1: Typical channel characteristics for different environments at 5 GHz.................................... 33 Tab. 2.2: System considerations............................................................................................................ 34 Tab. 2.3: Parameters of a well designed OFDM system. ...................................................................... 41 Tab. 3.1: Simulation parameters for the conventional system. ............................................................. 61 Tab. 3.2: Alamouti scheme. .................................................................................................................. 70 Tab. 4.1: Simulation parameters for response analysis. ........................................................................ 86 Tab. 4.2: Simulation parameters for SFTF............................................................................................ 89 Tab. 4.3: Comparison of SFTF approaches........................................................................................... 97 Tab. 5.1: Example for parameters of a future wideband system. ........................................................ 107 Tab. 5.2: Simulation parameters for transmit beamforming. .............................................................. 119 Tab. 5.3: Appellations of the different versions of the covariance matrix. ......................................... 119 Tab. 5.4: Properties of single-user beamforming approaches. ............................................................ 127 Tab. 6.1: Puncturing patterns for convolutional code (G1=171, G2=133, KC=7, R’C=1/2) [IEEE99]. 130 Tab. 6.2: Simulation parameters for the system comparison. ............................................................. 134 Tab. A.1: Power delay profile of channel A........................................................................................ 151 Tab. A.2: Power delay profile of channel E. ....................................................................................... 152 Tab. A.3: Simulation parameters for MATRICE chain. ..................................................................... 155 Tab. A.4: Channel parameters for MATRICE chain........................................................................... 156


1 Introduction

1.1 The future of wireless mobile communications

‘What will mobile wireless communications be like in the future ?’ – At the end of the last century the answers to this question seemed quite obvious: ‘Higher bit rates, better coverage, more subscribers !’. This is basically a continuous view of the way peoples’ lives were conquered by mobile wireless technology during the preceding century.

Since the first experiments on electromagnetic waves carried out by H. Hertz in 1886, which were rapidly followed by the demonstration of their potential for wireless communications by G. Marconi, the evolution of wireless technology had been marked by an enormous progress. The first successful commercial application of wireless technology was broadcasting. The arrival of radio and television already lead to a considerable change in daily life. The next milestone was the commercialisation of wireless cellular systems for personal communications in the 1980s. Here, various analogue standards can be cited such as the C-450 in Germany, Radiocom2000 in France, the Advanced Mobile Phone System (AMPS) in the USA, and the Nippon Telephone and Telegraph (NTT) system in Japan. About ten years later, this first generation of mobile cellular systems was followed by the second generation comprising the following standards: Global System for Mobile communications (GSM) in Europe, Interim Standard (IS-) 54 in the USA, and Personal Digital Cellular (PDC) in Japan [Rap02]. This second generation (2G) is characterised by the paradigm shift from analogue to digital technology. The progress in digital technology made the 2G systems ready for the mass market with current penetration rates up to 80% and more in Western Europe. The next paradigm shift from purely voice oriented systems to data transmission seemed also programmed within a ten-years-step. Besides the extensions of 2G systems, e.g. General Packet Radio Service (GPRS) and Enhanced Data rates for GSM Evolution (EDGE), new data services with rates up to 2 Mbit/s are to be provided by the third generation (3G) standards called Universal Mobile Telecommunications System (UMTS) by the European Telecommunications Standard Institute (ETSI) and International Mobile Telecommunications 2000 (IMT-2000) by the International Telecommunications Union (ITU). This system and its evolutions are currently standardised by in the Third Generation Partnership Project (3GPP) [3GPP]. Commercial cellular systems based on 3G technology were first launched in Japan in 2001 but are still in their trial phase in most European countries at the time being. In parallel, Wireless Local Area Network (WLAN) standards, e.g. IEEE802.11a [IEEE99], IEEE802.16a [IEEE03], and HIPERLAN/2 [ETSI01], providing high-speed data services with rates up to 54 Mbit/s in a limited range and the Bluetooth standard with rates around 500 kbit/s for very short range communications have come to their maturity [Cha01].

At the beginning of this new millennium, the paradigm shift from 2G (voice) to 3G (data services) is achieved at the technology level but not yet in the commercialisation. Furthermore, the industry of telecommunications and information technology suffers from a general downturn,

Boy, you guys in sales are all the same. You remind me of the farmer in 1850.If you asked him what he wanted, he would say he wanted a horse that was

half as big and ate half as many oats and was twice as strong. And there would be no discussion of a tractor.

(David T. Kearns, former CEO of Xerox)

Chapter 1: Introduction


which drastically shows that an enhanced technology is not the only key for the success of wireless communications. So, keeping this in mind, we can again ask the question about the future of mobile wireless communications: Will there be a new paradigm shift to 4G? What will future systems look like? Finding answers to this question is the aim of research forums, e.g. the Wireless World Research Forum (WWRF) [WWRF01] and standardisation bodies, e.g. ETSI and ITU [ITU-R03]. In its book of visions [WWRF01], the WWRF adopted a user-centred approach based on the possible ways a user may interact with wireless systems. This view shall provide a support for the identification of new services and applications and associate them with emerging technologies. In the user-centred approach, the user is surrounded by several spheres representing the systems with which he may want to interact. These spheres range from its personal devices (headset, watch, cellular phone,…) over different LAN environments (home, office,…) to a nationwide cellular network. Already from this view, it can be concluded that the convergence of systems and their interconnectivity will be one of the major issues to be solved in the future. Trends in this direction are the generalisation of the Internet Protocol (IP) for mobile applications [IPv6-forum] enabling a convergence on the protocol layer, Software Defined Radio (SDR) [SDR-forum] facilitating the reconfigurability of devices, and ad-hoc networking [HuGr01].

Concerning new air interfaces, flexibility is obviously a key property [ITU-R03][WINNER]. New air interfaces should be able to provide a seamless service between different environments, e.g. indoor and outdoor environments. Furthermore, new physical layers should support the transmission of several bit streams with different Quality of Service (QoS). This implies a shift from a classical channel-switched system suited for voice to a packet-switched system, which is only partially realised in current 3G systems. The data rates for future systems may range from 10 Mbit/s for high speed with wide area coverage to 1 Gbit/s in static short range scenarios [ITU-R03]. Here, a future system should be suited for asymmetric traffic and achieve the very high peek data rates required by download applications. Among the various technologies currently considered for meeting these requirements, several key research topics seem particularly promising: Fast adaptive coding and modulation can adjust their modes to the actual transmission conditions. Antenna array technology achieves high data rates by benefiting from the spatial dimension of the radio channel. Multi-carrier modulation provides robustness against multi-path propagation and a flexible platform for different multiple user access schemes.

Within this work we focus on a promising radio access technology incorporating the three key features identified above. The basis is a radio access combining Code Division Multiple Access (CDMA), which is already an integral part of current 3G systems, and multi-carrier modulation. The different versions of this combination are distinguished in the following section and the general appellation Multi-Carrier CDMA (MC-CDMA) employed here encompasses all versions within the considered framework. The aim of this thesis is to explore the potential of antenna array technology in conjunction with the MC-CDMA scheme for the design of a new air interface suited for mobile radio systems beyond 3G.

1.2 Multi-Carrier CDMA (MC-CDMA)

The principle of Multi-Carrier (MC) communications is to divide a data stream into several parallel streams which are transmitted on different carrier frequencies. The first articles mentioning data transmission over several carriers date from the analogue area. However, it was not until the apparition of digital transmitters and receivers that MC systems started to pave their way into the domain of wireless transmission systems [Bin90]. The main technical reasons for this success are the simplified equalisation in multipath propagation and their robustness to impulse noise and fast fading as a benefit of the longer symbol period. Nowadays, many examples of wireless communication systems employing the MC principle can be cited: There are the European standards for Digital Audio Broadcast (DAB) and Terrestrial Digital Video Broadcast (DVB-T)

1.2 Multi-Carrier CDMA (MC-CDMA)


[ETSI97a,b] and the standards for WLAN (IEEE802.11a [IEEE99] and HIPERLAN/2 [ETSI01]). The air interface of all these standards is based on Orthogonal Frequency Division Multiplex (OFDM) [HaMü03] [NePr00]. An MC option also figures in the standards for 3G wireless cellular systems. This standard employs Direct-Sequence CDMA (DS-CDMA), where a data symbol is spread into several consecutive versions called chips by user-specific spreading codes. In the MC option, several DS-CDMA systems are allocated on a low number of parallel subcarriers [HoTo00]. An overview over the whole spectrum of wireless MC communications can be found in [WaGi00].

Various hybrids of MC modulation and CDMA have been proposed for current and future wideband wireless cellular systems. Basically, three different approaches have to be distinguished. It is interesting to observe that all three were proposed almost simultaneously in the autumn of the year 1993. The first one is MC-DS-CDMA and was already mentioned above [DaSo93]. Its principle is to create several parallel DS-CDMA systems of moderate bandwidth. Thus, MC-DS-CDMA uses symbol spreading in the time domain and a low number of orthogonal subcarriers with moderate bandwidth. The second technology is referred to as Multi-Tone CDMA (MT-CDMA). In contrast to MC-DS-CDMA, MT-CDMA is based on overlapping subcarriers or tones. It uses symbol spreading in the time domain and a low number of overlapping tones with large bandwidth. The interference between the tones can be mitigated as a benefit of the large spreading gain in this system [Van93]. Finally, there is MC-CDMA, which is based on a large number of orthogonal subcarriers of low bandwidth, and generally uses OFDM as underlying MC modulation scheme. In contrast to the other two systems, symbol spreading is performed in the frequency domain, i.e. the chips obtained from symbol spreading are transmitted on different subcarriers. Comparisons of the three presented technologies can be found in [HaPr97] and [FaKa03].

MC-CDMA was introduced in 1993 by several authors independently [ChBr93][FaPa93][YiLi93]. At the time this thesis is written, MC-CDMA celebrates its 10th anniversary. During these ten years, MC-CDMA has evolved from a theoretical proposition to the phase of prototyping and pre-standardisation. The MC-CDMA system considered in the framework of this thesis is described in detail in chapter 3, where references for each particular aspect are provided. The following table summarises several selected references, which from the author's point of view provide a representative picture of the state of the art in MC-CDMA research.

General aspects and books [FaKa03][HaMü03][HaPr97][Kai98]

System aspects and prototypes [AtMa02][MaKi03][HaSch01]

Current research projects [MATRICE][4MORE]

Tab. 1.1: Selected references on MC-CDMA.

The framework of this thesis is closely related to current European research projects considering MC-CDMA for future air interfaces providing very high data rates with moderate to high mobility [MATRICE][4MORE]. Such a new air interface can complement existing mobile radio systems as shown in Fig. 1.1, which corresponds to the vision elaborated by the ITU [ITU-R03][MAT,D1.4]. The major advantage of the MC-CDMA scheme in this context is its high flexibility. Thanks to the underlying OFDM and the CDMA realised by symbol spreading in the frequency domain, this scheme can be adapted to various propagation conditions, e.g. indoor and outdoor environments. Furthermore, the use of variable spreading factors allows an adaptation of the bit rate and the QoS of different transmitted data streams, which may belong to different users or to different services of the same user. In this way, an air interface based on MC-CDMA can provide a versatile platform for future mobile radio systems and services. The main focus of this work is the downlink, where successful field trials already proved the efficiency of this scheme [MaKi03].



0.1 101 100Transmission Bit Rate [Mbit/s]

Dep

loym

ent

Are

a/M

obili

ty

Highspeed/Nationwide

ModerateSpeed/ Citywide

Walking/Premises

Static/Indoor

2GGSM

3GUMTS/

IMT 2000

WirelessLAN Millimeter-wave

LAN

Beyond3G

based onMC-CDMA

0.1 101 100Transmission Bit Rate [Mbit/s]

Dep

loym

ent

Are

a/M

obili

ty

Highspeed/Nationwide

ModerateSpeed/ Citywide

Walking/Premises

Static/Indoor

2GGSM

3GUMTS/

IMT 2000

WirelessLAN Millimeter-wave

LAN

Beyond3G

based onMC-CDMA

Fig. 1.1: Complement-type vision adopted in MC-CDMA research [MATRICE].

1.3 Multiple antenna techniques and receiver-oriented systems

From their beginning, radio communications and the underlying information theory were basically one-dimensional. This historical dimension is time. Signals can be modulated, equalised, and detected in the time domain. The success of digital communication systems and the progress in signal processing opened the way to a second dimension, frequency. Clearly, the use of the frequency dimension for modulating signals, separating different systems, and ensuring full duplex mode is not a recent idea. But the emergence of wideband MC systems as described in the previous section really marks a milestone in radio communications. The third dimension that is about to be conquered by radio communication systems is space. This is enabled by the use of multiple antennas at the transmitter, at the receiver, or on both sides [FoGa98].

The benefits of the spatial dimension for radio communication systems are manifold. Depending on the application, the propagation environment, and the tolerable implementation complexity, very different strategies may be adopted. Basically, there are three different ways to exploit the spatial dimension: diversity combining, spatial multiplexing, and spatial filtering. Fig. 1.2 schematically represents these approaches. Note that various combinations of these schemes are possible.

. . .

Diversitycombining

. . .

Spatial multiplex

. . .

Spatial filtering

. . .

Diversitycombining

. . .

Spatial multiplex

. . .

Spatial filtering

Fig. 1.2: Approaches for exploiting the spatial dimension.

The principle of spatial diversity is well known and already applied to current radio communication systems in various ways [Pro95]. Here, the quality of the received signal in fading channels is enhanced by combining several signal versions that reach the receiver through independent paths. The different transmission paths are generally created by employing multiple antennas at one end of the transmission system, either at the receiver side or at the transmitter side. The benefit arises from the fact that several independent transmission paths are less likely to fade

1.4 Content and major achievements of this thesis


away than a single one. Spatial multiplexing aims at higher data rates by transmitting several data streams in parallel using multiple antennas for transmission and reception. A famous example for spatial multiplexing is the BLAST (Bell-Labs Layered Space-Time) architecture proposed in [Fos96]. For spatial filtering or beamforming, the multiple antennas are considered as an antenna array whose directivity pattern acts as a spatial filter [God97]. The fundamental benefits of this concept are the antenna gain obtained with the array and the reduction of interference by spatially-selective reception and transmission.

In the downlink system considered in this work, the basestation transmits signals to mobile receivers. Since the constraints in terms of cost, size, and power consumption are very tight for mobile user terminals, a major goal of this thesis is to investigate transmission strategies allowing a light mobile receiver design. From a general point of view, the time-varying channel in mobile radio systems is given by physical laws and the transmitter-receiver pair has to be adapted to this channel to enable the communication. Traditionally, the transmitter has to transform the information into a signal that is suitable for the transmission over a given type of channel. Then, the receiver extracts this information from the captured signal by compensating the actual channel distortions and mitigating interference. For doing so, the receiver acquires information about the current channel state and adapts itself to the variations of the channel. This classical repartition of roles may be qualified as transmitter-oriented, i.e. the receiver adapts itself to the transmitted signal and the current channel state. In the downlink, this repartition of roles has the drawback that complex signal processing tasks have to be performed by the mobile terminal. An alternative solution may consist in already adapting the transmitted signal to the current channel state in order to simplify the signal detection at the receiver. Such a concept can then be qualified as receiver-oriented [BaQi03]. In the downlink, this allows a transfer of implementation complexity from the mobile terminal to the basestation, where it can be tolerated more easily.

The crucial requirement for a receiver-oriented system is the availability of channel state information at the transmitter side prior to transmission. In the considered system, this knowledge can either be acquired by the basestation in the uplink or obtained by feedback of the mobile. In either of these cases, it is important that the channel variations are sufficiently slow so that there are no considerable variations between the instant of acquisition and the usage of channel knowledge. An example of a system, where instantaneous channel state information acquired by the basestation in the uplink may be used directly for transmission in the downlink is Time Division Duplex (TDD). Here, uplink and downlink use the same carrier frequency. Therefore, if the channel variations are sufficiently slow, the channel can be assumed reciprocal for successive uplink and downlink transmission periods. In other system configurations, there may still be the possibility of using long-term or average channel state information for the adaptation of the transmitted signal.

Within the framework of this thesis, we consider a light design of the mobile terminal. Here, the terminal is equipped with a single antenna and uses detection techniques of low complexity. The basestation is endowed with multiple antennas and is assumed to have some information about the channel state at its disposal. Based on these assumptions, we develop and evaluate transmission strategies exploiting the spatial dimension for an MC-CDMA downlink system.

1.4 Content and major achievements of this thesis

The remainder of this work comprises six chapters whose contents and major achievements are summarised in the sequel:

In chapter 2, the system considerations and models are defined. A particular focus is put on the modelling of the radio channel and its characteristics in time, frequency and space. A spatial vector channel model is proposed as an extension of a time-domain channel model that is currently employed for WLAN studies. Besides reproducing the fast fading of the radio channel,



this model enables a simplified drawing of the spatial channel characteristics, required for the performance evaluation of the proposed approaches.

The conventional single-antenna MC-CDMA system is described in detail in chapter 3. The major characteristics and aspects of this system in uplink and downlink are presented and related references are provided. The emphasis is put on the trade-off between diversity and multiple access interference, which is a major issue in the design of MC-CDMA systems. Based on the characteristics of the conventional system, the potential benefits of multiple antenna approaches for MC-CDMA are evaluated and an overview of current research in this field is provided. Chapter 3 concludes with a description of the choices and assumptions that represent the framework of this thesis.

A first transmission strategy termed Space Frequency Transmit Filtering (SFTF) is proposed in chapter 4. This strategy is suitable for a downlink scenario where the basestation has instantaneous knowledge of the channel fading at its disposal, which is typically the case for TDD systems in indoor environments. Several optimisation criteria are derived and compared. The SFTF approach can optimally exploit the spatial diversity offered by the channel and simultaneously mitigate the multiple access interference, which may even allow an increase of the user capacity by code overloading.

The transmit beamforming strategy proposed in chapter 5 corresponds to purely spatial transmit filtering. This approach can be applied if only spatial covariance knowledge of the channel is available at the basestation, e.g. in outdoor scenarios with moderate to high mobility. After addressing the aspects of beamforming for wideband systems, optimisation criteria for covariance based transmit beamforming suitable for the MC-CDMA downlink are developed and discussed. It is shown that the combination of single-user transmit beamforming and direction-based code allocation achieves promising performance results.

The innovative approaches SFTF and covariance based transmit beamforming are compared in chapter 6 for typical indoor and outdoor scenarios. In particular, this system comparison accounts for channel coding and imperfect channel knowledge at the basestation Chapter 6 additionally provides a discussion of open issues that could be the subject of future studies.

Finally, chapter 7 concludes this thesis with a summary of the obtained results and prospects on future work.


2 Modelling of mobile radio systems and channels

In this chapter, we present an overview of the physical layer of modern wireless cellular systems. We define the system considered within this thesis and provide the reader with some notions that will be used throughout the following chapters. An important part concerns the modelling of the mobile radio channel, which is a crucial point in all physical layer studies.

2.1 Transmission chain of cellular communication systems

A typical digital cellular communication system, where a Basestation (BS) communicates with a certain number of Mobile Terminals (MT), is depicted in Fig. 2.1. This simplified view allows us to identify the main entities and the principal functionalities of the system. Note that the transmitter and the receiver of the mobile terminals basically have the same functionalities as their equivalents at the basestation, except the management of the multiple user access. For simplicity, only the basestation transceiver is detailed here.

Multi-useraccess

&Pilot

insertion

Basebanddemodulation

Binarysource g

Channelcoding

Symbolmapping Baseband

modulationD/A &RF Mod

Binary signal g

Channeldecoding

Symbolde-mapping A/D &

RF Demod

Equalisation &

Detection of all users

Downlink

Uplink

Discrete equivalent baseband channel

Channelestimation

Symbols of other users k≠g

Basestation

Mobileterminals

Transmitter

Receiver

Focus of the thesisFrequency domain channel for OFDM


Multi-useraccess

&Pilot

insertion

Basebanddemodulation

Binarysource g

Channelcoding

Symbolmapping Baseband

modulationD/A &RF Mod

Binary signal g

Channeldecoding

Symbolde-mapping A/D &

RF Demod

Equalisation &

Detection of all users

Downlink

Uplink

Discrete equivalent baseband channel

Channelestimation


Basestation

Mobileterminals

Transmitter

Receiver

Focus of the thesisFrequency domain channel for OFDM


Fig. 2.1: Overview of the physical layer.

Starting at the transmitter of the basestation, a binary information stream has to be delivered to a given user g. The bit stream is first encoded by the channel coder. The role of channel coding is to protect the information stream against errors occurring in the transmission. Therefore, the channel coder adds redundancy to the original stream that can be used for detecting and

Everything should be made as simple as it is, but not simpler.Albert Einstein (1879-1955)

Chapter 2: Modelling of mobile radio systems and channels


correcting transmission errors [GlJo99][Pro95]. The code rate RC is a measure for the redundancy added by the channel coding and defined as

number of information bitsnumber of coded bitsCR = (2.1)

Note that RC equals 1 in the uncoded case. The coded bit stream is then mapped to a symbol alphabet, which is used to modulate the carrier signal. Modern digital communications systems generally use complex alphabets, i.e. points out of a constellation in the complex plane. Fig. 2.2, shows three examples of such constellations.

ℑ

ℜ

0 1

BPSK

ℑ

ℜ

01 00

1011

QPSK

ℑ

ℜ

16-QAM

0000

0001

0101

0100

0010

0011

0111

0110

1010

1011

1111

1110

1000

1001

1101

1100

ℑ

ℜ

0 1

BPSK

ℑ

ℜ

01 00

1011

QPSK

ℑ

ℜ

16-QAM

0000

0001

0101

0100

0010

0011

0111

0110

0000

0001

0101

0100

0010

0011

0111

0110

1010

1011

1111

1110

1000

1001

1101

1100

1010

1011

1111

1110

1000

1001

1101

1100

Fig. 2.2: Complex symbol constellations.

For the first two constellations, the information corresponds to the phase of the complex symbol. They are therefore called Phase Shift Keying (PSK), and the depicted constellations correspond to Binary PSK (BPSK) and Quaternary PSK (QPSK), respectively. For the third constellation, the symbol amplitude also contains information. This family is called Quadrature Amplitude Modulation (QAM), and Fig. 2.2 shows the constellation for 16-QAM. The symbol mapping assigns bits or groups of bits to the different constellation points. Within this thesis, we always use the depicted Gray mapping, where neighbour points in the constellation only differ in a single bit [Pro95]. The data symbol of user k is denoted by dk. This symbol carries a certain number of bits. If the size of the constellation is denoted by MC , the number of bits per symbol is given by

2log CMβ = (2.2)

For performance comparison, it is important to be aware of the power spent for the transmission of an information bit. The energy of a data symbol is given by its squared amplitude. Since the amplitude varies for QAM constellations, the mean energy of a data symbol is defined as its mean squared amplitude, i.e.

2ES kE d= (2.3)

From (2.3), the energy per information bit is obtained by taking into account (2.1) and (2.2) as

Sb

C

EERβ

= (2.4)

At this point, the basestation transmitter disposes of the complex data symbols of all active users. These data symbols have to be transmitted within the same system bandwidth. Multiple access schemes (cf. section 2.4.2) provide us with a variety of possibilities to share the bandwidth among the different users. A major goal of this thesis is to optimise the signals transmitted to the different users as a whole in order to enable the mobile terminals to easily extract the data symbols of the corresponding users. Furthermore, pilot symbols are generally inserted in the transmitted signal at this stage. Pilot symbols are known to the mobile receiver and used for

2.1 Transmission chain of cellular communication systems


synchronisation and channel estimation purposes. Once the multiplexing of pilot and user symbols is performed, the symbol stream modulates a carrier signal in the baseband. Many single and multi-carrier modulations are known from the literature, e.g. [Pro95][Rap02]. Within this thesis we consider Orthogonal Frequency Division Multiplex (OFDM) modulation, which is detailed in section 2.5.

After the modulation stage, the transmitted signal is composed of complex samples in the baseband. In the further stages, this signal is converted to the analogue domain and transformed into a bandpass signal around the carrier frequency, fC , by the Radio Frequency (RF) modulation stage. The RF signal is then ready for transmission over the radio channel.

The radio link between a mobile and the basestation is composed of two parts. In the Down-Link (DL) or forward link, the basestation sends information to the mobile terminals, and in the Up-Link (UL) or reverse link the mobiles send information to the base. Since the basestation communicates with multiple users, there is an important difference between these two links. In the downlink, a mobile terminal receives a signal from the basestation that contains the signal parts of all active users. All these signal parts have travelled through the same channel and arrive at the terminal with the same amplitude and delay. In the uplink, however, the signals of the multiple users travel from the diverse terminal positions towards the basestation over different channels. For this reason, the multi-user management is generally more difficult in the uplink, which can be noticed at several points in this work.

For the description of the receiver, the focus is also put on the basestation while keeping in mind that the receiver at the terminal has the same basic functionalities. However, the mobile receiver is much simpler since it only receives a single signal from the basestation, from which it has to extract its own part. The first stage of the receiver is the counterpart of the RF modulation and D/A conversion at the transmitter. Within this thesis, we stay with the complex baseband representation of the system. The pass-band signals and especially the radio channel at the considered carrier frequencies, are modelled by their equivalent baseband representation [GlJo99] [Pro95][Rap02]. Note that the discrete equivalent baseband channel also includes the effects of the RF components at the transmitter and the receiver, as illustrated in Fig. 2.1. The channel characteristics and models are detailed in section 2.2. In the baseband part of the receiver, the signal is demodulated by the counterpart of the modulation stage in the transmitter. A further simplified representation of the radio channel in the frequency domain is obtained by assuming an ideal transmission through an underlying OFDM system (cf. section 2.5.2).

The demodulated signal contains the contributions of all users, which arrive at the basestation through different channels. According to the multiple access scheme, the basestation receiver has to extract and detect the symbols of the different users. Before detection, the channel effects are generally mitigated by an equalisation stage. The equalisation is based on knowledge about the channel state, which is acquired by channel estimation. Depending on the system configuration and the detection technique, different kinds of channel knowledge may be required. Irrespective of these differences, Channel State Information (CSI) is used here as a general term. Note that at the terminal, it is sufficient to acquire CSI of a single channel, while at the basestation the CSIs of all users have to be estimated. The knowledge of the channel states can not only be used for signal equalisation at the receiver but may, in some cases, also be used for adapting the transmit signal to the current channel state. This represents the key idea for the techniques studied in this thesis and is detailed in the following chapters.

Once the desired signal is detected, the complex data symbols are de-mapped, and the coded bit stream is decoded to reconstitute the original information bit stream. An important indicator for the quality of the detected signal at the receiver is the Signal to Noise Ratio (SNR). The SNR is defined as the signal energy divided by the energy of the noise, which is also present in the received signal. Denoting the spectral density of the noise by N0, the SNR can be defined per data symbol γS , or per information bit, γb , i.e.



0

SS

EN

γ = and 0

bb

EN

γ = (2.5)

2.2 The mobile radio channel

In mobile radio communication systems, the link between a basestation and a mobile terminal is called the mobile radio channel. The intrinsic aim of all studies concerning the physical layer of communication systems is to find an appropriate technology for sending a maximum of information over the available channel. The capacity of a transmission channel was defined by Shannon as the maximum number of bits per second and Hertz that can be transmitted through a channel with an arbitrary low probability of error [Pro95]. For example, the capacity of a channel only affected by Gaussian noise is given by

2log (1 )SC γ= + (2.6)

The channel capacity and the transmission strategy that may approach this capacity highly depend on the considered channel. Therefore, the modelling of the channel plays a key role in telecommunications research. In contrast to fixed transmission channels like wires, optical fibres, or directional radio lines, the mobile radio channel may change its characteristics dramatically during the communication period, and a mobile radio system has to be able to cope with a large variety of transmission conditions.

A signal transmitted over a mobile radio channel is subject to the rules of electromagnetic wave propagation. In the considered frequency ranges and environments, three fundamental propagation mechanisms determine the way a wave travels through the channel: reflection on large surfaces like buildings, walls, or the ground, diffraction on edges, and scattering on rough surfaces, on groups of small objects, or on other irregularities in the channel [Rap02]. These mechanisms lead to three basic effects that can be observed on a signal having passed the radio channel:

Multipath propagation occurs as a result of the multiple propagation paths created by the three mechanisms described above. Hence, the received signal is a superposition of a multitude of waves arriving from different directions with different delays, phases and attenuations. Especially the phases of the different waves change quickly when the mobile is moving, which gives rise to a variation in the signal strength arising through constructive and destructive superposition of the waves. In general, at two points spaced by more than the carrier wavelength, an independent superposition can be assumed. The corresponding variation of the signal strength is referred to as fast fading. Shadowing is caused by obstacles in the propagation path. While the mobile is moving, some paths disappear while other new paths appear. This also gives rise to a variation of the signal strength. Two main channel configurations are distinguished: The configuration, where a direct path between the basestation and the terminal exists, is called Line-Of-Sight (LOS) configuration. If there is no direct path, the configuration is called Non-Line-Of-Sight (NLOS) configuration. A change in the number of paths generally requires that the mobile covers a distance, which is large compared to the carrier wavelength. Therefore, the fading caused by the shadowing effect is called slow fading. Path loss describes the attenuation of the signal strength due to the distance between the mobile terminal and the basestation. In free space, the signal strength decreases with the square of the covered distance. In mobile radio channels, the signal strength generally decreases with a power higher than two (typically 3 to 5) [Jak94].

The transmission system has to cope with these three effects in order to ensure an acceptable quality of the information bearing signal after detection at the receiver side. A possible countermeasure for the variation of the signal strength is the control of the transmitted power.



The transmitter can adjust its power according to some feedback of the receiver about the signal quality. However, this power control procedure is generally too slow to cope with fast fading. Furthermore, the bit rates of today’s wireless systems require a rapid modulation of the transmitted signal, which already leads to signal variations that are on the same temporal scale than the fast fading [Rap02]. Within this work, we assume that the path loss and the slow fading can be compensated by power control mechanisms, which are out of the scope of this thesis. Thus, we focus on the fast fading effects of the mobile radio channel.

In the sequel, we expose the statistical description of the channel adopted for this thesis and present the channel models used for the system simulation.

2.2.1 The fast fading channel model and its characteristic functions

The channel characteristics highly depend on the propagation environment. For the derivation of the channel model, we use the example of a typical outdoor environment depicted in Fig. 2.3. Here, a basestation with multiple antennas communicates with a mobile equipped with a single antenna. This situation is mostly considered throughout this thesis, but the derived model is general enough to be applied in other environments, and the extension to systems using multiple antennas at both ends is straightforward.

v

local-to-mobile scatterers

remote scatterer

remote scatterer

basestation

mobile

θM,p,s

Path p, τp Sub-path s, αp,s

θB,p,s

v

local-to-mobile scatterers

remote scatterer

remote scatterer

basestation

mobile

θM,p,s

Path p, τp Sub-path s, αp,s

θB,p,s

Fig. 2.3: Example of an outdoor propagation environment.

The derived model is based on the equivalent complex representation of the channel in the baseband, as illustrated in section 2.1. The fading statistics are assumed to be constant over short time periods and small spatial distances. Such a channel is called wide sense stationary [Bel63].

Fig. 2.3 illustrates the different propagation paths between the mobile and the basestation created by different obstacles in the propagation environment, which are all called scatterers for simplicity. In the sequel, a path is defined as a group of propagation paths called sub-paths. The NSP sub-paths of a path p are assumed to have a negligible difference in their propagation delays compared to the system’s sampling time. Thus, they can be assumed to arrive with the same delay τp . Note that the delay is always given with respect to the path having the shortest absolute propagation delay. Each sub-path is characterised by its angle at the basestation, θB,p,s , measured with respect to the antenna array. These angles are referred to as Directions Of Arrival (DOA) in the uplink and Directions Of Departure (DOD) in the downlink, respectively. When no explicit distinction is needed, we only refer to the DOAs for simplicity. At the mobile terminal, each sub-path has an angle, θM,p,s , measured with respect to the mobile’s moving direction. Note that only azimuth angles are considered here. Thus, we assume that the transmitter, the receiver and the obstacles



are located in the same horizontal plane. This assumption is justified for most propagation environments [ErCa98]. However, the channel model can easily be generalised to three dimensions, if necessary. Each sub-paths also owns a real amplitude αp,s , and a phase ϕp,s . Furthermore, each sub-path is subject to a Doppler shift arising from the movement of the terminal. Denoting the mobile speed by v and the carrier-wavelength by λC , this Doppler shift is given as

( ), , , ,cosD p s M p sC

vf θλ

= (2.7)

In a first step, a single antenna is considered at both ends so that the channel can be modelled in the conventional way by scalar functions. The time-varying impulse response of the mobile radio channel is given by the sum of the components over all NP paths and their sub-paths:

( ) ( ), , ,11

( 2 ),

0 0

, eSPP

D p s p sNN

j f tB p s p

p s

h t π ϕτ α δ τ τ−−

+

= =

= −

∑ ∑ (2.8)

Equivalently, the channel can also be characterised by the time variant channel transfer function HB(f,t), which is the Fourier transform of hB(τ,t) with respect to τ and defined within the system bandwidth B.

( ) ( ), , ,11

( 2 ),

0 0

, eSPP

D p s p p sNN

j f t fB p s

p s

H f t π τ ϕα

−−− +

= =

= ∑ ∑ (2.9)

hB(τ,t) and HB(f,t) are illustrated by their magnitude in Fig. 2.4.

|hB(τ,t)|

τ f

|HB(f,t)|

τmax B

|hB(τ,t)|

τ f

|HB(f,t)|

τmax B Fig. 2.4: Channel impulse response and transfer function.

2.2.2 Delay spread and frequency selectivity

The impulse response depicted in Fig. 2.4 illustrates how a short impulse sent through the multipath channel is spread in time. This phenomenon is called delay spread and essentially caused by the remote scatterers, which introduce significant differences in the delays of the paths (cf. Fig. 2.3).

To quantify the delay spread, we start with the time spaced autocorrelation function of the impulse response given by

( ) ( ) ( ) *1 2 1 2

1, ; E , ,2A B Bt h t h t tτ τ τ τφ ∆ ∆= + (2.10)

For the considered channels, the phases and attenuations at the two delays τ1 and τ2 can be assumed uncorrelated, which is called uncorrelated scattering. This restricts our statistical model to the so-called Wide Sense Stationary Uncorrelated Scattering (WSSUS) model [Bel63]. Incorporating this



assumption in the above equation and taking the autocorrelation function at ∆t =0, the power delay spectrum of the channel is defined as

( ) ( ) ( ) ( ) *1; 0 E , ,2B A B Bh t h tρ τ τ τ τφ= =

The power delay spectrum gives the average output power of the channel as a function of the delay. This important function is the basis of most statistical channel models. From the power delay spectrum we can obtain two important parameters of the multipath channel. Firstly, the delay range for which the power delay spectrum, and equivalently the channel impulse response, is essentially non zero is called the maximum channel delay τmax (cf. Fig. 2.4). Secondly, the so-called Root-Mean-Square (RMS) delay spread στ is defined as the standard deviation of the power delay spectrum with respect to the mean delay, τ . The definitions of the RMS delay spread and the mean delay are respectively

( ) ( )

( )

2

0

0

B

B

d

dτ

τ τ ρ τ τσ

ρ τ τ

∞

∞

−=

∫

∫ and

( )

( )0

0

B

B

d

d

τ ρ τ ττ

ρ τ τ

∞

∞=∫

∫ (2.11)

The delay spread gives rise to Inter Symbol Interference (ISI). Considering a transmitted signal that consists of successive symbols each having a duration TS, the long delayed versions of a given symbol will arrive at the receiver at the same time as the shorter delayed versions of the succeeding symbol and interfere with them. This effect gets negligible if the maximum channel delay is small compared to the symbol time, i.e. τmax <<TS. Multi-carrier systems take advantage of this property by using parallel transmission streams with longer symbol times.

Equivalently, the distortion due to the delay spread can also be described as a frequency selectivity of the channel, i.e. variations in the transfer function. The frequency range in which the transfer function can be considered as constant is called the coherence bandwidth and denoted by Bcoh. The coherence bandwidth depends on the form of the power delay spectrum. Approximate values are given by:

15cohB

τσ≈ [Rap02] or

max

1cohB

τ≈ [Pro95] (2.12)

A channel is considered as frequency non-selective or flat if the signal bandwidth, B, is small compared to the coherence bandwidth of the channel, i.e. B <<Bcoh. Note that this condition is equivalent to the condition for negligible ISI since the signal bandwidth can be approximated by B =1/TS. In the case, where the system sees a flat fading channel all paths become sub-paths with a common delay and the impulse response has a single coefficient at τ =0. Omitting the indices for p=0 for simplicity, the flat fading channel is given by

( ) ( ),

1( 2 )

0

, eSP

D s s

Nj f t

B ss

h t π ϕτ α δ τ−

+

=

= ∑ (2.13)

The counterpart of ISI or frequency selectivity is path or frequency diversity, respectively. Path diversity is obtained, when the receiver is able to separately detect several versions of the same symbol arriving at different delays and to combine them coherently. An example of such a receiver is the RAKE receiver employed in DS-CDMA [Pro95]. Equivalently, a system can benefit from frequency diversity if different versions of the same symbol are transmitted on carriers spaced by more than the coherence bandwidth.



2.2.3 Doppler spread and time selectivity

The time variation, or time selectivity, of the channel is determined by the movement of the mobile terminal and to some extend by moving obstacles. Since we focus on the fast fading of the channel, we only have to account for the variations due to the Doppler shift (cf. (2.8) and (2.9)) The Doppler shifts are specific to each sub-path and depend on their angle with respect to the moving direction of the mobile (cf. (2.7)). Since the mobile is generally surrounded by a large number of local-to-mobile scatterers (cf. Fig. 2.3), there is variety of angles and consequently Doppler shifts. The different Doppler shifts lead to an effect called Doppler spread. Indeed, a narrowband signal sent through the multipath channel is spread in frequency by the different Doppler shifts. The maximum magnitude of the Doppler shift fD,max is obtained from (2.7) for the angles θp,s =0 and θp,s =π, i.e.

,D maxC

vfλ

= (2.14)

In the same way as for the delay, a Doppler power spectrum ρD(fD) and a Doppler spread σD of the channel can be defined, which depend on the distribution of the angles of incidence of the different sub-paths [Pro95]. Considering the range of the Doppler frequencies for angles θp,s∈[0,2π[ yields the following inequality

,2D D maxfσ ≤ (2.15)

An important case for which the Doppler power spectrum can easily be derived is for a large number of sub-paths (NSP→∞) with angles that are uniformly distributed in the range [0,2π[. Then the Doppler spectrum can be obtained either for a single path p or for the flat fading channel. The time spaced autocorrelation function for a given delay τp is given by

( ) ( ) ( ) *1 E , ,2A B p B pt h t h t tφ τ τ∆ ∆= + (2.16)

The mathematical derivation can be found in appendix A.1.1. Finally, the normalised time spaced correlation function is obtained as

( ) ( )( ) ( ), 0 ,J 20

AA norm D max

A

tt f t

φφ π

φ∆

∆∆ = = (2.17)

Here, Jk(x) denotes the k-th order Bessel function of the first kind. The Doppler power spectrum is the Fourier transform of φA,norm(∆t) and given by

( ) ( ), ,2

, ,

1 ,1 /

0 otherwise

D D max D max

D D D max D D max

f f ff f f fρ π

∀ ∈ − = −

(2.18)

This classical Doppler power spectrum is often called the Jakes spectrum [Jak94].

A measure of the time selectivity of the channel is the coherence time, Tcoh , i.e. the time range in which the channel fading is strongly correlated. The coherence time depends on the form of the Doppler power spectrum. It can be approximated by [Rap02][Pro95]:

,

12coh

D max

Tf

≈ (2.19)

Considering again a transmitted signal with symbol time TS and bandwidth B =1/TS , the channel can be considered as time non-selective if the symbol duration is much shorter than the



coherence time of the channel, i.e. TS <<Tcoh, or equivalently if B >>2fD,max . Otherwise the channel is time-selective, which gives rise to signal distortions.

A system can take advantage of the time selectivity of the channel and benefit from time diversity. To obtain time diversity, several versions of a symbol are transmitted at different instants spaced by more than the coherence time of the channel.

2.2.4 Vector channel modelling

In the previous sections, the channel was represented by the scalar impulse response and the scalar channel transfer function given in (2.8) and (2.9), respectively. When multiple antennas are added to the system, the model has to be extended to a spatial channel model. The different multi-antenna configurations are identified by the following acronyms: The conventional system with a single transmit and a single receive antenna is called Single-Input-Single-Output (SISO). When there are multiple transmit antennas but a single receiver antenna it is a Multiple-Input-Single-Output (MISO) system. Accordingly, there are also Single-Input-Multiple-Output (SIMO) and finally Multiple-Input-Multiple-Output (MIMO) configurations. The model described here extends the scalar channel model to a vector channel model that can directly be applied to MISO and SIMO configurations The matrix model required for the MIMO case is a straightforward extension of this vector approach.

Without loss of generality, we consider here the system with multiple antennas at the basestation depicted in Fig. 2.3. Then, the vector channel model additionally takes into account the DOAs of the sub-paths at the basestation θB,p,s , which generally lead to different impulse responses and transfer functions at the different antennas. Therefore, we have to shift from a scalar to a vector representation of the multipath channel. An overview of different vector channel models can be found in [ErCa98].

The vector channel model we use throughout this thesis is based on several assumptions: The narrowband assumption of array processing states that the inverse signal bandwidth, i.e. 1/B, has to be large compared to the travelling time across the array [LiLo96]. It is further assumed, that the signal sources are located in the far-field of the antenna array and in the same horizontal plane. The array is assumed to consist of M omni directional (at least in the horizontal plane) elements with identical gain and without mutual coupling between them.

Uniform Linear Array

θ

1 2 M-10 3 rS

2

M-1

τ

θ 0

1

Uniform Circular Array

τ dS

Fig. 2.5: Uniform array geometries.

The so-called array response vector represents the array response per element for a signal impinging from a distinct angle θ. Fig. 2.5 shows two uniform array configurations: the Uniform Linear Array (ULA) and the Uniform Circular Array (UCA). The array response vector consists of phase rotations arising from the propagation delay of the impinging signal at a certain element m with respect to a reference point.



An ULA consists of M elements which are aligned linearly. The spacing between two elements is denoted by dS and identical for all elements. Thus, the propagation delay, τ, between two neighbour elements is also identical and can be expressed by

( )0

cosSdv

τ θ= (2.20)

v0 is the velocity of light. Taking the element 0 as reference point, the array response vector of a ULA is given by

( ) ( ) ( ) ( ) ( )2 cos 2 1 cos2 121, , e , , e 1, , e , , e

S S

CC C C

Td dj m j MTj f Mj f mπ θ π θ

π τπ τ λ λθ−

−

= = a K K K K (2.21)

It is easy to see that the array response vector is non-ambiguous only in the range of θ∈[0,π[. Furthermore, when applied to beamforming, the ULA has the drawback that its beamwidth varies with the main direction. Indeed, the ULA produces a narrow beam at broadside, which broadens when the look direction moves away from broadside. Thus for beamforming, the ULA is mainly used in sectored systems, with a range that is generally limited to 120°. However, the ULA has some nice properties facilitating the estimation of the angles of incidence [God97][KrVi96] and is by far the most common structure employed for multiple antenna systems.

The array response vector for the UCA can be derived in the same way. Here, the array elements are uniformly placed on a circle with radius rS. Hence, the angle positions of the elements are ϕm=2πm/M. It has to be noted that the propagation delay between two neighbour elements of the UCA is not identical. The delay at the m-th element with respect to the centre of the array takes the form

( )0 0

cos cos 2S Sm

r r mv v M

τ θ ϕ θ π = − = −

(2.22)

and the array response vector for the UCA turns out to be

( )( ) 12 cos 2 cos 2 2 cos 2

e , , e , , eS S S

C C C

Tr r rm Mj j jM M

π θ π θ π π θ πλ λ λθ

− − − − − −

=

a K K (2.23)

The vector channel model is now obtained by inserting the directional information of the array response vector into the scalar model given by (2.8) and (2.9). Each sub-path generally has a different DOA θΒ,p,s requiring its proper array response vector. This yields the following expression for the vector channel impulse response [ErCa98]:

( ) ( ) ( ), , ,11

( 2 ), , ,

0 0

, eSPP

D p s p sNN

j f tB B p s p s p

p s

t π ϕτ θ α δ τ τ

−−+

= =

= −

∑ ∑ ah (2.24)

This vector of length M represents the time variant channel impulse response at each antenna element. The vector form of the channel transfer function can be obtained analogously.

2.2.5 Angle spread and space-selective fading

Depending on the propagation environment, the channel impulse response at adjacent elements may differ significantly. This is caused by the different DOAs of the sub-paths and leads to spatial selectivity of the channel. In the same way as for the delay and the Doppler shift, one can define a power azimuth spectrum and an angle spread σθ around a mean angle of incidence θ [Fle00]. From Fig. 2.3, it is evident that remote scatterers introduce a moderate angle spread (in this example, at



the basestation), while scatteres close to the antenna cause severe angle spread (in this example, at the mobile). Note that the notion of angle spread applies to both ends of the channel, so that it is not necessary here to distinguish the angles at the basestation and at the mobile. Since there exist different definitions of the angle spread, we often use the more convenient notion of the maximum angle separation ∆θmax given by the range in which the power azimuth spectrum is essentially non zero. ∆θmax represents an upper bound of the angle spread, i.e.

θσ θ∆≤ max (2.25)

The equality is given for a uniform power azimuth spectrum within the range of ∆θmax. The angle spread is a crucial parameter for multiple antenna systems since it determines the correlation of the channel fading at different antennas. This spatial correlation is an important factor in the choice of the strategy that should be adopted to exploit the spatial dimension of the channel.

The correlation of the channel fading at different antennas was widely studied in literature, e.g. [SaWi94][ShFo00]. The fading correlation between two antennas spaced by dS is a function of the angle spread and the mean angle of incidence θ . Based on the assumption of a flat fading channel (cf. (2.13)), the m-th element of the vector channel for an ULA is expressed using (2.21) and (2.24) as

( ) ( ) ( ) ( ),

1 2 cos2,

0

, e eSSP s

D s s C

dN j mj f tB m s

s

h tπ θπ ϕ λτ δ τ α

−+

=

= ∑ (2.26)

The spatial correlation function between two elements spaced by dS is given in the following way

( ) ( ) ( ) *, , 1

1 E , ,2C S B m B md h t h tφ τ τ+= (2.27)

The normalised spatial correlation function, φC,norm(dS), is derived in appendix A.1.2 for the assumption of an infinite number of sub-paths (NSP→∞) with a uniform power azimuth spectrum in the range of [θ -∆θmax/2, θ +∆θmax/2]. The obtained results for the real and the imaginary part are

( ) ( ) ( ) ( )

( ) ( ) ( )( ) ( )( )

, 0 2 max1

, 2 1 max0

J 2 2 1 J 2 cos 2 sinc

2 1 J 2 cos 2 1 sinc 2 1 /2

kS SC norm S k

kC C

k SC norm S k

k C

d dd k k

dd k k

φ π θ θλ λ

φ π θ θλ

π∞

=

∞

+=

∆

∆

ℜ = + −

ℑ = − − + +

∑

∑ (2.28)

Fig. 2.6 shows the magnitude of the spatial correlation for several values of ∆θmax and for θ =90° and θ =30°. The figures show that as the angle spread decreases the spatial coherence of the vector channel increases. If the angles are uniformly distributed in azimuth, i.e. ∆θmax= 360°, the first zero occurs at dS/λC ≈ 0.4. This can be seen as the minimum spacing required for independent fading at the antennas. When θ moves away from broadside, the correlation increases for constant angle spread. In particular, there is no zero in correlation for angle spreads lower than 360°. Note that a zero in correlation occurs only if both, the real and the imaginary, parts of the spatial correlation are zero.



30θ = °

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

dS /λC

∆θmax= 0°

∆θmax= 20°

∆θmax= 10°

∆θmax= 120°∆θmax= 360°

90θ = °

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

dS /λC

∆θmax= 0°

∆θmax= 10°∆θmax= 20°∆θmax= 120°∆θmax= 360°

|φC,norm(dS)| |φC,norm(dS)| 30θ = °

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

dS /λC

∆θmax= 0°

∆θmax= 20°

∆θmax= 10°

∆θmax= 120°∆θmax= 360°

90θ = °

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

dS /λC

∆θmax= 0°

∆θmax= 10°∆θmax= 20°∆θmax= 120°∆θmax= 360°

|φC,norm(dS)| |φC,norm(dS)|

Fig. 2.6: Spatial correlation.

The maximum distance between two antenna elements for which the fading remains strongly correlated is called the coherence distance [Fle00]. In appendix A.1.2, we derive a rule of thumb for the coherence distance by assuming a uniform distribution of the angle within [θ -∆θmax/2, θ +∆θmax/2], where the mean angle corresponds to the broadside, i.e. θ =90°. An upper bound for the coherence distance is then obtained by the first zero in the spatial correlation function for different values of 0°<∆θmax<360°. This upper bound is given by

( )

2sin / 2

Ccoh

max

d λθ

θ∆

≤ ∀ (2.29)

It is easy to see that the larger ∆θmax the lower the coherence distance and vice-versa. The coherence distance indicates the minimum antenna spacing required to obtain independent fading channels. Then, a system can benefit from space diversity by transmitting or receiving versions of the same symbol over different antennas.

2.2.6 Channel fading statistics

The fading of wireless communication channels is often modelled with random variables using specific distributions. Here, we will introduce the two most important distributions. More details can be found in [Pro95][Rap02].

Rayleigh fading distribution The Rayleigh distribution can be used to model the amplitude of a flat fading channel or the amplitude of a given path p, provided that there is a large number of sub-paths. Then, using the central limit theorem the channel fading can be considered as a complex-valued Gaussian process. In a NLOS configuration, it can further be assumed that this process has zero mean. The flat fading channel is given by (2.13), and its amplitude is here denoted by α(t)=|hB(0,t)| or simply α. The random variable α can be shown to follow a Rayleigh distribution with the probability density function

( )ααα α

− Ω≥

Ω=

2 /2p( ) e ; 0 (2.30)

where 2E αΩ = is the mean power. The phase of the flat fading channel or the path is then uniformly distributed in the interval [0,2π[.



Ricean fading distribution If a LOS path exists, the assumption that the fading process is of zero mean does not hold anymore. This affects the amplitude of the flat fading channel or the amplitude of the first path (p=0), respectively. Under the same assumptions as above, α follows then a Ricean distribution, with the probability density function

( )ααα α α

− + Ω≥

Ω Ω

=

2 /0

2p( ) e I 2 ; 0RiceK RiceK (2.31)

where I0 denotes the modified Bessel function of order 0. The Ricean factor KRice denotes the ratio between the power of the LOS path and the mean power of the scattered paths. The phase is again uniformly distributed in the interval [0,2π[.

2.2.7 Propagation environments

Today’s wireless communication systems generally split their service area into multiple geographically separated cells. Within these cells a basestation serves several mobile terminals. According to the propagation environment and the number of users to be served, the cells vary in size and shape [Rap02]. Generally three typical cell types are distinguished:

Macrocells are found in outdoor suburban or rural environments and have a radius starting from several hundreds of meters and going up to several tens of kilometres. The basestation antenna is generally located high above the rooftop level, where local-to-base scattering effects are negligible. The mobile terminal speed corresponds to that of vehicles and can attain up to 300 km/h for high speed trains. A LOS path is rarely present since the mobile is mostly surrounded by big structures like houses or hills. The macrocell environment is characterised by a moderate or high delay spread, which depends on the presence of remote scatterers, high Doppler spread and low to moderate angle spread at the basestation.

Microcells have a cell radius of typically 50 metres to 500 metres and correspond to outdoor propagation environments like urban areas or city centres. The basestation is often located below rooftop level, and the maximum terminal velocities correspond to city traffic, i.e. around 50 km/h. A LOS path is often present but NLOS situations also occur frequently. Hence in microcells, there is a moderate delay spread and Doppler spread and a considerable angle spread at the basestation.

Picocells are very small cells and generally used in indoor environments, where the range is typically up to several tens of meters. A LOS path may be present if the mobile and the basestation are located in the same room. Otherwise, NLOS situations are generally found. Both, basestation and mobile terminals are surrounded by a large number of scatterers. The mobile speed is very low and does not exceed that of pedestrians, i.e. around 3 km/h. In such indoor environments, the Doppler spread and the delay spread are low, while very large angle spreads occur at the basestation.

Environment RMS Delay Spread [ns]

Angle Spread [deg]

Max. Doppler frequency [Hz]

Macrocell (Outdoor) Up to 500 5 up to 1000

Microcell (Outdoor) 120 10-30 200

Picocell (Indoor) 50 360 10

Tab. 2.1: Typical channel characteristics for different environments at 5 GHz.



Tab. 2.1 summarises values for the channel characteristics at 5 GHz in the three typical environments. The first two columns correspond to channel measurements carried out within COST-259 [Cor01], and the third column was directly calculated from the considered mobile speeds using (2.14).

2.3 Practical channel modelling

The simulation of wireless systems necessitates the development of mathematical models for the generation of the impulse response or the transfer function of the time varying channel. Basically three different kinds of models can be found in the literature: Statistical channel models use random variables to reproduce the channel behaviour. The laws for these variables are obtained by assumptions on the radio propagation. Statistical models are generally easy to implement and allow fast simulations. Empirical models are based on real channel measurements. The mathematical model then tries to imitate the measured radio channel. Their complexity and accuracy depend on the level of detail of the measurements. Deterministic models aim at reproducing the physical wave propagation and generally employ ray tracing algorithms together with knowledge about the propagation environment. Deterministic models achieve a high accuracy at the price of a very high complexity and long simulation times. There also exist hybrids of these models, which are a trade-off between computational complexity and accuracy.

As for spatial channel models, basically two approaches can be found in the literature. There are models based on directional information, i.e. the DOAs of the propagation paths, and models based on a statistical description of the fading correlation at different antennas. The directional models correspond to the vector channel description presented in section 2.2.4. A good overview of these models can be found in [ErCa98]. The directional information can be generated by a geometrical approach, where scatterers are randomly placed in the propagation environment according to spatial distributions. Then, ray tracing yields the propagation paths from the transmitter to the receiver and the corresponding power azimuth spectrum [Cor01] [LiRa99][ZoMa00]. Another possibility is to randomly choose the directions according to a probability density function obtained from assumptions about the locations of the scatterers [Cor01][FuMo98][SCM03]. Correlation based models use covariance matrices obtained from assumptions about the environment in order to draw the elements of the channel vector from a multivariate probability distribution [ShFo00][Schu00]. A hybrid of the directional and the correlation based approaches is the Gaussian Wide Sense Stationary Uncorrelated Scattering (GWSSUS) model, where the signal impinges from several clusters of scatterers, each of them being characterised by a mean DOA and a covariance matrix [ZeOt95].

In the following, we introduce the two channel models selected for the computer simulations in this thesis. Besides the complexity and the expected simulation time, the criteria for the selection of the channel models are system considerations like the carrier frequency, the bandwidth and the targeted environments. Furthermore, we also have to take into account practical arguments like the comparability with existing results and the possibility to produce reference curves in order to facilitate comparison with the analysis. We only consider models based on directional information, since this information is required for the studied beamforming approaches. The system considerations are basically those used in [MAT,D1.4] and given in Tab. 2.2.

Carrier frequency 5 GHz

Bandwidth Around 50 MHz

Environments Indoor(Picocell)/Outdoor (Microcell)

Tab. 2.2: System considerations.

2.3 Practical channel modelling


For this kind of system, there exits a channel model that has been worked out at ETSI for the standardisation of HIPERLAN/2 [Med98a]. However, this model is only suited for SISO systems and thus has to be extended to a vector model for MISO and SIMO. The second model used in this thesis is the wideband spatial channel model proposed by the combined 3GPP/3GPP2 Spatial Channel Model Ad-Hoc Group [SCM03].

2.3.1 The HIPERLAN/2 model and its vector extension

The channel model used in the standardisation of HIPERLAN/2 [Med98a] is a hybrid of a statistical and an empirical channel model. The channel impulse response is given by an expression similar to (2.8):

( ) ( )1

( )

0

, ( ) ep

p

Nj t

B p pp

h t t ϕτ α δ τ τ−

=

= −∑ (2.32)

Here, it is assumed that each path contains a large number of sub-paths so that it has a time varying Rayleigh fading amplitude, αp(t), of variance Ωp and a phase ϕp(t) that is uniformly distributed in [0,2π[ (cf. section 2.2.6). The Doppler spectrum assumed for each path is the classical Jakes spectrum given in (2.18). The power delay spectrum of the model, i.e. the variances Ωp and the delays τp , was obtained empirically, and several power delay spectra were specified for different environments in [Med98b]. For the simulations in this thesis, we will refer to the channel model A and the channel model E. The details of these models can be found in the appendix A.2 and Fig. 2.7 illustrates the power delay spectrum of channel model E. Note that the variances of the different paths are always given with respect to the strongest one.

0

0,2

0,4

0,6

0,8

1

1,2

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Delay (ns)

Var

iance

of p

aths

0

0,2

0,4

0,6

0,8

1

1,2

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Delay (ns)

Var

iance

of p

aths

Fig. 2.7: Power delay spectrum of HIPERLAN/2 channel model E [Med98b].

In order to extend this model for MISO and SIMO configurations, directional information can be added by allocating an angle, θp , i.e. a DOA, to each path with respect to the antenna array. Then, the vector channel impulse response is obtained in analogy to (2.24) as

( ) ( ) ( )1

( )

0

, ( ) ep

p

Nj t

B p p pp

t t ϕτ θ α δ τ τ−

=

= −∑h a (2.33)

Thereby it is assumed that the angle spread of the sub-rays arriving at the same delay is negligible. The angles θp are chosen according to a uniform distribution within an angular range of ∆θmax around a mean angle θ , which is defined as



1

01

0

p

p

N

p ppN

pp

θθ

−

=−

=

Ω=

Ω

∑

∑ (2.34)

Note that this definition fails if the mean angle is close to the discontinuity of the considered angular notation, e.g. close to 0 for θp∈[0,360°[ or close to 180° for θp∈[-180,180°[ and that the notation has to be chosen accordingly. The mean angle itself is chosen uniformly distributed in the operating range of the array antenna, e.g. [0,360°[ for an UCA and [30°, 150°] for an ULA.

This vector channel model is easy to implement and facilitates comparison with single-antenna results since it is based on a scalar model that is very common in literature. However, this model does not ensure the consistency of the angle distribution with respect to the power delay spectrum, since the angles are chosen independently of the power delay spectrum. To give a simple example, two paths having a large difference of their delays are also likely to impinge from very different directions and vice versa. A more sophisticated model that ensures the consistency between the spatial and temporal description and that can also be used for MIMO configurations is cited in the next section.

2.3.2 The 3GPP/3GPP2 Spatial Channel Model

The model proposed by the combined 3GPP/3GPP2 Spatial Channel Model Ad-Hoc Group [SCM03] is one of the most elaborated direction based channel models at the time being. It is a statistical model and based on the superposition of waves (or sup-paths) that are drawn with respect to carefully chosen probability density functions. This principle is similar to the description of Fig. 2.3.

In contrast to the previous section, the sub-paths are explicitly modelled. This means that the amplitudes, phases and angles of the sub-paths are modelled by random variables and chosen from probability density functions, which are specified for different propagation scenarios. Note that the statistical laws of theses variables are correlated. The model ensures the consistency of the probability density functions by the use of correlation matrices [SCM03]. Once all random variables are drawn, the channel model evolves in time in a completely deterministic manner with the movement of the mobile terminal.

Details about the probability density functions of the different variables can be found in [SCM03] and appendix A.5. Note that a specific parameterisation of the model is used to adapt it to the propagation conditions at 5 GHz and to ensure the backward compatibility with the HIPERLAN/2 model. This parameterisation was specified in the MATRICE project [MATRICE].

2.4 Multiple access techniques

Modern cellular systems are intended to enable simultaneous communications of multiple users. These users have to share the bandwidth available for a wireless communication system. The aim of multiple access techniques is to efficiently use the bandwidth, while ensuring good transmission quality for all active users.

2.4.1 Duplexing

Duplexing is a property known from the conventional telephone system, where the user can speak and listen simultaneously, and is provided by most wireless systems. The duplex mode in wireless

2.4 Multiple access techniques


communications defines the way the bandwidth is shared between the downlink and the uplink. Two basic duplex modes are depicted in Fig. 2.8.

DL

Time

Guard band

UL

Frequency

Frequency Division Duplex (FDD) Time Division Duplex (TDD)

UL

Time

Guard time

DL

Frequency

UL

Guard time

DL

Time

Guard band

UL

Frequency

Frequency Division Duplex (FDD) Time Division Duplex (TDD)

UL

Time

Guard time

DL

Frequency

UL

Guard time

Fig. 2.8: Duplex modes.

Frequency Division Duplex (FDD) In FDD the up- and down-links are allocated in different frequency bands. These frequency bands are separated by a guard band. FDD requires a special device in the transceiver called duplexer that separates the RF chains of the receiver and the transmitter so that they can operate simultaneously [Rap02]. Other drawbacks of FDD are the loss in bandwidth due to the guard band and a lack of flexibility due to the fact that a constant bandwidth is always allocated to the UL and the DL regardless of the traffic conditions. On the other hand, the independent simplex links of FDD facilitate synchronisation and may have some advantages in multi-cellular contexts. These are the reasons why FDD is generally used in outdoor systems with large ranges [Rap02]. Another important point concerns the channel states of UL and DL in FDD. Channel state information is obtained from estimation at reception and may, in some cases, be used for adapting the transmitted signal to the channel (cf. Fig. 2.1). In FDD, the channel fading in one link generally differs considerably from the fading in the other link, since the difference between the carrier frequencies generally exceeds the coherence bandwidth of the channel. However, it can still be assumed that the propagation conditions are similar and that at least the number of paths and the DOAs are identical in UL and DL. This property can, thus, be exploited for beamforming at transmission (cf. chapter 5).

Time Division Duplex (TDD) TDD uses the same frequency band for UL and DL and allocates them in different time slots. Thus, this system is not real duplex, but the UL and DL transmissions alternate so quickly that the user is not aware of the difference. TDD requires a precise time synchronisation of the mobile and the terminal to ensure that the UL and DL transmission slots are well respected. Additionally, a guard time is generally left between the slots as shown in Fig. 2.8. The advantages of TDD are the simplified transceiver, which does not require the duplexer, and an increased flexibility to cope with variable traffic, since the length of UL and DL slots can be varied. However, because of its high demands in terms of synchronisation TDD is generally limited to indoor transmissions within a short range [Rap02]. Since UL and DL use the same carrier frequency in TDD, the channel state can be assumed identical for consecutive UL and DL time slots, provided that the UL and DL slots lie within the coherence time of the channel. Then, a system can benefit from channel reciprocity and use channel estimates obtained at reception to adapt the transmitted signal with respect to the current channel conditions (cf. section 3.4 and chapter 4).



2.4.2 Multiple access schemes

The duplex modes are used to allocate the UL and DL of a single user within the considered frequency band. Similar principles can also be used to allocate the signals of different users sharing the same system resources. Fig. 2.9 illustrates three multiple access principles [Rap02]. The three dimensions representing the system resources are frequency, time and the spreading code. The code dimension may equivalently be seen as the dimension of transmitted power. Thus, the figures show how the transmitted power of each user is distributed in time and frequency.

Code

Frequency

Time

User 3

User 2

User 1

Time

Code

FrequencyUse

r 1

Use

r 2

Use

r 3

User 1

Code

Frequency

Time

User 2User 3

TDMA CDMAFDMA

Code

Frequency

Time

User 3

User 2

User 1

Time

Code

FrequencyUse

r 1

Use

r 2

Use

r 3

User 1

Code

Frequency

Time

User 2User 3

TDMA CDMAFDMA Fig. 2.9: Multiple access schemes.

The two dimensions, frequency and time, were already used for the duplexing mode. When the users are separated in frequency the multiple access scheme is called Frequency Division Multiple Access (FDMA), and when they are separated in time the scheme is called Time Division Multiple Access (TDMA). For transmitting the same amount of information FDMA uses a narrow bandwidth and a long duration, while TDMA uses a large bandwidth and a short duration. Note here that the transmit power per user is relatively lower in FDMA than in TDMA. The disadvantage of these techniques is the lack of flexibility. Indeed, if a user is idle, a part of the available time-frequency space is unused. Furthermore in these schemes, the users transmit a relatively high power, when they are active and no power otherwise. This leads to interference peaks in multi-cellular contexts, where the users interfere with the neighbour cells. Thus, TDMA and FDMA require a careful cell planning in multi-cellular systems.

The third scheme is called Code Division Multiple Access (CDMA). It allows multiple users to access the channel at the same time and on the same frequency, by allocating a distinct spreading code to each of them. It is thus more flexible than the previous two techniques and ensures that the complete time-frequency space is always used for signal transmission. Hence, the power of an active user is spread over the whole time frequency space, and the interference created in a multi-cellular context is averaged in the same way. This interference can be further reduced by using different scrambling codes in the cells, which considerably facilitates the cell planning task [HoTo00].

Recently, the use of multiple antennas for beamforming brought up a new access scheme called Space Division Multiple Access (SDMA). The principle of SDMA is illustrated in Fig. 2.10. The basestation communicates with several users by using a different antenna pattern, i.e. a beam, for each of them. Indeed, this scheme can be seen as an extension of cell sectorisation when fixed beams are used. More sophisticated systems use adaptive antenna arrays with beams that can follow the users’ movement. In contrast to the three previous schemes, SDMA does not actively separate the signals of users, but rather benefits from the fact that they are spatially-separated. Indeed, if two users are located at similar positions, SDMA is not applicable and other schemes have to be used. Therefore, SDMA is mostly used in conjunction with other multiple access schemes [Far99].

2.5 Orthogonal Frequency Division Multiplex (OFDM)


BasestationBasestation

Fig. 2.10: Principle of SDMA.


The MC-CDMA system considered in this thesis relies on OFDM as baseband modulation scheme. The OFDM scheme is the most prevalent multi-carrier system in today’s wireless communications and has proved its efficiency especially for DAB, DVB-T, and in WLAN standards [ETSI97a,b][IEEE99][ETSI01].

2.5.1 OFDM basics

The principle of multi-carrier systems is to divide an initial stream into NC parallel sub-streams of lower transmission rate and, thus, longer symbol time, TS , and smaller bandwidth B. These streams are transmitted over different subcarriers regularly spaced in the frequency domain. Thanks to this principle, multi-carrier modulations are robust to multipath propagation and frequency selective fading. Indeed, the use of a large number of subcarriers resulting in a small bandwidth and equivalently a long symbol time, can ensure that the channel fading on each subcarrier is flat (cf. section 2.2.2).

OFDM uses a spacing between the frequencies equal to the Nyquist bandwidth of the parallel sub-streams, i.e. ∆f =1/TS. Hence, the frequencies of the NC subcarriers in the baseband are given by

/ ; 0... 1n S Cf n f n T n N∆= = = − (2.35)

Denoting the complex data symbol at instant i on subcarrier n by xi,n and assuming a rectangular pulse shaping, the modulated OFDM signal is given by the following expression

1 2

,0

1( ) rect ( ) eC

S

S

nN j tT

i n T Sn i S

s t x t iTT

π− +∞

= =−∞

= −∑ ∑ (2.36)

The power density spectrum of s(t) can be obtained as

( ) ( )1

2

0

sinc ( )CN

S Sn

S f E f T n−

=

= −∑ (2.37)



S(f )

fBOFDM

S(f )

fBOFDM

Fig. 2.11: Power density spectrum of OFDM. The power density spectra of the different subcarriers are depicted in Fig. 2.11. The orthogonality of the subcarriers arises from the fact that the power density spectrum of each subcarrier has zeros at the maxima of all other subcarriers. S(f ) as the sum of these spectra decreases with 1/f 2 outside the interval [-(NC+1)/(2TS),(NC+1)/(2TS)]. Hence, the bandwidth of the OFDM signal is given as

( 1)/ /OFDM C S C SB N T N T= + ≈ (2.38)

The approximation holds for a large number of carriers. In this case, OFDM has the same spectral efficiency than classical single-carrier QAM modulation [Pro95].

Baseband modulation is generally done in the digital domain, i.e. before D/A conversion. OFDM has the nice property that the digital realisation is very simple, since the algorithms for Discrete Fourrier Transform (DFT) can be employed. Denoting the sampling time by TC and assuming that TS is a multiple of it, i.e. TS =NSTC , the sampled version of the modulated signal in (2.36) is

1 12 ( ) 2

, ,0 0

1 1( ) e eC CS C

S C

n nN Nj iT T jT N

S C i n i nn nS S

s iT T x xT T

ςπ ς πς

− −+

= =

+ = ⋅ = ⋅∑ ∑ (2.39)

Hence, the sampled modulated signal is just the Inverse DFT (IDFT) the complex data symbols transmitted over the NC subcarriers. Note that the Nyquist sampling theorem requires NS ≥NC. For NS >NC , a DFT size of NS is performed and zero padding is done on the overhead bins. In the same way, the OFDM demodulation can be represented by the DFT operation. For a further reduction of complexity, the algorithms for Fast Fourrier Transform (FFT) and Inverse FFT (IFFT) are generally employed in practice.

The use of the longer symbol period with OFDM already reduces the impact of the ISI arising from the delay spread of the channel. To completely cancel the ISI in the system, it is common to insert a guard interval between the consecutive OFDM symbols, which is illustrated in Fig. 2.12.

The duration of the guard interval is denoted by TG . It is simply a cyclic prefix using the tail samples of the modulated signal as depicted in Fig. 2.12. The new duration of the overall OFDM symbol is defined as TS' =TS+TG . In order to completely cancel the ISI introduced by the delay spread of the channel, the duration of the guard interval has to be longer than the maximum channel delay, i.e.

maxGT τ> (2.40)



tTG TS

cyclic prefix cyclic prefix

Overall durationTS'

s(t)

tTG TS

cyclic prefix cyclic prefix

Overall durationTS'

s(t)

Fig. 2.12: Insertion of a guard interval.

Note that the insertion of a guard interval leads to a loss in spectral efficiency, because it reduces the transmission rate. Furthermore, the overhead of the cyclic prefix increases the signal power spent for the transmission of a bit, Eb. As a rule of thumb, the guard interval is generally kept shorter than a quarter of the symbol time, i.e. TG ≤ TS/4, which leads to an increase of transmit power of less than 1dB [NePr00].

An important drawback of OFDM is the non-constant envelope of the modulated signal, which makes the A/D conversion difficult and reduces the efficiency of the RF power amplifier. In this context, the Peak-to-Average Power Ratio (PAPR) is defined as the peak power of the modulated signal divided by its average power [HaMü03][NePr00]. Indeed, the OFDM signal is a sum of a large number of signals with different carrier frequencies. When these signals add coherently, it results a power peak which equals NC times the average power. Thus, the PAPR increases for an increasing number of subcarriers. Countermeasures are the clipping of high signal peaks and the use of special encoding and scrambling schemes to avoid coherent signal addition [HaMü03] [NePr00].

The choice of the parameters of an OFDM system is a trade-off between various conflicting requirements. A typical design is based on a given system bandwidth BOFDM and a given maximum channel delay τmax [NePr00]. To ensure an ISI free system, the guard interval is chosen according to (2.40). Then, the symbol time, TS , is set to at least four times the guard interval, TG , to limit the loss due to the overhead. The upper limit for TS is equivalent to the maximum number of subcarriers, since NC =BOFDMTS from (2.38). Recalling that the carrier spacing for OFDM is ∆f =1/TS, the limit is given by the minimum carrier spacing that is tolerable by the system requirements. Indeed, the Doppler spread broadens the spectrum of the received signal and the spectra of closely spaced subcarriers may overlap for high velocities. This gives rise to Inter Carrier Interference (ICI). To avoid this effect, the subcarrier spacing has to be chosen much larger than the range of the Doppler power spectrum, i.e. ∆f >>2fD,max (cf. section 2.2.3). A low carrier spacing also makes the system more sensitive to frequency offsets and phase noise [NePr00]. Furthermore, a high number of subcarriers induces a high PAPR and requires a more complex implementation. In the sequel, we refer to a well designed system as ideal OFDM system. In such a system, the receiver is well synchronised to the transmitted signal in time and frequency, the system is free from ISI and ICI, and that the channel is stationary during the OFDM symbol period. The corresponding requirements for the system parameters are summarised in Tab. 2.3.

TG >τmax ISI free

∆f >>2fD,max ICI free

TS+TG <<TC Time invariance

Tab. 2.3: Parameters of a well designed OFDM system.



2.5.2 Frequency domain channel

Within this thesis, we often represent the multipath channel in the frequency domain (cf. Fig. 2.1). This representation is valid for a well designed system as defined in Tab. 2.3. The frequency transfer function of the channel given in (2.9) and sampled at frequencies n∆f and for each OFDM symbol duration iTS’ is

( ) ( ), , ,11

( 2 ' ), , ,

0 0

, ' eSPP

D p s S p p sNN

j f iT n fB i n B S p s

p s

H H n f iT π τ ϕα

−−− ∆ +

= =

= ∆ = ∑ ∑ (2.41)

This means that the frequency-domain channel can be represented by a complex flat fading coefficient on each subcarrier n and for each OFDM symbol i. The baseband transmission scheme obtained with the frequency-domain channel model is depicted in Fig. 2.13.

The input stream is serial to parallel converted into NC parallel sub-streams, whose symbols at instant i are denoted by xi,0,…, xi,Nc -1. These symbols are transmitted over parallel flat fading channels. Indeed, each of them is multiplied by the corresponding channel coefficient, and a noise sample denoted by χi,n is added. The noise samples can be assumed to correspond to Additive White Gaussian Noise (AWGN) and to have an identical variance of σC

2. This variance is identical to the noise spectral density at the receiver, i.e. σC

2=N0 [Pro95]. The received samples on each sub-channel are given by

, , , , , ; 0... 1i n B i n i n i n Cy H x n Nχ= + = − (2.42)

S/P P/S

xi,0

xi,Nc-1

HB(0, iTS')

HB((NC -1)∆f, iTS')

yi,0

yi,Nc-1

χi,Nc-1

χi,0

S/P P/S

xi,0

xi,Nc-1

HB(0, iTS')

HB((NC -1)∆f, iTS')

yi,0

yi,Nc-1

χi,Nc-1

χi,0

Fig. 2.13: Frequency domain channel representation.

The frequency-domain channel model considerably simplifies the implementation of simulation chains for OFDM based systems, since it replaces IFFT and FFT operations, the time domain convolution with the channel impulse response, and the guard interval insertion and cancellation by a simple multiplication. The channel coefficients in the frequency domain can be calculated from the time domain channel response by a single FFT operation. However, it has to be verified that the frequency-domain model is valid for the considered channel parameters. This is especially sensitive when high Doppler variations occur like in scenarios with high mobility. Unless otherwise stated, we use the frequency-domain channel representation throughout the following chapters of this thesis.



The frequency-domain channel obtained with OFDM can also be represented by the following two dimensional scheme:

Time

TS'

∆f

Frequency

BOFDM =NC ∆f

HB(n∆f, iTS')

Tcoh

Bcoh

TF = NF⋅TS'

Time

TS'

∆f

Frequency

BOFDM =NC ∆f

HB(n∆f, iTS')

Tcoh

Bcoh

TF = NF⋅TS'

Fig. 2.14: OFDM time-frequency frame representation.

Fig. 2.14 represents an OFDM frame of duration TF that consists of NF OFDM symbols, each of them spanning NC subcarriers within a bandwidth of BOFDM . Each square within this frame corresponds to a time-frequency position (iTS',n∆f ) spanning a bandwidth ∆f and a duration TS'. These positions can carry different complex data symbols and are affected by distinct channel coefficients Hb(n∆f, iTS' ). Around a given frame position, a rectangle spanning Bcoh/∆f subcarriers and Tcoh/TS' symbol durations represents the time-frequency range in which the channel coefficients are highly correlated. As a consequence, time and frequency diversity can be achieved by transmitting redundant information over positions that cannot be covered by one and the same rectangle. Redundancy is added to the data symbols by creating different versions of the same symbol, i.e. spreading, or by creating symbols containing redundant information, i.e. by channel coding. To ensure that redundant versions of the same information are transmitted over uncorrelated positions a symbol interleaving is generally performed. The maximum degree of diversity offered by one time-frequency OFDM frame, DO , can be approximated as the product of the diversity degrees in time, DT , and in frequency, DF , i.e.

O T FD D D= , with /T F cohD T T= and /F cohD B B= . (2.43)


3 The Multi-Carrier CDMA system The combination of OFDM and CDMA has been subject to intensive research during the past ten years, and we already gave an overview in the introduction. Here, we describe and compare the different schemes proposed for the transmitter and the receiver including an assessment of channel estimation techniques. Starting from these conventional SISO systems, we evaluate the potential benefits arising from the use of the spatial dimension.

3.1 Transmitter structure

A general structure of the MC-CDMA transmitter covering several variants of this transmission scheme is considered in the sequel. Fig. 3.1 shows the general structure of the basestation transmitter employed in the DL, where K users are served simultaneously. The transmitter structure used at the mobile in the UL is, thus, simply obtained by setting K =1.

user 1d1

user KdK

↑ L

c1,l

↑ L

cK,l

. . .

Chip-wisesumming

Chipmapping

0

NC -1

OFDM+

Guard Interval

xl

. . .

user 1d1

user KdK

↑ L

c1,l

↑ L

cK,l

. . .

Chip-wisesumming

Chipmapping

0

NC -1

OFDM+

Guard Interval

xl

. . .

Fig. 3.1: General structure of the MC-CDMA transmitter at the basestation.

The complex data symbols of the K users are denoted by dk . Note that for simplicity, time indices are omitted in this description wherever possible, but obviously symbol streams are always considered. First, these data symbols are spread into L chips by up-sampling and multiplying with the user-specific spreading code. The spreading code is given by a normalised code vector of length L composed of elements ck,l and defined as follows:

,0 , 1, ...,T

k k k Lc c − = c with 2 1k =c (3.1)

Several choices for the spreading codes are presented in section 3.1.3. The role of this code is to separate the signals of the different users so that each of them can be extracted from the received signal by despreading with the user-specific code. Since orthogonal spreading codes are commonly used for this kind of system, spreading ensures the orthogonality of the users’ signals or simply the orthogonality of users. The chips of all users are summed in order to obtain the

An expert is a man who has made all the mistakes that can be made, in a narrow field.

Niels Bohr (1885-1962)

Chapter 3: The Multi-Carrier CDMA system


information bearing symbols transmitted by the underlying OFDM system. These symbols are denoted by xl and gathered in the symbol vector of length L given by

[ ]0 11

, ...,K

TL k k

kx x d−

=

= = ∑x c (3.2)

The following chip mapping allocates the elements of the symbol vector to L positions in the OFDM frame. Within this work the term MC-CDMA is used in a general sense for a combination of OFDM and CDMA irrespective of the different variants for the chip mapping. Unless otherwise stated, we adopt a system description based on these L frame positions. This description can be applied without loss of generality in the case when the bits of each data symbol, dk, are detected independently and the respective position of consecutive data symbols in the OFDM frame is not of importance. This condition is satisfied in particular when no channel coding and no feedback of the decisions taken on preceding data symbols is considered.

The underlying OFDM transmission is assumed to be ideal in the sense that the multipath fading channel in the frequency domain can be represented by a complex flat fading coefficient on each frame position (cf. section 2.5.2). The coefficients corresponding to the channel between the basestation and the mobile terminal g on the chip positions l =0…L-1 are denoted by hg,l and gathered in the vector

,0 , 1, ...,T

g g g Lh h − = h (3.3)

3.1.1 Downlink signal

In the downlink, the signals of all users travel from the basestation to mobile terminal g through the same channel hg . Using expression (2.41), the received signal vector of the L chip positions is given by

1

K

g g k kk

d=

= + = +

∑y h x n h c no o (3.4)

where n gathers the AWGN terms on the L positions and o denotes the element-wise vector product. The different channel fading on each chip breaks the orthogonality of users’ signals installed by the spreading code. As a consequence, the signal obtained by despreading at the receiver not only contains the desired users’ signals but also interference from the other users’ signals. This interference is called Multiple Access Interference (MAI). Nevertheless in the downlink, the signal contributions of all users are subject to the same fading, and the MAI can be mitigated at the mobile receiver by appropriate equalisation techniques preceding the despreading operation, which can completely or partly restore the orthogonality among users’ signals.

3.1.2 Synchronised uplink signal

In the uplink, the signals of the different users are transmitted by their mobile terminals and reach the basestation through independent channels. The received signal at the basestation is a superposition of all these signals. In contrast to the downlink, the signals may arrive at the basestation with different time delays due to the different positions of the mobile terminals. This is referred to as an asynchronous uplink. In a synchronised uplink, the mobiles are aware of their respective propagation delay to the basestation and compensate this delay by a timing advance. Assuming that the guard interval absorbs the remaining delays between the users’ signals, these signals can be jointly OFDM demodulated. Then, the received signal in the synchronised uplink is given by the following expression

3.1 Transmitter structure


( )1

K

k k kk

d=

= +∑y h c no (3.5)

Comparing with (3.4), the channel vector has moved into the sum as a consequence of the different channels between each mobile and the basestation. This has an important impact on the MAI. Indeed, the MAI after despreading is generally increased compared to the downlink case. Furthermore, it can not be mitigated by equalising techniques aiming at the restoration of orthogonality, since only one fading channel can be equalised at once.

3.1.3 Spreading

The spreading code vector defined in (3.1) can be chosen from a variety of code sets. The choice of the spreading code depends on several factors such as the orthogonality and correlation properties of the codes, the synchronism of users, the implementation complexity, and the impact on the PAPR of the resulting signal. In the downlink, where the signals of the different users are synchronously transmitted, orthogonal code sets are generally used. Examples of such orthogonal codes are Walsh-Hadamard codes, Golay codes, and orthogonal Gold codes [Nob03][Pop99]. In the uplink, code orthogonality is less important since the users’ signals propagate through different transmission channels, which irreparably breaks their orthogonality. Here, simple Pseudo Noise (PN) sequences [Pro95] can be chosen. For asynchronous uplink systems, codes with a good cross-correlation property, e.g. Gold codes [Pro95], are required.

Concerning the influence of the spreading codes on the PAPR, several studies show that Golay or Zadoff-Chu sequences can considerably reduce the PAPR, especially in the uplink [NoHe02][Pop99]. Note however that the PAPR is also influenced by the scrambling, which is used to separate signals of different cells in a multi-cellular context and may be optimised with respect to the resulting PAPR [NePr00].

In order to accommodate users with different requirements in terms of bit rate and QoS, different spreading factors can be used for different users. The use of such a variable spreading factor was proposed in [AtMa02]. Furthermore, when the fading on the different chips is correlated, the choice of the spreading codes has an impact on the resulting MAI level. Taking the example of a downlink transmission with a Walsh-Hadamard code set and a number of users inferior to the size of the set, it was shown in [MoCa00] that the order in which the codes are allocated strongly influences the MAI (cf. section 5.5.1).

Walsh-Hadamard (W-H) code sets are the most common orthogonal codes for the downlink and are simple to generate. When the spreading factor is a power of two, the W-H matrices are obtained by the iterative rule

/2 /2

/2 /2

2 , 1L L mL

L L

L m

= ∀ = ≥ −

C CC

C C with 1 1=C . (3.6)

The spreading code vectors defined in (3.1) simply correspond to the lines, or equivalently the columns, of this quadratic matrix, which are normalised accordingly. The maximum number of users, K, that can be allocated with W-H codes is thus equal to L. W-H matrices also exist for spreading factors others than powers of two, which is detailed in appendix A.3. Furthermore, W-H spreading can easily be implemented using the Fast Hadamard Transform algorithm. Within this thesis, we mostly employ W-H spreading codes.



3.1.4 Chip mapping

The role of chip mapping is to allocate the L chips of the spread signal to positions in the OFDM frame. Different mapping schemes are illustrated in Fig. 3.2 using the two dimensional representation of the OFDM frame introduced in section 2.5.2.

time

frequency

Chips of symb. 2

Tcoh

Bcoh

a) spreading in time b) spreading in frequency

c) spreading in time and frequency

d) spreading and interl.in time and frequency

Chips of symb. 0

Chips of symb. 1

LT

LF

time

frequency

Chips of symb. 2

Tcoh

Bcoh

a) spreading in time b) spreading in frequency

c) spreading in time and frequency

d) spreading and interl.in time and frequency

Chips of symb. 0

Chips of symb. 1

LT

LF

Fig. 3.2: Chip mapping schemes.

Spreading in time

The first mapping (a) corresponds to a symbol spreading in the time dimension only. A system employing this scheme can be considered as synchronous MC-DS-CDMA [FaKa03]. In practice, spreading in the time dimension yields a high correlation of the channel coefficients affecting the different chips since the coherence time of the channel generally spans a large number of OFDM symbols. A strong correlation of the fading coefficients affecting the chips has the advantage that the orthogonality of the users’ signals is almost conserved, which leads to a low MAI at the receiver. Note that this holds for both, the uplink and the downlink. The disadvantage of correlated fading on the chips is that only a low diversity gain is obtained from spreading. In this case, a strong channel coding and an efficient bit interleaving is required to benefit from the diversity offered by the channel.

Spreading in frequency

Spreading in frequency according to the scheme (b) was used in the original propositions for MC-CDMA [HaPr97]. Depending on the relation of the spreading factor and the coherence bandwidth of the channel, this scheme can benefit from a high frequency diversity by spreading over subcarriers spanning several times the coherence bandwidth. However, the diversity is obtained at the price of a high MAI level. This penalises spreading in frequency, especially in the uplink, where the MAI cannot be mitigated by equalisation.

3.2 Receiver structure and detection algorithms


Spreading in time and frequency

Scheme (c) represents two dimensional spreading in time and frequency. Here, the overall spreading factor is the product of the spreading factors in the two dimensions.

F TL L L= (3.7)

For two dimensional spreading, the code vectors can be built from different spreading codes in frequency and time of lengths LF and LT , respectively [EgRe97]. Alternatively, the chips of a single spreading code of length L can be consecutively mapped to the frame positions. There is again the trade-off between diversity and MAI. A large spreading factor together with two dimensional spreading in the OFDM frame can collect the maximum diversity offered by the channel [EgRe97]. In contrast, two dimensional spreading within the rectangle given by the coherence time and bandwidth (cf. Fig. 2.14) yields a high correlation of the fading affecting different chips and consequently a low MAI level [PeOt02]. In [AtMa02], LF and LT are adapted to the channel characteristics and the data symbol constellation. The principle is to apply spreading within the coherence rectangle for the usage with a high constellation size in good propagation conditions (small cells), whereas a robust constellation, e.g. QPSK, with high diversity is used in bad propagation conditions (large cells with high mobility).

Chip interleaving

In contrast to chip mapping on adjacent frame positions, the chips can be interleaved in order to transmit them on distant positions in the OFDM frame (d). The aim of interleaving is to obtain an independent fading on the different chips, which is the case when the chips are transmitted on positions that cannot be covered by one and the same coherence rectangle (cf. section 2.5.2). In this way, a diversity order corresponding to the spreading factor can be achieved, provided that the channel offers this degree of diversity [Kai98]. Note that time interleaving may cause a latency in the transmission since despreading has to be done from a large number of consecutive OFDM symbols.


Fig. 3.3 shows the structure of the general MC-CDMA receiver employing linear detection techniques. After removing the guard interval, OFDM demodulation, and chip de-mapping, the downlink and uplink signal on each chip position is given by (3.4) and (3.5), respectively.

Chipde-

mapping

0

NC -1

RemoveGuard Int.

&OFDM-1

0

L -1

ˆgd

. . .

. . .

*,0gq

*, 1g Lq −

Chipde-

mapping

0

NC -1

RemoveGuard Int.

&OFDM-1

0

L -1

ˆgd

. . .

. . .

*,0gq

*, 1g Lq −

Fig. 3.3: MC-CDMA receiver structure with linear detection.

The linear detector corresponds to a recombination of the L elements of vector y yielding the decision variable for the desired user g denoted by ˆ

gd . This is done by complex combining weights qg,l , which ensure despreading and frequency-domain equalisation. These weights are gathered in a vector defined as

,0 , 1, ...,T

g g g Lq q − = q (3.8)



Note that the complex conjugate of these weights are used for combining and the decision variable for both links is given by the following scalar product

ˆ Hg gd = q y (3.9)

Using this expression together with (3.4) and (3.5) respectively, the decision variable of the downlink is

DL: ( ) ( )1,

NoiseDesired part MAI

ˆK

H H Hg g g g g g g k k g

k k g

d d d= ≠

= + +∑q h c q h c q no o

1442443 144424443

(3.10)

and the corresponding expression of the uplink is

UL: ( ) ( )1,


ˆK

H H Hg g g g g g k k k g

k k g

d d d= ≠

= + +∑q h c q h c q no o

1442443 144424443

(3.11)

Both decision variables are composed of three characteristic terms: the desired signal part, the interference from users other than g, i.e. the MAI, and the residual noise after despreading. Note that the residual noise after combining stays Gaussian, but its variance is modified by the combining weights. Thus, from the variance of the noise on each subcarrier, σC

2, the variance of the residual noise is given by

22 2

n C gσ σ= q (3.12)

3.2.1 Single-User Detection

Single-User Detection (SUD) techniques only use knowledge about the signal of the desired user for optimising the combining vector qg . To ensure the operations of despreading and frequency-domain equalisation, SUD requires knowledge of the spreading code vector cg and the channel vector hg . Here, the most common approaches are presented together with an assessment of their influence on the three characteristic terms and their fields of application.

3.2.1.1 Maximum Ratio Combining

Maximum Ratio Combining (MRC) is a well known technique for diversity combining. The combining weight is simply the complex conjugate of the product of the channel coefficient and the spreading code element on the corresponding position, i.e.

MRC: , , ,g g gq c h=l l l (3.13)

MRC maximises the SNR by coherently summing the signals received on the chip positions and weighting them with respect to their amplitude [Pro95]. This strategy is optimum when only a single user is active (K=1). With multiple users, MRC has a disastrous effect on the MAI in the downlink case. Indeed, the MAI is caused by the variations of the elements of hg and MRC amplifies these variations by weighting again with the amplitude of the channel coefficients. However in the uplink, the orthogonality among the users is already completely broken due to the different channel vectors hk . In this case, the MAI can be considered as noise, which makes MRC a good choice for an uplink SUD technique.

3.2.1.2 Equal Gain Combing

Equal Gain Combing (EGC) also uses coherent combining of the chips but avoids the weighting by ensuring an identical amplitude for all elements of qg [HaPr97]. The corresponding combining weights are



EGC: ,, ,

,

gg g

g

hq c

h= l

l l

l

(3.14)

EGC is often used as a reference technique in the downlink, since it is the simplest technique providing an acceptable performance thanks to its neutrality with respect to the MAI and the noise.

3.2.1.3 Orthogonality Restoring Combining

Orthogonality Restoring Combining (ORC) is also known under the name Zero Forcing (ZF) equalisation, since it completely restores the orthogonality of the users’ signals or, equivalently, forces the MAI term to zero. This is achieved by an inversion of the channel fading with the coefficients

ORC: ,, , , 2*

, ,

1 gg g g

g g

hq c c

h h= = l

l l l

l l

(3.15)

This technique has the important drawback that the inversion may result in high amplitudes of the coefficients, especially for the chips affected by a deep fade. Having a look at relation (3.12), it is easily seen that this causes a considerable amplification of the residual noise. Furthermore, this technique cannot be applied to the uplink, as a consequence of the different channels appearing in the MAI term. Note that derivations of this approach, called controlled equalisation, have been proposed that try to avoid excessive noise amplification by discarding the chips affected by deep fades or by using EGC on them [Kai98].

3.2.1.4 Minimum Mean Squared Error Combining

Minimum Mean Squared Error Combining (MMSEC) aims at minimising the Mean Squared Error (MSE) between the transmitted symbol and the equalised received symbol on each chip position. The cost function is given by

,

2*EggJ d q y= −ll l (3.16)

The coefficient minimising this cost function is given by the corresponding one-tap Wiener filter [Hay96]. Assuming, for instance, that the data symbol power of all users is unity, the coefficients are obtained as

MMSEC: ,, , 2 2

,

gg g

g C

hq c

K h σ=

+

l

l l

l

(3.17)

Note that MMSEC additionally requires the knowledge of the noise variance on the chip positions. MMSEC realises a trade-off between MRC and ORC. Indeed, the coefficients tend towards MRC for high noise levels and towards ORC for σC

2=0. Several variants of the per-chip MMSEC approach have been proposed, which namely take into account a difference in the power levels of the users and an estimation of the interference power on the chip level, respectively. Up to a scalar factor, which does not impact the performance, the general coefficient of all MMSEC variants can be expressed as

,, , 2

,

gg g

g g

hq c

h κ=

+

l

l l

l

(3.18)

Here, κg is a real scalar calculated from additional knowledge [MoCa01] or estimated in advance [FaKa03]. Note that if knowledge about other signals than the one of user g is required, the corresponding techniques have to be considered as multi-user detection.



3.2.2 Multi-User Detection

While SUD techniques basically consider the signals of other users as unpredictable noise, Multi-User Detection (MUD) techniques use knowledge about other users’ signals for MAI mitigation [Ver98], which is obtained at the price of a higher complexity. This penalises MUD approaches for the downlink, where the mobile receiver is subject to tight constraints concerning implementation complexity and power consumption. However, MUD techniques can be advantageously applied to mitigate the strong MAI in the uplink, all the more as a higher complexity can be tolerated at the basestation. Examples for the application of MUD in the MC-CDMA uplink can be found in [AkAs98][CoGr01].

For the following sections, we reformulate the received signals of up- and downlink given in (3.4) and (3.5) by a common equivalent matrix notation

C= +y A d n (3.19)

The data symbol vector of length K is given by

[ ]1 , ...,T

Kd d=d (3.20)

and the combined channel and spreading matrix AC of size L×K is given for the two links as

DL: 1 , ...,g gC K = A h c h co o (3.21)

UL: 1 1 , ...,C K K = A h c h co o (3.22)

3.2.2.1 Maximum Likelihood detection

Optimum MUD is achieved with the Maximum A Posteriori (MAP) criterion or the Maximum Likelihood (ML) criterion, respectively [Pro95][Ver98]. Here, we present a Maximum Likelihood Sequence Estimator (MLSE), which estimates the data vector d. The extension of the MLSE to a MAP sequence estimator is straightforward by taking into account the a priori probabilities of the transmitted symbols. When the a priori probabilities of all possible sequences are equal, the MLSE and MAP sequence estimators are identical. The MLSE minimises the joint symbol error probability for the symbols in vector d by minimising the Euclidian distance between the estimated symbol vector and the received signal vector y given by (3.19). Thus, the estimated data vector, d , is given by the following minimisation

( )2

ˆˆmin C −

dA d y (3.23)

Note that, if we assume that the K users all have the same constellation size MC , the number of possible sequences equals (MC )K and the complexity of this estimator gets rapidly prohibitive as the number of users increases. A considerably lower complexity can be obtained using sphere decoders, which have been proposed for MC-CDMA by [Bru02]. If reliability information for each data symbol is required by subsequent soft input detection or decoding stages, a symbol by symbol ML estimator as proposed by [FaKa03] can be employed.

3.2.2.2 Linear multi-user detection

Compared to ML detection, linear MUD is a sub-optimum MUD technique based on the knowledge of the matrix AC . The linear MUD matrix gathering the combining vectors of all users is defined as

[ ]1 , ..., K=Q q q (3.24)

The estimated data vector, d , is then obtained from the received vector by



ˆ H=d Q y (3.25)

There exist basically two different approaches for choosing the matrix Q:

The ZF-MUD method is the multi-user extension of the ORC SUD scheme. Here the interference is cancelled as good as possible by choosing Q as the pseudo-inverse of AC [GoLo96], i.e.

ZF-MUD: ( ) 1H H HC C C

−=Q A A A (3.26)

In the same way as ORC, ZF-MUD also suffers from the noise enhancement resulting from the channel inversion. Note that in the downlink case ZF-MUD and ORC are equivalent for K=L.

The optimum linear MUD method is given by the Wiener solution [Hay96] minimising the MSE between the estimated and the transmitted data vector. The approach is close to MMSEC and will be called MMSE-MUD in the sequel. Different formulations of this approach have been proposed in the literature [BaHe00][ChBr93][MoCa01]. Here, we will stick to the simplified version of [MoCa01], where the matrix to be inverted has the same size as for ZF-MUD, i.e. K×K. Assuming that the data symbols of all users have unit power, the linear MUD matrix for MMSE-MUD is

MMSE-MUD: ( ) 12H H HC C C K Cσ

−= +Q A A I A (3.27)

MMSE-MUD realises a trade-off between interference cancellation and noise enhancement, which maximises the Signal over Interference plus Noise Ratio (SINR). Similar to ZF-MUD and ORC, MMSE-MUD and MMSEC are equivalent in the downlink for K=L.

3.2.2.3 Interference Cancellation

The principle of Interference Cancellation (IC) is to estimate the MAI term and to subtract it from the received signal before detecting the desired signal. Fig. 3.4 shows the example of a two stage Parallel Interference Cancellation (PIC) with hard decision. Before the detection stage of the desired user g, the signals of the other users k≠g are detected by a SUD or MUD stage [BaHe00][Faz93][KaPr96]. The signals in the interference estimation stage are denoted as prime, which means that the components of user g are missing. The interference data vector, d', is obtained by hard decision from the estimated data vector, ˆ 'd . Then, the interference signal y' is generated by multiplying with the combined spreading and channel matrix, AC'. The so estimated interference is subtracted from the received signal. The decision value of the desired user g can then be obtained from the remaining signal by SUD or MUD schemes. In the ideal case, where the signals of users k≠g are perfectly estimated, the signal provided to the detection stage for user g is free from MAI and SUD MRC is the optimum strategy. However in the non-ideal case, MRC performs poorly. Promising schemes are obtained using MMSEC schemes based on equation (3.18), which can be adapted to the interference level in the different stages [Kai98]. The scheme of Fig. 3.4 is called PIC, because the interfering signals are all detected and subtracted in parallel. Another possibility is to detect and subtract the interference signals successively. This is called Successive Interference Cancellation (SIC). SIC is particularly advantageous if the different signals are received with unequal powers. Then, the signal with the highest power is detected and subtracted first and the others follow successively [Ver98]. Both PIC and SIC can be applied in several iterations and hybrid schemes of them are also possible. To improve the reliability of the estimated interference, the channel decoding can also be included in the interference regeneration process. Finally, instead of taking hard decisions on the interfering signals soft values taking into account the reliability of the interference can be used for its regeneration, which considerably reduces the effects of error propagation [KaHa97]. Obviously, these improvements come along with a considerable increase of complexity.



SUD or MUD

SUD of g y

y'Interference detection

and regeneration for k≠g

ˆgd

ˆ 'd

d'AC'

SUD or MUD

SUD of g y

y'Interference detection

and regeneration for k≠g

ˆgd

ˆ 'd

d'AC'

Fig. 3.4: Parallel interference cancellation with hard decision.

3.3 Channel estimation

Within this thesis we focus on coherent detection [Pro95]. Indeed, all presented detection techniques require the knowledge of the channel fading coefficients. An alternative would be differential modulation and detection, where the information is coded in the transitions between consecutive data symbols. Differential detection avoids channel estimation on each chip at the price of a somewhat poorer performance [Pro95]. Note that the application of a differential scheme is not trivial in MC-CDMA, since it impacts on the orthogonality among users’ signals. Propositions for differential schemes for the MC-CDMA downlink can be found in [CoGr00] and for the uplink in [ToKr98].

In the same way as coherent detection in pure OFDM, coherent detection in MC-CDMA requires a channel estimate on all chip positions in the time-frequency frame. Thus, most channel estimation techniques known from pure OFDM systems are directly applicable to MC-CDMA. For these systems, it is natural to perform the channel estimation in the frequency domain, i.e. after the DFT operation. However, some approaches for an estimation of the channel impulse response in the time domain are also proposed [EdSa98][YeLi99].

The receiver generally acquires information about the channel coefficients from known symbols multiplexed in the transmitted signal (cf. Fig. 2.1). From the observations of the channel at pilot positions, the channel estimates for the data positions are obtained by interpolation. These approaches, which are called pilot-symbol based, are detailed in the following sections. In addition to real pilot symbols, which are known to the receiver, channel estimation can be decision directed. Indeed, once a decision has been taken on a data symbol, this symbol can be fed back to the channel estimation unit and used for a refinement of the estimation in iterative approaches or as observation for the channel estimation of the following OFDM symbol [KaSt98].

An alternative to pilot-symbol based channel estimation are blind approaches, which generally rely on some statistical properties of the transmitted signal [HeGi99][MuCo02]. The main disadvantages of blind approaches are their long convergence time and the computational effort.

3.3.1 Pilot-symbol based channel estimation

Pilot-symbol based channel estimation places known symbols on pilot positions in the OFDM frame, from which an observation of the channel fading coefficient can be obtained [NePr00]. The insertion of these symbols leads to a reduction of the spectral efficiency of the system since the pilot positions cannot be used for data transmission and they consume a part of the transmit power. To minimise the loss from pilot insertion, the channel estimation takes advantage of the correlation of the channel fading on the frame positions. The pilots are placed according to a



predefined pilot symbol grid, and the channel coefficients for the data positions between them are obtained from interpolation. Fig. 3.5 shows several examples of such grids.

In the first two examples, entire subcarriers (a) and entire OFDM symbols (b) are dedicated to pilot transmission. Then, interpolation has to be done in frequency and time, respectively. A generalisation of these two possibilities is the rectangular grid (c), where interpolation is done in both dimensions. The fourth depicted example is a diagonal grid (d), which is obtained from the rectangular grid by a subcarrier shift of the positions between successive OFDM symbols. The advantage of this grid is the fact that different carriers are used for the estimation from one OFDM symbol to another. This avoids that a pilot is always placed on a subcarrier that is subject to a deep fade. The diagonal grid is used, for example, in the European DVB-T standard [ETSI97b]. In WLAN systems, a combination of (a) and (b) is often applied. Indeed, a typical WLAN frame is shorter than the coherence time of the channel, and a pilot OFDM symbol at the beginning of each frame is sufficient. Pilot subcarriers are used during the whole frame to track phase variations, which are essentially due to frequency variations in the oscillators [ETSI01].

Time

Frequency

Tcoh

Bcoh

a) Pilot sub-carriers b) Pilot symbols

Pilot position

d) Diagonal gridc) Rectangular grid

NPF

NPT

Data position

e) Typ. WLAN grid

Time

Frequency

Tcoh

Bcoh

a) Pilot sub-carriers b) Pilot symbols

Pilot position

d) Diagonal gridc) Rectangular grid

NPF

NPT

Data position

e) Typ. WLAN grid Fig. 3.5: Pilot symbol grids.

Taking the example of the rectangular grid (c), it is easy to see that the pilots provide the receiver with a sampled version of the time varying channel transfer function HB(f,t ) (cf. (2.9)). In order to reconstruct this function at each frame position by interpolation, the sampling theorem has to be respected in both dimensions, time and frequency. Denoting the pilot spacing in time by NPT and in frequency by NPF , their maximum values are given by

PT S cohN T T≤ and PF cohN f B∆ ≤ (3.28)

In other words, there must be at least one pilot in every coherence rectangle (cf. section 2.5.2). However, since the observations at these positions are affected by fading and noise, it has been shown that a two-times oversampling is generally a good choice [HoKa97]. This leads to following values for the pilot spacing

/ 2PT S cohN T T≈ and / 2PF cohN f B∆ ≈ (3.29)



The overhead introduced by this pilots is defined by the number of pilot symbols per frame divided by the number of frame positions. Thus, excluding edge effects, the overhead for the rectangular grid is

( ) ( )/ / 1C PF F PTP

C F PF PT

N N N NO

N N N N⋅

= = (3.30)

The overheads of modified rectangular patterns, e.g. the diagonal pattern, are identical to the rectangular one, if edge effects are also excluded. This overhead leads to an SNR loss given in dB by the following expression

, 1010 log 1(1 )P p

P dBS P

E OK E O

∆γ

= + ⋅ − (3.31)

Here, the data symbol energy, ES , is assumed to be the same for all K active users, and EP denotes the energy of a pilot symbol. In general, the pilot symbols are boosted, which means that their energy is higher than the data symbol energy [ETSI97b]. The impact of boosted pilots on the system performance has been studied in [Säl00][SäMo01], where a simple rule for adapting the pilot energy with respect to the data symbol energy and the number of active users is proposed.

From the pilot symbols, the channel estimation obtains observations of the channel coefficients at the pilot positions. The pilot symbols are denoted by xP,i,n , where i is the time and n the frequency index. From (2.41), the observations are then given by

, ', ' ', ' , ', ' , ', ' ', ' , ', '' / / ; ', ' pilot-gridB i n i n P i n B i n i n P i nH y x H x i nχ= = + ∈ (3.32)

The channel coefficients on all frame positions can be estimated by interpolating the observations. In the most general case, these estimations are obtained from the observations by a two dimensional shift variant filter, which is proper to each frame position. The estimated coefficients are then given as

*, , , , ', ' , ', '

', ' pilot-grid

ˆ ' ; 1... , 1...B i n i n i n B i n F Ci n

H H i N n Nϖ∈

= = =∑ (3.33)

The most general filter is different for each position and its number of coefficients is equal to the number of observations in the frame. However, due to the fact that the correlation between two channel coefficients decreases with their distance in time and frequency and for complexity reasons, only a subset of observations is generally used for estimating a given coefficient.

The optimum linear filter for (3.33) is a two dimensional Wiener-filter [Hay96][HoKa97]. Joint two-dimensional filtering has the main drawback that the filtering spans several OFDM symbols, which introduces a latency in the system, since several OFDM symbols have to be received before the estimation can start. Furthermore, joint filtering leads to a large number of filtering coefficients and, thus, a high implementation complexity. These drawbacks can be avoided by employing two cascaded one-dimensional filters, which successively perform the filtering in frequency and time. A comparison of the performance of a two-dimensional Wiener filter and two cascaded one-dimensional filters shows that the one-dimensional filters can achieve almost the same performance with a lower number of filter taps [FaKa03]. Note that the order of application has no importance for the performance of linear filters. However, filtering in frequency is generally performed first to avoid the latency arising from filtering over consecutive OFDM symbols. Different kinds of filters can be used in the two dimensions. A common approach for WLAN is to use an efficient filtering in the frequency domain in order to obtain a good first estimate of the channel and to simply track the variations in the time direction by a few pilot subcarriers [ETSI01].



3.3.2 One-dimensional Wiener-filter design

Here, we present a common approach for a one-dimensional Wiener filter in the frequency dimension, which is used for studying the impact of real channel estimation in this work. Note that the principles can be directly applied for a filter design in the time dimension or even extended for a two-dimensional filter.

Omitting the time dimension in expression (3.33), the channel estimates for a single OFDM symbol with interpolation in frequency are given by

*, , ' , '

' pilot-grid

ˆ ' ; 1...B n n n B n Cn

H H n Nϖ∈

= =∑ (3.34)

The Wiener filter is designed so as to minimise the MSE between the channel coefficients and their estimates according to the following cost function [Hay96]

2

, ,ˆEn B n B nJ H H= − (3.35)

The filter is based one cross-correlation function between the channel coefficients and its observations, i.e.

( ) *, , ', ' E 'C B n B nn n H Hφ = , (3.36)

and on the autocorrelation function of the observations, i.e.

( ) *, ' , ''', '' E ' 'A B n B nn n H Hφ = . (3.37)

The number of coefficients or, equivalently, the number of filter taps is denoted by Ntap . Shifting to a vector notation, the cross-correlation coefficients are gathered in the vector ϕn of length Ntap , and the auto-correlation coefficients in the Toeplitz matrix Φ of size Ntap×Ntap . Then, the vector of length Ntap gathering the filter coefficients for position n is given by [Hay96]

1n n

−=ϖ Φ ϕ (3.38)

The principle of one-dimensional Wiener filtering with a limited number of taps is depicted in Fig. 3.6.

estimated position, n

ϖn,-2 ϖn,-1 ϖn,0 ϖn,1 ϖn,2

cross-correlations

positions using sameobservations

predictedpositions

border positions

border positions

Pilot positions (observations)

estimated position, n

ϖn,-2 ϖn,-1 ϖn,0 ϖn,1 ϖn,2

cross-correlations

positions using sameobservations

predictedpositions

border positions

border positions

Pilot positions (observations)

Fig. 3.6: Example of a 5-tap Wiener filter.

In the example, a 5-tap Wiener filter is used with a pilot spacing of NPF =3. Thus for the central region, the same observations are used for the estimation of three adjacent positions. Note that always the 5 nearest observations are used for the interpolation, and the filter is shifted accordingly. Consequently, three different filters have to be designed, while two of them are symmetric versions of the same filter. At the border positions, where the filter cannot be shifted



anymore, asymmetric filters have to be used. In the example, five border filters are required on the left side and can be reused by symmetry on the right side. At the right border, two more filters are required, which are called prediction filters since the corresponding positions are not framed by observations. It has been shown in [Säl00] that such prediction filters have quite poor performance. Hence, these situations should be avoided by a proper design of the pilot grid.

The design of the filters is based on the cross- and auto-correlation functions given in (3.36) and (3.37), respectively. These functions are generally unknown, and have to be estimated or obtained from assumptions about the frequency correlation function of the channel. An approach, where these functions are estimated directly from the observations can be found in [MaGa03][Säl00]. However, this requires a frequent update of the filter coefficients. A robust and low complex design can be obtained from assumptions about the power delay spectrum of the channel and the noise variance in the observations [HoKa97][LiCi98]. Assuming a power delay spectrum of the channel having a rectangular shape, i.e.

( )1 0

0 otherwise

maxmaxBρ τ

τ ττ

< <=

(3.39)

the discrete cross-correlation function of (3.36) and the discrete auto-correlation function of (3.37) are given as

( ) ( )( ) ( )', ' sinc ' e maxj f n nC maxn n f n n πτ ∆φ τ ∆ − −= − (3.40)

( ) ( )( ) ( ) ( )' '' 2', '' sinc ' '' e ' ''maxj f n nA max Cn n f n n n nπτ ∆φ τ ∆ σ δ− −= − + − (3.41)

This robust filter design allows to pre-calculate the filter taps with estimates of the maximum channel delay, τmax , and the noise variance on each subcarrier, σC

2. An assessment of the filter performance with a mismatch of these values with respect to the real channel conditions can be found in [Säl00]. There it is shown that a very robust design is achieved by slightly overestimating τmax while using a lower estimate for σC

2. An adaptive version of this design is proposed by [SaSp00], where τmax is regularly estimated by the receiver and the filter is updated accordingly.

3.3.3 Pilot-based estimation for the synchronous uplink

The synchronous uplink received signal given in (3.5) is a superposition of the signals of the K active users that reach the basestation through specific channels. Thus, a coherent detection of the users’ signals requires a parallel estimation of K different channels. The approaches presented for pilot-based estimation in the downlink can directly be applied to the uplink if dedicated pilot positions are employed. A possible pilot grid with dedicated pilot positions for the synchronous uplink is depicted in Fig. 3.7. With this scheme, the number of users whose pilots can be allocated simultaneously within an OFDM symbol equals the pilot frequency spacing NPF . As a consequence, the scheme requires K/NPF entire OFDM symbols to allocate the pilots of all users. This simple example shows that the pilot overhead is significantly increased in the uplink and may get prohibitive for large K. Instead of using dedicated pilot positions, the channels for different users can also be estimated with user-specific training sequences which are transmitted on the same OFDM symbol [Stei99] [StVa98]. These sequences are designed such that the channel impulse responses of the users are estimated on different fractions of the OFDM symbol. Then, the corresponding transfer functions are simply obtained in the frequency domain by re-multiplying with the complex conjugate of the training sequence and appropriate filtering. For this approach, the number of parallel channels that can be estimated is the ratio between the OFDM symbol duration and the maximum channel delay, i.e. TS/τmax . Comparing this value with the maximum allowable

3.4 Pre-equalisation for the uplink


frequency spacing of the pilots in (3.28), i.e. NPF ≤ Bcoh/∆f =TS/τmax , it gets clear that the pilot overhead cannot be reduced by this approach. However, the use of a larger number of observations generally improves the quality of estimation.

Time

Frequency

NPT

NPF

Pilot foruser x

Data position

x

1

21

34

21

34

65

78

65

78

21

34

21

34

65

78

65

78

Time

Frequency

NPT

NPF

Pilot foruser x

Data position

x

1

21

34

21

34

65

78

65

78

21

34

21

34

65

78

65

78

Fig. 3.7: Example for an uplink pilot grid.

3.4 Pre-equalisation for the uplink

Two major difficulties of uplink MC-CDMA systems have been mentioned in the previous sections: The high MAI created due to the different propagation channels and the high overhead required for estimating these channels with pilot symbols. To overcome these difficulties, pre-equalisation has been proposed recently for TDD systems, where reliably instantaneous channel knowledge is available at the transmitter due to the reciprocity of the channel. Pre-equalisation can principally be applied in the downlink and the uplink. The principle of pre-equalisation in the downlink is addressed in detail in chapter 4. In this section, we introduce pre-equalisation as an alternative for the uplink. Here, the basestation first sends a downlink frame including pilot symbols, from which the mobile estimates the channel coefficients of the downlink. Then, these estimates not only serve to detect the downlink frame but are reused to pre-equalise the transmitted signal in the uplink. This yields the advantages that channel estimation can be avoided at the basestation and that the MAI level is considerably reduced, because the orthogonality of users’ signals can be conserved [MoCa02][CoSch03].

user gdg

↑ LChip

mapping

0

NC -1

OFDM+

Guard Interval

. . .

S/P

cg,0

cg,L-1

gg,0

gg,L-1

user gdg

↑ LChip

mapping

0

NC -1

OFDM+

Guard Interval

. . .

S/P

cg,0

cg,L-1

gg,0

gg,L-1

Fig. 3.8: Terminal transmitter with pre-equalisation.

The transmitter structure of the mobile terminal with pre-equalisation is depicted in Fig. 3.8. In addition to the multiplication with the spreading code element, each chip is weighted by a pre-equalisation coefficient. These coefficients are gathered in vector

,0 , 1, ...,T

g g g Lg g − = g (3.42)



Then, the received signal in the uplink is given by an expression similar to equation (3.5), i.e.

( )1

K

k k k kk

d=

= +∑y h g c no o (3.43)

When pre-equalisation at the terminal is applied there is no need for equalisation at the basestation, which simply despreads the received signal with the user-specific code vector. Thus the decision value for user g is given by

( ) ( )1,


ˆK

H H Hg g g g g g g k k k k g

k k g

d d d= ≠

= + +∑c h g c c h g c c no o o o

144424443 14444244443

(3.44)

From (3.44) it is evident that the MAI can be completely cancelled by employing a ZF pre-equalisation that simply inverts the channel similar to the ORC technique in the DL. The weights for the ZF pre-equalisation are given by

,,

1g

g

gh

=l

l

(3.45)

The disadvantage of this technique is the prohibitively high transmit power required for the channel inversion when deep fades occur. In practice, the transmit power has to be controlled, which can be done by introducing a power constraint to the pre-equalisation vector [MoCa02]. Here, the pre-equalisation vector is assumed to be normalised so that the transmitted signal power is not modified, i.e.

2

g L=g (3.46)

Basically, the same approaches as those used for SUD can be applied for pre-equalisation. In this way, the vectors for Maximum Ratio Transmission (MRT), Equal Gain Transmission (EGT), and ZF pre-equalisation are given by

MRT: *, ,g g gg hκ=l l , EGT:

*,

,,

gg g

g

hg

hκ= l

l

l

, ZF: ,,

gg

g

ghκ

=l

l

(3.47)

where the scalar κg ensures the power constraint. A promising single-user approach is proposed in [MoCa02] as sub-optimum SINR-based pre-equalisation. The coefficients employed by this approach are given by

SINR-based: *,

, 2 2,( 1)

g gg

g C

hg

K h L

κ

σ=

− +

l

l

l

(3.48)

where κg ensures again the power constraint. This approach can be seen as the analogue of MMSEC at reception, since it realises a trade-off between the limited transmit power and channel inversion. For a single user and full system load, i.e. K=L, this approach is identical to the optimum, but more complex multi-user SINR based pre-equalisation [MoCa02]. Note that, the implementation of multi-user pre-equalisation schemes at the terminal is difficult for two reasons: Firstly, there are limitations in terms of complexity and, secondly, knowledge about the other users’ signals is generally not available.

3.5 Performance of the conventional single-antenna system



In this section, we present the performance of the conventional single-antenna system, which was described in the paragraphs above. These results give insight in the properties of MC-CDMA and are used as references for the following chapters.

3.5.1 Simulation scenarios

The simulation parameters correspond to typical values used in the studies of MC-CDMA for future air interfaces. Most of them are chosen according to the propositions in the MATRICE project [MAT,D1.4]. The parameters are summarised in Tab. 3.1.

The channel models considered here, are the classical HIPERLAN/2 models A and E described in section 2.3.1, and the corresponding power delay profiles are given in appendix A.2. Note that Doppler variations are not considered in this chapter. The underlying OFDM system is designed such that the guard interval absorbs the delay introduced by the considered channels. The OFDM spectrum is well shaped by zero padding of the subcarriers on the boundaries. Therefore, the number of subcarriers available for data transmission is lower than the FFT-Size. Several MC-CDMA subsystems each of them comprising L subcarriers are allocated in parallel in one OFDM symbol. Concerning the mapping scheme, we focus on spreading in frequency either on adjacent subcarriers or with chip interleaving (cf. section 3.1.4). In this way, we can compare the two characteristic configurations: With chip interleaving the system achieves a high diversity order but suffers from MAI. When the chips are placed on adjacent subcarriers, the diversity order is low but the system benefits from a lower MAI level. Here, we focus on an uncoded system in order to clearly identify the effects of diversity and MAI. The system performance taking into account channel coding is considered in chapter 6. Therefore, the performance can be averaged by redrawing the fast fading amplitudes of the channel for each OFDM symbol. For the uncoded system, we generally compare the performance at the operation point of BER=10-2, which can be considered as a typical input BER for channel decoders. The BER presented in the following sections is always an average BER of all active users.

Carrier frequency, fC 5 GHz Sampling frequency 57.6 MHz FFT-size 1024 Number of available subcarriers, NC 736 Carrier spacing, ∆f 56.3 kHz Overall symbol time, TS’ 21.5 µs Guard time, TG 3.75 µs Symbol alphabet QPSK Channel coding not considered. Spreading factor, L 32

Chip mapping Spreading in frequency adjacent or interleaved.

Channel models HIPERLAN/2 Channel A: τmax=0.39µs Channel E: τmax=1.72µs

Tab. 3.1: Simulation parameters for the conventional system.

Unless otherwise stated the average BER performance is evaluated with respect to the average SNR per bit. In a system including power control with respect to the slow fading, the average



SNR per bit, γb , is defined as the transmitted energy per bit divided by the noise spectral density at the receiver, i.e.

0

bb

EN

γ = (3.49)

Since the data symbols are spread over L chips with a normalised spreading vector, their energy is spread accordingly and the SNR per chip is obtained for the un-coded system (RC =1) as (cf. section 2.1)

20

S bC b

C

E EL LN L

β βγ γ

σ= = = (3.50)

3.5.2 Single-user performance and theoretical bounds

The performance of the system with a single user and MRC yields lower bounds for the BER. These bounds can be used to estimate the diversity offered by the different channels in the case of chip mapping on adjacent positions or with chip interleaving. Several theoretical curves can be used for comparison. These curves are derived from statistical laws and indicate the Bit Error Probability (BEP), which can then be compared to the BER obtained by simulations. According to the modulation schemes considered in this thesis, we focus on the BEP of BPSK and QPSK with coherent detection. Note that the BEP for these two schemes is identical for the considered cases.

The first basic bound is given by the BEP for the AWGN channel, i.e. a channel only adding noise to the signal. The BEP of an AWGN channel is given by [Pro95]

( )1 erfc2E bP γ= (3.51)

Here, erfc(x) denotes the complementary error function. Another important bound is obtained for a flat fading channel, whose amplitude follows a Rayleigh distribution with unit mean power, i.e. Ω=1. The BEP is given by [Pro95]

1

11 11 2 4

bb

Eb b

Pγγ

γ γ+

= − ≈

(3.52)

where the approximation holds for high SNR. This bound corresponds to symbol transmission over an ideal OFDM system without spreading (cf. section 2.5.2), i.e. a symbol is transmitted on a single position in the frame. The considered MC-CDMA system exploits frequency diversity by transmitting several versions of the symbols over different subcarriers. If the fading on these carriers is independent, the diversity order corresponds to the spreading factor, L. In this case, the performance with MRC is given by [Pro95]

1

0

11 11 12 2

LL

b bE

b b

LP

L Lγ γ

γ γ

−

=

− + = − + + +

∑l

l

l

l (3.53)

where (x over y) denotes the binomial coefficient. For high SNR this BEP can be approximated as

2 1

4

L

Eb

LLPLγ

− ≈

(3.54)

Fig. 3.9 shows the single-user performance of the considered system for the two channel models, A and E. The AWGN bound (3.51) and the diversity curves of (3.53) for several values of L are also depicted. It can be noticed that the diversity curves approach the AWGN curve for



increasing L. Since the diversity curve for L=10 is already close to the AWGN curve, it is obvious that higher degrees of diversity only lead to a small performance gain. A frequency diversity of DF=10 is achieved on channel E with chip interleaving. As expected from the maximum channel delay, the degree of diversity offered by channel A is a bit lower. Without chip interleaving, i.e. chip transmission on adjacent subcarriers, the system only obtains DF ≈ 2 on channel E and almost no diversity on channel A.

4 6 8 10 12 14 16 18 20

10-3

10-2

10-1

Channel E, interl.Channel E, adjac.Channel A, interl.Channel A, adjac.AWGN boundDivers ity bounds

SNR, γb

BER

L=1

L=2L=4L=10

AWGN

4 6 8 10 12 14 16 18 20

10-3

10-2

10-1

Channel E, interl.Channel E, adjac.Channel A, interl.Channel A, adjac.AWGN boundDivers ity bounds

SNR, γb

BER

L=1

L=2L=4L=10

AWGN

Fig. 3.9: Single-user performance bounds (MRC, K=1).

3.5.3 Multi-user performance in the downlink

When multiple users are simultaneously active, the frequency selective fading of the channel gives rise to MAI. The impact of MAI can be mitigated by choosing an appropriate detection technique. In Fig. 3.10, we present performance results of a fully-loaded system, i.e. K=L=32, for channel E with chip interleaving, where the MAI is particularly important. The figure shows curves for different SUD techniques, which are compared to the single-user bound.

As expected MRC performs very badly in the multi-user case, since the chip weighting leads to an increased MAI. EGC avoids this weighting and yields a considerably better performance. Both techniques, MRC and EGC present an error floor at high SNR as a result of the MAI. The channel inversion with ORC amplifies the noise, which leads to a high BER at low SNR. At high SNR, however, where the influence of MAI is more important than the noise, ORC has a better performance than EGC and MRC. Note that ORC has no error floor thanks to complete MAI cancellation. MMSEC yields the best performance of the presented techniques for the whole SNR range. It is about 4 dB from the single-user bound at a BER of 10-2. Thus, MMSEC is a very efficient SUD technique, because it achieves a trade-off between noise enhancement and MAI mitigation. Note that for the fully-loaded downlink system MMSEC is identical to the MMSE-MUD scheme.

Fig. 3.11 shows the performance for a variable number of users over channel E with and without chip interleaving. When EGC is employed, the trade-off between diversity and MAI is clearly visible. For low loads, chip interleaving benefits from diversity and the MAI plays a minor role. Starting from half-load (K=16), the tendency is inverted. The impact of the MAI is more important than the diversity gain and the performance rapidly deteriorates for higher loads. Thus, chip mapping on adjacent subcarriers is clearly preferable for high loads. However, the situation



is different when the orthogonality between users is partly restored by MMSEC and MMSE-MUD. Note that already from their construction MMSEC and MMSE-MUD have the same performance in the single-user case (K=1) and for full load (K=32). For intermediate loads, the MUD scheme clearly outperforms the SUD scheme. Both schemes allow to conserve the diversity gain of the chip interleaving for the whole range of K. Thus, if these techniques can be envisaged in the receiver, it is preferable to exploit the frequency diversity of the channel. Note, however, that the QPSK constellation used for the simulations is quite robust and the conclusions may be different for QAM constellations of higher order. Furthermore, a strong channel coding in conjunction with bit interleaving has also the capacity to benefit from diversity, which makes the diversity on the chip level less important (cf. chapter 6).

0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1

MRCEGCORCMMS EC

BER

Single user bound

SNR, γb

0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1

MRCEGCORCMMS EC

BER

Single user bound

SNR, γb Fig. 3.10: Downlink performance of the fully-loaded system

(K=L=32, interl., channel E).

Requ

ired

SNR

at B

ER=

10-2

Number of active users(K)1 4 8 12 16 20 24 28 32

6

8

10

12

14

16

18EGC interl.EGC adjac.MMS EC interl.MMS EC adjac.MMS E-MUD interl.MMS E-MUD adjac.

Requ

ired

SNR

at B

ER=

10-2

Number of active users(K)1 4 8 12 16 20 24 28 32

6

8

10

12

14

16

18EGC interl.EGC adjac.MMS EC interl.MMS EC adjac.MMS E-MUD interl.MMS E-MUD adjac.

Fig. 3.11: Downlink performance as a function of system load

(adjac./interl., channel E).



3.5.4 Multi-user performance in the synchronised uplink

In the uplink, the impact of the MAI is more important as a consequence of the different channels between the mobiles and the basestation. For the same reason, approaches aiming at a restoration of the orthogonality, like ORC and MMSEC, are useless in the uplink. However, the MMSE-MUD approach can be applied here, because it accounts for the different channels of the users. Fig. 3.12 shows the performance of a half loaded system, i.e. K=16, on channel E with and without chip interleaving. The MRC single-user curves are again given as a reference.

BE

R

SNR, γb

0 2 4 6 8 10 12 14 16

10-3

10-2

10-1

MRC interl.MRC adjac .EGC interl.EGC adjac.MMS E-MUD interl.MMS E-MUD adjac.K=1 interl.K=1 adjac.

BER

SNR, γb

0 2 4 6 8 10 12 14 16

10-3

10-2

10-1

MRC interl.MRC adjac .EGC interl.EGC adjac.MMS E-MUD interl.MMS E-MUD adjac.K=1 interl.K=1 adjac.

Fig. 3.12: Uplink performance for half load

(K=16, adjac./interl., channel E).

In contrast to the downlink, MRC outperforms EGC in the uplink because it maximises the power of the desired signal part. Here, the impact of the power weighting on the MAI is irrelevant since the orthogonality is already broken by the different channels. Note, however, that there is still a difference between symbol transmission on adjacent subcarriers and chip interleaving. Indeed, the MAI arises from the difference in the fading coefficients affecting the chips. In the limiting case, where the fading is identical for all chips, there is no MAI, even if the fading differs from one user to another. For this reason, MRC and EGC perform much better when the chips are placed on adjacent subcarriers [ChMo04].

Since the effectiveness of SUD is very limited, MUD schemes are often applied in the uplink. Fig. 3.12 shows that good results are obtained with the linear MMSE-MUD scheme, whose curves achieve a loss compared to the single-user curve at BER=10-2 of 3 dB and 1 dB with and without chip interleaving, respectively. Since MMSE-MUD effectively separates the users’ signals, the uplink system can still benefit from frequency diversity when chip interleaving is applied.

3.5.5 Impact of channel estimation in the downlink

To assess the impact of channel estimation in the downlink, we start with an evaluation of the performance of the fixed Wiener filter design (cf. section 3.3.2) in the considered system configuration. The performance of the filter is given in terms of the MSE at its output defined in (3.35) with respect to the SNR of the pilot symbols defined as



2P

PC

Eγ

σ= (3.55)

Fig. 3.13 concerns filtering in the frequency dimension on channel E with a pilot symbol spacing of NPF=4. It shows the MSE at the output with respect to γP for different numbers of filter taps. Border effects are not considered. The MSE of the observations obtained for NPF=1, where all estimates can be directly obtained from the observations without filtering, is used as a reference. Compared to this curve the Wiener interpolation filters have gain of 5 dB at γP=0 dB thanks to their noise reduction capacity. As the pilot SNR increases the quality of the interpolation gets more important than noise reduction and a considerable difference can be noticed with respect to the number of filter taps. The interpolation quality clearly improves when the number of taps is increased. On the other hand, Fig. 3.13 does not consider a mismatch between the filter design and the actual channel parameters. It has been shown in [Säl00] that an increasing number of taps also leads to a higher sensitivity with respect to a mismatch in the parameters used for the filter design. Thus, for the considered case, a 5-tap Wiener filter seems to be a good trade-off between the quality of the interpolation and robustness with respect to a parameter mismatch.

0 5 10 15 20 25 30 35 40-45

-40

-35

-30

-25

-20

-15

-10

-5

03 taps5 taps7 taps15 tapsobs erv.

Pilot SNR,γP

MSE

[dB]

0 5 10 15 20 25 30 35 40-45

-40

-35

-30

-25

-20

-15

-10

-5

03 taps5 taps7 taps15 tapsobs erv.

Pilot SNR,γP

MSE

[dB]

Fig. 3.13: MSE performance of fixed Wiener filter design

(channel E, NPF=4).

The impact of an error in the channel estimates on the performance of different detection techniques is illustrated by Fig. 3.14. We considered a downlink system at half load, i.e. K=16, on channel E with chip interleaving. The SNR of the pilot symbols is directly related to the SNR per chip and consequently to the SNR per bit by the following relation

CP PP C b

S S

RE EE E L

γ γ γβ

= = (3.56)

Here, we use boosted pilots whose energy equals two times the average signal energy on a subcarrier at full load, i.e. EP=2LES. We further assume a pilot spacing of NPF=4 and a 5-tap Wiener filter, whose gain is given by the curves in Fig. 3.13 and can be approximated by 3 dB in the considered SNR range. The curves in Fig. 3.14 do not account for the SNR loss on the data symbols caused by pilot insertion. The comparison of the curves obtained with perfect channel estimates and real channel estimates shows that the loss can be kept below 2 dB at BER=10-2 for



the considered SUD and MUD schemes. Furthermore, the loss is almost identical for the three considered schemes.

BER

SNR, γb

0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1

EGC perfect CEEGC real CEMMS EC perfect CEMMS EC real CEMMS E-MUD perfect CEMMS E-MUD real CE

BER

SNR, γb

0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1

EGC perfect CEEGC real CEMMS EC perfect CEMMS EC real CEMMS E-MUD perfect CEMMS E-MUD real CE

Fig. 3.14: Downlink performance with channel estimation errors

(K=16, interl., channel E).



3.6 Multiple antenna concepts

In the previous sections, we presented the conventional MC-CDMA system with a single antenna at the transmitter and the receiver. To meet the requirements of future radio communication systems, this system can be endowed with multiple antennas at the basestation, at the mobile terminal, or on both ends. Such a system can exploit the spatial dimension of the mobile radio channel basically in three different ways: As an additional source of diversity, for spatial multiplexing, and for a spatial separation of users. These concepts and their application to MC-CDMA are exposed in the following sections together with an assessment of their potential benefits in the considered context.

The general structure of a MIMO system employing MT antennas at transmission and MR at reception is depicted in Fig. 3.15. Here, M symbols are MIMO encoded at the transmitter and the resulting signals are transmitted on the MT antenna branches. At the receiver the M symbols are obtained by MIMO decoding from the MR received signals. Note that this general MIMO encoding and decoding stands for the different schemes presented in the following sections.

MIMOencoding

...

1

MT

...

1

MR

Symbol 1

Symbol M

Symbol 1

Symbol M

Transmitter Receiver1,1h

,T RM Mh

1, RMh

,1TMh MIMOdecoding

MIMOencoding

...

1

MT

...

1

MR

Symbol 1

Symbol M

Symbol 1

Symbol M

Transmitter Receiver1,1h

,T RM Mh

1, RMh

,1TMh MIMOdecoding

Fig. 3.15: MIMO system structure.

Assuming flat fading, the radio channel between the antennas of the transmitter and the receiver can be described by MRMT channel coefficients, which are gathered in the following matrix

1,1 1,

,1 ,

T

R R T

M

M M M

h h

h h

=

H

K

M O M

L

(3.57)

The capacity of a concrete realisation of this MIMO channel is given by [Fos96]

2log detR

HSM

T

CMγ

= + I HH (3.58)

where det[.] is the determinant of a matrix. This formula is analogue to the Shannon capacity for an AWGN channel given in (2.6), which is easily obtained from this formula by setting MT =MR =1 and h1,1=1. The capacity of a MIMO system depends on the correlation of the elements of the matrix H. The highest capacity is achieved if the channel fading on different antennas is uncorrelated at both ends. Then, the MIMO capacity corresponds to the capacity of min(MT,MR) independent SISO channels. Uncorrelated fading is obtained if the array is placed in an environment with rich scattering and for large spacing between the antennas. It may also be obtained by using different polarisations of the antennas. Indeed the fading of signals received at orthogonal polarisations (e.g. horizontal and vertical) is independent in common propagation



environments. Polarisation diversity has the advantage that no spatial separation of the antennas is required, which is particularly interesting for small mobile terminals. Spatially-correlated fading reduces the number of independent channels and, thus, considerably degrades the capacity of MIMO systems. A recent overview of capacity limits on MIMO channels in the single and multi-user case can be found in [GoJa03].

3.6.1 Spatial multiplexing

The spatial multiplexing approach exploits the MIMO capacity by transmitting several data streams in parallel and thereby increases the bit rate of the system. The maximum number of parallel streams that can be transmitted in a MIMO system is equal to M=min(MT,MR). Assuming for instance M=MT =MR, the transmitter simply sends the M different symbols in parallel over its antennas, which superpose at the receive antennas. This leads to cross-talk between the streams, which is an important difference compared to the transmissions of parallel streams with OFDM. In ideal OFDM, signals transmitted on different subcarriers do not interfere and, thus, there is no cross-talk between the streams. Here, the detector has to extract the M transmitted data streams from the superposed signals at the receiver antennas. Note that sophisticated receiver schemes, in general IC schemes, are required to solve this task. Additional transmit or receive diversity can be obtained by using more transmit or receive antennas, respectively. The most famous example for spatial multiplexing is the BLAST (Bell-Labs Layered Space-Time) architecture proposed in [Fos96].

Since current studies on spatial multiplexing mostly assume flat fading channels between the antennas, it seems natural to combine this approach with OFDM as underlying modulation scheme. Recent work on this subject can be found in [BöGe02][LiWi02]. The application of spatial multiplexing for MC-CDMA is also suggested by [AtSa03]. However, the complexity of the corresponding receiver seems very high, since it has to cope with two types of interference, the cross-talk of the spatial multiplexing and the MAI.

3.6.2 Diversity schemes and space-time coding

In contrast to spatial multiplexing, pure spatial diversity schemes yield no direct increase of the transmitted bit rate. Here, the transmission of M symbols requires MT ≥M consecutive channel uses. Receive diversity techniques are straightforward and similar to the combining schemes used for time and frequency diversity or for chip combining in the considered MC-CDMA systems. Thus, MRC is the optimum scheme in the absence of interference. The drawback of combining the signals received over all antennas is that all these signals have to be demodulated in parallel. Thus, antenna selection based on rough estimates of the signal powers at the antennas can considerable reduce the complexity of the receiver [MoWi03]. Exploiting diversity at transmission, when no CSI is available at the transmitter, is a bit more challenging. Several examples for transmit diversity schemes applied to OFDM can be found in [Kai00] and [LiCh99]. These schemes are particularly interesting when the radio channel only provides a low degree of frequency diversity, e.g. in LOS situations with a short maximum channel delay. Then, the spatial diversity branches can be exploited so that they are seen by the receiver as additional propagation paths. An example is the delay diversity scheme depicted in Fig. 3.16. Here, delayed versions of the signal are transmitted over the different antennas and perceived by the receiver in the same way as additional paths [Wit91]. It is clear that the sum of the artificially introduced delay and the maximum channel delay must be shorter than the guard time to ensure ideal OFDM transmission.



OFDM ...

1

MT

OFDM-1

DelayMT -1

Delay1

2

Transmitter Receiver

OFDM ...

1

MT

OFDM-1

DelayMT -1

Delay1

2

Transmitter Receiver

Fig. 3.16: OFDM system with delay diversity.

Very efficient transmit diversity schemes are obtained by Space-Time Coding (STC). The STC schemes encode an original data stream so that redundant information is transmitted over the different antenna branches and in consecutive symbol periods. The receiver is not necessarily equipped with multiple antennas, since the STC scheme allows a decoding in the time dimension. This makes the STC scheme particularly attractive for small mobile receivers in mobile communications. It can be shown that the STC schemes can achieve the capacity in (3.58) for the MISO case, i.e. MR=1, but cannot reach the MIMO capacity for MR >1 [GeSh03]. Thus, from a pure information theoretic point of view, spatial multiplexing schemes should rather be employed if multiple receive antennas are available.

The simplest STC scheme would be a repetition code, where the same symbol is transmitted successively over the different antennas during subsequent symbol periods. Then, the receiver successively receives the versions from the different transmit antennas over a single receiver antenna, and the diversity gain is obtained by a coherent combining. However, this code has a rate of only 1/MT . More sophisticated STC schemes have higher rates and additionally achieve a coding gain. The two families of STC are Space-Time Trellis Codes (STTC) and Space-Time Block Codes (STBC). Powerful examples of STTC can be found in [TaSe98]. The disadvantage of STTC is the decoding complexity since the number of states increases exponentially with the number of transmit antennas. Due to the complexity of the decoder for STTC, current approaches in literature mostly consider STBC [GeSh03]. STBCs are designed as pure diversity schemes and provide no coding gain. Yet, they are much simpler to implement. A well-known scheme for MT=2 was proposed by Alamouti in [Ala98]. Denoting two subsequent data symbols by d(0) and d(1), the symbols transmitted on the transmit antenna branches during two symbol periods are given by Tab. 3.2.

Instant t t+TS

Antenna 1 d(0) d(1)

Antenna 2 -d(1)* d(0)*

Tab. 3.2: Alamouti scheme.

This scheme allows to achieve a diversity of 2 for MR=1 with rate 1. Note that for the detection of the two data symbols, two consecutive symbols have to be received and the channel has to be stationary during two symbol periods. Thanks to the orthogonality of this STBC, the receiver can separate the two symbols by simple linear combining. From a practical point of view, this scheme is very robust as it transmits the whole information even when one of the two branches is inactive. In this case, the scheme simply falls back to SISO transmission. Similar orthogonal schemes exist for more than two transmit antennas [TaJa99]. However, it can be shown that schemes for MT >2 only exist for rates lower than one.



When applied to MC-CDMA, the STBC is generally placed before the spreading operation. The corresponding transmitter structure is depicted in Fig. 3.17 and the receiver structure in Fig. 3.18.

user 1d1

↑ L

c1,l

Chipmapping

0

NC -1

OFDM+

Guard Interval

x1,l

. . .c1,l

Chipmapping

OFDM+

Guard Interval

xM,l

. . .↑ L

Contributionsof users 2...K

Space

Time

Coding

. . .

1

M

user 1d1

↑ L↑ L

c1,l

Chipmapping

0

NC -1

OFDM+

Guard Interval

x1,l

. . .c1,l

Chipmapping

OFDM+

Guard Interval

xM,l

. . .↑ L↑ L

Contributionsof users 2...K

Space

Time

Coding

. . .

1

M

Fig. 3.17: Transmitter structure with space-time coding.

Chipdemapping

0

NC -1

RemoveGuard Int.

&OFDM-1

0

L -1

ˆgd

. . .

. . .

Equal.

&

SpaceTime

Decoding

Chipdemapping

0

NC -1

RemoveGuard Int.

&OFDM-1

0

L -1

ˆgd

. . .

. . .

Equal.

&

SpaceTime

Decoding

Fig. 3.18: Receiver structure with space-time decoding.

Note that the receiver has to jointly perform the operations of equalisation, despreading, and decoding of the STBC, which leads to several linear combining matrices for the successive symbols of the desired user. An application of the Alamouti scheme to MC-CDMA can be found in [CaAk00] and more than two transmit antennas are considered in [NiAu03].

In OFDM systems and also in MC-CDMA, the STBC scheme can be applied in a more general way. Instead of transmitting the STBC symbols on consecutive symbol periods, the symbols can generally be transmitted on frame positions having identical fading coefficients. Indeed, the frame positions on which the chips of the MT STBC symbols are mapped have to be chosen such that their channel vectors h(1),…,h(MT) are identical. This leads to a generalised space-time-frequency block code [MoWi02].

3.6.3 Spatial filtering

The spatial filtering or Beamforming (BF) concept [God97][VeBu88][WiMa67] differs from the previously described concepts, which were both based on spatial diversity, by the fact that the multiple antennas are primarily considered as one antenna array. The purpose of spatial filtering is to optimise the directivity pattern of the antenna array, which can also be seen as the spatial response of a filter. Spatial filtering can be applied at reception, i.e. in SIMO systems, at transmission, i.e. in MISO systems, and both, i.e. in MIMO systems. For SIMO and MISO systems, the spatial filter transforms the multiple channels to a single channel and thus leads to an equivalent SISO system with a modified overall channel. In MIMO systems, several such sub-channels can be obtained in parallel each corresponding to a distinct pair of spatial transmit and receive filters.



Spatial filtering requires knowledge about the spatial channel characteristics, i.e. spatial CSI. Depending on the considered approach, this can be instantaneous knowledge of the channel fading at the different antennas, long-term spatial channel statistics, or the DOAs of the paths forming the radio channel. At the receiver, the required CSI can be obtained from estimation, or alternatively adaptive approaches may be considered. At transmission, spatial filtering requires the CSI prior to transmission. Here, the CSI has to be obtained from reception in the uplink or from feedback of the mobile terminal. Note that the spatial multiplexing and diversity schemes presented above exploit the spatial dimension without any a priori knowledge of the CSI at the transmitter. If such knowledge is available, its usage for spatial filtering yields considerable advantages compared to the diversity and multiplexing schemes. Indeed, spatial filtering has been shown to be the optimum strategy for a single receive antenna, i.e. in MISO systems, when the transmitter disposes of reliable CSI [JaVi01]. For MIMO systems, spatial filtering applied at both ends can get close to the maximum capacity if several parallel streams are transmitted using a distinct spatial transmit and receive filtering pair for each stream [Tel99]. Furthermore, spatial filtering is particularly beneficial in multi-user systems where it provides an additional dimension for the separation of user’s signals, i.e. SDMA. Here, employing user-specific spatial filters at the basestation for reception and also for transmission considerably increase of the user capacity [NaPa94][FaNo98].

When applied to OFDM-based systems, spatial filtering can be applied in the frequency domain, i.e. before the OFDM modulation at the transmitter and after OFDM demodulation at the receiver, or in the time domain, i.e. on the OFDM modulated signal (cf. Fig. 3.19). Examples for both approaches can be found in [LiSo99] and [KiCh99], respectively. The time-domain approach has the advantage, that only a single OFDM stage is required for all antennas. However, in a multi-user system where a distinct spatial filter is applied for each user, this would lead to separate OFDM stages for the different users. Since the number of users generally exceeds the number of antennas, the frequency-domain approach seems preferable for a multi-user system with respect to the system complexity. Furthermore, the frequency-domain approach allows to combine filtering in the dimensions space and frequency and to jointly optimise this combined filter.

OFDM

...

1

MT

Time-domain spatial filter Frequency-domain spatial filter

Spatialfilter

OFDM ...

1

MT

Spatialfilter

OFDM

OFDM

...

1

MT

Time-domain spatial filter Frequency-domain spatial filter

Spatialfilter

OFDM ...

1

MT

Spatialfilter

OFDM

Fig. 3.19: Spatial filtering approaches applied to OFDM.

3.6.4 Channel estimation with multiple transmit antennas

A multi-channel estimation similar to the synchronous uplink case is required if multiple antennas are used for transmission and the channel coefficients of all transmit antennas are required at the receiver. This is the case for spatial multiplexing and STC schemes. However, when the same signal is transmitted on the different antennas, i.e. for spatial transmit filtering and transmit diversity, the estimation of a single resulting response is sufficient. As far as multiple antennas are only considered at the basestation, the number of transmit antennas is generally much lower than the number of users in the uplink, and the resulting overhead stays in a tolerable range.

The multi-channel estimation can basically employ the same schemes as presented in section 3.3.3. Thus, a possible solution is to use distinct pilot positions for the different antennas according to Fig. 3.7 [JoRa98][MiKi02]. Approaches using pilot sequences, which result in an

3.7 Conclusion and choices for this work


estimation of the channel impulse responses of the different antennas on distinct fractions of the OFDM symbol are presented in [LiY02]. Concerning the design of the interpolation filter, it can be assumed that the power delay spectra of the channels corresponding to different antennas are identical, which leads to an enhanced filter design [LiWi02].

3.7 Conclusion and choices for this work

It has been shown in this chapter that MC-CDMA is a very flexible multi-user access scheme thanks to its CDMA component. Furthermore, as a benefit of the underlying OFDM scheme, it is not only robust to multipath propagation but exploits the diversity of such channels efficiently with different possible chip mapping schemes. An important drawback of MC-CDMA is the MAI arising through the loss of orthogonality among users’ signals when their chips are affected by different fading coefficients. Hence, there is a trade-off between the achieved diversity and the impact of the MAI. Especially in the uplink, the impact of MAI is important and its mitigation is also more difficult than in the downlink.

Mitigation of MAI, synchronisation, and channel estimation are important issues for the MC-CDMA uplink, which require further intensive research. In the sequel of this work, we focus on the downlink where the efficiency of MC-CDMA has been proved by field trials. Here, MC-CDMA can be considered as a very promising scheme for future wireless systems.

Among the different possibilities to exploit the spatial dimension, user separation by spatial filtering seems to be a very promising approach for the MC-CDMA downlink for several reasons.

Firstly, the mitigation of MAI is an important and complex task, which has to be carried out by the receiver in a conventional downlink system. A separation of users’ signals in space obtained by spatial filtering at transmission can reduce the MAI at the receiver and keep the complexity and power consumption of the receiver low. In this way, the complexity is somehow transferred to the basestation, where it can more easily be tolerated.

Furthermore, antenna array technology also comes with high demands in terms of complexity and power consumption as a result of the multiple RF parts required for the antenna branches and the additional spatial signal processing. This, together with the additional space required by multiple antennas, makes its implementation at mobile terminals fairly difficult. In order to achieve a light receiver design, we only consider a single antenna at the receiver.

For the considered MISO system, diversity and spatial filtering schemes are possible candidates. Since we assume in this work, that some CSI is available at the transmitter, spatial filtering is generally the better choice. Even without taking into account the benefit of spatial user separation, spatial transmit filtering is preferable since it almost reaches the maximum channel capacity already with long-term channel knowledge and partially-correlated fading.

In the following chapters, we propose spatial filtering approaches for different scenarios. Space-frequency transmit filtering is a combination of spatial filtering and pre-equalisation and can be applied in a scenario with low mobility and TDD, where instantaneous channel knowledge is available at the transmitter side from the uplink. When instantaneous knowledge of the channel fading is not available, e.g. in FDD systems or in scenarios with high mobility, we propose transmit beamforming. This spatial filtering approach avoids pre-equalisation and only requires knowledge of the spatial covariance matrices at the transmitter side.


4 Space-Frequency Transmit Filtering Space-Frequency Transmit Filtering (SFTF) combines pre-filtering at the transmitter in two dimensions: space and frequency. This approach requires knowledge of the instantaneous channel fading at the transmitter and is, therefore, well suited for systems with channel reciprocity between uplink and downlink, e.g. TDD systems with low mobility.

4.1 Principles of multi-user pre-filtering

An important drawback of transmission systems based on CDMA is MAI arising from an imperfect separation of users’ signals. The important impact of MAI in MC-CDMA systems was already observed in chapter 3. Efficient MAI mitigation at the receiver involves MUD techniques, which are based on knowledge about the interfering signals [Ver98]. However, these techniques generally require an increased complexity and power consumption that may not be tolerable at mobile receivers. An alternative exists for the considered downlink case, when the basestation has instantaneous CSI prior to transmission. Here, the users’ signals can already be pre-filtered at the transmitter with respect to their different channels so that the MAI level at their terminals is reduced [VoJa98]. Pre-filtering can also take into account the data symbols of the different users and is then generally non-linear, e.g. [IrRa03]. However, due to the complexity of the non-linear approaches, only linear pre-filtering based on CSI is considered in this work. Such pre-filtering techniques can be applied to single and multi-antenna transmission. In the multi-antenna case, pre-filtering at the basestation can benefit from the spatial separation of the terminals, which leads to very efficient MAI mitigation. Note that the situation is different at the terminal. Here, there is no benefit from the spatial dimension for MAI mitigation since the terminal communicates with a single point, the basestation.

For a single transmit antenna, pre-filtering reduces to pre-equalisation and may also be called pre-coding. Multi-user pre-coding for single-antenna downlink systems was presented by [VoJa98], where it is shown that a ZF pre-coding at the transmitter together with SUD techniques at the receiver can achieve the same performance as a conventional system with MUD schemes at the receiver. In this way, the complexity of MUD can be shifted to the transmitter, where it can be tolerated more easily.

In multi-antenna transmission over flat fading channels, pre-filtering is carried out in the spatial dimension only. For a single user, it can equivalently be seen as a transmit diversity scheme. This diversity scheme outperforms other spatial diversity schemes by ensuring that the signals transmitted over the different antenna branches always add coherently at the receiver [Cav00]. Multi-user spatial pre-filtering is similar to the classical beamforming approach and, thus, provides an effective separation of users’ signals [ScBo04].

Combing pre-equalisation and spatial pre-filtering yields a two-dimensional pre-filtering scheme. While pre-filtering for a single-antenna system does not provide a significant improvement, apart

Knowledge is power.Francis Bacon (1561-1626)

Chapter 4: Space-Frequency Transmit Filtering


from the transfer of complexity to the transmitter, two dimensional pre-filtering with multiple antennas can provide a substantial gain compared to MUD at the receiver even when the CSI at the transmitter is imperfect [ViMa01]. In single-carrier systems, the pre-filtering is generally performed in the dimensions space and time. Recent propositions of space-time pre-filtering approaches can be found in [MoGa02] and [TrWe01].

Here, we consider linear pre-filtering for MC-CDMA in the frequency domain. A user-specific transmit filter is placed before the OFDM stages of the different antenna branches. This enables spatial pre-filtering on each chip. Since we focus on spreading in frequency in this chapter, the pre-filtering is done in the dimensions space and frequency. Note however, that the proposed approaches can directly be applied to all other chip mapping schemes cited in section 3.1.4.

4.2 System model

The schematic view of the MC-CDMA system with SFTF over several antenna branches is depicted in Fig. 4.1. The system model is an extension of the conventional single-antenna system introduced in section 3.1. Like in the conventional system, the data symbols dk of users 1 to K are spread into L chips using orthogonal codes ck .

qg*(0)

qg*(L-1)

OFD

M +

∆

.

.M..

.

.K..

OFD

M +

∆

user 1d1

user KdK

Channel State h1,...,hK

OFD

M-1

-∆

Mobile Terminal gReceiver

.

.

.

.

L

Channel

dg^

Basestation Transmitter

Spreadingc1

Transmit-filter

Contributions of users 2...K


L

.

.M..

Copy

1w%

Channelestimation

(if required)

L

L

L

L

Single userdetection

gh%

qg*(0)

qg*(L-1)

OFD

M +

∆

.

.M..

.

.K..

OFD

M +

∆

user 1d1

user KdK

Channel State h1,...,hK

OFD

M-1

-∆


.

.

.

.

L

Channel

dgdg^


Spreadingc1

Transmit-filter

Transmit-filter

Transmit-filter



LL

.

.M..

Copy

1w%

Channelestimation

(if required)

LL

LL

LL

LL


gh%

Fig. 4.1: MC-CDMA downlink system with Space Frequency Transmit Filtering (SFTF).

The different antennas are used in SFTF to transmit filtered versions of the same signal. Therefore, the chips are copied M times to supply the antenna branches. Both operations, spreading and copying, are represented mathematically by an extended version of the code vector ck. The resulting vector of length ML is an M-times repetition of ck and given as follows:

, ,TT T

k k k = c c c% K (4.1)

The notation ~ is generally used to indicate a vector representation of the two dimensions space and frequency. In this way, ML chips of the data symbol dk are obtained. The following linear transmit filter enables a complex weighting of each of these chips with a coefficient wk,m,l . Here, m is the antenna and l the subcarrier index. These coefficients are gathered in the vector kw% of length ML, which is ordered in the same way as the code vector in (4.1). The transmit filters for the different users are calculated using instantaneous channel knowledge according to the criteria detailed in sections 4.3 and 4.4. After filtering, the contributions of all users are summed chip-by-chip on each antenna branch. Hence, the vector gathering the transmit signal is

4.2 System model


( )*

1

K

k k kk

d=

= ∑x w c%% % o (4.2)

The vector x% is of length ML and ordered as in (4.1). This means that its first L elements are mapped to L subcarriers of the first antenna branch, the next L elements to the second branch, and so on. Note that, without loss of generality, we focus here on spreading in frequency only, but keep the two alternative schemes of adjacent chip mapping and chip interleaving. In Fig. 4.1, the chip mapping and de-mapping operations are included in the OFDM module for simplicity.

The underlying OFDM transmission uses a guard interval ∆ and is assumed to be ideal in the sense that the channel can be represented in the frequency domain by a single flat fading coefficient on each subcarrier (cf. section 2.5.2). Hence, the channel between the M antennas of the basestation and the single antenna of terminal g is represented by ML complex fading coefficients hg,m,l gathered in vector gh% .

The mobile terminal is equipped with a single antenna and implicitly recombines the M signals from the transmit array in space. After OFDM demodulation and a potential channel estimation, the receiver equalises and despreads the signals of the L subcarriers using vector qg=[qg,0,…,qg,L-1]T. In analogy to (4.1), we use an expanded vector gq% =[qg

T,…,qgT ]T of size ML to mathematically

represent the signal recombination in space and frequency. Then, the resulting decision variable for mobile terminal g is given by

( ) ( )

* *

1,

NoiseDesired Signal MAI

ˆ K

H H Hg g g g g g g g k k k g

k k gd d d

= ≠

= + +

∑q h w c q h w c q n% %% % % %o % o o % o

144424443 1444442444443

(4.3)

where vector n gathers the noise samples on the L subcarriers. Comparing (4.3) to the decision variable of the conventional system (cf. (3.10)), there are again the three characteristic terms: the desired signal, the MAI and the noise after subcarrier combining. Note that the noise term is identical to the conventional system since the noise is still recombined from the L subcarriers in frequency.

In contrast to the conventional system, the desired signal and the MAI terms are now a function of the transmit filter. In fact, their amplitude depends on the combination of the channel gh% and the transmit filter kw% . This has important consequences, especially for the MAI term. In a conventional system, the MAI term only depends on the channel vector, which is identical for all signal components (desired and interference) arriving at a given terminal from the basestation. Here, we introduce the appellation overall frequency response for the combination of the transmit filter and the common channel on the L subcarriers. For a user-specific transmit filter, the overall frequency response is also specific to each user. Defining the vectors for the channel and the transmit filter on each subcarrier as

, ,0, , 1,' [ , ..., ]Tg g g Mh h −=h l l l and , ,0, , 1,' [ , ..., ]Tg g g Mw w −=w l l l (4.4)

the overall frequency response of user k at terminal g is then given by the vector

, , ,0 , , 1 ,0 ,0 , 1 , 1, ..., ' ' , ..., ' 'T TH H

k g k g k g L k g k L g Lu u − − − = = u w h w h (4.5)

The property of having different frequency responses for each user is known from the MC-CDMA uplink system (cf. 3.1.2). So, roughly speaking, the user-specific transmit filter transforms the downlink system into an uplink system. Since the loss of orthogonality is generally worse in the uplink, this represents an important drawback of the presented approach at first sight. Indeed, we show in the performance results that pre-filtering may actually lead to an increased MAI in some cases, because the orthogonality of the users’ signals is already broken at



transmission. However, we show as well that the advantage of pre-filtering clearly prevails for well-designed filters.

The vector qg for equalisation and despreading is chosen according to the considered combining technique just as in the conventional system. Striving for a low-complexity terminal, we focus on SUD techniques. Note that, as a consequence of the user-specific overall frequency response, ORC cannot restore the orthogonality here, which is analogue to the uplink case, and for the same reason, MMSEC is not advantageous, either. Hence, suitable techniques in conjunction with SFTF are EGC and MRC.

The SFTF approaches are derived under the assumption that the transmitter perfectly knows the channel vectors gh% . In this case, SFTF can perfectly pre-equalise the channel and avoid channel estimation and frequency equalisation at the terminal. Then, the vector qg simplifies to pure despreading, i.e.

g g=q c and g g=q c% % (4.6)

Pre-filtering generally results in a varying power of the transmitted signal. Especially, approaches based on ZF may lead to excessive power peaks that are not tolerable in practice [MoCa02] [VoJa98]. Since power control is out of the scope of this work, we ensure that all transmit filters are power normalised, i.e.

= = ∀ =% % % 2 1...H

k k k L k Kw w w (4.7)

Yet, it is worth noting that the presented techniques can readily be used in joint pre-filtering and power control schemes as proposed for example in [ScBo04].

4.3 Single-user criteria

The considered single-user criteria are obtained from the maximisation of the SNR with respect to the decision value in (4.3). Since the noise at the receiver is not a function of the transmit filter, SNR maximisation is equivalent to maximising the desired signal power under the power constraint in (4.7).

Several single-user criteria are presented in the sequel. The first one represents a theoretical bound for single-user transmission in the case when instantaneous CSI is exploited at both sides, the transmitter and the receiver. The second approach exploits CSI only at the transmitter and applies a simple despreading at the receiver according to (4.6). This criterion maximises the SNR of the decision value given in (4.3) and is, therefore, a joint space-frequency approach including pre-equalisation. The third approach is a per-carrier criterion that does not make any assumption about the combining technique used at the terminal and maximises the desired signal part on each of the L subcarriers separately. Hence, it only aims at performing a spatially-selective transmission on each subcarrier without pre-equalisation in frequency.

4.3.1 Optimum single-user bound

The optimum strategy to adopt for a single-user in the case where instantaneous CSI is exploited at both ends of the considered transmission system can be derived by considering the dimensions frequency and space separately. This approach provides insight in the different properties of the two dimensions.

Fig. 4.2 depicts the simplified single-user system structures for pre-filtering in frequency and space separately. For simplicity, the user index of the symbols is omitted along with the space or frequency indices for pre-filtering in frequency and space, respectively. From this figure, it can be observed that there is an important difference between the two dimensions. In the frequency



dimension, the L subcarriers can be seen as independent transmission channels, each of them having its own fading coefficient and noise process. At the receiver, the signals of the subcarriers are combined explicitly with the weights ql . In the spatial dimension however, the signals transmitted over the antenna branches add implicitly at the single receiver antenna and, thus, there is only one equivalent transmission channel and one noise process in this case.

d

w0*

w*L-1 hL-1

h0 n0

nL-1

q0*

q*L-1

Transmitter Channel

d

Receiver

d

w0*

w*M -1 hM-1

h0

n q*

Transmitter Channel

d

Receiver

Frequency Space

d

w0*

w*L-1 hL-1

h0 n0

nL-1

q0*

q*L-1

Transmitter Channel

d

Receiver

d

w0*

w*M -1 hM-1

h0

n q*

Transmitter Channel

d

Receiver

Frequency Space

Fig. 4.2: Pre-filtering in frequency or space for a single user.

4.3.1.1 Optimisation of transmit and receive weights in frequency

The joint optimisation of the transmit and receive weights for the system exploiting the frequency dimension only is a special case of the power loading problem generally considered in pure OFDM systems. The strategy maximising the capacity is the transmission of multiple parallel streams using the so-called water-filling approach [Gal68]. In the considered system, the same stream is transmitted on the L subcarriers, and the power loading problem gets trivial. The optimum solution is to select the subcarrier providing the highest transmission gain and allocate the total transmit power to this subcarrier, i.e.

max/ for 0 otherwise

h hw

==

l l

l

l l and max1 for

0 otherwiseq

==

l

l l where ( )maxmax h= l

ll (4.8)

This solution is equivalent to selection diversity [Bre59]. Note that the pre-filter weight includes the phase equalisation of the channel, which can equivalently be done by the combining weight at the receiver. It can easily be demonstrated, that this solution maximises the general expression for the SNR per data symbol, i.e.

2 21 1* * * *

0 0, freq. 1 222

0

L L

S S

S LC

C

E w h q E w h q

qγ

σσ

− −

= =−

=

= =∑ ∑

∑

l l l l l ll l

ll

(4.9)

Here, it has been assumed, without loss of generality, that the noise variance after combining is kept constant by normalising the combining weights, i.e.

1

2

0

1L

q−

=

=∑ ll

(4.10)

Then, the maximisation of the SNR is demonstrated by the following sequence of inequalities for the squared sum in the numerator



21 1 1 22 2* * *

0 0 0max

L L L

w h q w h q h− − −

= = =

≤ ≤∑ ∑ ∑l l l l l l ll l l

(4.11)

The first inequality can easily be proved using the well-known inequality of Cauchy-Schwarz and equality holds for wl =κ hl ql , where κ is a real scalar factor. The second inequality is also easy to see with (4.7) and (4.10). Consequently, the optimised SNR for the frequency dimension is obtained with (4.8) and given by

2

, opt. freq. 2maxS

SC

E hγ

σ= l (4.12)

For large L and independent Rayleigh fading on the employed subcarriers, this SNR can be quite high, theoretically infinite. In practice however, this SNR stays obviously limited since a transmission channel itself does never amplify a signal.

4.3.1.2 Optimisation of transmit weights in space

The situation is different for the system exploiting spatial diversity only. Here, the signals transmitted over the M antenna branches are recombined implicitly at the receiver antenna, and only the transmit weights can be adapted. The corresponding SNR per data symbol is given by

2 21 12* * *

0 0, space 2 22 *

M M

S m m S m mm m

SCC

E q w h E w h

qγ

σσ

− −

= == =∑ ∑

(4.13)

Note that this SNR is independent of the receiver weight q, which is only required for phase equalisation in coherent detection. The maximum is obtained from an inequality similar to (4.11), i.e.

21 1 12 2*

0 0 0

M M M

m m m mm m m

w h w h− − −

= = =

≤∑ ∑ ∑ (4.14)

In analogy to (4.11), the equality is obtained for

m mw hκ= (4.15)

where κ is again a real scaling factor. This condition is similar to the MRC technique generally used for receive diversity [Bre59][Pro95]. It also ensures phase compensation so that the multiplication with q* can be omitted at the receiver. Here at the transmitter, we can use the appellation Maximum Ratio Transmission (MRT) [Cav00]. The maximised SNR is then given by

12

0, opt. space 2

M

S mm

SC

E hγ

σ

−

==∑

(4.16)

This SNR increases with the number of transmit antennas. The above expression shows that MRT is the optimum transmission strategy for both cases, correlated and uncorrelated fading at the antennas. For highly correlated fading, MRT achieves the classical array gain compared to single-antenna transmission. This gain is given in dB by [God97]

dB 10=10 log ( )a M (4.17)

For uncorrelated fading, MRT yields a coherent combination of the diversity branches without increasing the number of noise sources, which is an important difference to receive diversity.



While classical diversity schemes tend towards AWGN performance as the number of diversity branches increases, MRT is not limited by this bound.

4.3.1.3 Optimisation of transmit and receive weights in space and frequency

Combining the approaches in frequency and space leads to the optimum solution in the case where both dimensions are exploited jointly. This solution consists in applying MRT on the subcarrier providing the maximum transmission gain. With the definitions in (4.4), the transmit and receive filters are given by

max' / ' for 0 otherwise

==

h hw l l

l

l l and max1 for

0 otherwiseq

==

l

l l where ( )max 'max = h l

ll (4.18)

and the corresponding SNR is

2

, opt. space-freq. 2

'maxS

SC

Eγ

σ=

h l (4.19)

Note that the subcarrier selection is done with respect to the SNR obtained by MRT on the different subcarriers. As the number of antennas increases, MRT benefits from a high spatial diversity, which reduces the dynamic range of the SNRs on the different subcarriers, i.e. it leads to an equalisation of the overall frequency response. This effect clearly reduces the advantage of subcarrier selection.

This combination of MRT and subcarrier selection represents the optimum solution for a single user in the case where instantaneous CSI is exploited at the transmitter and the receiver. However, it will be used as a theoretical reference only. Indeed, this optimum approach results in a spreading factor of one, i.e. no spreading at all. Then in the multi-user case, the multiple access itself has to be managed with respect to the actual channel state, i.e. selection of the optimum subcarrier allocation for the different users. Such multiple access schemes have been proposed especially for wire-line OFDM systems, e.g. [Pfl03] and [WoCh99], and are beyond of the scope of this thesis, where we focus on CDMA.

4.3.2 Joint Maximum Ratio Transmission (J-MRT)

The single-user criterion J-MRT is the optimum solution when despreading without equalisation, cf. (4.6), is applied at the receiver. It is based on the decision variable given in (4.3). Assuming, without loss of generality, that the data symbols have unit power, the desired signal power for terminal g is given by

( ) ( ) 2*, H T H H H

D g g g g g g g g g g gP = ⋅ =w c h c c h c w w h% % %% % % %% o o o o % % (4.20)

Now, PD,g has to be maximised under the power constraint in (4.7), which corresponds exactly to the situation in (4.13) for spatial diversity. The solution is completely analogue and leads to the transmit filter

J-MRT: g g gκ=w h%% (4.21)

where the real scalar κg is given by the power constraint in (4.7). J-MRT involves spatially-selective transmission and pre-equalisation in frequency. When applied in the multi-user case, even this single-user approach can implicitly mitigate interference by reducing the signal power transmitted towards other terminals. However, the pre-equalisation in frequency may aggravate the loss of orthogonality among the users signals, which is a disadvantage of user-specific transmit filtering in the downlink that was already observed in section 4.2.



4.3.3 Per-Carrier Maximum Ratio Transmission (PC-MRT)

In contrast to J-MRT, PC-MRT only aims at spatially-selective transmission on each subcarrier independently, without pre-equalising the signal in frequency. The criterion is based on the maximisation of the desired signal power on each subcarrier separately. It considers the received signals on the L subcarriers before they are combined and consequently there is no assumption about the combining vector qg applied at the terminal, which yields an additional degree of freedom for the choice of the detection technique. This vector can then be chosen according to the combining techniques presented in section 3.2.1. Consequently, PC-MRT requires a channel estimation on each subcarrier at the terminal.

The amplitude of the desired signal on each subcarrier is given by the elements of the overall frequency response vector ug,g defined in (4.5). In analogy to (4.20), the term , ,' 'H

g gw hl l has to be maximised on each subcarrier, which leads to the solution

PC-MRT: , , ,' 'g g gµ=w hl l l (4.22)

In contrast to (4.21), the scalar µg,l is now complex and not only normalises the power but also the phase of the resulting transmit filter. The magnitude of µg,l ensures an equal transmit power on all subcarriers, i.e. |w΄g,l|2 =1 ∀l, and the phase a zero imaginary part of the transmit weight wg,0,l . In this way, the transmit filter is forced to be idle for a single transmit antenna, where the weights are equal to 1 for all users on all subcarriers. In the same way as J-MRT, PC-MRT modifies the resulting overall frequency response at the terminal.

4.4 Multi-user criteria

Multi-user criteria are intended for explicit interference reduction. Hence, they not only consider the desired signal but also the MAI terms. The joint optimisation of the transmitter and the receiver in multi-user systems exploiting instantaneous CSI at both ends is still a challenging issue of research. However, such approaches generally apply multi-user schemes at both ends and involve high computational complexity also at the terminal side. Since our aim is to transfer the complexity from the terminal to the basestation, we focus on multi-user approaches at the basestation assuming that SUD techniques are applied at the terminal.

Multi-user pre-filtering is different from multi-user post-filtering, i.e. linear MUD schemes, since it requires a joint optimisation of the transmit filters for all users. Indeed, it can be observed that the decision variable in (4.3) of a given user is a function of the transmit filters of all users, while a decision variable for linear MUD at the reception only involves the filter of the desired user (cf. section 3.2.2). Thus, one major difficulty in the optimisation of pre-filters for the multi-user case is to find criteria leading to a mathematically-tractable weight optimisation.

Two basic criteria are employed for the weight optimisation: Zero Forcing (ZF) and Maximisation of the SINR (MSINR). In the same way as for single-user criteria, multi-user criteria can be formulated jointly, assuming despreading at the terminal, or separately on each subcarrier without any assumption about the combining techniques employed at the terminal.

4.4.1 Joint Zero Forcing (J-ZF)

The ZF criterion is known from MUD techniques. It aims at cancelling the MAI, or equivalently at installing an orthogonality of users’ signals at the receiver. When used as MUD technique, this principle leads to an amplification of the noise. For ZF pre-filtering, this disadvantage does not exist since the noise at the receiver side is not modified by the transmit filter. However, an unconstrained ZF approach at transmission may lead to very high transmit powers, and the



constraint introduced in (4.7) is therefore essential [VoJa98]. The application of joint ZF in space and frequency to the multi-antenna downlink of MC-CDMA was presented in [SiGa03] and [SäSi03] under slightly different names. Here, we derive the corresponding transmit weights in an intuitive way and give some remarks about the expected performance.

The J-ZF criterion is directly applied to the decision variable of Mobile Terminal (MT) g in (4.3). Forcing the MAI terms to zero while keeping the desired signal power constant yields the following equations:

( )( )

*

*

1 desired signal of MT MAI at MT 0

Hg g g g

Hg g k k

ggk k g

=

= ∀ ≠

c h w c

c h w c

%% %o % o

%% %o % o (4.23)

Here, we assumed that the desired signal power is forced to unity. Note that this set of equations involves the transmit filters of all users, which was already stated in the general remarks above. For the ZF approach, the conditions for a separate optimisation of each transmit filter can be found easily. Since the above set of equations has to be satisfied at all terminals, the equations involving a distinct transmit filter can simply be grouped together. After a convenient reformulation, the conditions to be satisfied by a distinct transmit filter are

( )( )

*

*

1 desired signal of MT MAI at MT 0

Hg g g g

Hg k k g

gkk k g

=

= ∀ ≠

w c h c

w c h c

%% %% o o

%% %% o o (4.24)

For convenience, we define the vectors

*,k g k k g=v c h c%% %o o of length ML, and [ ]

-th el.0, ..,1, .., 0 T

gg

=b of length K (4.25)

bg has a single one in element g and all other elements are zero. The above system of linear equations can be rewritten in the following way

Hg g g=A w b% with 1, ,, ...,g g K g = A v v (4.26)

This system has K equations and ML degrees of freedom. In general, we can assume that Ag has rank K due to the independent channel vectors. For multiple transmit antennas, the system is generally underdetermined, since K<ML. A unique solution exists for M=1 and a fully-loaded system (K=L). The solution for both cases is obtained from the pseudo-inverse of matrix Ag and given by

1( )Hg g g g g

−=w A A A b% (4.27)

The above expression yields the unique solution for K=ML and minimises the norm of the transmit filter in the underdetermined case. The matrix to be inverted is of size K×K and hermitian so that efficient algorithms can be employed [GoLo96]. Up to now the power constraint of (4.7) is not yet included in the criterion. Relaxing the constraint on the desired signal power at the receiver, the above solution can be normalised by a real scalar κg , and the J-ZF vector is finally obtained as

J-ZF: 1( )Hg g g g g gκ −=w A A A b% (4.28)

This normalisation has no impact on the MAI, which stays zero independently of κg , but the desired signal power may vary considerably with respect to the channel conditions and the number of constraints. Indeed, J-ZF forces MAI to zero at any cost even if the MAI level is already lower than the noise level. Thus, J-ZF is sub-optimum especially at low SNR. Numerical results show that J-ZF leads to an inefficient use of transmit power in particular for the case



where only a unique solution exists. A multi-user criterion that does not suffer from this drawback is presented in the next section.

4.4.2 Joint Maximisation of the SINR (J-MSINR)

The disadvantage of the ZF criterion is the inefficient use of transmit power resulting from the fact that the MAI at other terminals is forced to zero at any cost. In contrast, the J-MSINR approach additionally takes into account the noise level at the receiver and in this way can avoid that transmit power is wasted to cancel MAI terms that are already concealed in the receiver noise [SäSi03].

J-MSINR is based on the SINR at the terminal. Using vk,g defined in (4.25) and assuming that the data symbol power is unity, the interference power of user k at terminal g can be written as

( ) 2*

, ,( ) H H HMAI g g k k k g k g k kP k g→ = =c h w c w v v w%% %o % o % % (4.29)

From (4.3) and (4.20), we can now write the SINR at mobile terminal g as

,,

2

1,

( )

D gI g K

MAI nk k g

P

P k gγ

σ= ≠

=→ +∑

(4.30)

Like in the previous section, the SINR of user g is a function of the transmit filters, kw% , of all active users. A criterion based on this SINR would result in a joint multi-variate optimisation of the SINRs of all active users. Here, we consider an intuitive approach that decouples the joint problem into K separate optimisation tasks, i.e. one for each user. Motivated by the fact that the ZF transmit vector of a given user g was obtained using the MAI created by this user at other terminals (cf. (4.24)), we define a modified SINR where the MAI created by user k at a terminal g, i.e. PMAI(k→g), is replaced by the MAI that user g creates at other terminals, i.e. PMAI(g→k). The expression obtained for this modified SINR is then

2

,,

2 2, ,

1, 1,

( )

Hg gD g

MI g K KH H

MAI n g k g k g g nk k g k k g

P

P g kγ

σ σ= ≠ = ≠

= = → + +

∑ ∑

w h

w v v w

%%

% %

(4.31)

In contrast to the conventional SINR, the modified SINR only depends on the transmit filter gw% of the considered user. This general property is known from filtering at reception. Indeed, the modified SINR can be seen as the SINR of the equivalent uplink, where a receive filter is employed at the base station. Therefore, we may also call it the SINR of the ‘virtual uplink’ as proposed by [RaTa98]. A more general paper addressing the duality of the downlink and uplink problem for SINR based algorithms was published recently [BoSc02], and an example where this concept is advantageously applied to pre-filtering in the uplink of MC-CDMA systems can be found in [MoCa02]. The J-MSINR filter is now obtained from a maximisation of the modified SINR subject to the power constraint in (4.7). Including this constraint in (4.31), the optimisation task is formulated as follows:

2

2, ,

1,

maxg

Hg g

KH H Hg k g k g g g g n

k k gσ

= ≠

+

∑

w

w h

w v v w w w%

%%

% % % %

subject to Hg g L=w w% % (4.32)



The term to be maximised stays unchanged if the transmit filter is multiplied by a scalar. Defining the auxiliary vector /g g gκ=w w% and setting 1H

g g =w h% , the maximisation task is given by

2

2, ,

1,

maxg

Hg g

KH Hg k g k g n ML g

k k gLσ

= ≠

+

∑w

w h

w v v I w

% subject to 1H

g g =w h% (4.33)

The solution to this problem is well known from the Minimum Variance Distortionless Response (MVDR) filter design [Hay96]. In this way, a first formulation of the J-MSINR transmit filter is obtained as

1

2, ,

1,

KH

g g g g k g k g n ML gk k g

Lκ κ σ−

= ≠

= = +

∑w w v v I h%% (4.34)

where the real scalar κg ensures the power constraint. This expression of J-MSINR involves a matrix inversion of size ML×ML. However, the problem only has K constraints, and it is easily seen from the sum over the interfering users that the matrix to be inverted is of rank K-1 for very high SNR, where the noise variance tends to zero. This motivates the search for a simplified expression. The derivation of the simplified result is given in appendix A.4. Using the definitions in (4.25) and (4.26), we finally obtain a simplified expression for the J-MSINR as

J-MSINR: 2 1( )Hg g g g g n K gLκ σ −= +w A A A I b% (4.35)

This is a very interesting result for two reasons: On one hand, the matrix to be inverted is reduced to a size of K×K. On the other hand, it proves that the modified SINR criterion leads to a solution that tends towards J-ZF for high SNR, i.e. (4.35) gets equivalent to (4.28) in the noise-free case, and towards J-MRT for low SNR, where the matrix to be inverted tends towards a diagonal matrix with identical entries. Hence, for a given transmit power the J-MSINR filter yields a trade-off between MAI reduction and SNR maximisation, which is analogue to the MMSE-MUD scheme at reception (cf. section 3.2.2.2).

4.4.3 Per-carrier multi-user criteria

The two multi-user criteria presented above for a joint optimisation of the transmit filters in space and frequency can also be formulated on each subcarrier separately. This is analogue to the per-carrier single-user criterion and leads to a transmit filtering that is only selective in space and avoids pre-equalisation in frequency, which leaves a degree of freedom for the choice of the detection technique at the mobile terminal [SäMo03a]. Here, we define the channel matrix of size M×K for each subcarrier l as

1, ,' , ..., 'K = H h hl l l (4.36)

In analogy to the per-carrier single-user criterion, the corresponding multi-user criteria are based on the overall frequency response (cf. (4.5)) of the desired user, i.e. ug,g , and the overall responses of the interfering users, i.e. uk,g for k≠g. Starting with the Per-Carrier MSINR criterion (PC-MSINR) the modified SINR on each subcarrier, cf. (4.31), is obtained with the elements of the overall frequency response vectors as

2

, ,, ,

2, , , ,

1,

' ''

' ' ' '

Hg g

MI g KH Hg k k g C

k k g

γ

σ= ≠

=

+

∑

w h

w h h w

l l

l

l l l l

(4.37)



Like in (4.22), we ensure that the transmitted power is identical on all subcarriers, which leads to the following formulation of the maximisation task

,

2

,

'2

, , , ,1,

' 'max

' ' ' 'g

Hg g

KH Hg k k C M g

k k gσ

= ≠

+

∑

w

w h

w h h I wl

l

l l l l

subject to 2

,' 1g =w l (4.38)

The solution is completely analogue to the previous section. Note, that the desired signal part can be added to the sum in the denominator without any modification of the normalised solution vector, which was shown for J-MSINR in appendix A.4. Using definition (4.36), the transmit filter for the PC-MSINR criterion is then obtained as

PC-MSINR: ( ) 12, ,' H

g g C M gµ σ−

= +w H H I H bl l l l l (4.39)

Here, the complex scalar µg,l ensures the power and phase normalisation as already exposed for PC-MRT. Note that the matrix to be inverted is of size M×M and hermitian. A reformulation of this approach is not advantageous, since the number of users generally exceeds the number of antennas. In analogy to J-MSINR, PC-MSINR tends towards PC-MRT for low SNR, and the Per-Carrier ZF (PC-ZF) solution is obtained for the noise free case as

PC-ZF: ( ) 1

, ,' Hg g gµ

−=w H H H bl l l l l (4.40)

Note however, that the per-carrier criteria are limited by the degrees of freedom given by the number of transmit antennas M. Therefore when M<K, the MAI mitigation capacity of the per-carrier multi-user criteria is quite limited.

4.5 Comparison of SFTF approaches

4.5.1 Analysis of the transmit filter responses in space and frequency

The aim of this section is to provide a qualitative evaluation of the SFTF criteria presented in the previous sections. Here, the transmit filters are calculated for an artificial scenario. This yields the advantage that the results can be graphically represented, which gives deep insight in their respective properties.

Number of carriers, NC 512 Spreading factor, L 32 Chip mapping adjacent subcarriers Antenna array λC/2 spaced ULA, M=16 Number of users, K 17 Channel delays 0 0.03TS 0.09TS 0.14TS Channel powers -0.5 dB 0 dB -7 dB -4.5 dB Channel DOAs, MT g 120° 45° 120° 120° Channel DOAs, MTs k≠g random among 120° and 45°

Tab. 4.1: Simulation parameters for response analysis.

Tab. 4.1 summarises the relevant simulation parameters. The channel comprises four paths with amplitudes chosen randomly from a Rayleigh distribution according to the indicated power delay profile. The desired user has two fixed DOAs (45° and 120°), and the DOAs for the paths corresponding to the channels of interfering users are chosen randomly among the same DOAs. From this spatial distribution of the users’ DOAs, we expect a high interference level, which varies between the DOAs of the desired user for different subcarriers.



SubcarrierDirection [deg]

norm

. Am

plitu

de


norm

. Am

plitu

de

J-MRT


norm

. Am

plitu

de


norm

. Am

plitu

de

PC-MRT


norm

. Am

plitu

de


norm

. Am

plitu

de

J-MSINR


norm

. Am

plitu

de


norm

. Am

plitu

de

PC-MSINR


norm

. Am

plitu

de


norm

. Am

plitu

de

J-ZF


norm

. Am

plitu

de


norm

. Am

plitu

de

PC-ZF

Fig. 4.3: Transmit filter responses in space and frequency.



Fig. 4.3 shows the amplitude of the transmit filter response for terminal g in the dimensions space and frequency for the different criteria. In space, the directions are given in degrees with respect to the ULA in the range of [30°,150°], and in frequency, the 32 adjacent subcarriers used for chip mapping are represented.

To start with the single-user criteria, the amplitude of the J-MRT response is obviously proportional to the amplitude of the channel transfer function of terminal g in space and frequency. As it can be expected from the power delay distribution of the channel, the amplitude is flat at the DOA of 45°, where only a single path is present, and it varies in frequency at 120° due to the superposition of the three other paths. In contrast, PC-MRT acts as an independent spatial filter on each subcarrier and its amplitude is also normalised on each subcarrier, i.e. the integral of the response taken over the spatial dimension is identical for all subcarriers. Nevertheless, the spatial response of PC-MRT varies from one subcarrier to another with respect to the frequency selectivity of the channel. In the considered case, PC-MRT in some sense switches between the DOAs of terminal g , i.e. the maxima of the filter response at 45° correspond to deep fades in the channel transfer function at 120° and the minima at 45° correspond to maxima of the transfer function at 120°.

For the multi-user criteria, the filter responses not only depend on the channel of terminal g but also on the interference created at other terminals. The joint criteria modify their response in both dimensions to mitigate the interference. For J-MSINR and J-ZF this modification is clearly observed by an increased frequency selectivity of the responses at both DOAs. Here, the J-MSINR response is still close to the response of J-MRT and thereby realises a trade-off between the desired signal power for terminal g and the interference created at other terminals. In contrast, the J-ZF response shows a high frequency selectivity and is quite different from the channel transfer function. This shows that an important part of the desired signal power at terminal g is sacrificed for MAI cancellation. The per-carrier criteria can only mitigate the interference by a modification of the spatial filter response. In the depicted situation, transmitting towards the DOA of 45° creates a high interference at other terminals. Therefore, PC-MSINR and PC-ZF minimise their response towards this direction. The response of PC-MSINR still has a considerable amplitude at 45° when deep fades occur in the transfer function of the channel for terminal g at 120° to ensure a sufficient level of the desired signal power. Due to the created interference, the response of PC-ZF at 45° is very small, and the filter has a high response towards the DOA of 120° even when deep fades occur. In the same way as for J-ZF, this leads to an inefficient use of transmit power.


The SFTF approaches are suitable for TDD systems with low mobility and channel reciprocity, which are typical properties of an indoor scenario. This context is considered for the simulations. Here, we assume a perfect knowledge of the instantaneous fading, i.e. the vectors kh% (cf. section 4.2), at transmission and we do not consider any mismatch arising from variations due to the mobility of the terminal. The impact of mobility is discussed in detail in chapter 6. The system parameters chosen for the simulations are basically those introduced in section 3.5.1, and summarised in Tab. 4.2. The HIPERLAN/2 channel model is here extended to a vector channel model according to section 2.3.1. The DOAs of the different paths are uniformly distributed within the operating range of the ULA employed at the transmitter. This large angle spread is typical for indoor scenarios. The performance is averaged over a large number of channel states, which include here the fast fading and the spatial channel properties and are redrawn for each user at each OFDM symbol. Unless otherwise stated we evaluate the performance in terms of BER, which is averaged over the active users as a function of the average SNR per bit. Note that in the considered system model including a power control with respect to the slow fading, the average SNR corresponds



to the transmitted energy per bit divided by the noise spectral density at the receiver (cf. equation (3.49)). For the un-coded system, we generally compare the performance at the operation point of BER=10-2, which can be considered as a typical input BER for channel decoders.

Carrier frequency, fC 5 GHz Sampling frequency 57.6 MHz FFT-size 1024 Number of avail. subcarriers, NC 736 Carrier spacing, ∆f 56.3 kHz Overall symbol time, TS' 21.5 µs Guard time, TG 3.75 µs Symbol alphabet QPSK Channel coding not considered Spreading factor, L 8, 16

Chip mapping Spreading in frequency adjacent or chip-interleaved

Channel models Extended indoor HIPERLAN/2 Channel A: τmax=0.39µs

Angle spread (AS) 120° Array configuration ULA Element spacing, dS λC/2 Number of transmit antennas, M 1, 2, 4, 8

Tab. 4.2: Simulation parameters for SFTF.

4.5.3 Single-user performance and diversity

When only a single user is active, the optimum bound presented in section 4.3.1 can be achieved by exploiting the instantaneous channel knowledge at both ends of the transmission system. As a first step, we compare this bound to the single-user performance of SFTF, i.e. J-MRT, which is the optimum single-user criterion for despreading without equalisation at the terminal.

Fig. 4.4 shows the BER performance for the optimum single-user bound, which corresponds to PC-MRT and subcarrier selection, and for J-MRT with 1, 2, and 4 transmit antennas. For the optimum bound, the subcarrier providing the highest SNR with PC-MRT is selected out of L=16 available subcarriers. We consider a chip-interleaved system, which provides a large dynamic range for the subcarrier selection. For a single antenna (M=1), J-MRT with despreading is about 4.5 dB from the optimum bound at BER=10-2. The difference would obviously be much lower if a set of adjacent subcarriers was considered, where the fading is highly correlated. As the number of antennas increases, J-MRT benefits from the array gain. At high SNRs, there is also a diversity gain resulting in a steeper slope of the curves, especially when stepping from M=1 to M=2. The difference between J-MRT and the optimum bound decreases as the number of antennas increases, because the spatial diversity obtained from MRT enhances the SNR on all subcarriers. This leads to a reduced dynamic range of the SNRs on the different subcarriers and thereby reduces the advantage of subcarrier selection. For 4 antennas, the difference is still about 2.5 dB. We can conclude from these results that the selection-based adaptive scheme may be an interesting alternative for systems with instantaneous knowledge at both ends. However, as already stated before, this requires a completely different management of the multiple user access, which is out of the scope of this work.



-10 -8 -6 -4 -2 0 2 4 6 8 10

10-3

10-2

10-1

P C-MRT - S electionJ-MRT - Des pr.

SNR, γb

BER

M=1M=4 M=2

-10 -8 -6 -4 -2 0 2 4 6 8 10

10-3

10-2

10-1

P C-MRT - S electionJ-MRT - Des pr.

SNR, γb

BER

M=1M=4 M=2

Fig. 4.4: Single-user performance of SFTF and theoretical bounds

(K=1, L=16, interl.).

In Fig. 4.5, we consider the single-user performance of J-MRT for chip mapping on adjacent subcarriers compared to chip interleaving. The diversity gain observed for an increasing number of antennas in addition to the array gain is considerably higher when adjacent subcarriers are chosen. Here, the lack of frequency diversity is compensated by the spatial diversity obtained with an increasing number of antennas. With the interleaved set, diversity is already well exploited in frequency and the use of additional antennas basically results in an SNR shift of the curves that corresponds to the array gain, while their slope stays almost constant. As a consequence, the advantage in terms of required SNR at BER=10-2 of the interleaved set reduces from 7 dB for M=1 to less than 2 dB for M=4. Thus, it seems interesting to consider both chip mapping schemes also in the case of multiple users, where we have again the trade-off between frequency diversity and MAI, which was already observed in the conventional system presented in the previous chapter.

SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1

adjacentinterleaved

M=1M=4 M=2

SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1

adjacentinterleaved

SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1

adjacentinterleaved

M=1M=4 M=2

Fig. 4.5: Single-user performance of SFTF with different chip mapping

(K=1, L=16).



4.5.4 Multi-user performance with chip interleaving

For a single transmit antenna, the joint pre-filtering approaches are equivalent to a pre-equalisation in frequency only. This case is considered in Fig. 4.6, where J-MRT, J-ZF, and J-MSINR with despreading at the terminal are compared to the conventional system with EGC and MMSE-MUD for a fully-loaded system, i.e. K=L=16. The single-user performance with J-MRT, which is equivalent to the single-user performance of the conventional system with MRC, is given as a reference. The comparison of J-MRT with the conventional system employing EGC shows the impact of the user-specific pre-filtering on the MAI. Indeed, J-MRT has an error floor above BER=10-1, while the conventional system with EGC achieves a BER of about 2⋅10-2. This shows that J-MRT considerably increases the MAI for a single-antenna system, where there is no possibility of spatial user separation. The multi-user criteria J-MSINR and J-ZF outperform the conventional system with EGC for higher SNR since they can completely cancel the MAI and have no error floor. However, compared to the conventional system with MMSE-MUD, the multi-user pre-filtering approaches require a considerably higher SNR. At BER=10-2 J-MSINR requires about 6 dB more than MMSE-MUD and J-ZF as much as 15 dB, which emphasises the inefficient use of the transmitted power by J-ZF. These results show that multi-user pre-equalisation in frequency at the transmitter can cancel the MAI in the downlink, but requires a considerably higher SNR than a conventional system with MUD at the receiver. Thus, the advantage of the considered pre-filtering approaches in single-antenna downlink systems is limited to the case where SUD is employed at the receiver.

SNR, γb

BER

0 5 10 15 20 25

10-3

10-2

10-1

BS:J-MRT MT:Despr.K=1BS:J-MRT MT:Despr.BS:J-MSINR MT:Despr.BS:J-ZF MT:Despr.BS:Conv MT:EGCBS:Conv MT:MMSE-MUD

SNR, γb

BER

0 5 10 15 20 25

10-3

10-2

10-1


Fig. 4.6: Multi-user performance with pre-equalisation in frequency only

(K=16, M=1, L=16, interl.)

The situation is different when multiple antennas are available at the transmitter. Fig. 4.7 compares the joint pre-filtering approaches with two and four antennas to the conventional single-antenna system.



-5 0 5 10 15

10-3

10-2

10-1


SNR, γb

BER

M=1M=4 M=2

-5 0 5 10 15

10-3

10-2

10-1


SNR, γb

BER

M=1M=4 M=2

Fig. 4.7: Multi-user performance of joint SFTF approaches

(K=16, L=16, interl.).

For M=2, the error floor of J-MRT is considerably reduced compared to Fig. 4.6, and for M=4 it is lower than the floor for the conventional system with EGC, which is a benefit of the implicit separation of user’s signals by spatially-selective transmission. J-MSINR and J-ZF clearly outperform the conventional system with MMSE-MUD. At BER=10-2, they achieve gains of 5 dB and 10 dB for M=2 and M=4, respectively. Here, there is only a slight difference between the two multi-user approaches, and J-ZF tends towards J-MSINR for higher SNR as expected from the equations derived above. Note that the multi-user approaches are very close to their single-user performance, i.e. about 2.5 dB for M=2 and 1 dB for M=4, which shows that these approaches can efficiently mitigate MAI even in the fully-loaded system. This underlines the efficiency of the proposed joint multi-user pre-filtering schemes when multiple antennas are employed at the basestation.

The per-carrier approaches result in a spatially-selective transmission on each subcarrier without pre-equalisation in frequency. These approaches are compared to the joint approaches in Fig. 4.8 for M=4 transmit antennas and a fully-loaded system. Comparing the single-user approaches, PC-MRT has a slightly lower error floor than J-MRT, which can be explained by the power weighting on the different subcarriers performed by J-MRT leading to an increased MAI. In the considered configuration, the per-carrier multi-user criteria PC-ZF and PC-MSINR with EGC have an error floor slightly below BER=10-2 and converge already at low SNRs. Obviously, there are not enough degrees of freedom for MAI mitigation with these algorithms, since the number of antennas (M=4) is much lower than the number of users (K=16). In this case, the multi-user approaches have a similar behaviour as the single-user approaches. Since the per-carrier approaches are independent of the detection technique employed at the receiver side, we also considered the combination of PC-MSINR at the transmitter with MRC at the receiver, which would be advantageous in the case of good spatial interference reduction, where the link towards each terminal can be seen as a single-user system. However, here this combination yields no advantage since the MAI level is still very high.



SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1

BS :J-MRT MT:Des pr.K=1BS :J-MRT MT:Des pr.BS :J-MS INR MT:Des pr.BS :P C-MRT MT:EGCBS :P C-MS INR MT:EGCBS :P C-MS INR MT:MRCBS :P C-ZF MT:EGC

SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1


Fig. 4.8: Multi-user performance of per-carrier SFTF approaches (1)

(K=16, M=4, L=16, interl.).

SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1


SNR, γb

BER

-5 0 5 10 15

10-3

10-2

10-1


Fig. 4.9: Multi-user performance of per-carrier SFTF approaches (2)

(K=8, M=8, L=8, interl.).

The same approaches as above are compared in Fig. 4.9 for a different system configuration. Here, the number of antennas (M=8) equals the number of users (K=8), while the system is still fully-loaded (L=8). Due to the higher number of antennas, there is a high degree of spatial diversity, which reduces the dynamic range of the overall frequency response. Thus, the power weighting effect with J-MRT almost disappears and its performance meets the one of PC-MRT. Note that the error floor for both criteria is again reduced as a benefit of the higher spatial selectivity. At BER=10-2, these single-user criteria are only about 1.5 dB from PC-MSINR and 3.5 dB from J-MSINR. PC-ZF and PC-MSINR have now enough degrees of freedom to completely cancel the MAI and have no error floor anymore. Again, the ineffective use of transmit power is observed for the ZF criterion, which has a loss of about 8.5 dB compared to PC-MSINR at BER=10-2. At the same BER, PC-MSINR is only about 2 dB from the J-MSINR performance, which itself is already very close to the single-user curve. Combining PC-MSINR



and MRC is slightly better than PC-MSINR with EGC, as a benefit of the low MAI level. Yet, MRC yields no considerable improvement as a consequence of the high spatial diversity. Indeed, for a large number of antennas, the spatial diversity reduces the dynamic range of the overall frequency response, which leads to a convergence of the combining techniques MRC and EGC.

The results in Fig. 4.8 and Fig. 4.9 show that the per-carrier criteria are clearly outperformed by the joint criteria. Therefore, the per-carrier criteria are not considered in the following sections. A detailed comparision of per-carrier and joint approaches accounting for imperfections due to Doppler variantions can also be found in [SäMo03b].

4.5.5 Multi-user performance with adjacent chip mapping

In the conventional MC-CDMA system, chip mapping on adjacent subcarriers is advantageous with respect to the MAI, since the orthogonality of users’ signals is almost conserved when the fading on the different chip positions is highly correlated. However, mapping on adjacent subcarriers cannot exploit the frequency diversity of the channel without channel coding. This drawback looses its importance when the system can benefit from spatial diversity obtained with multiple antennas, which was observed for the single-user performance presented in Fig. 4.5.

-5 0 5 10 15 20

10-3

10-2

10-1

BS :J-MRT MT:Des pr.K=1BS:J-MRT MT:Des pr.BS :J-MS INR MT:Des pr.BS :Conv MT:EGCBS:Conv MT:MMSE-MUD

SNR, γb

BER

M=1M=4 M=2

-5 0 5 10 15 20

10-3

10-2

10-1

BS :J-MRT MT:Des pr.K=1BS:J-MRT MT:Des pr.BS :J-MS INR MT:Des pr.BS :Conv MT:EGCBS:Conv MT:MMSE-MUD

SNR, γb

BER

M=1M=4 M=2

Fig. 4.10: Multi-user performance of joint SFTF approaches

(K=16, L=16, adjac.).

Here, we consider adjacent chip mapping in the multi-user case. The system configuration for Fig. 4.10 corresponds to the one used for Fig. 4.6 and Fig. 4.7 with the only difference that adjacent chip mapping is employed here. Thus, the single-user reference curves obtained with J-MRT suffer from reduced diversity. For K=16, the conventional single-antenna system with MMSE-MUD also suffers from reduced diversity. In contrast, the conventional system with EGC SUD benefits from the lower MAI and has no error floor. For M=1, the J-MRT scheme only has a small loss compared to the conventional system with EGC. Indeed, for highly correlated fading on the subcarriers, the impact of user-specific pre-filtering on the MAI is less important. For the same reason, the performance of J-MSINR is almost identical to the conventional system with EGC. For M>1, the performances of J-MRT and J-MSINR are close to the single-user performance. In this case, the orthogonality among users’ signals is nearly conserved, which makes J-MRT the optimum strategy since the higher complexity involved by multi-user criteria can be avoided. Comparing Fig. 4.7 and Fig. 4.10, J-MRT and J-MSINR with adjacent chip mapping achieve a similar performance as J-MSINR with chip interleaving.



Especially for adjacent chip mapping, SFTF clearly benefits from spatial transmit diversity as the number of antennas increases. Since a large angle spread can be assumed in the considered indoor scenario, the employed antenna spacing of dS=0.5λC is generally sufficient to achieve a low correlation of the fading on different antennas and consequently a high spatial diversity. However in situations with small angle spreads, the coherence distance is increased and a larger antenna spacing may be required to benefit from spatial diversity. Such a scenario is shown in Fig. 4.11, where Channel E (τmax=1.72µs) with an angle spread of AS=30° and a mean DOA uniformly distributed in the range [30°,150°] is considered for a fully-loaded system. The spacing of the elements in the ULA is dS=0.5λC and dS=2.0λC , respectively. Here, the benefit of the larger element spacing is clearly observed. The gain for the single-user performance of J-MRT and for J-MSINR is about 2 dB at BER=10-2. As for J-MRT, it has to be noted that channel E is more selective in frequency than channel A employed for the previous results. Thus, the orthogonality among users’ signals cannot be entirely conserved with adjacent chip mapping. However, J-MRT with multiple users still achieves an acceptable performance and gains around 3 dB at BER=10-2 from the larger spacing.

Further results for J-MSINR obtained with the simulation chain of the MATRICE project also show the impact of the antenna spacing and are presented in appendix A.5.

-6 -4 -2 0 2 4 6 8 10 12 14

10-3

10-2

10-1 BS :J-MRT MT:Des pr. K=1

BS:J-MRT MT:Des pr.BS :J-MSINR MT:Des pr.

SNR, γb

BER

dS=0.5λCdS=2.0λC

-6 -4 -2 0 2 4 6 8 10 12 14

10-3

10-2

10-1 BS :J-MRT MT:Des pr. K=1

BS:J-MRT MT:Des pr.BS :J-MSINR MT:Des pr.

SNR, γb

BER

dS=0.5λCdS=2.0λC

Fig. 4.11: Influence of antenna spacing on SFTF performance

(K=16, M=4, L=16, adjac., channel E, AS 30°).

4.5.6 System overloading by code reallocation

The user-capacity in conventional single-antenna MC-CDMA systems is limited by the number of available spreading codes. In the case of W-H codes, the number of users referred to as full system load equals the length of the spreading codes. The transmit antenna array used for spatially-selective filtering endows the system with an SDMA component or, equivalently, with additional degrees of freedom to separate the users’ signals. As a consequence, the user capacity can be increased by the allocation of additional spreading codes. Optimal code reallocation generally has to take into account the spatial properties of the different channels. Then, the same code can be allocated to users that are well separated in space. For the considered approaches, the spatial transmit filters and consequently the resulting spatial separation of users’ signals already depend on the codes allocated to the different users. Hence, an optimum code allocation would require a joint optimisation of the code allocation and the transmit filters, which is a non-trivial task. As a



sub-optimum but easily feasible solution, we propose to use an overloading scheme allowing the allocation of additional codes without taking into account the spatial channel properties of the different users. The transmit filters are then optimised with respect to this new code set.

The notion of overloading in CDMA systems is used to describe the allocation of additional spreading codes to a fully-loaded system. Here, the extended code set may loose some of the properties of the original set. In the considered case of W-H codes, the additional codes can obviously not be orthogonal to the original set. There are several possibilities to generate extended code sets from orthogonal sets with a given spreading factor, e.g. [VaMo03]. Here, the extended set is obtained from several W-H sets of size L allocated in parallel and separated by a random scrambling code of length L. The code vectors of the extended set are given as follows:

X ,k p q k= ∀c c ro with p=mod(k,L) and q=div(k,L) (4.41)

mod(x,y) and div(x,y) denote the reminder and the integer part of the integer division x/y, respectively, and cp denotes a code of the original W-H set. The random scrambling code, given by vector rq , is different for each of the W-H sets. Thus for K ≤ L, the extended set is equivalent to the original set and completely orthogonal. For higher K, there is orthogonality of the codes belonging to the same W-H set, i.e. having the same scrambling code, but not between codes from different W-H sets, which are multiplied by different scrambling codes. This allocation scheme provides an arbitrary number of additional codes, but its performance is obviously limited by the MAI, which increases rapidly when the number of users exceeds the spreading factor.

Fig. 4.12 shows the tolerable system load with code reallocation for one and two transmit antennas with chip interleaving and channel A. The curves represent the SNR required to achieve the operation point BER=10-2 as a function of the number of users, which is equivalent to the number of allocated codes. The considered approaches are J-MSINR, J-ZF and the conventional system with MMSE-MUD.

1 4 8 12 16 20 24 28 32

5

10

15

20

25 BS:Conv MT:MMSE-MUDBS:J-MSINR MT:Despr.BS:J-ZF MT:Despr.BS:J-MSINR MT:Despr.BS:J-ZF MT:Despr.

Number of users (K)

Requ

ired

SNR

at B

ER=

10-2

Full load of conv. system(K=L=16)

M=2M=1

1 4 8 12 16 20 24 28 32

5

10

15

20

25 BS:Conv MT:MMSE-MUDBS:J-MSINR MT:Despr.BS:J-ZF MT:Despr.BS:J-MSINR MT:Despr.BS:J-ZF MT:Despr.

Number of users (K)

Requ

ired

SNR

at B

ER=

10-2

Full load of conv. system(K=L=16)

M=2M=1

Fig. 4.12: Tolerable system load with code reallocation

(L=16, interl.).

For a single antenna, none of the considered techniques allows to achieve the operation point with a number of users beyond the conventional full load limit given by K=L=16. Indeed, the MAI level increases drastically even if only a single user is added to the fully-loaded system.

4.6 Conclusion on Space-Frequency Transmit Filtering


Comparing the SNR required by the three approaches, it can be noticed that the conventional system with MMSE-MUD performs best with a single antenna for all system loads. Here, the multi-user pre-filtering approaches require considerably higher SNRs for medium to full load, i.e. K≥8. J-MSINR outperforms J-ZF, which requires an excessive SNR when the number of users approaches full load. For M=2, the tolerable system load basically doubles when J-MSINR and J-ZF are employed. Here, J-MSINR also yields a considerable gain compared to J-ZF and tolerates a load that is slightly beyond the limit of K=2L. Thus, even with sub-optimum code reallocation, the multi-user SFTF techniques efficiently exploit the additional degrees of freedom for jointly separating the users’ signals in the two dimensions, space and frequency.

Note that code re-allocation requires an explicit separation of the users’ signals by multi-user criteria. Therefore, it cannot be applied for the combination of J-MRT and adjacent chip mapping, where the orthogonality of the employed code set is crucial for the performance. With J-MSINR however, code allocation is also possible for adjacent chip mapping.

4.6 Conclusion on Space-Frequency Transmit Filtering

Several criteria for SFTF in conjunction with SUD at the receiver were derived and analysed in the case of perfect instantaneous channel information at the transmitter. Four basic approaches can be distinguished: Single- and multi-user approaches, which are applied separately on each subcarrier or jointly on all subcarriers. The advantages and drawbacks of these features are briefly summarised in Tab. 4.3.

Single-user criteria Multi-user criteria

Pro

s - Independent on detection technique. - Benefits from spatial diversity.

Per

Car

rier

SF

TF

Con

s - Impacts on the code orthogonality. - Requires channel estimation at the

terminal.

- Impacts on the code orthogonality. - Requires channel estimation at the

terminal. - Limited number of degrees of

freedom for user separation (M). - Increased complexity due to matrix

inversion (M×M).

Pro

s

- Optimum single-user technique. - Benefits from spatial and frequency

diversity. - Achieves close to single-user

performance with adjacent chip mapping and multiple antennas.

- Efficient user separation in space and frequency irrespective of chip mapping.

- Benefits from spatial and frequency diversity.

- Allows an increased user capacity with code reallocation.

Join

t SF

TF

Con

s

- Impacts on the code orthogonality. - Increased complexity due to matrix inversion (K×K).

Tab. 4.3: Comparison of SFTF approaches.



The SFTF approaches are efficient transmit diversity schemes and benefit from diversity in space (per-carrier and joint approaches) and frequency (only joint approaches). Therefore, uncorrelated fading on the antennas is favourable for these algorithms.

In its optimum version, SFTF yields an efficient separation of users’ signals in space and frequency. However, in some cases the user-specific transmit filter of SFTF can induce an increased MAI since it impacts on the orthogonality among users’ signals installed by the spreading code. This drawback is particularly important for a system with chip interleaving and for the single-user criteria. As a consequence, SFTF yields no particular performance improvement compared to the conventional system if only a single-antenna is employed at the basestation. Note that with a single antenna, SFTF results in pre-equalisation in frequency only. For multiple transmit antennas, however, the advantages of STFT clearly prevail over this drawback.

For multiple transmit antennas, the joint approaches perform considerably better than the per-carrier approaches. Note that the per-carrier approaches are equivalent to the conventional system for a single transmit antenna. Furthermore, the fact that the per-carrier criteria are optimised on each subcarrier separately and are free from any assumption about the detection technique yields no particular advantage compared to the joint criteria, but requires additional complexity at the receiver, e.g. for channel estimation. Therefore, the per-carrier criteria are of minor interest for the considered system.

The joint criteria in conjunction with multiple transmit antennas can provide a considerable gain compared to the conventional system. When adjacent chip mapping is employed, the single-user J-MRT approach almost attains the performance of a single user even with a fully-loaded system. J-MSINR yields a very efficient separation of the users’ signals in space and frequency irrespective of the chip mapping and allows an increase of the user capacity with code re-allocation.

The joint SFTF approaches enable a very simple receiver design for the mobile terminal. These approaches are optimised for a pure despreading at the terminal and, in the ideal case of perfect channel information at the transmitter, require no channel estimation at the receiver. In this way, the joint approaches allow a transfer of the complexity from the terminal to the basestation. Even with a pure despreading at the terminal, J-MRT outperforms the conventional system with MMSE-MUD at the terminal for adjacent chip mapping. The same performance is obtained with J-MSINR, but here independently of the chip mapping employed.

In this chapter, we concentrated on the un-coded system with perfect channel knowledge. A further assessment of the joint SFTF approaches including channel coding and erroneous channel knowledge due to the mobility of the terminal is presented in chapter 6.


5 Transmit beamforming Transmit beamforming is a purely spatial pre-filtering approach that allows a spatially-selective transmission based on instantaneous or long-term channel knowledge. Consequently, this approach can be applied not only in TDD scenarios with channel reciprocity but also in scenarios with higher mobility and in FDD schemes, where instantaneous channel knowledge is generally not available at the transmitter side.

5.1 Beamforming in wireless multi-user communications

In wireless multi-user communications, the mobile terminals are generally located at distinct positions within the area covered by the basestation. Therefore, the channels between these mobiles and the basestation have different characteristics. In particular, the DOAs of the propagation paths forming the radio channel vary considerably from one user to another. Beamforming with antenna arrays exploits this property to spatially separate the signals belonging to different users.

Firstly introduced as an analogue spatial filtering concept, e.g. [WiMa67], beamforming emerged as a promising concept for multi-user communications thanks to the advances in digital signal processing [LiLo96]. A very good overview on beamforming techniques and the closely related topic of DOA estimation can be found in [God97]. The principle of beamforming can be applied at transmission and at reception. It consists in adapting the spatial response of the antenna array with respect to the DOAs of the different users’ channels. Such a spatial response generally has maxima towards desired directions and minima towards undesired ones. The benefit of beamforming is twofold, it yields an antenna gain and a reduction of interference. The antenna gain is obtained at transmission by concentrating the signal power towards the desired direction and at reception thanks to the large aperture obtained by coherently combining the signals received on the antennas of the array. Interference is reduced by placing minima of the spatial response towards undesired directions so as to avoid signal transmission or reception to and from these directions, respectively. In this way, beamforming yields a variety of applications, especially in multi-user systems [LiLo96][LiRa99]: Fixed beams can be used to sectorise a cellular system with each beam covering a distinct part of the cell. Adaptive beamforming can reduce interference among users of the same cell by applying a different spatial response for transmitting or receiving the signals of each user, which leads to the already presented SDMA scheme [Far99][NaPa94] [ZeOt95]. Note that MAI mitigation through spatial user separation can only be obtained at the basestation as a benefit of the different locations of mobile terminals. The terminal, however, cannot do any better than orienting its beam towards the basestation. In cellular systems, beamforming also allows to reduce the inter cell interference. Indeed, spatially-selective reception of signals reduces the interference received from other cells and a reciprocal reasoning holds for spatially-selective transmission.

The aim of science is not to open the door to infinite wisdom, but to set a limit to infinite error.

Bertolt Brecht (1898-1956)

Chapter 5: Transmit beamforming


Beamforming applied to OFDM and MC-CDMA is a subject that came up only recently. Most publications concern receive beamforming at the basestation in the uplink. The use of receive beamforming for co-channel interference rejection in the frequency domain of an OFDM system is studied in [LiSo99]. In contrast, an adaptive time-domain beamforming for OFDM is proposed by [KiCh99] and extended to MC-CDMA in [KiKi00]. Yet, for multi-user systems, beamforming at the basestation in the time domain requires a separate OFDM stage for each user, which seems disadvantageous in terms of implementation complexity. Receive beamforming for MC-CDMA in the frequency domain is addressed by several authors, e.g. [KiCh00a][KiCh00b][LiLe01]. [LiLe01] considers beamforming in conjunction with MUD at the receiver side, where groups of users with similar DOAs are separated through beamforming and separately processed in the following MUD stages. [KiCh00a] and [KiCh00b] investigate an estimator for the spatial covariance matrix in the case of small angle spreads, which is employed for receive beamforming at the basestation. As for the forward link, a recent assessment of adaptive transmit beamforming for OFDM compared with other space-time schemes can be found in [KaAs03]. However, the authors only consider a single link and do not mention the possibility of MAI mitigation in multi-user systems. The combination of OFDM with SDMA through adaptive beamforming in the frequency domain is covered in detail by [HaMü03], where the potential of MAI mitigation is clearly pointed out. For MC-CDMA, [Fuj03] presents a beam-space diversity scheme using fixed beams and STBC, which also benefits from spatial user separation. The usage of the beamforming vector obtained at reception for transmission in the MC-CDMA forward link is suggested in [KiCh00a], and a similar approach based on direction finding was recently proposed in [RaCa03]. In both cases, a small angle spread was assumed so that the beam can be directed towards a single DOA.

Here, we propose transmit beamforming at the basestation in the frequency domain based on spatial covariance matrices obtained from an instantaneous estimation, e.g. in TDD systems with low mobility, or a long-term estimation, e.g. in TDD systems with high mobility and FDD systems. Covariance-based beamforming can cope with a large angle spread arising, for instance, in urban outdoor and in indoor scenarios. In the same way as in the previous chapter, the aim of a user-specific transmit beamforming is the reduction of MAI in the downlink, which enables the use of very simple terminals and at the same time increases the user capacity of the system.

5.2 System Model

The system model is quite similar to the one used in the previous chapter for SFTF. Fig. 5.1 depicts a schematic view of the MC-CDMA downlink system with transmit beamforming at the basestation employing M antennas.

The data symbol dk of each user k is subject to beamforming over the M branches, which is represented by a vector wk defined as follows:

,0 , 1[ ,..., ]−= Tk k k Mw ww (5.1)

The beamforming vectors of the different users are calculated on the basis of channel state information, for instance the spatial covariance matrices of the users’ channels. In contrast to SFTF, the beamforming operation is placed before the spreading, which indicates that the same beamforming vector is applied to all chips. Hence, the M versions of the symbols are spread on each antenna branch separately using the code vector ck of length L defined in (3.1). After the spreading operations on the M antenna branches, there is a total of ML chips per data symbol, which is completely analogous to SFTF. The contributions of all users are added chip by chip, and the transmitted signal vector in the frequency domain can be expressed in the same way as for SFTF, i.e.

5.2 System Model


( )*

1

K

k k kk

d=

= ∑x w c%% % o (5.2)

The extended code vector kc% is here also given by (4.1). In contrast, the transmit filtering vector kw% of length ML is different from SFTF and obtained from the beamforming vector, wk , by

repeating its elements L times for each antenna branch, i.e.

times times,0 ,0 , 1 , 1[ , ..., ]L L T

g g g g M g Mw w w w− −= ←→ ←→w% (5.3)

The vector x% is ordered as before. Thus, its first L elements are transmitted on the L subcarriers of the first antenna branch, the next L elements on the second branch, and so on. Again, we focus on spreading in frequency only, but the results can be extended easily to other chip mapping schemes. In Fig. 5.1, the mapping and de-mapping operations have been included in the OFDM module for simplicity. To ensure that the transmitted signal power per user is normalised, the condition (4.7) established for SFTF has also to be respected here. From the expression of the transmit filter kw% , the normalisation of the beamforming vector is obtained as

= = ∀ = 2 1 1...Hk k k k Kw w w (5.4)

qg*(0)

qg*(L-1)

OFD

M +

∆

.

.M..

.

.K..

OFD

M +

∆

user 1d1

user KdK

Channel State R1 ,...,RK

OFD

M-1

-∆


.

.

.

.

L

Channel

dg^


Spreadingc1

Beamforming



.

.M..

1w

Channel estimation

L

L

Spreadingc1


gh%

qg*(0)

qg*(L-1)

OFD

M +

∆

.

.M..

.

.K..

OFD

M +

∆

user 1d1

user KdK


OFD

M-1

-∆


.

.

.

.

L

Channel

dg^


Spreadingc1

Beamforming



.

.M..

1w

Channel estimation

L

L

Spreadingc1


qg*(0)

qg*(L-1)

OFD

M +

∆

.

.M..

.

.K..

OFD

M +

∆

user 1d1

user KdK


OFD

M-1

-∆


.

.

.

.

L

Channel

dgdg^


Spreadingc1

Beamforming



.

.M..

1w

Channel estimation

LL

LL

Spreadingc1


gh%

Fig. 5.1: MC-CDMA downlink system with transmit beamforming.

The underlying OFDM transmission is assumed ideal so that the multipath channel between the M transmit antennas and the receive antenna of terminal g on the L considered subcarriers can be represented by vector gh% . In analogy to (4.4) and (4.5), we define the overall frequency response as the combination of the beamforming vector of user k with the channel of terminal g on each subcarrier

, ,0 , 1' , ..., 'TH H

k g k g k g L − = u w h w h with , ,0, , 1,' [ , ..., ]Tg g g Mh h −=h l l l (5.5)

We focus on a low-complexity terminal equipped with a single antenna and SUD techniques. At a given terminal g, the signal is OFDM demodulated and channel estimation is carried out for each subcarrier. Then, the signal components can be recombined from the different subcarriers using the vector qg=[qg,0,…,qg,L-1]T, which corresponds to equalisation and despreading. In this way, the decision variable is obtained as

( ) ( )

, ,1,


ˆ K

H H Hg g g g g g g k g k k g

k k gd d d

= ≠

= + +

∑q u c q u c q no o

1442443 14444244443

(5.6)



This decision variable is composed of the three characteristic terms: The desired signal, the MAI and the noise after subcarrier combining. Concerning the MAI term, it has to be noticed that the overall frequency response is specific to each user as a consequence of the user-specific transmit beamforming. Thus, the MAI term here is similar to the MAI term obtained in a conventional uplink system, which is a disadvantage that is common to all user-specific transmit filtering schemes.

Transmit beamforming does not include any pre-equalisation in frequency. Hence, equalisation has to be ensured by the combining vector qg . Due to the user-specific overall frequency response, SUD schemes based on orthogonality restoring, e.g. ORC and MMSEC, are not advantageous. Therefore, we consider EGC and MRC SUD schemes, which are here given by

MRC: , , , , , 'Hg g g g g g g,q c u c= = w hl l l l l (5.7)

EGC: , , , ,,

, ,

'

'

Hg g g g g g,

g Hg g g g,

c u cq

u= =

w h

w h

l l l l

l

l l

(5.8)

Note that estimates of the overall frequency response (cf. (4.5)) of the desired signals are required for both techniques. Thus, channel estimation at the receiver is mandatory for transmit beamforming.

5.3 Beamforming principles

Suitable criteria for beamforming in the frequency domain of the MC-CDMA system described above have to respect the fundamental principles of array processing and take into account the particularities of a wideband multi-carrier system. In the following, we address these issues and present classical single- and multi-user beamforming criteria.

5.3.1 Spatial sampling theorem

The output of an antenna array is a spatially-sampled version of the signal impinging on the array. Similar to sampling in time, the spatial sampling has to respect the Nyquist-criterion to avoid aliasing effects. A plane wave in the far field is characterised by its wavelength λC and its direction of propagation. If such a wave impinges on an ULA from a direction θ, the ULA takes probes of the impinging signal spaced by the distance |dS cos(θ )| (cf. section 2.2.4). This corresponds to a sampling time of |dS cos(θ )|/v0 . To satisfy the sampling theorem, the sampling time has to be smaller than 1/(2fC ), which leads to the following condition for the element spacing

( ) λθ ≤ =0cos

2 2C

SC

vdf

(5.9)

Hence, for spatial sampling without aliasing effects in the range of θ=[0,π], the maximum element spacing for an ULA is dS=λC /2, which is the value commonly employed in literature. In the case of an UCA, the M elements are placed on a circle of radius rS at every 2π/M radians and the distance between two elements is given by 2rS sin(π/M). Thus, to satisfy the sampling theorem, the radius of an UCA has to be chosen according to the following condition

4 sin

CSr

M

λπ

≤

(5.10)

If the spatial sampling theorem is not respected, the array response develops so-called grating lobes due to spatial aliasing [God97]. In this case, the relation between the DOAs and the array response vector is ambiguous, which should generally be avoided.



5.3.2 Classical beamforming approaches

The beamforming criteria for MC-CDMA are derived from classical approaches for receive beamforming in flat fading single-carrier systems that can be found in literature. In this section, these approaches are introduced, and their properties are investigated with a focus on their suitability for transmit beamforming in the considered MC-CDMA system. Single- and multi-user criteria are considered in two scenarios. The first scenario corresponds to a small angle spread, where a single DOA can be assumed for each user. The second scenario considers a large angle spread and consequently several DOAs per user.

5.3.2.1 Criteria for small angle spreads

For a small angle spread, it can be assumed that the paths forming the channel of a given user impinge from a single DOA at the basestation. In this case, the beamforming vector can be directly related to the mean DOA gθ of a given user g. Hence, the beamforming criteria presented here are optimum in the case of a single DOA per user and their performance degrades as the angle spread increases.

The optimum single-user criterion for beamforming in the presence of a single DOA is straightforward. Given the mean DOA gθ , the beamforming vector maximising the SNR is obtained from the array response vector (cf. section 2.2.4). This solution is referred to in literature as conventional beamforming [God97][KrVi96], and the beamforming vector is given as

SU-Conv: ( )1g gM

θ=w a (5.11)

As a single-user criterion, the conventional beamforming does not take into account the interference from and towards other users directions, respectively. However, it implicitly mitigates the interference by spatially-selective transmission. Compared with the single-antenna system, the conventional beamforming yields an array gain in the SNR given in dB by [God97]

dB 10=10 log ( )a M (5.12)

This gain was already observed for the MRT approach presented in section 4.3.1.2. Note that, for a single DOA, i.e. completely correlated fading at the antennas, MRT and SU-Conv are identical. The SU-Conv criterion is general enough so that it can directly be applied for transmit beamforming, and it is also suited for the considered MC-CDMA downlink system when the angle spread is sufficiently small.

The optimum beamforming for a single DOA in the presence of interference and noise at reception can be obtained by the MVDR filter [Hay96]. This criterion minimises the total output power of the spatial filter, while keeping a constant response with respect to the signal impinging from the desired direction. In this way, it maximises the SINR of the output signal. Defining the vector representing the received signal on the M antennas as y(t )=[y1(t),…,yM(t)], the spatial covariance matrix of size M×M for the received signal is given by

E ( ) ( )Hy t t=R y y (5.13)

Then, the MVDR solution is obtained from the following minimisation

( )ming

Hg y g

ww R w subject to ( ) 1H

g gθ =w a (5.14)

This yields the beamforming vector as

MU-MVDR: ( )

( ) ( )1

1

y gg H

g y g

θ

θ θ

−

−=

R aw

a R a (5.15)



In principle, the MVDR criterion can be extended to transmit beamforming, provided that a suitable spatial covariance matrix representing the interfering directions can be constructed. In contrast to conventional beamforming, this criterion is not directly applicable for transmit beamforming in the considered system since the representation of the interference with a spatial covariance matrix is generally not sufficient. This issue is addressed in detail in section 5.4.3. Nevertheless, the MVDR criterion derived here provides insight in the interference rejection capacity of beamforming. Indeed, according to the degrees of freedom of the minimisation task above, an array composed of M elements can mitigate the interference of M-1 directions, while keeping a constant response to one desired direction.

5.3.2.2 Criteria for large angle spreads

For large angle spread, the DOAs of the different paths forming the radio channel cannot be merged to a single mean DOA anymore. As a consequence, beamforming for large angle spreads has to be done with respect to the spatial covariance matrices of the considered signals. The spatial covariance matrix corresponding to the desired signal of user g can be obtained from its vector channel. Assuming a normalised power for the desired signal, the spatial covariance matrix of user g is given by

( ) ( ) , ,E Hg B g B gt t=R h h (5.16)

Here, the vector channel of user g for flat fading results from definition (2.33) for a negligible delay spread, where τ can be omitted. Note that the criteria presented here also cover the special case of a small angle spread, where the spatial covariance matrix of the desired signal has rank one.

The optimum single-user criterion maximises the output SNR of the spatial filter given the covariance matrix Rg of the desired user. The beamforming vector is then obtained from the following maximisation

( )maxg

Hg g g

ww R w subject to

21g =w (5.17)

Hence, the beamforming vector has to be proportional to the principal eigenvector of the spatial covariance matrix and is given by

SU-Eigen: m_eig( )g g gκ=w R (5.18)

m_eig(X) denotes the principal eigenvector of a matrix X, i.e. the eigenvector corresponding to the largest eigenvalue [GoLo96], and κg ensures the normalisation. In the same way as the single-user criterion in the previous section, this criterion also holds for transmit beamforming due to the reciprocity of the spatial response of the antenna array. Furthermore, it is directly applicable to the considered MC-CDMA system, which is shown in section 5.4.2. It is interesting to note that there exist efficient solutions for estimating and tracking the principal eigenvector of the hermitian matrix Rg , which avoid an explicit eigenvalue decomposition of the covariance matrix [GoLo96][Utsch02].

The multi-user criterion for large angle spreads is given by the maximisation of the output SINR taking into account the covariance matrix covering the interfering signals of the other users and the noise. This covariance matrix is the sum of the covariance matrices belonging to the other users and the noise, i.e.

2

1,

K

I k k n Mk k g

P σ= ≠

= +∑R R I (5.19)

Here, Pk denotes the signal power of user k. The optimum beamforming vector is then obtained by maximising the SINR, i.e.



maxg

Hg g gHg I g

w

w R w

w R w (5.20)

The solution must be proportional to the principal generalised eigenvector of the matrix pair (Rg ,RI) [GoLo96], and the corresponding beamforming vector is given by

MU-Eigen: gm _eig( , )g g g Iκ=w R R (5.21)

where gm_eig(X,Y) denotes the principal eigenvector of a matrix pair (X,Y), and κg ensures the normalisation. Even if the SINR maximised in (5.20) corresponds to receive beamforming in the uplink, this criterion can be extended to transmit beamforming in the downlink, provided that the matrix RI is appropriately chosen with respect to the interference and noise powers [BoSc02][FaNo98]. A possible approach for MC-CDMA employing this criterion is discussed in section 5.4.3.

5.3.2.3 Assessment of spatial responses

The spatial responses resulting from the beamforming approaches presented above are here illustrated by concrete examples for situations with a small angle spread, i.e. a single DOA per user, and a large angle spread, i.e. multiple DOAs per user. For instance, we consider an UCA with radius 0.7λC composed of 12 elements. Desired and interfering signals have identical and normalised powers and the SNR is set to 6 dB.

30

210

60

240

90

270

120

300

150

330

180 0

-10 dB

-5 dB

0 dBDesired DOA

Interfering DOA

SU-Conv

MU-MVDR

30

210

60

240

90

270

120

300

150

330

180 0

30

210

60

240

90

270

120

300

150

330

180 0

-10 dB

-5 dB

0 dBDesired DOA

Interfering DOA

SU-Conv

MU-MVDR

Fig. 5.2: Spatial responses for a small angle spread (UCA, M=12, 1 desired DOA, 5 interfering DOAs).

Fig. 5.2 shows the situation for a small angle spread, i.e. a single desired DOA, and five interfering DOAs. The response of SU-Conv beamforming has its maximum of 0 dB towards the desired direction, i.e. 210°. As for the interfering directions, the gain of the SU-Conv response is quite high, up to –1 dB for the closest one at 220° lying in the main lobe of the response and around –10 dB for three others. In contrast, the response of the MU-MVDR criterion shows a slight loss of about 3 dB towards the desired direction. Towards the closest interfering direction, the response is about 10 dB lower, and for all other interfering directions, the response is more than 18 dB lower. Thus, the MU-MVDR criterion realises the trade-off between maximising the desired signal power and mitigating the interference, which globally enhances the SINR.



The situation for a large angle spread is shown in Fig. 5.3, where the desired signal power is distributed on two DOAs (0.6 at 210° and 0.4 at 100°). The SU-Eigen criterion yields a response with a maximum towards the desired DOA with the highest power. Note however, that the response to the second DOA is also increased compared with Fig. 5.2. Again, the interfering DOA at 220° lies in the main lobe and several side-lobes lead to relatively high responses towards interfering DOAs. In contrast, the MU-Eigen criterion yields a main lobe towards the second DOA at 100° that corresponds to a lower part of the desired signal power but has no interfering DOA in its vicinity. Towards the interfering directions, the gain of the MU-Eigen response is always lower than –20 dB. Hence, the MU-Eigen criterion achieves again a good trade-off between the maximisation of the desired signal power and interference mitigation.

30

210

60

240

90

270

120

300

150

330

180 0

-10 dB

-5 dB

0 dBDesired DOA

Interfering DOA

SU-Eigen

MU-Eigen

30

210

60

240

90

270

120

300

150

330

180 0

-10 dB

-5 dB

0 dBDesired DOA

Interfering DOA

SU-Eigen

MU-Eigen

Fig. 5.3: Spatial responses for a large angle spread

(UCA, M=12, 2 desired DOAs, 4 interfering DOAs).

5.3.3 Wideband beamforming aspects

The vector channel model used in this thesis and the considered beamforming techniques are based on the narrowband assumption of array processing, which states that the signal bandwidth has to be much lower than the inverse of the travelling time across the array. For the example of a half-wavelength spaced ULA, this condition turns out to be

0 2( 1) cos( ) ( 1)cos( )

C

S

v fBM d Mθ θ

<< =− −

(5.22)

Note that for an ULA, this condition depends on the considered DOA θ. Tab. 5.1 gives an example for parameters of a future wireless wideband systems, for which bandwidths up to 100 MHz are currently considered [AtMa02]. With these parameters, the ratio between the travelling time across the array and the signal bandwidth is about 10%, which reaches the limit of the narrowband assumption. Even if the parameters are chosen very roughly they indicate that wideband array processing is an issue for the design of future wideband systems.



Carrier frequency, fC 5 GHz Carrier wavelength, λC 6 cm Bandwidth, B 100 MHz = 0.02 fC Antenna array 10 element ULA, λC /2 spacedTravelling time across the array 1 ns Ratio travelling time/bandwidth 0.1

Tab. 5.1: Example for parameters of a future wideband system.

Two basic approaches are known from literature that enable array processing for wideband signals. Firstly, a tapped delay line can be placed after each array element in order to equalise the array response for a certain frequency range. The second possibility is to perform the processing in the frequency domain after an FFT operation, which has to be carried out on each antenna branch. In this way, the wideband signal is split into narrowband components, which can be processed separately. A comparison of both approaches for an adaptive receive array can be found in [Com88], where it is shown that the approaches are basically equivalent but that the frequency domain approach leads to a less complex filter design. In the multi-carrier system considered in this work, the array processing is also carried out on the narrow-band subcarriers in the frequency domain. Hence, we can conclude that it is sufficient to respect the narrow-band assumption on each subcarrier provided that array processing is done on each subcarrier separately. Then the narrowband assumption gets

0 2( 1) cos( ) ( 1)cos( )

C

C S

v fBN M d Mθ θ

<< =− −

(5.23)

which is generally satisfied in practice. This is the case for the SFTF approaches presented in the previous chapter, where transmit weights are adapted with respect to the channel fading on each subcarrier.

For the beamforming approaches, however, the same beamforming vector is used for a group of L subcarriers and its optimisation is based on an estimate of the covariance matrix obtained from subcarrier averaging. Thus, depending on the range spanned by these subcarriers this can require a joint array processing over the whole bandwidth of the underlying OFDM system. In this case, there may be an impact arising from the violation of the narrowband assumption. The following two sections evaluate this impact and show possible countermeasures.

5.3.3.1 Coherent wideband array processing

If the subcarriers of the considered OFDM system span a large bandwidth, the array response vector varies with respect to the actual subcarrier frequency. Neglecting this variation results in non-coherent wideband array processing and may lead to a degradation of the beamforming performance. This impact can be avoided by coherent wideband array processing, which aims at a compensation of the frequency variation in the array response [WaKa85]. Thereby, the array response at a given frequency, fn , is transformed into an equivalent response at a common processing frequency f0 . This is achieved by a so-called focusing matrix of size M×M verifying

( ) ( ) ( )0, ,n nf f fθ θ=T a a (5.24)

Here, the condition is only established for a single DOA, θ , while coherent processing of signals impinging from several different directions requires focusing matrices that can be used for a whole range of DOAs. The construction of focusing matrices for large DOA ranges is a challenging research subject in wideband array processing [WaKa85]. Here, we focus on two approaches for frequency compensation in the whole operating range of an array: Response matching based on the MSE, which is independent of the array geometry [AsFo98], and spatial re-sampling, which is limited to ULAs [KrSw91]. Considering a single focusing matrix for a large



range is obviously sub-optimum, but it enables a pre-calculation of this matrix. Otherwise different matrices have to be calculated for smaller angular sectors and applied with respect to a rough estimation of the actual DOAs.

The response matching approach finds an approximate solution for equation (5.24) for all values of θ within a considered angle range by minimising the MSE. For instance, we take the example of an ULA. Note that the approach can be applied to any other array configuration without major modifications. The angular range in which the approximation is valuable may vary according to system requirements. For an ULA, the operating range is generally θ∈[30°,150°]. To ensure a good transformation of an arbitrary array response vector within this range, P equidistant angles θp are taken from this range and the corresponding array responses at frequency fn are stacked into the following matrix of size M×P

( ) ( ) ( )0 1, , , ,P n n P nf f fθ θ −= A a aK (5.25)

Now, the focusing matrix has to respect the condition in (5.24) for the whole set of angles given by θp ; p=0..P -1, i.e.

( ) ( ) ( )0n P n Pf f f=T A A (5.26)

This over-determined system can in general only be solved approximately. The focusing matrix for response matching is given by the solution minimising the MSE, i.e.

Response matching: ( ) ( ) ( ) ( ) ( )( ) 1

0HH

n P P n P n P nf f f f f−

=T A A A A (5.27)

The basic idea of spatial re-sampling is to compensate the frequency dependence by virtually adapting the antenna spacing. Indeed, the array response is independent of frequency if the ratio between the antenna spacing and the wavelength, i.e. dS/λn , stays constant, which is easily verified from the array response vector defined in (2.21). Then, the virtual spacing is frequency dependent an given by d(fn )=dSf0/fn . This principle is illustrated in Fig. 5.4. The physical array spacing is given by dS at the reference frequency f0. The frequency corrected array response at fn >f0 has to be obtained from element positions spaced closer than dS. Thus, the frequency corrected response can be obtained from the original response by interpolation. For fn <f0, there is an additional difficulty since the virtual element positions lie outside the physical array. In this case, the frequency correction involves prediction, which leads to performance degradation. Thus, the transposition towards a lower frequency (f0 <fn ) is generally more accurate than the transposition to a higher frequency (f0 >fn ).

Interpolated positions

Predicted positions affected by higher resampling error

Physical positions at f0 dS

Virtual positions fn > f0 dS f0/fn

dS f0/fnVirtual positions fn < f0

Interpolated positions

Predicted positions affected by higher resampling error

Physical positions at f0 dS

Virtual positions fn > f0 dS f0/fn

dS f0/fnVirtual positions fn < f0

Fig. 5.4: Spatial re-sampling.

The focusing matrix for spatial re-sampling is then obtained from the interpolation filter used for the frequency correction. A detailed derivation of a suitable interpolation filter is given in



[KrSw90]. Assuming that the number of antennas is odd, i.e. M=2P+1, the shift variant filter coefficients are given by

0

0

sin1( , ) ; ,

nn

n

f m pf

m p m p Kf m pf

ψ

ϖπ

− = ≤

− with ψn =min(π,(f0/fn )π). (5.28)

The corresponding focusing matrix is then given by

Spatial re-sampling: ( ) ( )1, 1 ; , 1...n pqf p P q P p q Mϖ= − − − − =T (5.29)

where Xp,q denotes the element at row p and column q of the matrix X.

The focusing matrices derived above are employed for frequency compensation in the case where the subcarriers of the considered system span a large bandwidth. For instance, these matrices can be applied to the spatial covariance matrices of each subcarrier before frequency averaging and also to the beamforming vector calculated for a given frequency before it is used on the different subcarriers. Note that the same frequency compensation can be employed in FDD systems, when an uplink estimate of the covariance matrix on frequency fn shall be employed for beamforming on the downlink frequency f0 [AsFo98][LiaCh01].

5.3.3.2 Evaluation of the performance loss with frequency compensation

The performance of the frequency compensation techniques in the presence of a considerable frequency variation is evaluated here for the example of two different frequencies f0 and f1 , where f1=(1+∆f ) f0. We apply the single- and multi-user beamforming criteria presented in section 5.3.2.2 on frequency f0 using a covariance matrix obtained at the higher frequency f1 with and without compensation.

0 20 40 60 80 100 120 140 160 180-70

-60

-50

-40

-30

-20

-10

0

10

No compensationResponse matchingSpatial re-sampling

Angle [deg]

Gain

[dB]

Desired DOA

Interfering DOA

0 20 40 60 80 100 120 140 160 180-70

-60

-50

-40

-30

-20

-10

0

10

No compensationResponse matchingSpatial re-sampling

Angle [deg]

Gain

[dB]

Desired DOA

Interfering DOA

Fig. 5.5: Example of spatial responses with frequency compensation.

Fig. 5.5 shows the example of MU-Eigen beamforming (cf. (5.21)) with an ULA composed of M=7 elements in the case of a single desired DOA and 6 interfering DOAs. The frequency difference is ∆f =0.1. All signals are assumed to have the same normalised power and the SNR is set to 10 dB. If no correction is applied to the covariance matrix obtained at f1 , the frequency mismatch is clearly visible in the spatial response obtained with the MU-Eigen criterion at f0. In particular, the main lobe of the response is broadened and the minima are shifted away from the interfering DOAs. These effects are aggravated for angles close to the borders, which is



intuitively clear from the fact that the frequency variation of the array response vector for an ULA increases as the angle moves away from broadside. Both frequency compensation techniques result in considerably better spatial responses. Their responses have a narrower main lobe towards the desired DOA and the minima are placed towards interfering DOAs. The response obtained with spatial re-sampling has more marked minima and thus achieves a better interference suppression than the response matching approach.

Fig. 5.6 considers the same configuration as above with the only difference that two desired DOAs maximally spaced by 30° are present. Apart from this constraint, the two desired DOAs and the five interfering DOAs are randomly chosen within the operating range of θ∈[30°,150°]. The SINR loss with respect to a response obtained without frequency mismatch was calculated for a large number of Monte Carlo draws. Fig. 5.6 depicts the cumulative probability of the SINR loss for single-user and multi-user criteria, i.e. the curves give the probability that the SINR loss is higher than the corresponding value. Without compensation the loss with SU-Eigen is lower than 0.5 dB in nearly all cases for ∆f =0.05 and lower than 1.5 dB for ∆f =0.1. A much higher loss is expected for MU-MVDR, here the loss exceeds 4 dB in 15% of the cases for ∆f =0.05 and in almost half of the cases for ∆f =0.1. The response matching approach leads to a considerable reduction of the loss for MU-MVDR, especially at ∆f =0.05. However, no amelioration is obtained for SU-Eigen, where the loss for ∆f =0.1 is slightly aggravated. Spatial re-sampling leads to a considerable reduction of the loss for MU-MVDR compared to the other two approaches. Here, the loss is kept lower than 1.5 dB for ∆f =0.0.5 and lower than 3.75 dB for ∆f =0.1. For SU-Eigen, it only leads to a slight improvement compared to the approach without compensation. Thus, the spatial re-sampling approach clearly outperforms the response matching approach as far as an ULA is employed.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1SU-Eigen, ∆f=0.05SU-Eigen, ∆f=0.1MU-MVDR, ∆f=0.05MU-MVDR, ∆f=0.1

Loss [dB]

Cum

ulativ

e pr

obab

ility

Nocompensation

Responsematching

Spatialre-sampling

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1SU-Eigen, ∆f=0.05SU-Eigen, ∆f=0.1MU-MVDR, ∆f=0.05MU-MVDR, ∆f=0.1

Loss [dB]

Cum

ulativ

e pr

obab

ility

Nocompensation

Responsematching

Spatialre-sampling

Fig. 5.6: Performance loss with frequency compensation.

We may conclude from these results that the loss for SU-Eigen without frequency compensation may be tolerable for moderate frequency differences (lower than ∆f =0.05), and that the considered compensation techniques cannot really mitigate the loss in this case. For MU-MVDR

5.4 Transmit beamforming criteria for the MC-CDMA downlink


a much higher loss is expected, and spatial re-sampling is an efficient approach to mitigate this loss when an ULA is employed. In the system parameters given in Tab. 5.1, the maximum frequency gap between two subcarriers is about ∆f =0.02. Here, the loss arising from non-coherent array processing is clearly negligible as far as SU-Eigen approaches in scenarios with moderate angle spreads are considered.


The general beamforming approaches of section 5.3.2 are here refined for their application to transmit beamforming in the considered MC-CDMA downlink. We focus on criteria suited for large angle spreads to match realistic propagation scenarios. The presented beamforming techniques exploit different versions of spatial covariance matrices obtained from instantaneous and long-term estimations.

5.4.1 Spatial covariance matrices in multi-carrier systems

Transmit beamforming requires information about the spatial properties of the channels of the different users served by the basestation. Such spatial knowledge is always related to the DOAs respectively DODs of the multipath components with respect to the antenna array (cf. section 2.2.1). In contrast to the fast fading amplitude of the mobile channel, these directions vary only slowly with respect to the movement of the terminal and are almost identical within a relatively large frequency range. As a consequence, the DOAs of the uplink channel can be assumed identical to the DODs of the downlink channel in most practical cases even when high mobile velocities and FDD systems are considered [LiaCh01]. For simplicity, we only mention the DOAs in the sequel and keep in mind this correspondence. Detailed spatial channel information generally involves knowledge about the DOAs and the distribution of the signal power among them, i.e. an estimate of the power azimuth spectrum. However, the estimation of DOAs and the associated powers for a multitude of paths requires a large computational effort. All the more as this requires DOA estimation for a single source, which is not trivial due to the correlation of signals [KrVi96]. A less demanding alternative for transmit beamforming is to employ an estimate of the spatial covariance matrix. This matrix represents the averaged spatial correlation of the channel fading at the different array elements and is the basis of most DOA estimation algorithms [God97].

Recalling definition (5.16), the spatial covariance matrix of the flat fading multipath channel is given as

( ) ( ) E HB Bt t=R h h (5.30)

Note that the user index is omitted here for simplicity. For instance, we consider the channel model derived in section 2.3.1, where the channel consists of NP independent Rayleigh fading paths each having a DOA θp and a variance Ωp . Using the expression of the vector channel in (2.33) in the case of flat fading, we can omit the delay τ and write the spatial covariance matrix as

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( )

'

'

1 1

' '0 ' 0

1 1*

' '0 ' 0

1

0

E ( )e ( )e

= E ( )e ( )e

P Pp p

P Pp p

P

HN Nj t j t

p p p pp p

N Nj t j tH

p p p pp p

NH

p p Pp

t t

t t

ϕ ϕ

ϕ ϕ

θ α θ α

θ θ α α

θ θ

− −

= =

− −−

= =

−

=

=

= Ω

∑ ∑

∑ ∑

∑

a a

a a

a a

R

(5.31)



This matrix is hermitian and its rank depends on the number of distinct DOAs. The matrix is full rank when the number of DOAs is superior or equal to the number of antennas. The expectation is taken in time, i.e. with respect to the fast fading channel statistics. As a consequence, the practical estimation of this matrix involves time averaging over a period that has to be much longer than the coherence time of the channel. Hence, R is called the long-term spatial covariance matrix. This matrix can advantageously be exploited for transmit beamforming in scenarios with high mobility since it is independent of the instantaneous channel fading. Furthermore, for transmit beamforming in FDD systems, the long-term spatial covariance matrix obtained at the uplink frequency can be used at the downlink frequency through transposition (cf. [LiaCh01] and section 5.3.3). In the considered MC-CDMA system, the long-term spatial covariance matrix is identical for all flat fading subcarriers, which motivates the use of a common beamforming vector for the set of L subcarriers employed for chip mapping.

In system configurations where the transmitter can exploit instantaneous channel knowledge, transmit beamforming can also be performed with respect to the instantaneous subcarrier averaged covariance matrix. Using definition (5.5), this matrix is given by

1

0

1 ' 'L

HL L

−

=

= ∑R h hl ll

(5.32)

Note that the user index is dropped for simplicity. This matrix is obtained from averaging over the instantaneous channel fading on the L subcarriers employed for chip mapping within a single OFDM symbol. Since this matrix represents the instantaneous channel state, it leads to an improved beamforming performance. The instantaneous covariance matrix is nearly identical to its long-term version for small angle spreads, where LR can also directly be related to the mean DOA. For large angle spreads however, LR varies considerably with the channel fading as a result of the superposition of different DOAs. Hence, this matrix is sensitive to Doppler variations and may only be available in TDD systems with low mobility and channel reciprocity between up- and downlink, i.e. in similar scenarios as those assumed for SFTF. A third version of the covariance matrix providing spatial information that is less sensitive to Doppler variations can be obtained by averaging over a larger number of subcarriers. In practice, many subsystems, each of them comprising L subcarriers, are allocated in parallel in the underlying OFDM transmission. Hence, we define the instantaneous covariance matrix averaged over the whole set of NC available subcarriers in the underlying OFDM system as

1

0

1 ' 'C

C

NH

N n nnCN

−

=

= ∑R h h (5.33)

To analyse the properties of this matrix, we express the channel vector in the frequency domain using the vector channel impulse response in the time domain given in (2.33). In analogy to (2.9), the vector channel transfer function in frequency is obtained from (2.33) by Fourier-Transform and given by

( ) ( ) ( )1

( 2 )

0

, ( ) eP

p pN

j t fB p p

p

f t t ϕ π τθ α−

−

=

= ∑ aH (5.34)

The vector h'n gathers the M samples of this vector function at instant iTS' and on frequency n∆f, which is analogue to (2.41). Hence, it is given by

( ) ( ) ( )1

( ' 2 )

0

' , ' ( ')eP

p S pN

j iT n fn B S p p S

p

n f iT iT ϕ π τθ α−

− ∆

=

= ∆ = ∑ ah H (5.35)

Using the above equation in (5.33) yields



( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

' '

' '

1

0

1 1 1( ' 2 ) ( ' 2 )

' '0 0 ' 0

( ' ' ) 2 ( )*' '

phase rot

1= ' '

1= ( ' )e ( ' )e

1 = ( ' ) ( ' ) e e

C

C

C P Pp S p p S p

p S p S p p

NH

N n nnC

HN N Nj iT n f j iT n f

p p S p p Sn p pC

j iT iT j n fHp p p S p S

C

N

iT iTN

iT iTN

ϕ π τ ϕ π τ

ϕ ϕ π τ τ

θ α θ α

θ θ α α

−

=

− − −− ∆ − ∆

= = =

− ∆ −

∑

∑ ∑ ∑a a

a a

R h h

( ) ( )

1 1 1

0 0 ' 0 ation with

1 2

0

( ' )

C P P

P

N N N

n p p n

NH

p p p Sp

iTθ θ α

− − −

= = =

−

=

≈

∑ ∑ ∑

∑ a a

14243

(5.36)

Here, the delay difference between distinct paths leads to a different phase rotation on each subcarrier. Due to this phase rotation, the contributions of the different paths can be dissociated from each other, i.e. the cross-terms for p’≠p in the sums over the paths vanish with the subcarrier average. This requires that the average is done over a large number of subcarriers and that the product of the delay difference and the subcarrier spacing, i.e. ∆f (τp’−τp ), is large enough. In this case, the instantaneous spatial covariance matrix can be represented in a similar way as its long-term version. Comparing (5.31) to (5.33), the variance of each paths Ωp is here replaced by its instantaneous power, |α(iTS’ )|².

This representation shows under which conditions the instantaneous subcarrier averaged spatial covariance matrix is closely related to long-term spatial channel properties, i.e. the DOAs of the propagation paths, even for large angle spreads. Indeed, for an average over a low number of subcarriers the directional information is concealed by the fast fading effect. In contrast, an average over a large number of realisations of the fading process reveals the directional information, which is similar to the long-term averaged spatial covariance matrix. Note that the bandwidth of the OFDM system generally spans several times the coherence bandwidth of the channel. In this case, the subcarrier averaged covariance matrix is robust with respect to Doppler variations.

The possibility to dissociate the DOAs of different channel paths by frequency averaging is a very interesting property that can be exploited for DOA estimation. Here, the DOAs can be obtained from a one shot estimate, i.e. from a single OFDM symbol, of the spatial covariance matrix, which avoids averaging over a long time period as required in flat-fading single-carrier systems. Note that this principle is similar to the spatial smoothing approach known from DOA estimation of correlated sources in single-carrier systems [KrVi96].

In principle, all three versions of the spatial covariance matrix given by (5.31), (5.32), and (5.33) can be employed for transmit beamforming. However, there are important differences in the properties of these matrices: Already from their construction it is observed that these three versions converge in scenarios with small angle spreads, but differ considerably for large angle spreads. Furthermore, a reliable estimate of these matrices may not always be available at the transmitter side depending on the considered scenario.

5.4.2 Single-user criterion

The Single-User Beamforming (SU-BF) criterion only concerns the desired signal part of the decision variable in (5.6). Assuming that the data symbol power is unity, the power of the desired signal for MRC and EGC is given as follows



( )

21 2

,2 0

, , 21

,0

1 ' with MRC

1 ' with EGC

LHg g

HD g g g g g

LHg g

LP

L

−

=

−

=

= =

∑

∑

w h

q u c

w h

ll

ll

o (5.37)

In both cases, the desired signal power is maximised by maximising the term

1 1 12

, , , , , ,0 0 0

1 1 1' ' ' ' 'L L L

H H H H H Hg g g g g g g g g g g L g gL L L

− − −

= = =

= = =

∑ ∑ ∑w h w h h w w h h w w R wl l l l ll l l

(5.38)

Hence, the desired signal power is maximised by choosing the transmit beamforming vector as the principal eigenvector of the instantaneous subcarrier averaged spatial covariance matrix ,L gR defined in (5.32). Taking into account the power constraint in (5.4), the optimum SU-BF vector is given as

SU-BF: ,m_eig( )g g L gκ=w R (5.39)

The real scalar κg ensures the power constraint in (5.4). Depending on the considered scenario, it may be necessary to replace the covariance matrix ,L gR by the other two versions of the spatial covariance matrix, i.e. Rg defined in (5.31) and ,CN gR defined in (5.33), which leads to sub-optimum SU-BF variants. Note that there exist efficient solutions for estimating and tracking the principal eigenvector of a hermitian matrix, which avoid an explicit eigenvalue decomposition of the covariance matrix [GoLo96][Utsch02].

The optimum SU-BF approach is closely related to the PC-MRT SFTF approach derived in the previous chapter. Indeed, when no spreading is performed, i.e. L=1, ,L gR is of rank one, and the two approaches are identical. Note that this equivalence also holds for small angle spread, i.e. a single DOA. In the same way as the single-user SFTF criteria, SU-BF is expected to provide an implicit reduction of MAI thanks to spatially-selective transmission, which reduces the interference power at other terminals.

5.4.3 Multi-user criterion

Deriving a multi-user criterion for transmit beamforming basically involves the same difficulties as those mentioned in the previous chapter for multi-user SFTF criteria. Indeed, a modification of the beamforming vector of a given user g impacts the desired signal of user g itself and the MAI terms in the decision variables of all other users k≠g. Thus, the principal challenge is again to decouple the optimisation tasks for the beamforming vectors of different users. This decoupling was achieved for SFTF thanks to the application of a modified SINR, which in some sense represents the SINR of a virtual uplink (cf. section 4.4.2). Here, we investigate the possibility of adopting an analogue approach for Multi-User Beamforming (MU-BF). The modified SINR differs from the classical SINR obtained from the decision variable in (5.6) by the fact that the interference created by a user k on the considered user g, i.e. PMAI(k→g) is replaced by the interference that user g creates on user k, i.e. PMAI(g→k). Considering EGC at the receiver, the modified SINR for MU-BF is obtained as

21

,, 0

, 2 2 2

1, 1,

'

( ) ( )

LHg g

D gMI g K K

MAI g n MAI nk k g k k g

P

P g k P g kγ

σ σ

−

=

= ≠ = ≠

= =

→ + → +

∑

∑ ∑

w h

q

ll (5.40)



Here, the interference term PMAI(g→k) is given as

( ) ( ) ( )2

12 , *, , , ,

0 ,

'( ) '

'

HLk kH H

MAI k g k g g k k gHk k

P g k c c−

=

→ = = ∑w h

q u c w hw h

l

l l ll l

o (5.41)

This term shows that the decoupling of the optimisation tasks with the modified SINR approach is not successful here since the modified SINR for the optimisation of the beamforming vector wg still depends on the other beamforming vectors wk|k≠g. This results from the fact that the combining vector for user k, qk , is always a function of the beamforming vector wk . Thus, without further assumptions, the modified SINR approach seems not tractable for MU-BF in MC-CDMA.

A possible solution for MU-BF consists in assuming that the MAI principally depends on the spatial separation of users signals. Then, PMAI(g→k) is approximated by

,( ) HMAI g L k gP g k→ ≈ w R w (5.42)

and the modified SINR is given by

2 21 1

, ,0 0

,2 2

, ,1, 1,

' 'L L

H Hg g g g

MI g K KH Hg L g g n g L g n M g

k k g k k g

γ

σ σ

− −

= =

= ≠ = ≠

= =

+ +

∑ ∑

∑ ∑

w h w h

w R w w R I w

l ll l (5.43)

Note that the power constraint in (5.4) is used for the simplification. This version of the modified SINR achieves the desired decoupling since it only involves vector wg. It can then be maximised in analogy to the multi-user criterion presented in section 5.3.2.2. The covariance matrix for interference and noise is here given as

2, ,

1,

K

L I L k n Mk k g

σ= ≠

= +∑R R I (5.44)

Due to the homogeneous approximation of the MAI term, the covariance matrices of all users identically enter into ,L IR , i.e. there is no user-specific weighting as in (5.19). Then, the MU-BF vector is obtained as

MU-BF: ( ), , gm _eig ,g g L g L Iκ=w R R (5.45)

The real scalar κg again ensures the normalisation. Several variants of this solution are obtained employing the different versions of the spatial covariance matrices given in (5.31) and (5.33). However, this approach is clearly limited by the fact that the interference created at a given terminal k, i.e. PMAI(g→k), not only depends on the spatial channel properties but also on the overall frequency responses and the spreading codes of users g and k, which is completely omitted in the construction of ,L IR .

It has to be remarked that the maximum number of users that can be separated by MU-BF criteria is always limited by the number of antennas. This limitation was already observed for the PC-MSINR criterion presented for SFTF, which is also a purely spatial transmit filtering criterion. Consequently, MU-BF approaches with a low number of transmit antennas seem of minor interest for the considered MC-CDMA system. Due to this conceptual limitation, we do not strive for more sophisticated MU-BF criteria within this work.



5.5 Direction-based spreading code assignment

An additional mean to reduce MAI in the downlink consists in optimising the assignment of spreading codes required by the different active terminals. In [MoCa00], such an optimisation was proposed for downlink MC-CDMA systems with a single transmit antenna. The authors showed that for a non-fully loaded system, given a set of available spreading codes, e.g. W-H, the system performance considerably depends on the subset of codes chosen to satisfy the needs of all terminals. In the considered system with transmit beamforming, the users’ signals are partly but in general not perfectly separated in space. Thus, for a given terminal g, there is generally a group of other terminals whose DOAs are similar to those of terminal g and whose signals cannot be spatially-separated from the signal of terminal g. The signal of terminal g interferes strongly with the signals of this group, while the interference with other terminals is considerably lower. This principle is depicted in Fig. 5.7, where the strongly interfering signals are represented by overlapping beams. Thanks to transmit beamforming the number of strongly interfering terminals is reduced compared to the number of active users. As a consequence, even in a fully-loaded system a distinct terminal only suffers from the interference of part of the other users, just as in a partially-loaded system. The idea of direction-based code assignment is to optimise the code subsets of these strongly interfering groups using the criteria proposed in [MoCa00]. Hereby, we assume that the basestation employs SU-BF techniques which do not take into account the MAI created at other terminals. Note that section 5.4.3 revealed that MU-BF schemes are not particularly interesting for the considered system where the number of transmit antennas is generally much lower than the number of users. The spreading codes are assigned with respect to the spatial information employed for SU-BF, for instance the DOAs. From this code assignment we expect a reduction of the resulting MAI level.

BasestationMT g strong

interference

weakinterference

BasestationMT g strong

interference

weakinterference

Fig. 5.7: MAI with transmit beamforming.

5.5.1 Code assignment in the conventional single-antenna system

It was demonstrated in [MoCa00] that a correlation of the L subcarriers involved in the chip mapping allows an optimised selection of the spreading codes out of a given code set ΩC for a non-fully-loaded system. This active code set is then given by

( ) 1 , ...,A KK =Ω c c (5.46)

In the conventional single-antenna system, a given terminal is subject to the interference of all other terminals. Therefore, subset ΩA(K) has to be optimised as a whole and the way the codes are ordered, i.e. distributed among the different terminals, has no impact.

An optimisation of the required subset based on an exhaustive search involves the analysis of L!/[(L-K)!K!] different candidate subsets. In [MoCa00], a simplified cost function ( )( )AJ KΩ related to the MAI level caused by the codes of ΩA(K) is introduced, which allows to select an

5.5 Direction-based spreading code assignment


optimised subset of codes without knowledge of the propagation channels. It only assumes a correlation of the fading on the subcarriers employed for chip mapping that decreases with respect to the distance between these subcarriers. This cost function is given by

( ) ( ),

2,

( , )

( )

( ) mini j

i jA

K i j

J K T∈Ω ≠

=c c

Ω ζ with ( ) ( )( ) ( )( )1

( , ) ( , ) ( , )

1

sgn 1 sgnL

i j i j i jT ς ς−

=

= + −∑ζl

l l (5.47)

where ζ (i,j )(l) is the l-th component of vector ζ(i,j )=ci*ocj . T(ζ(i,j )) is the number of sign changes

between consecutive components of ζ(i,j ). This is a measure of how a joint use of ci and cj impacts MAI: A good (respective bad) pair of codes ci and cj is such that T(ζ(i,j )) is maximum (respective minimum). A maximisation of ( )( )AJ KΩ over any candidate subset yields an optimum subset Ω0(K) defined as

( )0 ( )( ) arg max ( )

A CAK

K J K⊂

=Ω Ω

Ω Ω (5.48)

Applying (5.47) and (5.48) aims at reducing the maximum interference caused by any pair of codes belonging to any subset ΩΑ(K). It has to be noted that this optimisation process can be carried out off-line, once for all, for any value of K and stored in look-up tables. The application of the above code selection process is particularly simple in the case of W-H codes, where the code set ΩC is given by the W-H code matrix CL defined in (3.6). Here, the optimised set Ω0(K) is given by selecting the W-H codes in their natural order, i.e. the first K rows or columns of the W-H matrix [MoCa00]. Note that this optimised selection is always considered throughout this thesis.

5.5.2 Direction-based code allocation with transmit beamforming

For MC-CDMA systems using multiple antennas for transmit beamforming, the impact of fading correlation on the choice of spreading codes remains similar. However, a given terminal g is only subject to the interference of terminals that cannot be separated in space from terminal g by transmit beamforming (cf. Fig. 5.7). Hence, a subset of codes optimised for terminal g may be sub-optimum for terminal k (k≠g) and the way the spreading codes are ordered in ΩA(K), i.e. distributed among terminals, impacts the performance. Here, an optimisation of the required subset based on exhaustive search would involve the analysis of L!/[(L-K)!] different candidates, i.e. 1035 subsets for L=K=32. Moreover, the subset of codes has to be optimised on-line and periodically taking into account the variations of the DOAs of all terminals. Since this requires a prohibitive processing power, such an approach is not realistic. To simplify the problem, we propose an optimisation in three steps [MoSä04]: Step 1 We first assume that despite transmit beamforming all assigned spreading codes potentially interfere. Then, the subset Ω0(K) of spreading codes is selected as in a single-antenna scenario according to section 5.5.1. In this way, the exhaustive search only involves L!/[(L-K)!K!] subsets for any value of K and the optimum subsets can be stocked in look-up tables. Thus, for K<L, the selection of codes responsible for a large part of the MAI in a single-antenna system are avoided, which also reduces the MAI in a system with transmit beamforming.

Step 2 The basestation orders active terminals by their mean DOA so that terminal 1 has the smallest mean DOA and terminal K the largest one. Hereby, we assume that the difference of the mean DOAs is representative of the spatial separation of terminals’ signals obtained by transmit beamforming.



Step 3 From the selected subset Ω0(K), the basestation distributes, i.e. orders, the codes so that interference among terminals having similar mean DOAs is minimised. For that purpose, given any ordered subset ( )A KΩ =c1,...,cK, the distribution of codes must be jointly optimised for codes ci and cj only if the difference between i and j is low, i.e. if terminal i and terminal j have close mean DOAs. Thus, by introducing P subgroups ( )p

A KΩ of codes that are likely to interfere, an optimisation process similar to section 5.5.1 yields the optimum ordered subset

0( )KΩ as

( )0 ( ) ( )( ) ( ), 1..

( ) arg max min ( )p

A AA A

pAK K

K K p P

K J K⊂ ⊂ =

=

Ω ΩΩ Ω

Ω Ω (5.49)

Here, we aim at minimising the maximum of interference occurring within each subgroup of codes. The definition of these subgroups highly depends on the beamforming scheme. For the adaptive beamforming scheme considered here, one subgroup may be defined for each terminal including the codes assigned to neighbouring terminals. Besides, it has to be noted that the exhaustive search proposed here involves K ! different ordered subsets ( )A KΩ , which may still be a limitation in practice for systems with high loads. For the W-H code set considered in this work, the optimisation process is considerably simplified. The resulting steps for direction-based code assignment are summarised in Fig. 5.8. The first step is identical to optimised code selection in the single-antenna system. In the second step, the terminals are ordered with respect to their mean DOAs. For the final step, we consider the natural order of W-H codes, i.e. c1 is the first row of CL , c2 the second row etc. This order has the properties

( )( , 1) 1 odd/2 even

i i L iT

L i+ − ∀

= ∀ζ (5.50)

Thus, each code ci of CL has one neighbouring code that may induce a minimum interference with ci compared with any other code of CL. For 2≤i ≤L-1, the other neighbouring codes of ci may induce an interference level below the average level L/2 occurring between any pair of codes. Therefore, we choose to distribute the W-H codes in the natural order to the different ordered terminals, which ensures that each terminal has neighbouring terminals with weakly interfering codes.

Step 1Selection of the first K rows of CL

Ω0(K)=c1,...,cK

Step 2Ordering K MTs so that

m.DOA(MT 1)≤ m.DOA(MT 2) ≤ ....≤ m.DOA(MT K)

Step 3Distribution of ci to MT i ∀i=1...K

Step 1Selection of the first K rows of CL

Ω0(K)=c1,...,cK

Step 2Ordering K MTs so that

m.DOA(MT 1)≤ m.DOA(MT 2) ≤ ....≤ m.DOA(MT K)

Step 3Distribution of ci to MT i ∀i=1...K

Fig. 5.8: Direction-based assignment of Walsh-Hadamard codes.

5.6 Comparison of beamforming approaches




The system parameters chosen for the simulations are very similar to those introduced in the previous chapters (cf. sections 3.5.1 and 4.5.2) and summarised in Tab. 5.2. The beamforming approaches are intended for outdoor scenarios with moderate angle spreads. Here, channel model E is employed with angle spreads of 10° and 30° around a mean DOA, which is randomly chosen for each user in the operating range of the array. The performance is averaged over a large number of channel states including the fast fading and the spatial channel properties. As before, the performance is generally evaluated in terms of the user-averaged BER as a function of the average SNR per bit (cf. equation (3.49)). The uncoded performance is compared at the operation point of BER=10-2.

Carrier frequency, fC 5 GHz Sampling frequency 57.6 MHz FFT-size 1024 Number of available subcarriers, NC 736 Carrier spacing, ∆f 56.3 kHz Overall symbol time, TS' 21.5 µs Guard time, TG 3.75 µs Symbol alphabet QPSK Channel coding not considered. Spreading factor, L 16, 32


Channel models Extended Outdoor HIPERLAN/2 Channel E: τmax=1.72µs.

Angle spread (AS) 10°, 30° Distribution mean DOA uniformly in the range [30°,150°] Array configuration ULA Element spacing, dS λC/2 Number of transmit antennas, M 1, 4, 8

Tab. 5.2: Simulation parameters for transmit beamforming.

Here, we assume a perfect knowledge of the spatial covariance matrices employed for beamforming. The impact of Doppler variations due to the mobility of mobile terminals is discussed in detail in chapter 6. Unless otherwise stated, EGC is used for subcarrier combining at the terminal. To differentiate the different versions of the covariance matrix employed for beamforming, we use the appellations given in Tab. 5.3.

Appellation Definition

SU-BF-long / MU-BF-long R in (5.31)

SU-BF-inst / MU-BF-inst LR in (5.32)

SU-BF-instNc CNR in (5.33)

Tab. 5.3: Appellations of the different versions of the covariance matrix.



5.6.2 Single-user performance

The single-user performance of beamforming algorithms shows how the spatial dimension can be exploited with the different versions of the covariance matrix. For instance, only the two limiting cases, i.e. SU-BF-long and SU-BF-inst are considered. Fig. 5.9 and Fig. 5.10 concern the performance of these approaches for chip interleaving and adjacent chip mapping, respectively. The curve showing the performance of the conventional single-antenna system with EGC is given as a reference. In addition, we also present the performance of the SFTF PC-MRT approach with EGC, which corresponds to beamforming on each subcarrier separately and is thus equivalent to SU-BF for L=1. Note that PC-MRT is only considered for a large angle spread since it converges with SU-BF-inst for small angle spreads. As usual, we compare the curves showing the performance without channel coding at BER=10-2.

For chip interleaving and an angle spread of 10° (AS 10°), SU-BF-inst and SU-BF-long are almost identical, as expected from the construction of the covariance matrices. Here, both approaches achieve the classical array gain of 6°dB (cf. (5.12)) compared to the conventional single-antenna system. For an angle spread of 30° (AS 30°), this gain reduces to around 5 dB for SU-BF-inst and 4 dB for SU-BF-long. At AS 30°, PC-MRT has a gain of about 1 dB compared with SU-BF-inst. Indeed, while PC-MRT benefits from the larger angle spread in terms of diversity, SU-BF-inst uses a beamforming vector that is not adapted to the different superposition of the paths, i.e. DOAs, on the L different subcarriers. However, SU-BF-inst has a gain of about 1.5 dB compared to SU-BF-long, because it adapts its beam with respect to the DOA that instantaneously yields the highest transmission gain.

When chip mapping on adjacent subcarriers is considered, the difference between SU-BF-inst and SU-BF-long is more important. This is due to the fact that the instantaneous covariance matrix is now averaged over adjacent subcarriers that are subject to correlated fading, while the long-term covariance matrix is unchanged as a matter of course. For AS 10°, the SU-BF-inst and SU-BF-long are still quite close and again achieve about 6 dB gain compared with the conventional system. For AS 30°, the performance of SU-BF-long degrades for the same reasons as before. In contrast, SU-BF-inst can here benefit from the increased diversity in a similar way as PC-MRT and its performance improves by more than 1 dB compared with AS 10°.

SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10

10-3

10-2

10-1

AS10 SU-BF-instAS30 SU-BF-instAS10 SU-BF-longAS30 SU-BF-longAS30 PC-MRTM=1 Conv

SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10

10-3

10-2

10-1


Fig. 5.9: Single-user performance of beamforming

with chip interleaving (K=1, M=4, L=16).



SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10 12 14 16

10-3

10-2

10-1


SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10 12 14 16

10-3

10-2

10-1


Fig. 5.10: Single-user performance of beamforming

with adjacent chip mapping (K=1, M=4, L=16).

5.6.3 Multi-user performance

The same configurations as in the single-user case above are considered for a fully-loaded system (K=L=16) with chip interleaving in Fig. 5.11 and for chip mapping on adjacent subcarriers in Fig. 5.12. Again EGC is considered at the mobile receiver for all presented techniques.

SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1


SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1


Fig. 5.11: Multi-user performance of beamforming

with chip interleaving (K=16, M=4, L=16).

For chip interleaving and an angle spread of 10°, SU-BF-inst and SU-BF-long have almost identical performance. In this case, both beamforming approaches achieve a substantial gain compared to the conventional system. Indeed, the error floor due to MAI is reduced from a BER of 2⋅10-2 for the conventional system to a BER around 5⋅10-4 with beamforming. Furthermore, at BER=10-2, both approaches are only around 2 dB from their single-user performance given in



Fig. 5.9. This performance degrades considerably for a higher angle spread for two reasons: Firstly, the beamforming gain with respect to the SNR is reduced, which was observed in the single-user case and can be observed here for low SNRs. Secondly, the capacity of beamforming to separate the users’ signals decreases obviously when their DOAs span larger angle sectors, which leads to an increased MAI and consequently a higher error floor. At an angle spread of 30°, SU-BF-inst looses about 4 dB compared with its performance for AS 10° at BER=10-2. Here, SU-BF-long has an error floor that is almost the same as for the conventional system.

For adjacent chip mapping, a loss of frequency diversity is observed in the performance of SU-BF-inst and SU-BF-long for AS 10°. However, SU-BF-inst can recover this loss by benefiting from the spatial diversity. The reduced MAI for adjacent chip mapping leads to a lower error floor for all presented approaches. At BER=10-2 and for AS 10°, SU-BF-inst and SU-BF-long are less than 1 dB from their single-user performance given in Fig. 5.10. For AS 30°, the loss of SU-BF-inst compared to its single-user performance is around 1 dB, while SU-BF-long heavily suffers from the higher angle spread and has an error floor higher than BER=10-2.

In contrast to the single-user case, the PC-MRT approach is clearly outperformed by SU-BF-inst for multiple users irrespective of the chip mapping. Thus, if pre-equalisation in frequency ensured by joint SFTF, is not desired, a common transmit vector for all L subcarriers is the better choice with regard to the MAI.

SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1


SNR, γb

BER

-6 -4 -2 0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1


Fig. 5.12: Multi-user performance of beamforming with adjacent chip mapping (K=16, M=4, L=16).

Fig. 5.13 shows the performance of MU-BF compared to SU-BF for an angle spread of 10° and a half-loaded system (K=8). The number of antennas was chosen equal to the number of users, i.e. M=8. Thus, in conjunction with the small angle spread, this configuration has enough degrees of freedom to enable a spatial interference reduction. Furthermore, we consider chip interleaving, which is generally favourable for the assumption of a homogeneous interference among the users. Even in this rather favourable conditions for the derived MU-BF criterion, MU-BF-inst and MU-BF-long cannot improve the performance compared with SU-BF-inst and SU-BF-long, respectively. Indeed, the MU-BF approaches are close to their SU-BF versions for low SNR, where the noise level is higher than the MAI level. As the noise level decreases, the MAI term in the MU-BF criterion dominates more and more. Thus, from the increase of the BER observed when moving towards higher SNRs, we can conclude that the assumption of a homogenous



interference among the users leading to the simplified MU-BF criterion does not hold in the considered system. Thus, the presented MU-BF criterion is completely unsuited for transmit BF in the MC-CDMA downlink. As already mentioned in section 5.4.3, due to the limitations of the MU-BF principle with regard to the required number of antennas for efficient MAI mitigation, MU-BF criteria are not considered in this work any further.

-9 -7 -5 -3 -1 1 3 5 7 9 11 13 1510-4

10-3

10-2

10-1

SU-BF-instMU-BF-instSU-BF-longMU-BF-long

SNR, γb

BER

-9 -7 -5 -3 -1 1 3 5 7 9 11 13 1510-4

10-3

10-2

10-1

SU-BF-instMU-BF-instSU-BF-longMU-BF-long

SNR, γb

BER

Fig. 5.13: Comparison of SU-BF and MU-BF

(K=8, M=8, L=16, interl., AS 10°).

5.6.4 Direction-based spreading code assignment

Up to now, all performance results have been presented for a random assignment of the spreading codes with respect to the DOAs of the users’ channels. The influence of the code assignment on the performance of a conventional single-antenna system (M=1) and of SU-BF-inst with multiple transmit antennas (M=4) is shown in Fig. 5.14. A half-loaded system (K=16, L=32) with adjacent chip mapping and EGC at the receiver is considered. Note that here we have around 1.25⋅1022 possible assignments of the W-H codes, which excludes an optimisation employing an exhaustive search.

For the conventional system with M=1, a distribution according to spatial information has no impact and the assignment schemes only differ by the way they select the active subset of codes. We compare an optimised subset selection according to section 5.5.1 to a random selection and a particularly bad selection. To achieve BER=10-2, an optimised selection of codes provides a gain of 1.5 dB compared to a random selection and a gain of 6 dB compared to a bad selection. For SU-BF-inst with M=4, an optimised selection and distribution according to Fig. 5.8 achieves a gain of 4.5 dB, compared to a particularly bad selection and distribution. A slight loss is experienced when the codes are well selected but randomly distributed. Hence, there is a visible gain from distributing the codes according to the mean DOA of the users’ channels. Finally, a random selection and distribution lead to a loss of about 1 dB, which underlines the necessity to properly select the active code subset.



-4 -2 0 2 4 6 8 10 12 14 16 18 20

10-3

10-2

10-1

M=1 opt. selectionM=1 rand. selectionM=1 bad selectionM=4 opt. selection & opt. distributionM=4 opt. selection & rand. distributionM=4 rand. selection & rand. distributionM=4 bad selection & bad distribution

SNR, γb

BER

M=1M=4

-4 -2 0 2 4 6 8 10 12 14 16 18 20

10-3

10-2

10-1


SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14 16 18 20

10-3

10-2

10-1


SNR, γb

BER

M=1M=4

Fig. 5.14: Performance of SU-BF-inst with direction-based

code assignment (K=16, M=4, L=32, adjac.).

1 4 8 12 16 20 24 28 32

0

5

10

15

20opt. selection & opt. distributionopt. selection & rand. distributionrand. selection & rand. distributionbad selection & bad distribution

Number of users (K)

Requ

ired

SNR

at B

ER=

10-2

M=1

M=4

M=8

1 4 8 12 16 20 24 28 32

0

5

10

15


Number of users (K)

Requ

ired

SNR

at B

ER=

10-2

1 4 8 12 16 20 24 28 32

0

5

10

15


Number of users (K)

Requ

ired

SNR

at B

ER=

10-2

M=1

M=4

M=8

Fig. 5.15: Performance of SU-BF-inst with direction-based code assignment

as a function of load (L=32, adjac.).

Fig. 5.15 represents the required SNR per bit to achieve BER=10-2 as a function of the number of users for the different assignment strategies and with different numbers of antennas. When only a single user is active, the performance does obviously not depend on the selected code. For M=1, the gain provided by the optimised selection compared to a bad selection increases up to 6 dB for half-load and decreases regularly down to 0 dB for full load (K=L). Indeed, for full load, all codes are allocated and thus there is no degree of freedom for an optimised selection anymore. Note that M=1 results in the conventional system, which has no possibility of spatial signal separation, so that the distribution of codes has no impact on the performance. In contrast, for a larger number of antennas, even if the active subset is fixed at full load, an optimised distribution of the codes with respect to the mean DOAs of the users’ channels provides a significant performance improvement. For instance, with 4 antennas, the gain provided by an optimised selection and distribution of codes increases up to 4.6 dB compared to a particularly



bad assignment. It has to be noted that such a bad assignment may statistically occur in the system if the code assignment is not properly handled. Compared to a random assignment, the average gain of the proposed assignment grows with the system load up to more than 1 dB. With 8 antennas, there is a slight reduction of the performance improvement achieved by the proposed assignment since the efficient spatial separation obtained by SU-BF reduces the impact of code assignment on the residual MAI.

Direction-based code assignment with code reallocation is presented in Fig. 5.16 for L=16. Code reallocation is carried out as described in section 4.5.6, where the system is overloaded by allocating several W-H code sets in parallel, which are separated by a random scrambling code according to (4.41). As before, the figure represents the required SNR per bit to achieve BER=10-2 as a function of the number of users. The curve of the conventional single-antenna system with MMSE-MUD at the receiver is given as a reference. Note again that this reference system cannot tolerate loads higher than K=L=16. When SU-BF-inst with 4 antennas and EGC at the receiver is considered, the required SNR is almost constant for loads up to K=L=16. For higher loads, the required SNR increases considerably. Indeed, in contrast to SFTF with J-MSINR considered in section 4.5.6, SU-BF-inst relies on an implicit user separation only, which limits the tolerable user capacity with code overloading. Indeed for moderate angle spreads (AS 30°), the potential of spatial user separation is limited, and the assignment of non-orthogonal spreading codes leads to a steep increase of the required SNR for K>16. For small angle spreads (AS 10°), spatial user separation is more efficient, but the important increase of MAI for K>16 is still visible. If the required SNR is limited to 12 dB, up to K=22 users can be supported at AS 30°, and the user capacity basically doubles to K=32 for AS 10°.

1 4 8 12 16 20 24 28 32

2

4

6

8

10

12

14BS:M1,Conv MT:MMSE-MUDBS:M4,SU-BF-inst MT:EGC AS10BS:M4,SU-BF-inst MT:EGC AS30

Number of users (K)

Requ

ired

SNR

at B

ER=

10-2 Full load of conv. system

(K=L=16) M=4

M=1

1 4 8 12 16 20 24 28 32

2

4

6

8

10

12

14BS:M1,Conv MT:MMSE-MUDBS:M4,SU-BF-inst MT:EGC AS10BS:M4,SU-BF-inst MT:EGC AS30

Number of users (K)

Requ

ired

SNR

at B

ER=

10-2 Full load of conv. system

(K=L=16) M=4

M=1

Fig. 5.16: Performance of SU-BF-inst with code reallocation (L=16, adjac.).

5.6.5 Comparison of robust beamforming approaches

The results in the previous sections show that adjacent chip mapping yields a considerable advantage with regard to the MAI in the considered system with transmit beamforming. The lower frequency diversity offered by this mapping scheme is of minor importance if we take into account the fact that the performance is compared here without channel coding, which is another way to benefit from diversity. Thus, the combination of SU-BF with adjacent chip mapping emerges as a very promising approach. For this combination, we evaluate the performance of SU-BF in Fig. 5.17 employing the three different versions of the covariance matrix with different



angle spreads. An optimised code assignment is considered for all approaches. For comparison, the performances of the conventional single-antenna system with EGC SUD and MMSE-MUD as well as the single-user performance for SU-BF-inst are also represented.

-6 -4 -2 0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1

SU-BF-inst K=1SU-BF-instSU-BF-instNcSU-BF-longM=1 Conv EGCM=1 Conv MMSE-MUD

SNR, γb

BER

AS 10°

AS 30°AS 30°

-6 -4 -2 0 2 4 6 8 10 12 14 16 18

10-3

10-2

10-1

SU-BF-inst K=1SU-BF-instSU-BF-instNcSU-BF-longM=1 Conv EGCM=1 Conv MMSE-MUD

SNR, γb

BER

AS 10°

AS 30°AS 30°

Fig. 5.17: Performance comparison of robust SU-BF approaches

(K=16, M=4, L=16, adjac.).

Here, SU-BF-inst achieves a similar performance for a small angle spread (AS 10°) and a moderate angle spread (AS 30°). However, the comparison with its single-user reference curves shows that the residual interference is obviously higher for AS 30°. At BER=10-2, the gain of SU-BF-inst compared to the conventional system with MMSE-MUD and EGC is around 8 dB and 10 dB, respectively. For AS 10°, SU-BF-instNc and SU-BF-long are basically identical and only show a small loss compared to SU-BF-inst. Yet for AS 30°, the performance of SU-BF-instNc and SU-BF-long is considerably degraded. At BER=10-2, SU-BF-long has the same performance as the conventional system with MMSE-MUD, while SU-BF-instNc still gains around 4 dB. However, both approaches have a high error floor due to the MAI and are even outperformed by the conventional system with EGC SUD for high SNRs. Consequently, SU-BF yields a considerable improvement compared to the conventional system for small angle spreads. For large angle spreads, this improvement is only achieved when instantaneous channel knowledge can be exploited at the transmitter.

5.7 Conclusion on transmit beamforming

Transmit beamforming criteria for the downlink of MC-CDMA systems were derived from classical single-carrier receive beamforming criteria and their properties were assessed with respect to the requirements of future wideband wireless systems.

We showed that three different versions of the spatial covariance matrix can be employed for transmit beamforming. In this way, the beamforming scheme can be adapted to the available channel knowledge at the transmitter with respect to the considered system configuration. The proposed schemes can exploit instantaneous channel knowledge, e.g. in TDD systems with low mobility and channel reciprocity, as well as long-term channel knowledge, e.g. for a high mobility of the terminal and for FDD.

In contrast to the SFTF approaches presented in the previous chapter, the same transmit beamforming vector is applied to all subcarriers employed for the chip mapping. Hence, transmit

5.7 Conclusion on transmit beamforming


beamforming only results in spatially-selective transmission without pre-equalisation in frequency. Consequently, the number of degrees of freedom for the filter optimisation is given by the number of transmit antennas. This limitation especially concerns the MU-BF criterion, which requires for its effectiveness that the number of active users is lower than the number of transmit antennas. Taking into account the fact that a suitable MU-BF criterion for the MC-CDMA downlink should take into account the actual MAI, which is not possible with covariance knowledge, only SU-BF seems advantageous for the considered system.

The combination of SU-BF and adjacent chip mapping was shown to be a promising strategy with regard to MAI mitigation. Here, the MAI can additionally be reduced by a direction-based assignment of the spreading codes. Especially, when the transmitter benefits from instantaneous channel knowledge, the SU-BF scheme provides a considerable gain compared to the conventional system up to a moderate angle spread. However, if only long-term knowledge is available the performance improvement with SU-BF is limited to small angle spreads. The behaviour of the single-user beamforming approaches with respect to the angle spread and the exploitable channel knowledge is summarised in Tab. 5.4.

A detailed comparison of transmit beamforming and SFTF including the influence of channel coding and the mobility of the terminal is provided in chapter 6.

Small angle spread Large angle spread

Inst

anta

neo

us

know

led

ge

- benefits of spatial diversity.

- near optimum antenna gain.

- good spatial user separation.

Lon

g-te

rm

know

led

ge

- convergence of long-term and instantaneous covariance matrix.

- near optimum antenna gain.

- good spatial user separation. - reduced antenna gain.

- reduced capacity of user separation.

Tab. 5.4: Properties of single-user beamforming approaches.


6 System comparison The previous chapters provided deep insight in each of the proposed technologies separately. In this way, we were able to select promising approaches and optimise them for the considered application. The aim of this chapter is to compare the selected approaches in realistic scenarios for beyond 3G systems. A particular focus is put on the aspects of channel coding and imperfect channel knowledge at the transmitter due to the mobility of the terminals.

6.1 Channel coding and decoding

Channel coding was already mentioned in chapter 2 as an essential part of any mobile communication system. Channel coding schemes for wireless communications are mostly derived from two basic schemes: block codes and convolutional codes [GlJo99][Pro95]. These schemes can be combined to concatenated codes [Pro95] or employed as constituent codes in a so-called Turbocode [BeGl93][Hag97]. Recently, a particular type of block codes called Low-Density Parity Check (LDPC) codes was rediscovered for the use in mobile communications [RiUr03].

Channel coding schemes introduce a redundancy in the transmitted bit stream in order to benefit from diversity. In this way, codes with a good capacity of error correction together with maximum-likelihood decoding based on CSI at the receiver achieve a considerable performance gain in fading channels. Current studies of coding schemes for MC-CDMA mostly consider convolutional codes and Turbocodes [GoHe00][Kai02][KüKa00] [MAT,D3.1].

6.1.1 Convolutional coding

Within this work, we focus on a convolutional coding scheme [GlJo99][Pro95], which is currently considered in the standards of several OFDM based systems, e.g. HIPERLAN/2 [ETSI01], DVB-T [ETSI97b] and IEEE 802.11a [IEEE99].

An example of a convolutional encoder is depicted in Fig. 6.1. This encoder comprises a linear finite-state shift register and two modulo-2 adders. The information bits are passed through the shift register of length KC –1, where KC is called the constraint length of the convolutional code (here KC =7). For each input bit, the modulo-2-additions provide two output bits, which depend on the input bit and on the state of the shift register. A serial-to-parallel conversion of the outputs of the additions finally provides the encoded bit stream. In this way, the resulting code has a rate of RC=1/2. Besides its constraint length, a convolutional encoder is defined by its generators (here G1 and G2). The generators are obtained by noting the connections of the adders with respect to the stages of the shift register starting with the input as stage 0. Here, a connection is noted by a 1 and no connection by a 0. Then, the generators are given by the octal form of this notation. For the given example, the generator of the first adder is G1=1111001bin=171oct and the generator of the second adder is G2=1011011bin=131oct .

If it can't be expressed in figures,it is not science; it is opinion.Robert A. Heinlein (1907-1988)

Chapter 6: System comparison


1 2 3 4 5 6informationbits P/S encoded

bits

Modulo-2-addition

Modulo-2-addition

G2=133

G1=171

shiftregister1 2 3 4 5 6information

bits P/S encodedbits

Modulo-2-addition

Modulo-2-addition

G2=133

G1=171

shiftregister

Fig. 6.1: Convolutional encoder, RC=1/2.

In order to obtain convolutional codes of different rates, a so-called puncturing is often employed. Punctured convolutional codes with a variable code rate RC are derived from a mother convolutional code of rate R’C by removing a part of the introduced redundancy. The generation of the data symbols, dg , from the data bits of user g with punctured convolutional coding and block interleaving is illustrated in Fig. 6.2. Here, the data bits are first convolutionally encoded with a fixed code rate, R’C. Then, a variable code rate, RC , is achieved by deleting bits from the encoded stream according to a given puncturing pattern. Several patterns for different rates are given in Tab. 6.1 together with the minimum distance of the resulting code [Pro95]. A conserved bit is denoted by a 1 and a deleted bit by a 0. The patterns are obviously cyclically repeated.

Data bits ofuser g

convolutional encoder R'C=1/2

Random interleaving

of coded blockdg

PuncturingRC=2/3

Viterbi decoder R'C=1/2

Soft symbol de-mapping

De-puncturingRC=2/3

Symbol mapping

De-interleavingof coded block

Data bits ofuser g

ˆgd

Data bits ofuser g

convolutional encoder R'C=1/2

Random interleaving

of coded blockdg

PuncturingRC=2/3

Viterbi decoder R'C=1/2

Soft symbol de-mapping

De-puncturingRC=2/3

Symbol mapping

De-interleavingof coded block

Data bits ofuser g

ˆgd

Fig. 6.2: Punctured convolutional coding and decoding.

Code rate, RC Puncturing pattern min. distance [Pro95]

1/2 1111 10

2/3 1011 6

3/4 101110 5

Tab. 6.1: Puncturing patterns for convolutional code (G1=171, G2=133, KC=7, R’C=1/2) [IEEE99].

The punctured bit stream is interleaved to combat the effect of error bursts and ensure that the diversity offered by the channel is well exploited. We consider here an encoding carried out on the basis of blocks, each of them containing BC encoded bits. Then a random interleaving is applied within each coded block. Finally, the encoded bits are mapped to the data symbols of the considered alphabet (cf. section 2.1).

At the receiver side, the soft de-mapping of decision value ˆgd yields a soft estimated value for

each encoded bit, which can equivalently be represented by a log-likelihood-ratio [Hag97]. These

6.1 Channel coding and decoding


soft values are de-interleaved and de-punctured by adding zeroes for the missing bits. Finally, the soft estimates of the encoded bits are decoded using ML decoding with the Viterbi algorithm [Pro95].

6.1.2 Soft de-mapping and Log-Likelihood Ratio

The soft de-mapping produces soft estimates of the encoded bits, which can equivalently be represented by the Log-Likelihood-Ratio (LLR). Here, we derive an approximation of the LLR, which is suitable for the considered system. The decision variable for user g with SFTF and transmit beamforming can be written as (cf. (4.3) and (5.6))

( ) ( )

, ,1,


ˆ K

H H Hg g g g g g g k g k k g

k k gd d d

= ≠

= + +

∑q u c q u c q no o

1442443 14444244443

(6.1)

For simplicity, we consider a QPSK alphabet but the extension to other QAM constellations is straightforward. The soft estimates of the bits bg in bipolar form, i.e. bg∈-1,1, are obtained as the real or the imaginary part of the decision variable, respectively. Focusing on the real part, the soft de-mapped value is given by

ˆ ˆ MAI Hg g g g gd d bν′ = ℜ = + ℜ + ℜ q n (6.2)

where νg denotes the real amplitude of the desired symbol and is given by

1 1

, , , , , , ,0 0

1L L

g g g g g g g gc q u q uL

ν− −

= =

= =∑ ∑l l l l ll l

(6.3)

where ug,g,l denotes the l–th element of vector ug,g . The simplification takes into account the normalisation of the code vector in (3.1) and the coherent combining carried out by the vector qg . Assuming that both, the MAI term and the noise term can be considered as complex AWGN having the variances 2

MAIσ and 2nσ , respectively, the LLR of this soft-estimate is given as

[Hag97][Kai02]

( )

( ) 2 2MAI

ˆ1 4 ˆlnˆ1

g g gg g

ng g

P b dd

P b d

νσ σ

′= ′= = +′= −

L (6.4)

where P(x) denotes the probability of x. Here, the variance of the MAI term depends on the considered detection technique and on the efficiency of the separation of users’ signals at transmission. Approximations for the variance of the MAI in a conventional system can be found in [Kai98][Kai02]. However, already in the conventional system with enhanced SUD schemes like MMSEC, neglecting the MAI only has a small impact on the performance of the decoder [Kai02]. Since, we generally expect a lower MAI term thanks to the transmission strategies at the basestation, we also omit the MAI term here. Using the expression for the noise after subcarrier combining in (3.12) the approximation of the LLR employed throughout this thesis is given as

1

, , ,0

12 2 2,

0

44 ˆ ˆ

L

g g gg

g g gLn

g C

q ud d

L q

νσ σ

−

=−

=

′ ′≈ =∑

∑

l ll

ll

L (6.5)



6.2 Impact of imperfect channel knowledge due to mobility

The main requirement for the approaches presented in this work is that reliable CSI is available at the transmitter side. In the previous sections, perfect CSI at the basestation transmitter was assumed. In practice, the considered system has to deal with imperfections arising basically from estimation errors and the mobility of terminals. Especially the assumption that instantaneous knowledge of the channel fading is available prior to transmission in TDD systems is not realistic for a considerable velocity of the terminals. Here, the channel is generally not stationary between consecutive UL and DL transmission slots. This means that the instantaneous channel knowledge required for SFTF and for the transmit beamforming approach SU-BF-inst is outdated, which leads to a degradation in the performance of these techniques. Here, we assess the impact of imperfections in the channel estimates with a focus on the mobility of terminals, i.e. the variations arising from the Doppler effect.

The movement of mobile terminals results in Doppler variations and consequently a variation of the channel fading in time. Referring to section 2.2.3, it is obvious that as the mobility increases the coherence time, Tcoh , of the channel decreases. In the considered TDD system, there is a delay between the estimation of the CSI in the UL and the usage of this knowledge for pre-filtering during the following DL slot. This delay is denoted by τU and illustrated in Fig. 6.3. Here, CSI is obtained at the end of the UL slot and used during the following transmission slot, which is separated from the UL slot by a guard time.

ULt

Guard time betweenUL and DL slots

DL UL... ...τU

...

CSI estimation CSI usage

ULt

Guard time betweenUL and DL slots

DL UL... ...τU

...

CSI estimation CSI usage

Fig. 6.3: Delay between estimation and usage of CSI in TDD systems.

For τU <<Tcoh , there is no mismatch between the estimated CSI and the actual channel state at the instant when the CSI is used. If this cannot be guaranteed, the mismatch between the estimated CSI and the actual channel state leads to performance degradation. A measure of this mismatch is given by the correlation coefficient ρCE representing the fading correlation at two instants spaced by the delay time τU . Here, we assume that the channel consists of several paths with independent Rayleigh fading amplitudes and distinct DOAs (cf. section 2.3.1). The DOAs are assumed to stay constant within the considered time periods. For a classical Jakes Doppler spectrum (cf. (2.18)), the correlation coefficient is obtained from the normalised correlation function of the fading amplitudes and given by

( ) ( )*, 0 ,E ( ) ( ) J 2CE A norm U p p U D max Ut t fφ πρ τ α α τ τ= = + = (6.6)

Note that the Doppler spectrum is determined by the local-to-mobile scattering (cf. Fig. 2.3) and is in general not modified by spatially-selective transmission at the basestation. Recalling (2.14), the maximum Doppler frequency is directly related to the velocity of the mobile terminal, i.e.

,D maxC

vfλ

= (6.7)

The delay τU obviously increases during the transmission of the DL slot, which results in a decreasing correlation coefficient. Hence, the quality of the CSI is better at the beginning of the

6.3 Performance analysis


slot and degrades towards the end of the slot. This continuous degradation depends on the system parameters, e.g. the slot duration and the guard time between UL an DL. To keep our results general enough and to directly relate the performance degradation of the algorithms to the quality of the CSI, we focus on a performance assessment with respect to a fixed correlation coefficient ρCE. For the sake of tangibility, we relate this coefficient to the mobile’s velocity by choosing a typical fixed delay τU of 1 ms, which is slightly longer than the slot duration in the scenario of the MATRICE project [MAT,D1.4]. Note that this represents a worst case, since the degradation at the end of the DL slot is an upper bound for the regularly increasing degradation. For this case, Fig. 6.4 depicts the correlation as a function of the velocity.

0 10 20 30 40 50 600.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Velocity [km/h]

Corr

elatio

n, ρ

CE

0 10 20 30 40 50 600.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 600.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Velocity [km/h]

Corr

elatio

n, ρ

CE

Fig. 6.4: Relation between correlation and velocity for τU=1 ms.



The system parameters chosen for the simulations are very similar to those introduced in the previous chapters and summarised in Tab. 6.2.

The performance is averaged over a large number of channel states with respect to the fast fading and spatial channel characteristics. For the results without channel coding, the states are redrawn for each user at each OFDM symbol. When channel coding is employed, the channel states are redrawn for each coded block.

A coded block is mapped to the OFDM frame consisting of NC NF chip positions in frequency and time (cf. section 2.5.2). For the simulations, all available carriers were employed for data transmission. Here, NC /L (from Tab. 6.2: 46) subsystems of L carriers are allocated in parallel within each OFDM symbol. Then the number of OFDM symbols in each frame is given by NF =BC L/(βNC ) (from Tab. 6.2: NF=15), and the channel is redrawn every NFTS'. For illustration, the aggregate modulation bit rate for this configuration at full system load is 68.5 Mbit/s, which represents 4.3 Mbit/s per user, in an occupied bandwidth of 41.4 MHz.

The performance is generally evaluated in terms of BER averaged over the active users as a function of the average SNR per bit (cf. equation (3.49)). For the uncoded system, we compare the performance at the operation point of BER=10-2, and for the coded system, we choose the operation point of BER=10-4.



Carrier frequency, fC 5 GHz Sampling frequency 57.6 MHz FFT-size 1024 Number of available subcarriers, NC 736 Carrier spacing, ∆f 56.3 kHz Overall symbol time, TS' 21.5 µs Guard time, TG 3.75 µs Symbol alphabet QPSK

Channel coding (if considered) Punctured convolutional G1=171, G2=133, KC=7, RC=2/3 Blocksize, BC = 1380

Spreading factor, L 16


Channel models Extended HIPERLAN/2 Channel A: τmax=0.39µs Channel E: τmax=1.72µs

Angle spread (AS) 10°, 30°, or 120° Distribution of mean DOA Uniformly in the range [30°,150°] Array configuration ULA Element spacing, dS λC/2 Number of transmit antennas, M 1, 4

Tab. 6.2: Simulation parameters for the system comparison.

6.3.2 Coded performance with perfect channel knowledge

The performance with channel coding and perfect channel knowledge at the transmitter and the receiver side is represented in the following figures for SU-BF and SFTF using M=4 transmit antennas. We consider channel E in both cases, but adapt the angle spread with respect to the scenario of application, i.e. a large angle spread (AS 120°) for SFTF corresponding to an indoor scenario and reduced angle spreads (AS 30° and AS 10°) for SU-BF with regard to an outdoor scenario.

Fig. 6.5 shows the performance with adjacent chip mapping for a fully-loaded system when J-MRT and J-MSINR are used at the basestation and despreading at the terminal. The performances of the conventional single-antenna system employing EGC SUD and MMSE-MUD at full load and MRC SUD for a single user are given for comparison as well as the single-user curve for J-MRT. Both, J-MRT and J-MSINR almost attain the single-user performance, which shows that there is a very low residual MAI. In contrast, for the conventional single-antenna system, there is a significant difference between the single-user curve and the curves with full load. At BER=10-4, the MMSE-MUD scheme looses almost 1.5 dB and EGC more than 2 dB compared to single-user performance. At the same operation point, J-MRT and J-MSINR achieve a gain of 9 dB compared to the conventional system with EGC. This gain is 3 dB higher than the pure antenna gain (6 dB for M=4) thanks to the spatial diversity and the reduced MAI level.



-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

J-MRT K=1J-MRT K=16J-MSINR K=16Conv MRC K=1Conv EGC K=16Conv MMSE-MUD K=16

SNR, γb

BER

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1


SNR, γb

BER

Fig. 6.5: Performance of SFTF with channel coding and

adjacent chip mapping (M=4, channel E, AS 120°).

SNR, γb

BER

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1


SNR, γb

BER

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1


Fig. 6.6: Performance of SFTF with channel coding and

chip interleaving (M=4, channel E, AS 120°).

The same configuration as above but with chip interleaving is considered in Fig. 6.6. Here, the conventional system performs better in the single-user case as a benefit of the frequency diversity but suffers from a high MAI level at full load. EGC SUD has an error floor above BER=10-4, and MMSE-MUD is about 3 dB from single-user performance. Note, however, that the conventional system with MMSE-MUD achieves here a slightly better performance than for adjacent chip mapping in Fig. 6.5. The performance of J-MSINR at full load is 1 dB from its single-user performance and yields a gain of 8 dB compared to the conventional system with MMSE-MUD. This emphasises again the efficient MAI mitigation achieved with the multi-user J-MSINR approach. Due to its lower MAI mitigation capacity the single-user approach J-MRT



suffers from an error floor at BER=5⋅10-5 for chip interleaving but it still achieves the same performance as the conventional system with MMSE-MUD at BER=10-4.

Comparing Fig. 6.5 and Fig. 6.6, J-MSINR achieves almost the same performance in both cases, i.e. with adjacent chip mapping and chip interleaving. Thus, when channel coding is applied, chip interleaving yields almost no advantage in terms of diversity. Since J-MRT performs as well as J-MSINR for adjacent chip mapping and, as a single-user criterion, requires a much lower computational effort, it seems preferable to opt for the combination of adjacent chip mapping and J-MRT in the considered scenario.

For the performance assessment of SU-BF with channel coding, we focus on adjacent chip mapping and optimised spreading code assignment according to the conclusions in chapter 5. Indeed, SU-BF, as a single-user approach, has only a limited capacity of MAI mitigation, which favours adjacent chip mapping. The performance of SU-BF approaches employing different versions of the spatial covariance matrix (cf. Tab. 5.3) is shown in Fig. 6.7 for AS 10° and in Fig. 6.8 for AS 30°. The same curves as in Fig. 6.5 obtained with the conventional single-antenna system are given as a reference. Note that for this SISO system the angle spread has obviously no influence on the performance. For comparison, the single-user performance of SU-BF-inst is also represented.

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

SU-BF-inst K=1SU-BF-inst K=16SU-BF-long K=16Conv MRC K=1Conv EGC K=16Conv MMSE-MUD K=16

SNR, γb

BER

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

SU-BF-inst K=1SU-BF-inst K=16SU-BF-long K=16Conv MRC K=1Conv EGC K=16Conv MMSE-MUD K=16

SNR, γb

BER

Fig. 6.7: Performance of SU-BF with channel coding for AS 10°

(M=4, adjac., channel E, opt. assignment).

For AS 10° in Fig. 6.7, SU-BF-inst and SU-BF-long have similar performance due to the convergence of these approaches for small angle spreads. At BER=10-4, SU-BF-long only looses 0.5 dB compared to SU-BF-inst. SU-BF-inst itself has nearly no loss compared to its single-user performance thanks to the low residual MAI level. Compared with the conventional system employing EGC, SU-BF-inst has a gain of more than 7 dB at BER=10-4. SU-BF-long also achieves a gain higher than the pure antenna gain compared to the conventional system, i.e. 6.5 dB, which shows the benefit of implicit interference reduction since spatial diversity cannot be obtained here.

As expected from the results in chapter 5, the performance of SU-BF approaches differs considerably for the larger angle spreads. For AS 30° in Fig. 6.8, SU-BF-long ends in a relatively high error floor of BER=5⋅10-4, whereas SU-BF-inst performs slightly better than at AS 10° thanks to the increased spatial diversity. For AS 30°, it is also interesting to consider



SU-BF-instNc as a trade-off between robustness to fading variations and performance. At BER=10-4, SU-BF-instNc still achieves the classical antenna gain of 6 dB compared to the conventional system with EGC.

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

SU-BF-inst K=1SU-BF-inst K=16SU-BF-long K=16SU-BF-instNc K=16Conv MRC K=1Conv EGC K=16Conv MMSE-MUD K=16

SNR, γb

BER

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

SU-BF-inst K=1SU-BF-inst K=16SU-BF-long K=16SU-BF-instNc K=16Conv MRC K=1Conv EGC K=16Conv MMSE-MUD K=16

SNR, γb

BER

Fig. 6.8: Performance of SU-BF with channel coding for AS 30°

(M=4, adjac., channel E, opt. assignment).

6.3.3 Uncoded performance with imperfect channel knowledge at the basestation

In this section, we assess the influence of imperfect CSI due to mobility on the performance of SFTF and SU-BF. Here, the quality of the CSI at the basestation is given by the correlation coefficient ρCE introduced in section 6.2. For the cases where equalisation at reception is employed, we still assume a perfectly estimated CSI at the terminal in order to evaluate only the mismatch of the transmit filter. All results are obtained with adjacent chip mapping, M=4 transmit antennas, on channel E, and without channel coding. The following figures show the required SNR for achieving the operation point of BER=10-2 as a function of the correlation ρCE. The corresponding velocity for τU=1 ms is given for illustration.

The performance of the SFTF approaches is shown in Fig. 6.9 for AS 120°. In the ideal case, STFT includes pre-equalisation. Then, there is no need for equalisation at the receiver and the subcarrier combining is realised by a simple despreading. This case is considered in the first set of curves. Here, the system performance degrades drastically as the correlation decreases, which arises essentially from the fact that coherent detection is no more guaranteed. For ρCE=0.9, the loss compared to perfect CSI (ρCE=1.0) is already about 3.5 dB for J-MRT in the single-user case, 6 dB for J-MRT at full load, and 5 dB for J-MSINR at full load. The second set of curves was obtained with EGC at the terminal, which is a more realistic configuration in practice. For ρCE=0.85, the loss is about 2 dB for J-MRT in the single-user case and 4 dB for J-MRT and J-MSINR at full load. These results emphasise the sensitivity of the SFTF approaches with respect to the quality of CSI. As a consequence, SFTF cannot tolerate Doppler variations arising from vehicular velocities, i.e. superior to 15 km/h, and, as expected, is limited to scenarios where the velocities do not exceed those of pedestrians.



0.750.80.850.90.951

0

2

4

6

8

10

12

14BS:J-MRT K=1BS:J-MRT K=16BS:J-MSINR K=16

Correlation, ρCE

Requ

ired

SNR

at B

ER=

10-2

15 km/h 20 km/h 30 km/h 35 km/h25 km/h

MT: despreading

MT: EGC

0.750.80.850.90.951

0

2

4

6

8

10

12

14BS:J-MRT K=1BS:J-MRT K=16BS:J-MSINR K=16

Correlation, ρCE

Requ

ired

SNR

at B

ER=

10-2

15 km/h 20 km/h 30 km/h 35 km/h25 km/h

MT: despreading

MT: EGC

Fig. 6.9: Performance of SFTF with imperfect CSI

(M=4, adjac., channel E, AS 120°).

Correlation, ρCE

Requ

ired

SNR

at B

ER=

10-2

20 km/h 30 km/h 40 km/h 50 km/h

0.50.550.60.650.70.750.80.850.90.951

0

2

4

6

8

10

12

14

SU-BF-inst K=1SU-BF-inst K=16SU-BF-instNc K=1SU-BF-instNc K=16

Correlation, ρCE

Requ

ired

SNR

at B

ER=

10-2

20 km/h 30 km/h 40 km/h 50 km/h

0.50.550.60.650.70.750.80.850.90.951

0

2

4

6

8

10

12

14

SU-BF-inst K=1SU-BF-inst K=16SU-BF-instNc K=1SU-BF-instNc K=16

Fig. 6.10: Performance of SU-BF with imperfect CSI (M=4, adjac., channel E, AS 30°, rand. assignment).

Fig. 6.10 shows the performance of SU-BF for AS 30°. Here, we focus on the approaches SU-BF-inst and SU-BF-instNc, since SU-BF-long is independent of the variations in the instantaneous fading. SU-BF-instNc is quite insensitive to Doppler variations. For ρCE=0.5 and compared to perfect CSI, SU-BF-instNc only has a loss of about 0.7 dB at full load and shows a negligible loss in the single-user case. This confirms the robustness of the instantaneous covariance matrix averaged over the whole set of NC subcarriers, which was already expected from the analysis. In contrast, the covariance matrix employed for SU-BF-inst is only averaged on the L subcarriers employed for chip mapping and is thus sensitive to fading variations within



this subcarrier set. At ρCE=0.5 and for a single user, SU-BF-inst has a loss of about 3 dB compared to perfect CSI. For K=16, the degradation is more important. Here, SU-BF-inst already suffers from a loss of 8 dB at ρCE=0.7. Consequently, the more robust version SU-BF-instNc should be chosen for K=1 if ρCE ≤0.55 and for full load if ρCE ≤0.77. Nevertheless, all SU-BF approaches are more robust to Doppler variations than SFTF, as expected. Furthermore, if lower angle spreads are considered, the robustness of SU-BF increases due to the convergence of the three versions of the spatial covariance matrix. Consequently, in the presence of moderate angle spread, SU-BF can tolerate vehicular speeds, which makes it suitable for outdoor environments.

6.3.4 Coded performance with imperfect channel knowledge at the basestation

The performance of the proposed approaches with channel coding and imperfect channel knowledge at the basestation is compared here in two typical scenarios: An indoor scenario with low mobility and an outdoor urban scenario with velocities corresponding to city traffic.

The indoor scenario is characterised by a large angle spread (AS 120°) and mobile speeds correspond to those of pedestrians, i.e. are below 15 km/h. Concerning the channel model and chip mapping, we present two opposite cases: In Fig. 6.11, channel model A is employed together with adjacent chip mapping, which results in a highly correlated fading on the chips. In contrast, channel E with chip interleaving used for Fig. 6.12 is an example of a very low correlation of the fading on the chips. Both figures show the performance of J-MRT, J-MSINR, and SU-BF-inst (opt. assignment) with EGC at the mobile receiver for M=4 transmit antennas. The performance of the conventional single-antenna system is given as a reference. The two extreme cases of perfect channel knowledge at the basestation (ρCE=1.0) and imperfect knowledge (ρCE=0.95) due to a maximum speed of 15 km/h are represented. Note that perfect channel estimation is still assumed at the mobile station and the performance of the conventional system is independent of the considered speed.

In Fig. 6.11, the performance of the fully-loaded conventional system with EGC is close to its single-user MRC bound. Indeed, for highly correlated fading on the chips, the orthogonality between users’ signals is nearly conserved, which results in a low MAI level and makes MUD dispensable. In this situation, the three considered transmission strategies, i.e. the single-user approaches J-MRT and SU-BF-inst and the multi-user approach J-MSINR, achieve the same performance. All three strategies can here optimally exploit the spatial diversity offered by the large angle spread of the channel. For perfect channel knowledge at the basestation (ρCE=1.0), they yield a gain of 11 dB compared to the conventional system at BER=10-4, which is obviously much higher than the pure antenna gain (6 dB for M=4). For imperfect knowledge at the basestation (ρCE=0.95), they all suffer from the same loss of around 1.5 dB at BER=10-4. Thus, even with these pessimistic considerations for the quality of the channel knowledge at the basestation the proposed approaches still achieve a gain of 9.5 dB at BER=10-4 compared to the conventional system.

In Fig. 6.12, the low correlated fading on the chips leads to a high MAI, which is reflected by the performance of the conventional system represented here with EGC and MMSE-MUD (cf. comments on Fig. 6.6). In this case, the three transmission strategies J-MRT, J-MSINR, and SU-BF-inst have a very different behaviour. SU-BF-inst cannot cope with the combination of a large angle spread and a low fading correlation on the subcarriers and has a high error floor above BER=10-2, even for perfect channel knowledge (ρCE=1.0). J-MRT also suffers from the high MAI and has an error floor of BER=5⋅10-5 for ρCE=1.0 (cf. comments Fig. 6.6) and of BER=2⋅10-4 for ρCE=0.95. In contrast, the multi-user approach J-MSINR still performs very well thanks to its capacity to explicitly mitigate the MAI. Its performance is similar to Fig. 6.11. At BER=10-4 it has a loss of slightly less than 2 dB due to imperfect channel knowledge but still achieves a gain of 6.5 dB compared to the conventional system with MMSE-MUD.



-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

J-MRT K=16J-MSINR K=16SU-BF-inst K=16Conv MRC K=1Conv EGC K=16

SNR, γb

BER

ρCE=1.0 ρCE=0.95 (15 km/h)

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

J-MRT K=16J-MSINR K=16SU-BF-inst K=16Conv MRC K=1Conv EGC K=16

SNR, γb

BER

ρCE=1.0 ρCE=0.95 (15 km/h)

Fig. 6.11: Performance of SFTF and SU-BF-inst (opt. assignment)

in the indoor scenario (M=4, adjac., channel A, AS 120°).

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

J-MRTJ-MSINRSU-BF-instConv EGCConv MMSE-MUD

SNR, γb

BER

ρCE=1.0

ρCE=0.95 (15 km/h)

-2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

J-MRTJ-MSINRSU-BF-instConv EGCConv MMSE-MUD

SNR, γb

BER

ρCE=1.0

ρCE=0.95 (15 km/h)

Fig. 6.12: Performance of SFTF and SU-BF-inst (opt. assignment) in the indoor scenario (M=4, K=16, interl., channel E, AS 120°).

Fig. 6.13 and Fig. 6.14 concern the urban outdoor scenario, which is characterised by channel E and a moderate angle spread (AS 30°). The mobile speeds correspond here to city traffic. We consider again M=4 transmit antennas and adjacent chip mapping. The reference curves given for the conventional single-antenna system are identical to those in Fig. 6.5, Fig. 6.7, and Fig. 6.8, where it was already observed that the longer delay of channel E results in a considerable MAI level even with adjacent chip mapping. Therefore, we represent here the performance at full load with EGC SUD and MMSE-MUD at the receiver.



0 2 4 6 8 10 12

10-4

10-3

10-2

10-1

J-MSINRSU-BF-instConv EGCConv MMSE-MUD

SNR, γb

BER

ρCE=1.0

ρCE=0.82 (30 km/h)

0 2 4 6 8 10 12

10-4

10-3

10-2

10-1

J-MSINRSU-BF-instConv EGCConv MMSE-MUD

SNR, γb

BER

ρCE=1.0

ρCE=0.82 (30 km/h)

Fig. 6.13: Performance of SFTF and SU-BF-inst (opt. assignment) in the outdoor scenario (M=4, K=16, adjac., channel E, AS 30°).

Fig. 6.13 compares the performance of SU-BF-inst and J-MSINR for perfect channel knowledge at the basestation (ρCE=1.0) and for imperfect knowledge (ρCE=0.82) at a mobile speed of 30 km/h. For perfect channel knowledge, J-MSINR outperforms SU-BF-inst by 0.5 dB at BER=10-4 thanks to its capacity of explicit MAI mitigation. When imperfect channel knowledge is considered, the situation is inverted. Here, J-MSINR suffers from a high loss of 5 dB at BER=10-4 and has an error floor of BER=4⋅10-4. In contrast, SU-BF-inst shows a better robustness with a loss of less than 2 dB and it still outperforms the conventional system with MMSE-MUD by 5.5 dB.

For higher velocities, it is interesting to compare the performance of SU-BF-inst to the more robust versions SU-BF-instNc and SU-BF-long, which is shown in Fig. 6.14. Again we consider the performance with perfect channel knowledge at the basestation (ρCE=1.0) and imperfect channel knowledge for a speed of 45 km/h (ρCE=0.6). Note that SU-BF-long only relies on long-term channel knowledge and is not affected by the considered velocities. For perfect channel knowledge, SU-BF-inst obviously outperforms SU-BF-instNc, with a gain of 1.5 dB at BER=10-4. With imperfect channel knowledge, SU-BF-instNc only has a small loss of 0.5 dB while SU-BF-inst suffers from a loss of 3 dB and, thus, looses 1 dB compared to SU-BF-instNc. This emphasises again the robustness of SU-BF-instNc. Compared to the conventional system both approaches still have a considerable gain, i.e. 5 dB for SU-BF-instNc and 4 dB for SU-BF-inst. The fact that SU-BF-inst and SU-BF-instNc perform considerably better than SU-BF-long shows that the use of instantaneous knowledge in TDD systems is still beneficial for moderate velocities of the mobile terminal.



0 2 4 6 8 10 12

10-4

10-3

10-2

10-1

SU-BF-instSU-BF-instNcSU-BF-longConv EGCConv MMSE-MUD

SNR, γb

BER

ρCE=1.0 ρCE=0.60 (45 km/h)

0 2 4 6 8 10 12

10-4

10-3

10-2

10-1

SU-BF-instSU-BF-instNcSU-BF-longConv EGCConv MMSE-MUD

SNR, γb

BER

ρCE=1.0 ρCE=0.60 (45 km/h)

Fig. 6.14: Performance of SU-BF in the outdoor scenario (M=4, K=16, adjac., channel E, AS 30°, opt. assignment).

6.4 Open issues

The effectiveness of the proposed transmission strategies should not conceal the fact that several open issues should be further investigated. These issues are, of course, closely related to the assumptions made within this work and are briefly discussed here.

6.4.1 Uplink channel estimation

The proposed strategies all exploit different kinds of CSI at the transmitter. This knowledge has to be obtained from channel estimation in the uplink or from feedback of the mobile terminal. Feedback from the mobile introduces an additional signalling overhead in the uplink when precise CSI has to be reported. Furthermore, reporting of the mobile introduces an additional delay between the estimation of CSI and its usage, which reduces the reliability of the CSI. Thus, it seems preferable to acquire the CSI by estimation in the uplink.

Channel estimation in an MC-CDMA uplink is not straightforward and may require an important overhead for pilot symbols (cf. section 3.3.3). An efficient solution exists for adjacent chip mapping within the coherence rectangle of the underlying OFDM system (cf. 2.5.2), where spread pilots can advantageously be applied [ChMo04]. Furthermore, alternative systems may be considered for the uplink like DS-CDMA and Spread Spectrum Multi-Carrier Multiple Access (SS-MC-MA) [Kai98][FaKa03], for which efficient schemes for channel estimation are known.

The estimation of spatial covariance matrices in the uplink is less demanding than an estimation of the fast fading coefficients, especially if a covariance matrix averaged over the whole OFDM bandwidth or a long-term spatial covariance matrix is considered. However, it may also require a user-specific pilot signal. Here, simplified algorithms for calculation and tracking of the principal eigenvector employed for transmit beamforming could lead to efficient solutions [GoLo96][Utsch02].

6.5 Conclusions


The objective of further investigations is thus the acquisition of reliable CSI in the uplink of an MC-CDMA or an alternative system and its usage for the proposed downlink transmission strategies.

6.4.2 Channel reciprocity

In general, instantaneous CSI is only available at the basestation transmitter when the reciprocity of uplink and downlink channels can be assumed, e.g. in TDD systems with low mobility. Besides the investigated issues related to the variations of the channel state itself, differences in the RF chains for transmission and reception may also introduce a mismatch between the uplink and downlink channel responses.

Further studies should consider the additional constraints on the RF chains resulting from the required reciprocity and techniques to compensate an eventual mismatch.

6.4.3 Downlink channel estimation

Even if the proposed SFTF techniques can perfectly pre-equalise the channel in theory, post-equalisation at the mobile receiver may be necessary in practice, especially when Doppler variations occur. As for the SU-BF techniques, an equalisation at the terminal is required in any case. Yet, when user-specific pre-filtering is employed at the transmitter, the receiver has to estimate the overall frequency response (cf. (4.5)), which is then also user-specific. Consequently, the estimation task is here similar to uplink channel estimation. Nevertheless, the estimation at the receiver may still benefit from the downlink properties by employing a combined pilot scheme consisting of common pilots transmitted with an idle transmit filter, which may be used for synchronisation and coarse channel estimation, and dedicated pilots transmitted with the user-specific transmit filter from which the overall frequency response can be estimated. Thus, future work could address the application of such combined pilot schemes in conjunction with the proposed transmission strategies.

To overcome part of the degradations experienced by SFTF in the presence of Doppler variations, one can take advantage of the fact that the included pre-equalisation is almost perfect at the beginning of the downlink slot and the mismatch increases towards the end of the slot. Then, this mismatch may be compensated by an adaptive solution for tracking the Doppler variations during the downlink frame. The effectiveness of such an approach has already been demonstrated for pre-equalisation in the MC-CDMA uplink [MoCa03].

6.5 Conclusions

The system comparison accounting for channel coding and imperfect channel knowledge at the basestation transmitter allows us to identify advantageous system designs in the considered scenarios.

In the conventional system, the choice between adjacent chip mapping and chip interleaving is generally a result of the trade-off between diversity and MAI, especially when a channel code of high rate or no channel coding is considered (cf. section 3.5.3). When reliable instantaneous knowledge is available at the transmitter, SFTF benefits from spatial diversity. Thus, the frequency diversity obtained by chip interleaving in the conventional single-antenna system can in some sense be replaced by spatial diversity obtained with multiple transmit antennas. Then, the low MAI resulting from adjacent chip mapping may be advantageous since it allows to employ the low-complexity J-MRT strategy, especially when the frequency diversity of the channel is also exploited by channel coding. However, almost the same performance can also be obtained with chip interleaving, but this requires that the multi-user technique J-MSINR is employed. In



scenarios where only covariance knowledge is available and SU-BF is employed, adjacent chip mapping is generally preferable, especially when moderate or large angle spreads occur. Compared with the single-user J-MRT approach, the proposed SU-BF approach requires an increased complexity, since it involves an eigenvector calculation. However, efficient algorithms for estimating and tracking the principal eigenvector of a matrix are known from literature [Utsch02].

The Doppler variations arising from the mobility of the terminal impact on the reliability of the instantaneous channel knowledge available at the basestation. In particular, the performance of SFTF approaches rapidly deteriorates when velocities higher than those of pedestrians occur. The impact of Doppler variations on the SU-BF approaches depends on the angle spread. For small angle spreads there is only a negligible impact, since the different versions of the spatial covariance matrix converge. For moderate angle spreads, there is an important impact on the performance of SU-BF-inst, which only tolerates low vehicular speeds. SU-BF-instNc is much more robust to Doppler variations and easily tolerates speeds in the order of typical city traffic and higher.

As a consequence, J-MRT in combination with adjacent chip mapping or J-MSINR with chip interleaving seem advantageous combinations in indoor systems with large angle spreads and low mobility where almost perfect instantaneous channel knowledge can be assumed at the transmitter. In urban outdoor systems, where lower angle spreads but velocities corresponding to city traffic occur, adjacent chip mapping and SU-BF-instNc yields a good trade-off between performance and robustness. When only long-term covariance knowledge is available, SU-BF-long can achieve the same performance as SU-BF-intNc for small angle spreads. However, for moderate and large angle spreads long-term covariance knowledge cannot be advantageously exploited at the transmitter side.

Issues for future studies are mostly related to the acquisition of reliable channel knowledge at both ends of the considered system and have been briefly classified.


7 Conclusions and prospects In this thesis, we proposed and investigated new transmission strategies employing multiple antennas at the basestation for the downlink of a Multi-Carrier CDMA (MC-CDMA) system.

Current research activities and experiments underline the suitability of MC-CDMA for air interfaces of future mobile radio systems, especially in the downlink. Since the requirements of such new air interfaces can only be met by exploiting the spatial dimension of the radio channel, the combination of MC-CDMA with multiple antennas is a technology of high potential.

Investigations on multiple antenna technologies necessitate an accurate modelling of the spatial characteristics of the radio channel. Based on an analysis of these characteristics, we were able to extend time-domain channel models employed in current studies to vector channel models accounting for the directions of the path forming the radio channel.

A major issue in the design of conventional single-antenna MC-CDMA systems is the trade-off between frequency diversity and the performance degradation due to multiple access interference (MAI). Indeed, chip interleaving resulting in weakly correlated fading on the chips achieves a high frequency diversity but suffers from strong MAI. On the other hand, adjacent chip mapping resulting in a high correlation of the fading affecting different chips leads to a lower MAI but in return provides only low frequency diversity. In any case, the user capacity of the conventional system is limited by MAI and can only be increased by employing multi-user detection schemes. Yet, these schemes have the drawback that they involve a high implementation complexity, which may not be tolerable at the mobile receiver in the downlink. Striving for a light design of the mobile receiver, we investigated alternative transmission strategies employing multiple antennas at the basestation, which are based on the assumption that some channel knowledge is available at the transmitter side.

For the case where the basestation transmitter has instantaneous channel knowledge at its disposal, we developed the so-called Space-Frequency Transmit Filtering (SFTF) approach, which applies different spatially-selective filters to the subcarriers used for chip mapping. We showed that the application of a user-specific transmit filter influences the orthogonality of users’ signals installed by the spreading codes, which has important consequences for the system design. Single- and multi-user optimisation criteria were derived and applied to each subcarrier separately, or jointly on all subcarriers employed for chip mapping. While the per-carrier criteria turned out to be only of minor interest, the joint criteria including pre-equalisation can efficiently exploit spatial diversity and mitigate MAI.

Joint Maximum Ratio Transmission (J-MRT) is the optimum single-user criterion maximising the SNR after despreading at the receiver and can advantageously be applied in conjunction with adjacent chip mapping. This combination benefits from spatial diversity and implicitly ensures a low MAI as a benefit of the highly-correlated fading on the chips. For chip interleaving, on the contrary, user-specific transmit filtering with J-MRT further degrades the orthogonality of users’

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It means common understanding, a common tradition,common ideas, and common ideals.

Robert M. Hutchins (1899-1977)

Chapter 7: Conclusions and prospects


signals and leads to an increase of MAI. The multi-user criterion maximising the modified SINR (J-MSINR) achieves an efficient separation of users’ signals in space and frequency and therefore obtains a good performance irrespective of the chip mapping. J-MSINR can even cope with an overloaded system, where the number of users exceeds the spreading code length. J-MSINR has the drawback that it involves an increased complexity due to matrix inversion, which may nevertheless be tolerable at the basestation. Both, J-MRT and J-MSINR benefit from spatial diversity, i.e. uncorrelated fading at the antennas, which is obtained for wide angle spreads and large antenna spacing.

When only knowledge of the spatial covariance matrix of the channel is available at the transmitter, we proposed transmit beamforming employing a common spatial filter on all subcarriers used for chip mapping. We addressed the issue of wideband beamforming, which may arise when the same beamforming vector shall be employed on the whole set of subcarriers in a wideband multi-carrier system. We showed that efficient solutions for frequency compensation exist for the estimation of the spatial covariance matrix as well as for the application of a common beamforming vector. Single and multi-user optimisation criteria for transmit beamforming in the MC-CDMA downlink were investigated. A multi-user criterion seems not advantageous, since the number of users generally exceeds the number of antennas, which results in a lack of degrees of freedom for filter optimisation. The proposed single-user beamforming (SU-BF) approach can only implicitly reduce the MAI by spatially-selective transmission, which favours adjacent chip mapping especially when the channels have a considerable angle spread. Here, the MAI can be further reduced thanks to direction-based spreading code assignment.

Basically three different versions of the spatial channel covariance matrix can be employed for transmit beamforming. These versions differ in their robustness to fading variations, and their availability depends on the considered system configuration and scenario. SU-BF-inst employs a covariance matrix depending on the instantaneous fading on the subcarriers employed for chip mapping, SU-BF-instNc uses a covariance matrix averaged over all subcarriers of the underlying OFDM system, and SU-BF-long is based on the long-term averaged covariance matrix. These three versions converge for small angle spreads, where the fading on the different antennas is highly correlated and SU-BF benefits from the antenna gain compared to the single-antenna system. For considerable angle spreads, i.e. reduced fading correlation on the antennas, SU-BF-inst can exploit the spatial diversity of the channel leading to an improved performance, while the other two approaches suffer from a reduced antenna gain.

A comparison of the proposed approaches accounting for channel coding and imperfect channel knowledge at the transmitter due to Doppler variations allowed to identify their scenarios of application. The SFTF approaches require instantaneous channel knowledge, which is only available in TDD systems. Furthermore, they are very sensitive to imperfections arising from Doppler variations and limited to mobile velocities corresponding to those of pedestrians. Consequently, SFTF is well suited for TDD systems in indoor environments, where it can efficiently exploit the typically large angle spread. SU-BF-inst also relies on instantaneous channel knowledge but is less sensitive to Doppler variations than SFTF for moderate or small angle spreads. Thus, SU-BF-inst is suitable for outdoor TDD systems with low mobility. SU-BF-instNc is a trade-off between the benefits of instantaneous knowledge and robustness to Doppler variations. In this way, it can tolerate speeds up to typical city traffic and higher with moderate angle spreads. When only long-term covariance knowledge is available, e.g. in outdoor systems with high mobility or in FDD systems, SU-BF-long can be employed, which is almost as efficient as the other two versions of SU-BF for small angle spreads. Note that long-term covariance knowledge cannot be exploited for large angle spreads where the fading correlation on the different antennas is low.

Chapter 7: Conclusions and prospects


Further studies should account for real channel estimation at the transmitter and the receiver side. In particular, the acquisition of reliable channel knowledge in the uplink of MC-CDMA or alternative systems has to be considered. At the receiver side, channel estimation schemes suitable for estimating the overall channel response resulting from user-specific transmit filtering are to be developed. The channel reciprocity required to exploit instantaneous channel knowledge at transmission may impose additional constraints on the radio frequency parts of the transceivers, which should also be investigated in more detail.

In summary, we demonstrated in this work the potential of transmission strategies exploiting the spatial dimension of the radio channel and the available channel knowledge at the transmitter in the downlink of MC-CDMA. These approaches obtain a considerable performance improvement in typical indoor and outdoor scenarios with a light receiver design and allow a transfer of implementation complexity from the terminal to the basestation.


A Appendix

A.1 Some channel correlation functions

A.1.1 Time correlation and Doppler spectrum

Based on the derivations in section 2.2.3, the Doppler power spectrum can easily be derived in the case where a large number of sub-paths (NSP→∞) impinge from angles that are uniformly distributed in the range [0,2π[. Then the Doppler spectrum can be obtained either for a single path p or for the flat fading channel. The time spaced autocorrelation function for a given delay τp is given by

( ) ( ) ( ) *1 E , ,2A B p B pt h t h t tφ τ τ∆ ∆= + (A.1)

The impulse response at a given delay τp is the superposition of the sub-paths and given by

( ) ,

1( 2 )

0

, eSP

D s s

Nj f t

B p ss

h t π ϕτ α−

+

=

= ∑ (A.2)

Combining the two equations above yields

( ) ( ),max

12 2 cos

0

E eSP

D s

Nj f t

A ss

t π θφ α−

∆

=

∆ = ∑ (A.3)

Since an infinite number of paths is assumed, this expression can be written in its integral form and the expected value of the path power can be replaced by the corresponding density function. Denoting Ω the total power of all sub-paths, which are uniformly distributed in the range [0,2π[, we get

( ) ( ),max

22 cos

0

e2

Dj f tA t d

ππ θφ θ

π∆Ω

∆ = ∫ (A.4)

Then, the normalised time spaced autocorrelation function is given as

( ) ( )( )

( ) ( ),max

22 cos

, 0 ,max0

e J 20

Dj f tAA norm D

A

tt d f t

ππ θφ

φ θ πφ

∆∆∆ ∆= = =∫ (A.5)

where Jk(x) denotes the k-th order Bessel function of the first kind.

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Appendix


A.1.2 Spatial correlation and coherence distance

In a similar way as above, the spatial correlation function can also be derived for a single path or the flat fading channel. The spatial correlation function between two antenna elements spaced by dS was defined in (2.27) (section 2.2.5) as

( ) ( ) ( ) *, , 1

1 E , ,2C S B m B md h t h tφ τ τ+= (A.6)

The impulse response at a given delay τp including the array response at element m is given as

( )( )

,

1 2 cos( 2 )

0

, e eSSP s

D s s C

dN j mj f t

B p ss

h tπ θ

π ϕ λτ α−

+

=

= ∑ (A.7)

Here, again a large number of paths is assumed with the power azimuth spectrum given as

( )for ,

20 elsewhere

ASθ θ

θ

θ θ θρ θ

Ω∆ ∆

∆ ∈ − + + =

(A.8)

In analogy to the derivation in the previous section, the normalised spatial correlation function is given as

( ) ( )( ),

2 cos

0

1 1 cos 2 cos sin 2 cos2 2

S

C

C SC norm S

C

djS S

C C

dd

d de d j dθ θ

θ θ

θ θπ θλ

θ θθ θ

φφ

φ

θ π θ π θ θλ λ

∆ + ∆ +

−∆ + −∆ +∆ ∆

= =

= +

∫ ∫

(A.9)

Using relations

( )( ) ( ) ( ) ( ) ( )

( )( ) ( ) ( ) ( )( )

0 21

2 10

cos cos 2 1 cos 2

sin cos 2 1 cos 2 1

kk

k

kk

k

z x J z J z kx

z x J z k x

∞

=

∞

+=

= + −

= − +

∑

∑ (A.10)

the integration is simplified to

( )( )( ) ( )( ) ( ) ( )

sin sin1 cos cos sinc2 2

a aa d a a

a

θ

θ

θθ θ

θθ θθ

θ θθ θ θ

∆ +

−∆ +

∆ ∆∆

∆ ∆

+ − −= =∫ (A.11)

Then, the real and imaginary part of the normalised spatial correlation function are

( ) ( ) ( ) ( )

( ) ( ) ( )( ) ( )( )

, 0 2 max1

, 2 1 max0

J 2 2 1 J 2 cos 2 sinc

2 1 J 2 cos 2 1 sinc 2 1 /2

kS SC norm S k

kC C

k SC norm S k

k C

d dd k k

dd k k

φ π θ θλ λ

φ π θ θλ

π∞

=

∞

+=

∆

∆

ℜ = + −

ℑ = − − + +

∑

∑ (A.12)

In order to give an approximation of the coherence distance [Fle00], we evaluate the fading correlation between two antenna elements, when the mean angle is equal to the broadside direction, i.e. θ =90°. From (A.9) we obtain

A.2: Power delay profiles of HIPERLAN/2 models [Med98b]


( )2

,

2

1 cos 2 cos sin 2 cos 2

1 cos 2 sin sin 2 sin2

1 cos 2 sin2

S SC norm S

C C

S S

C C

S

C

d dd j d

d dj d

d d

θ

θ

θ

θ

θ

θ

π

πθ

θ

θ

φ π θ π θ θλ λ

π θ π θ θλ λ

π θλ

θ

∆ +

−∆ +

∆

−∆

∆

−∆

∆

∆

∆

= +

= +

=

∫

∫

∫

(A.13)

The last equality results from the fact that the sin-function is odd. We will now use the smallest value dS , for which the spatial correlation function is zero, as an approximation for the coherence distance dcoh . The first zero occurs if the cos-function is integrated over one period of 2π. This is the case if the following condition holds:

2 sinS

C

dθπ π

λ∆ = (A.14)

Thus, we obtain an upper bound for the coherence distance as

( )2sinC

cohdθ

λ∆

≤ (A.15)

A.2 Power delay profiles of HIPERLAN/2 models [Med98b]

A.2.1 Channel model A

Delay [ns] Variance [dB] 0 0 10 -0.9 20 -1.7 30 -2.6 40 -3.5 50 -4.3 60 -5.2 70 -6.1 80 -6.9 90 -7.8 110 -4.7 140 -7.3 170 -9.9 200 -12.5 240 -13.7 290 -18 340 -22.4 390 -26.7

Tab. A.1: Power delay profile of channel A.

Appendix


A.2.2 Channel model E

Delay [ns] Variance [dB] 0 -4.9 10 -5.1 20 -5.2 40 -0.8 70 -1.3 100 -1.9 140 -0.3 190 -1.2 240 -2.1 320 0 430 -1.9 560 -2.8 710 -5.4 880 -7.3 1070 -10.6 1280 -13.4 1510 -17.4 1760 -20.9

Tab. A.2: Power delay profile of channel E.

A.3 Existence and generation of Hadamard matrices

Walsh-Hadamard codes are the most common orthogonal spreading codes for CDMA systems. They are based on Hadamard matrices, which is a class of square matrices containing only 1s and –1s originally invented by Sylvester in 1867 [Syl67]. They have the property that if we take any two lines or columns of the matrix and put them side by side, half the adjacent cells are the same sign and half the opposite. This ensures the orthogonality of the resulting spreading codes. A common definition of a Hadamard matrix is the following

Tn n nn=C C I (A.16)

A necessary condition for the existence of a Cn is that n=1, 2 or a positive multiple of 4. It has been shown that for n < 428, Hadamard matrices exist for all n divisible by 4 [LiWi93]. Furthermore, Paley's theorem guarantees that there always exists a Hadamard matrix Cn when n is divisible by 4 and of the form 2ε(pm+1), for some positive integers ε and m and p an odd prime. In such cases, the matrices can be constructed using a Paley construction [Ger79].

A very simple iterative construction rule for higher order matrices is given as follows: Starting from the matrices Cm and Cn, Cmn can be constructed by replacing all 1s in Cm by Cn and all –1s by - Cn. For n<100, the matrices for n= 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, and 100 cannot be generated from lower order matrices. For example, C4 is generated in the following way:

2 22 4

2 2

1 1 1 11 1 1 1 1 1

; 1 1 1 1 1 1

1 1 1 1

− − = = = − − − − − −

C CC C

C C (A.17)

A.4: Simplification of the J-MSINR expression


As an example of a matrix where n is not a power of two, we just mention the matrix C12 , which is actually the lowest order where the matrix is unique except isomorphism:

12

1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1

− − − − − −− − − − − −

− − − − − −− − − − − −− − − − − −

=− − − − − −

− − − − − −− − − − − −

− − − − − −− − − − − −

−

C

1 1 1 1 1 1 1 1 1

− − − − −

(A.18)

A.4 Simplification of the J-MSINR expression

The term to be maximised for the J-MSINR is given in (4.33) (section 4.4.2) as

2

2, ,

1,

maxg

Hg g

KH Hg k g k g n ML g

k k gLσ

= ≠

+

∑w

w h

w v v I w

% ; subject to 1H

g g =w h% (A.19)

and the solution is obtained as

1

2, ,

1,

KH

g k g k g n ML gk k g

Lσκ−

= ≠

= +

∑w v v I h% (A.20)

where the real scalar κ ensures the constraint in (A.19). As a first step in the simplification, the term for k=g, i.e. H

g gh h% % , can be added in the sum representing the interference without any impact on the normalised solution. This is seen easily by multiplying the above solution from the left with the matrix to be inverted and adding the considered term

2 2, , , , , , ,

1 1, new term

K KH H H

g k g k g n ML g new k g k g n ML g new g g g newk k k g

L Lσ σλ= = ≠

= + = + + ∑ ∑h v v I w v v I w h h w% % % (A.21)

here the real scalar λ ensures again the constraint in (A.19). Using this constraint, the new solution vector can then be expressed as

2, , ,

1,

KH

g k g k g n ML g new gk k g

Lσλ= ≠

= + +

∑h v v I w h% %

1

2, , ,

1,

( 1)K

Hg new k g k g n ML g

k k gLσλ

−

= ≠

= − +

∑w v v I h%

,( 1)

g new gλ

κ−

=w w (A.22)

Appendix


Thus, the new solution is just a scaled version of the original one, and leads to an identical normalised transmit filter. Thus, (4.34) can be rewritten using the definitions in (4.25) and (4.26) as

( ) 12Hg g g g n ML gLκ σ

−= +w A A I h%% (A.23)

A further simplification is obtained by projecting the transmit filtering vector into the signal space spanned by the columns of Ag . Now, the auxiliary vector gw is defined as follows:

g g g gκ=w A w% (A.24)

Equation (A.19) can then be written as

2

2, ,

1,

max g

H Hg g g

KH H Hg g k g k g n ML g g

k k gLσ

= ≠

+

∑w

w A h

w A v v I A w

%; subject to 1H H

g g g =w A h% (A.25)

which leads to the solution

1

2, ,

1,

KH H H

g g k g k g n ML g g gk k g

Lσκ−

= ≠

= +

∑w A v v I A A h% (A.26)

Again adding the term for k=g in the sum, the solution in (4.34) can be written as

( )( )

( ) ( )

12 2

112

H H Hg g g g g n g g g g

H H Hg g g g n K g g g g

L

L

κ σ

κ σ

−

−−

= +

= +

w A A A A A A h

A A A I A A A h

%%

% (A.27)

From the definitions (4.25) and (4.26), one can obtain g g g=h A b% . Using this in the above expression, the simplified solution for J-MSINR as is given by

2 1( )Hg g g g g n K gLσκ −= +w A A A I b% (A.28)

A.5: Numerical results with the MATRICE simulation chain


A.5 Numerical results with the MATRICE simulation chain

In this section, we present exemplary numerical results obtained with the J-MSINR SFTF approach and the physical layer simulation chain developed in the MATRICE project [MAT,D3.1].

A.5.1 Simulation scenarios

The simulation parameters are similar to those employed in the previous chapters of this work and chosen according to [MAT,D1.4]. The parameters are summarised in Tab. A.3. The major differences with the parameters of chapter 6 are the coding scheme and the channel model, which is here based on the 3GPP/3GPP2 spatial channel model (cf. section A.5.2). In contrast to the previous chapters, the channel is not redrawn for each coded block but it evolves with respect to the terminal velocity starting from a randomly chosen initial state. The obtained results are averaged over a representative number of initial states and over simulation durations exceeding 50 times the coherence time, Tcoh , of the channel. Perfect CSI is assumed at the transmitter and the receiver. Thus, the velocity of the mobile terminal only concerns the evolution of the channel and has no impact on the CSI quality.

Carrier frequency, fC 5 GHz Sampling frequency 57.6 MHz FFT-size 1024 Number of available sub-carriers, NC 736 Carrier spacing, ∆f 56.3 kHz Overall symbol time, TS’ 21.5 µs Guard time, TG 3.75 µs Symbol alphabet QPSK

Channel coding UMTS convolutional code G1=753, G2=561, KC=9, RC=1/2 Blocksize, BC = 1380

Spreading factor, L 16

Chip mapping Spreading in frequency with chip interleaving

Channel model 3GPP/3GPP2 SCM (cf. sect. A.5.2) based on Channel E: τmax=1.72µs

Frame size, NF 15 Mobile velocity 60 km/h Array configuration ULA Element spacing, dS λC/2, 10λC Number of transmit antennas, M 1, 2, 4

Tab. A.3: Simulation parameters for MATRICE chain.

A.5.2 Spatial channel properties and parameters

The 3GPP/3GPP2 SCM channel model was briefly described in section 2.3.2. Here, we indicate the major parameters employed for the presented numerical results. A detailed description of the parameters and their dependencies can be found in [SCM03]. The parameters of this channel model originally proposed for the 2 GHz UMTS band were adapted to the propagation conditions at 5 GHz and to the high bandwidth of the considered system within the MATRICE

Appendix


project [MATRICE]. However, due to the confidentiality of these parameters we only indicate the principle employed for determining the spatial channel characteristics.

The model ensures the consistency between the time and angle dispersion of the channel at the mobile terminal and the basestation with respect to the considered scenario. The time dispersion of the channel is fixed according to the power delay spectrum of HIPERLAN/2 model E to ensure the comparability with the results of the conventional SISO chain. The spatial channel characteristics correspond to a typical outdoor scenario with large mean angle spread at the terminal and moderate mean angle spread at the basestation.

To determine the DOAs at the terminal and the basestation a LOS direction is randomly chosen according to a uniform distribution in the operation range of the antennas, i.e. [30°,120°] for a ULA at the basestation and within 360° at the single-antenna terminal. Then, the DOAs of the paths follow normal distributions around the LOS directions with different angle spreads, which are related to their delaysτp and powers Ωp (cf. section 2.3.1). Finally, the DOAs of sub-paths constituting the different main paths follow a fixed laplacian distribution around the DOAs of the main paths. The corresponding channel parameters are summarised in Tab. A.4, where

2(0, )η σ denotes a normal distribution with zero mean and variance σ 2.

Channel Scenario Urban Outdoor Channel E

Number of paths, NP 18 Number of sub-paths per-path, NSP 20 Co

mm

on

Power delay spectrum HIPERLAN/2, Channel E Mean AS at BS EσAS,BS=21.4° BS per-path DOA distribution 2

,(0, )AS BSη σ

DO

As a

t BS

Per-path AS at BS (fixed) (Sub-path DOAs are laplacian distributed) 5°

Mean AS at MT EσAS,MT=68° MT per-path DOA distribution 2

,(0, )AS MTη σ

DO

As a

t M

T

Per-path AS at MT (fixed) (Sub-path DOAs are laplacian distributed) 35°

Tab. A.4: Channel parameters for MATRICE chain.

A.5.3 Results

The performance results presented in Fig. A.1, Fig. A.2, and Fig. A.3 are given in terms of the user-averaged BER versus the average SNR per bit defined in (3.49). A variable number of antennas and two different element spacings are considered. Since channel coding is considered here, the performance is compared at BER=10-4.

Fig. A.1 shows the single-user performace of J-MSINR, which is here equivalent to J-MRT. For a single antenna and a single user, J-MSINR with despreading at the receiver is equivalent to the conventional system with MRC. Hence, the corresponding curve represents the single-user bound of the conventional system and can be used as a reference. Compared to this reference curve J-MSINR with M=2 and M=4 transmit antennas spaced by ds=0.5λC achieves gains of 3 dB and 6.5 dB, respectively, which is slightly higher than the pure array gain thanks to spatial diversity. For efficiently exploiting the spatial diversity in this outdoor scenario caracterised by a moderate angle spread at the bastestation, the spacing has to be further increased. With an element spacing of ds=10λC , additional gains of 1.5 dB and 2 dB are achieved with M=2 and M=4 transmit antennas, respectively.

A.5: Numerical results with the MATRICE simulation chain


SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

M=1M=2 ds =0.5λcM=2 ds =10λcM=4 ds =0.5λcM=4 ds =10λc

SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

M=1M=2 ds =0.5λcM=2 ds =10λcM=4 ds =0.5λcM=4 ds =10λc

Fig. A.1: Single-user performance of J-MSINR with MATRICE chain (K=1).

Half- and fully-loaded systems are considered in Fig. A.2 (K=8) and Fig. A.3 (K=16), respectively. Increasing the number of active users leads to a higher level of MAI. If only a single antenna is employed for transmission, J-MSINR can only separate the users’ signals in frequency by pre-equalisation, which is sub-optimum compared to MUD schemes at the receiver (cf. section 4.5.4). Here, the considered system looses 1.5 dB for K=8 and more than 14 dB (not shown) for K=16 compared to the single-user bound. However, an efficient separation of users’ signals in space and frequency is obtained for multiple transmit antennas. For M=2, there are losses compared to the single-user J-MSINR performance of 0.5 dB (ds=0.5λC) and 1 dB (ds=10λC) at K=8 and around 2.5 dB at K=16. For M=4, these losses are lower than 0.5 dB at K=8 and 1 dB at K=16, respectively. Note that for multiple transmit antennas J-MSINR always performs better than the single-user bound of the conventional system, even at full load.

The presented results obtained with the MATRICE simulation chain and a sophisticated spatial channel model confirm the results obtained in the previous chapters, where a simplified spatial channel model was employed. This emphasises the potential of the proposed approaches in realistic environments. Future versions of advanced MATRICE simulation chains will also account for imperfect channel knowledge and could be used to confirm the results presented in chapter 6.

Appendix


SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1

M=1M=2 ds=0.5λcM=2 ds=10λcM=4 ds=0.5λcM=4 ds=10λc

SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1


Fig. A.2: Performance of J-MSINR with MATRICE chain (K=8).

SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1


SNR, γb

BER

-4 -2 0 2 4 6 8 10 12 14

10-4

10-3

10-2

10-1


Fig. A.3: Performance of J-MSINR with MATRICE chain (K=16).


Symbols xy element-wise vector product. ^ estimate of a variable or vector. ~ extended vector of length ML. (.)* complex conjugate. (.)H hermitian matrix transposition. (.)T matrix transposition. Xp,q element of the matrix X, p-th row, q-th column. (x over y) binomial coefficient. E. expected value. ℑ[.] imaginary part. ℜ[.] real part. . largest integer smaller than or equal to expression.

div(x,y) integer part of the division x/y. erfc(x) complementary error function of x. gm_eig(X,Y) dominant generalised eigenvector of matrix pair (X,Y). mod(x,y) reminder of the division of integers x/y. m_eig(X) dominant eigenvector of matrix X. rectT(t) rectangle function, equals 1 for t∈[-T/2,T/2[ and zero otherwise. sgn(x) sign of x. sinc(x) sin(πx)/(πx).

adB array gain in dB. a(θ) array response vector. Ag combined spreading and channel matrix of size K×ML for transmit filter g. AC combined spreading and channel matrix of size L×K for MUD. AP matrix of array response vectors. bg bit of user g. bg vector of length K having a one at element g and zeros otherwise. B bandwidth. BC size of coded block. Bcoh coherence bandwidth. BOFDM overall OFDM bandwidth. ck,l l-th element of the spreading code vector for user k. ck spreading code vector of length L for user k. C channel capacity. Cn Hadamard matrix of size n×n. d data vector of length K. dcoh coherence distance. dk complex data symbol of user k. dS element spacing of an ULA. DF , DT , DO frequency diversity, time diversity, and overall diversity. Eb mean energy of a bit. ES mean energy of a symbol. EP energy of a pilot symbol. f , fn frequency variable, frequency of carrier n. fC carrier frequency. fD Doppler shift. fD,max maximum Doppler shift.

Symbols


g considered user. gg pre-equalisation vector for user g. gg,l pre-equalisation weight for user g on chip l. G code generator in octal form. hB(τ,t) baseband impulse response of multipath channel. hg,m,l complex fading coeff. between basestation antenna m and terminal g on chip l. hB(τ,t) impulse response vector of multipath channel in the baseband. hg frequency-domain channel vector of length L for terminal g. h'g,l channel vector of length M for terminal g on chip l. HB(f,t) baseband transfer function of multipath channel. HB(f,t) vector transfer function of multipath channel (size M). HB channel coefficients in frequency domain. H’B channel observations in frequency domain. H channel matrix of a MIMO system size MR×MT . Hl channel matrix of size M×K on chip l. Ik(x) k-th order modified Bessel function of the first kind. In identity matrix of size n×n. j 1− . J cost function. Jk(x) k-th order Bessel function of the first kind. k user index. K number of active users. KC constraint length of convolutional code. KRice Ricean factor. l chip index. L, LF , LT spreading factor, spreading factors in frequency and time dimension, respectively. m antenna index. M, MT, MR number of antennas, number of antennas at transmitter and receiver, respectively. MC QAM constellation size. n noise vector of length L. N0 spectral density of the AWGN. NC number of subcarriers. NF number of OFDM symbols per frame. NP number of paths in multipath channel. NPF , NPT pilot spacing in frequency and time dimension. NS number of samples. NSP number of sub-paths in multipath channel. Ntap number of filter taps. OP overhead introduced by pilot symbols. p path index. p(x) probability density function. P(x) probability of x. PE bit error probability. PD,g desired signal power after despreading at terminal g. Pk signal power of user k. PMAI(k→g) interference power of user k at terminal g. qg,l coefficient for chip combining on chip l. qg chip combining vector of length L for terminal g. Q linear MUD matrix of size L×K. rS radius of a circular array. r scrambling vector of length L.

Symbols


RC , R’C code rate, mother code rate. R log-term spatial covariance matrix of size M×M. RI long-term spatial covariance matrix of size M×M for interference and noise.

LR instantaneous covariance matrix averaged over L chip positions. CNR instantaneous covariance matrix averaged over NC subcarriers.

s(t ) modulated signal in the baseband. S(f ) power density spectrum. t time variable. Tcoh coherence time. TC sampling time. TF frame duration. TG guard interval duration. TS , TS' symbol time, overall symbol time. T(ζ) number of sign changes between consecutive elements of ζ. T focusing matrix for coherent wideband array processing. uk,g overall frequency response vector of length L for user k at terminal g. uk,g,l l-th element of uk,g. v mobile velocity. v0 velocity of light (∼3⋅108 m/s). vk,g combined spreading and channel vector of length ML for filter g. wk,m,l transmit filtering coefficient of user k, antenna m, and chip l. wk transmit filter of length M for terminal k. w'k,l transmit filter of length M for terminal k on chip l.

kw auxiliary filter vector according to some temporary definition. xi,n , xP,i,n complex symbol, or pilot symbol, at instant i on subcarrier n. x complex symbol vector in the frequency domain of length L. y received signal. y received signal vector.

α,αp real amplitude, amplitude of path n. β number of bits per symbol. χn,i noise sample of subcarrier n at instant i δ(t) Dirac delta function. ∆f frequency spacing. ∆t time spacing. ∆θmax maximum angular separation. ∆γP loss due to pilot insertion. φA(.),φA,norm(.) auto correlation function, normalised auto correlation function. φC(.),φC,norm(.) cross correlation function, normalised cross correlation function. Φ autocorrelation matrix. γb signal to noise ratio per information bit. γS signal to noise ratio per symbol. γC signal to noise ratio per chip. γI,g signal to interference plus noise ratio for user g. γMI,g modified signal to interference plus noise ratio for user g. γ 'MI,g,l modified signal to interference plus noise ratio for user g on chip l. γP signal to noise ratio on pilot symbols. ϕm discrete angle. ϕp phase of path p. ϕ cross correlation vector. κ real scalar.

Symbols


λ real scalar. λC carrier wavelength. µ complex scalar. νg amplitude of the desired symbol after soft de-mapping. θ azimuth angle. θB , θM angle at basestation and mobile, respectively. θ mean angle. ρAS(θ) power azimuth spectrum of the multipath channel. ρB(τ) power delay spectrum of the multipath channel. ρCE correlation between fading amplitudes of the channel.

2Cσ variance of the Gaussian noise on each chip.

σD Doppler spread. 2MAIσ variance of the multiple access interference. 2nσ variance of the Gaussian noise after chip combining.

σθ angle spread. στ RMS delay spread. τ,τp delay variable, delay of path p. τmax maximum channel delay. τU delay between estimation and usage of CSI. τ mean multipath delay. ϖ interpolation filter coefficient. Ω, Ωp power of the fading amplitude, power of the fading amplitude of path p. ΩA(K) active spreading code set. ΩC spreading code set. Ω0(K) optimised code set. ζ product vector of spreading codes.

Lg log-likelihood-ratio of bits for user g.

Acronyms


Acronyms A/D Analogue Digital conversion AS Angle Spread AWGN Additive White Gaussian Noise BEP Bit Error Probability BER Bit Error Rate BPSK Binary Phase Shift Keying BF Beamforming BS Basestation CDMA Code Division Multiple Access COST European Cooperation in the Field of Scientific and Technical Research CSI Channel State Information D/A Digital Analogue conversion DAB Digital Audio Broadcast DFT Discrete Fourier Transform DL Downlink DOA Direction of Arrival DOD Direction of Departure DS-CDMA Direct Sequence CDMA DVB-T Terrestrial Digital Video Broadcast EGC Equal Gain Combining EGT Equal Gain Transmission ETSI European Telecommunications Standard Institute FDD Frequency Division Duplex FDMA Frequency Division Multiple Access FFT Fast Fourier Transform GSM Global System for Mobile communications IC Interference Cancellation ICI Inter Carrier Interference IDFT Inverse Discrete Fourier Transform IFFT Inverse Fast Fourier Transform IMT-2000 International Mobile Telecommunications 2000 IP Internet Protocol ISI Inter Symbol Interference ITU International Telecommunications Union J-MRT Joint Maximum Ratio Transmission J-MSINR Joint Maximisation of the Signal to Interference plus Noise Ratio J-ZF Joint Zero Forcing LAN Local Area Network LLR Log-Likelihood Ratio LOS Line Of Sight MAI Multiple Access Interference MAP Maximum A Posteriori MC Multi-Carrier MC-DS-CDMA Multi-Carrier Direct Sequence CDMA MC-CDMA Multi-Carrier CDMA MIMO Multiple Input Multiple Output MISO Multiple Input Single Output ML Maximum Likelihood MLSE Maximum Likelihood Sequence Estimator MMSE Minimum Mean Squared Error MMSEC Minimum Mean Squared Error Combining MMSE-MUD MMSE based Multi-User Detection MRC Maximum Ratio Combining MRT Maximum Ratio Transmission MSE Mean Squared Error MSINR Maximisation of the Signal to Interference plus Noise Ratio

Acronyms


MT Mobile Terminal MU Multi-User MU-BF Multi-User Beamforming MU-BF-inst Multi-User Beamforming employing inst. cov. matrix averaged over L chip positions MU-BF-long Multi-User Beamforming employing long-term cov. matrix MU-Eigen Multi-User Eigenvector-based beamforming MU-MVDR Multi-User MVDR-based beamforming MUD Multi-User Detection MVDR Minimum Variance Distortionless Response NLOS Non Line Of Sight OFDM Orthogonal Frequency Division Multiplex ORC Orthogonality Restoring Combining PAPR Peak to Average Power Ratio PC-MRT Per-Carrier Maximum Ratio Transmission PC-MSINR Per-Carrier Maximisation of the Signal to Interference plus Noise Ratio PC-ZF Per-Carrier Zero Forcing PIC Parallel Interference Cancellation PSK Phase Shift Keying QAM Quadrature amplitude modulation QoS Quality of Service QPSK Quaternary Phase Shift Keying RF Radio Frequency RMS Root Mean Square SDMA Space Division Multiple Access SDR Software Defined Radio SFTF Space Frequency Transmit Filtering SIC Successive Interference Cancellation SIMO Single-Input-Single-Output SINR Signal to Interference plus Noise Ratio SISO Single-Input-Single-Output SNR Signal to Noise Ratio STBC Space-Time Block Codes STC Space-Time Coding STTC Space-Time Trellis Codes SU Single-User SU-BF Single-User Beamforming SU-BF-inst Single-User Beamforming employing inst. cov. matrix averaged over L chip positions SU-BF-instNc Single-User Beamforming employing inst. cov. matrix averaged over NC subcarriers SU-BF-long Single-User Beamforming employing long-term cov. matrix SU-Conv Single-User Conventional beamforming SU-Eigen Single-User Eigenvector-based beamforming SUD Single-User Detection TDD Time Division Duplex TDMA Time Division Multiple Access UCA Uniform Circular Array ULA Uniform Linear Array UL Uplink UMTS Universal Mobile Telecommunications System W-H Walsh-Hadamard WLAN Wireless Local Area Network ZF Zero Forcing ZF-MUD ZF-based Multi-User Detection 2G Second Generation of mobile wireless systems 3G Third Generation of mobile wireless systems 3GPP Third Generation Partnership Project

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[WWRF01] Wireless World Research Forum, ‘Book of visions 2001,’http://www.wireless-world-research.org/.

[YeLi99] C.S. Yeh, Y. Lin, ‘Channel Estimation using Pilot Tones in OFDM systems,’ IEEE Transact. on Broadcasting, vol. 45, no. 4, pp. 400-408, Dec 1999.

[YiLi93] N. Ye, J.P. Linnartz, G. Fettweis, ‘Multicarrier-CDMA in indoor wireless radio networks,’ IEEE Proc. of PIMRC’93, vol. 1, pp. 109-113, Sept. 1993.

[ZeOt95] P. Zetterberg, B. Ottersten, ‘The Spectrum Efficiency of a Base Station Antenna Array System for Spatially Selective Transmission,’ IEEE Transact. on Vehicular Technology, vol. 44, no. 3, pp. 651-660, Aug 1995.

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Publications of the author


Publications of the author [MoSä04] D. Mottier, T. Sälzer, ‘Spreading Sequence Assignment in the Downlink of OFCDM

Systems Using Multiple Transmit Antennas,’ to be presented at VTC’04 Spring, 2004.

[SäMo01] T. Sälzer, D. Mottier, L. Brunel, ‘Influence of system load on channel estimation in MC-CDMA mobile radio communication systems,’ IEEE Proc. of VTC’01 Spring, vol. 1, pp. 522-526, May 2001.

[SäMo03a] T. Sälzer, D. Mottier, ‘Transmit beamforming for SDMA in multi-carrier CDMA downlink on a per subcarrier basis,’ IEEE Proc. of ICT’03,vol. 1 , pp. 793-798, Feb. 2003.

[SäMo03b] T. Sälzer, D. Mottier, D. Castelain, ‘Comparison of antenna array techniques for the downlink of multi-carrier CDMA systems,’ IEEE Proc. of VTC’03 Spring, vol. 1 , pp. 316-320, April 2003.

[SäMo03c] T. Sälzer, D. Mottier, ‘Downlink Strategies Using Antenna Arrays for Interference Mitigation in Multi-Carrier CDMA,’ Proc. of int. Workshop on Multi-Carrier Spread Spectrum & Rel. Topics (MC-SS’03), pp. 315-325, Sept. 2003.

[SäSi03] T. Sälzer, A. Silva, A. Gameiro, D. Mottier, ‘Pre-Filtering Using Antenna Arrays for Multiple Access Interference Mitigation in Multi-Carrier CDMA Downlink,’ Proc. of IST Mobile & Wireless Communications Summit 2003, vol. 1, pp. 175-179, June 2003.

Patents of the author D. Mottier, T. Sälzer ‘Method of allocating transmission power level to pilot symbols used for estimating the channel of a transmission system of the multi-carrier type with spreading of the signal in the frequency domain by spreading sequences,’ European patent 1189370, publication Oct. 2002.

T. Sälzer ‘Multi-Carrier CDMA downlink transmission method,’ European patent 1396956, publication March 2004.

D. Mottier, T. Sälzer ‘Method of assigning one or more spreading sequences to users of a multi-carrier transmission network,’ European patent 03292148.8, filing Sept. 2003.

these doctorat d’electronique thomas sÄlzer … · frequency domain is a promising candidate for...

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