super orthogonal double space-time trellis coding
TRANSCRIPT
Super Orthogonal Double Space-Time Trellis
Coding
للأنظمة الزمكانية المزدوجة فائق التعامدالترميز الشبكي
By
Mohammed As’ad Tubail
Supervised by
Dr. Ammar M. Abu Hudrouss
Associate Prof. of Electrical
Engineering
Dr. Mohammed Taha El Astal
Assistant Prof. of Electrical
Engineering
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Engineering in Electrical Engineering
July/2018
زةــغ – ةــلاميــــــة الإســـــــــامعـالج
عمادة البحث العلمي والدراسات العليا
ة الهندســــــــــــــــــةــــــــــــــــــــليـك
ماجستيـــــــر الهندســــة الكهربائيـــة
The Islamic University–Gaza
Deanship of Research and Graduate Studies
Faculty of Engineering
Master of Electrical Engineering
I
إقــــــــــــــرار
أنا الموقع أدناه مقدم الرسالة التي تحمل العنوان:
Super Orthogonal Double Space-Time Trellis Coding
للأنظمة الزمكانية المزدوجة فائق التعامدالترميز الشبكي أقر بأن ما اشتملت عليه هذه الرسالة إنما هو نتاج جهدي الخاص، باستثناء ما تمت الإشارة إليه حيثما ورد، وأن هذه
لنيل درجة أو لقب علمي أو بحثي لدى أي مؤسسة تعليمية أو نالاخري الرسالة ككل أو أي جزء منها لم يقدم من قبل
بحثية أخرى.
Declaration
I understand the nature of plagiarism, and I am aware of the University’s policy on this.
The work provided in this thesis, unless otherwise referenced, is the researcher's own
work, and has not been submitted by others elsewhere for any other degree or
qualification.
:Student's name محمد أسعد طبيل اسم الطالب:
:Signature محمد طبيل التوقيع:
:July/2018 Date التاريخ:
II
III
Abstract
Multiple-Input-Multiple-Output (MIMO) technique is a technology that offers a good
solution for high data rate wireless systems. Space-Time Coding (STC) is a coding technique that
aims to benefit from the MIMO systems by introducing a correlation between the transmitted
signals. Space-Time Block Coding (STBC) and Space-Time Trellis Coding (STTC) are two main
approaches of STC and many of researches discussed them.
Super Orthogonal Space Time Trellis Coding (SO-STTC) and Super Orthogonal
Trellis Coded Spatial Modulation (SOTC-SM) are two schemes that combine the
advantages of STBC and STTC and provide high error performance. However, they suffer
from high decoding complexity and low performance in the high data rates due to the high
number of branches that occurred in the trellis structure.
In this research, a novel MIMO transmission scheme is proposed that directly
combines the Super Orthogonal-STBC (SO-STBC) and the trellis coding technique. The
new scheme reduced the number of branches in the trellis using double space diversity
approach. Hence, the decoding complexity was reduced and also the error performance
was improved in the high rates.
The encoding process of the proposed scheme passes through several steps. Dividing the
overall system into two identical and independent systems with a half of the rate for each is the
first step, then the set-partitioning for SO-STBC is performed. Finally, the encoder assigns the
trellis’s branches with the appropriate codes. In the decoding process, the receiver uses Minimum-
Mean-Square-Error (MMSE) algorithm with interference cancellation to decode the received
symbols.
Multiple designs of the new scheme were proposed and simulated using MATLAB
simulation environment. The simulation results showed that an improvement in the error
performance over SO-STTC and SOTC-SM was achieved in the high rate. Also, the complexity
calculations of the proposed designs were calculated and showed that they were less complexity
compared to the recently developed schemes.
IV
ملخص الدراسة
رسال البيانات إتعتبر تقنيات الاتصال متعددة المداخل والمخارج من التقنيات المهمة والتي ساهمت في زيادة سرعة رسال والاستقبال تهدف أنظمة الترميز الزمكانية لتوفير تقنيات للاستفادة من تعدد هوائيات الإ، و عبر الموجات اللاسلكية
نظام الترميز الزمكاني :شارات المرسلة، ويعتبر من أهم أنواع هذه الأنظمةبين الإحداث تداخل مدروس إمن خلال اللذين لقيا، و (space time trellis coding)والترميز الزمكاني الشبكي (space time block coding)الكتلي
كبيرين من قبل الباحثين. واهتماما رواجا
Super orthogonal space): نظام الترميز الشبكي فائق التعامد تستخدم أنظمة الترميز فائقة التعامد مثل
time trellis coding) ونظام الترميز المكاني المرمز شبكيا فائق التعامد(super orthogonal trellis coded
spatial modulation) إلا أن هذه الأنظمة تعاني بشدة منة الإرسالنظمأتحسن نوعي على كفاءة إضافة في ، العالية الارسال في الأنظمة ذات سرعات ةكفاءالفي عملية فك الترميز بالإضافة إلى محدودية مشكلة التعقيد الكبير
.نتيجة للزبادة الكبيرة االتي تحصل في عدد التفرعات الحاصلة في الشكل الشبكي للنظام
قة التعامد وأنظمة الترميز الشبكية، في هذا البحث، سنقدم ترميزا جديدا يدمج بين أنظمة الترميز الكتلية فائمن خلال استخدام طريقة الارسال التنوعي المزدوج بالتقليل من عدد التفرعات الحاصلة بحيث يقوم هذا النظام الجديد
سرعات العالية.العملية فك التشفير بالإضافة إلى تحسنا أكبر في كفاءة النظام في في تعقيدوبالتالي التقليل من ال
حلة الترميز للنظام الجديد بمجموعة من الخطوات تبدأ بتقسيم النظام الكلي إلى نظامين منفصلين تمر مر ومتماثلين يعمل كل منهما على نصف معدل ارسال البيانات، ثم يتم عمل تقسيم لأنظمة الترميز الكتلية فائقة التعامد
يستخدم المستقبل في عملية فك رمز المناسب له.كي يستطيع النظام في النهاية اسناد كل فرع من الشكل الشبكي بال مع خوارزمية الغاء التداخل لفك ترميز البيانات المستقبلة. (MMSE)الترميز خوارزمية أقل معدل تربيعي للخطأ
وقد أظهرت النتائج ،MATLABومحاكاة نتائجها باستخدام بيئة المحاكاة التصميمات من مجموعة عمل تم ،مقارنة بالأنظمة فائقة التعامد الأخرى لعاليةالحطأ وكفاءة النظام عند معدلات الارسال اتحسن في معدل وجود
بالإاضفة إلى أنه تم حساب معدلات التعقيد في عملية فك الترميز حيث أظهرت القيم المحسوبة أن درجة التعقيد في .الأخرى الشبيهة الأنظمة في نظيرتها من أقلالنظام الجديد
V
Dedication
To my country, Palestine
To my beloved father
Who taught me the value of study and perseverance ethic
To my beloved mother
Who gave me the most precious thing she has
To my dear wife
For her patience and endless support
To the soul of my dear brother, Ahmed
I ask Allah to make his abode in His spacious gardens
To my brothers and my sister
For their support
To my beloved son and daughter
For their sweet smiles
To my special friends
VI
Acknowledgment
First of all, without the enlightenment of ALLAH, this work would not have been
done successfully.
My sincere appreciation goes to Dr. Ammar M. Abu-Hudrouss and Dr. Mohammed
El Astal for their valuable guidance, motivation, patience and encouragement. I have
benefited tremendously from their enthusiasm, understanding, and patience. Also, I would
also like to thank the committee members, Dr. Talal Skaik and Dr. Yousef Hamouda for
their time in reviewing my thesis.
I would mostly like to thank my parents, my wife, my brothers and my sister who's
constant and endless support, motivation, and unwavering belief in me had a great part in
nurturing my dreams and bringing this work to completion. I regret that I cannot be with
them for most of the time. The only thing I can do is to work harder and make them feel
proud of me.
Last but not least, all thanks to anyone who prayed for me.
Mohammed As’ad Tubail
July, 2018
VII
Table of Contents
Declaration ......................................................................................................................... I
Abstract ........................................................................................................................... III
Dedication ........................................................................................................................ V
Acknowledgment ............................................................................................................ VI
Table of Contents ........................................................................................................... VII
List of Tables ................................................................................................................... X
List of Figures ................................................................................................................. XI
List of Abbreviations ................................................................................................... XIV
Chapter 1 Introduction ................................................................................................... 2
1.1 Introduction ........................................................................................................... 2
1.2 Motivations: .......................................................................................................... 3
1.3 Literature Review:................................................................................................. 4
1.4 Problem Statement: ............................................................................................... 6
1.5 Thesis Contribution: .............................................................................................. 6
1.6 Thesis Organization: ............................................................................................. 7
Chapter 2 Thesis’s Background .................................................................................. 10
2.1 Wireless Channel Characteristics: ...................................................................... 10
2.1.1 Additive White Gaussian Noise (AWGN): ........................................ 10
2.1.2 Large Scale Models: ........................................................................... 11
2.1.3 Multipath Channels: ........................................................................... 16
2.2 MIMO Systems: .................................................................................................. 18
2.3 Space Time Block Codes: ................................................................................... 20
2.3.1 STBC Encoder: ................................................................................... 20
2.3.2 Alamouti’s STBC: .............................................................................. 21
2.3.3 Super Orthogonal Space-Time Block Codes (SO-STBC): ................ 24
2.4 Spatial Modulation (SM): ................................................................................... 25
2.4.1 Spatial Modulation coding: ................................................................ 25
2.4.2 Spatial modulation decoding and performance: ................................. 27
VIII
2.5 Space-Time Block Coded Spatial Modulation (STBC-SM): .............................. 28
2.5.1 STBC-SM coding: .............................................................................. 28
2.6 Double Space-Time Transmit Diversity (DSTTD): ............................................ 29
2.6.1 DSTTD model: ................................................................................... 29
2.6.2 Minimum-mean square error (MMSE) interference cancellation for
DSTTD: 31
2.7 Conclusion: ......................................................................................................... 33
Chapter 3 Space-Time Trellis Coding Schemes ..................................................... 35
3.1 Trellis coded Modulation (TCM):....................................................................... 35
3.2 Space-Time Trellis Codes (STTC): .................................................................... 37
3.2.1 STTC Encoding: ................................................................................. 37
3.2.2 STTC Decoding: ................................................................................. 39
3.3 Super-Orthogonal Space-Time Trellis Coding (SO-STTC): .............................. 42
3.3.1 Set partitioning of SO-STBCs: ........................................................... 42
3.4 Spatial Modulation with trellis coding (SMTC): ................................................ 46
3.4.1 SMTC coding: .................................................................................... 46
3.4.2 SMTC decoding and performance: .................................................... 48
3.5 Super-Orthogonal trellis Coded Spatial Modulation (SOTC-SM): .................... 49
3.5.1 Construction of SOTC-SM codebooks: ............................................. 49
3.5.2 SOTC-SM decoding and performance: .............................................. 52
3.6 Conclusion: ......................................................................................................... 54
Chapter 4 Super Orthogonal Double Space-Time Trellis Coding (SO-DSTTC)56
4.1 SO-DSTTC Encoding: ........................................................................................ 57
4.2 Set partitioning of the super-set of STBCs: ........................................................ 59
4.3 SO-DSTTC Trellis structure for different states: ................................................ 62
4.4 Rotating angles optimization: ............................................................................. 65
4.5 ML decoding with interference cancellation (IC) for SO-DSTTC scheme: ....... 66
4.6 Complexity of SO-DSTTC decoder:................................................................... 69
4.7 Conclusion: ......................................................................................................... 73
Chapter 5 Simulation Results .................................................................................. 75
5.1 Results for spectral efficiency of 3 b/s.Hz: ......................................................... 75
5.2 Results for spectral efficiency of 4 b/s.Hz: ......................................................... 77
IX
5.3 Comparison between using two-step MMSI-IC and using only one-step: ......... 80
5.4 Conclusion: ......................................................................................................... 82
Chapter 6 Conclusion and Future Works............................................................... 84
6.1 Conclusion: ......................................................................................................... 84
6.2 Future Works: ..................................................................................................... 86
The Reference List ........................................................................................................ 88
X
List of Tables
Table (2.1): SM mapping table (R. Y. Mesleh et al., 2008). .......................................... 26
Table (2.2): The mapping rule for 2 b/s.Hz and BPSK modulation (Basar et al., 2011b).
......................................................................................................................................... 29
Table (3.1): The trellis state transition matrices for SOTC-SM (Başar, Aygölü, Panayırcı,
& Poor, 2012). ................................................................................................................. 52
Table (4.1): The offset array of O4 for 16QAM: ............................................................ 60
Table (4.2): The optimized rotating angles of SO-DSTTC in Figures (4.4) - (4.7) ........ 65
Table (4.3): Number of operations required by the stages of the branch metric for a rate
of 3 b/s.Hz ........................................................................................................................ 71
Table (4.4): Number of operations required by the stages of the branch metric for a rate
of 4 b/s.Hz ........................................................................................................................ 71
Table (4.5): Number of operations required by SO-STTC and SOTC-SM ML decoder:
......................................................................................................................................... 72
XI
List of Figures
Figure (2.1): Path Loss, Shadowing and Multipath versus Distance (Goldsmith, 2005).
......................................................................................................................................... 12
Figure (2.2): Friis transmission model. ........................................................................... 12
Figure (2.3): Two-Ray model (Kim, 2015). ................................................................... 14
Figure (2.4): Knife-Edge model (Goldsmith, 2005). ...................................................... 15
Figure (2.5): Transmitted signals and its reflected versions (Kim, 2015). ..................... 17
Figure (2.6): MIMO system model (Vucetic & Yuan, 2003). ........................................ 19
Figure (2.7): The general block diagram for STBC implementation. ............................ 21
Figure (2.8): The encoding block diagram of Alamouti’s STBC. .................................. 22
Figure (2.9): Symbol error probability of Alamouti’s STBC with QPSK symbols and one
receive antenna (Hamid Jafarkhani, 2005). ..................................................................... 24
Figure (2.10): SM system model. ................................................................................... 26
Figure (2.11): The BER of SM over ideal channel with 6 bits/s.Hz (R. Y. Mesleh, Haas,
Sinanovic, Ahn, & Yun, 2008) ........................................................................................ 27
Figure (3.1): Set partitioning of 8-PSK constellation (Hamid Jafarkhani, 2005). .......... 36
Figure (3.2): The trellis structure for the set-partitioning in Figure (3.1) (Hamid
Jafarkhani, 2005). ............................................................................................................ 37
Figure (3.3): Trellis diagram for 4-state STTC with QPSK symbols and 2 transmit
antennas. .......................................................................................................................... 38
Figure (3.4): Frame error rate of STTC for 4-PSK using two transmit antennas and two
receive antennas with rate 2 b/s.Hz (Tarokh, Seshadri, & Calderbank, 1998). ............... 41
Figure (3.5): Frame error rate of STTC for 4-PSK using two transmit antennas and two
receive antennas with rate 3 b/s.Hz (Tarokh et al., 1998). .............................................. 41
Figure (3.6): The set-partitioning of SO-STBCs for BPSK with θ = (0, π) (Hamid
Jafarkhani, 2005). ............................................................................................................ 43
Figure (3.7): The trellis structure for 4-state SO-STTC with r = 2 b/s.Hz using QPSK
codes (Hamid Jafarkhani, 2005). ..................................................................................... 44
Figure (3.8): The trellis structure for 4-state SO-STTC with r = 3 b/s.Hz using 8-PSK
codes (Hamid Jafarkhani, 2005). ..................................................................................... 44
Figure (3.9): FER of SO-STTCs for 2 b/s.Hz with two transmit antennas and two receive
antennas (Hamid Jafarkhani, 2005). ................................................................................ 45
Figure (3.10): FER of SO-STTCs for 3 bits/s.Hz with two transmit antennas and two
receive antennas (Hamid Jafarkhani, 2005). .................................................................... 46
XII
Figure (3.11): SMTC system model. .............................................................................. 47
Figure (3.12): The trellis structure for 4-state SMTC with 4 transmit antennas (Basar,
Aygolu, Panayirci, & Poor, 2011a). ................................................................................. 47
Figure (3.13): The BER performance of SM-TC with 4, 8 and 16 states at 2 b/s.Hz (Basar
et al., 2011a). .................................................................................................................... 48
Figure (3.14): The BER performance of SM-TC with 8 and 16 states at 3 b/s.Hz (Basar
et al., 2011a). .................................................................................................................... 49
Figure (3.15): The set partitioning of STBC-SM codewords for QPSK, 8-PSK and 16-
QAM (Başar et al., 2012). ................................................................................................ 50
Figure (3.16): The trellis diagram for 4-state SOTC-SM using QPSK for 2 bits/s.Hz or 8-
PSK for 3 bits/s.Hz or 16-QAM for 4 bits/s.Hz (Başar et al., 2012). .............................. 51
Figure (3.17): FER performance of SOTC-SM codes with 2, 4 and 8-state at 2 bits/s.Hz
(Başar et al., 2012). .......................................................................................................... 53
Figure (3.18): FER performance of SOTC-SM codes with 2, 4 and 8-state at 3 bits/s.Hz
(Başar et al., 2012). .......................................................................................................... 54
Figure (4.1): SO-DSTTC encoder’s block diagram. ...................................................... 57
Figure (4.2): The set partitioning of STBC codewords for 8-PSK. ................................ 61
Figure (4.3): The set-partitioning of STBC codewords for QPSK. ................................ 61
Figure (4.4): A 4-state SO-DSTTC with r = 3 b/s.Hz and QPSK (the first code trellis
structure). ......................................................................................................................... 62
Figure (4.5): An 8-state SO-DSTTC with r = 3 b/s.Hz and QPSK (the first code trellis
structure). ......................................................................................................................... 63
Figure (4.6): An 8-state SO-DSTTC with r = 3 b/s.Hz and QPSK (the first code trellis
structure). ......................................................................................................................... 64
Figure (4.7): A 4-state SO-DSTTC with r = 4 b/s.Hz and QPSK (the first structure only).
......................................................................................................................................... 65
Figure (4.8): A 4-state SO-DSTTC with r = 3 b/s.Hz using QPSK. .............................. 70
Figure (5.1): FER performance for 4- and 8-state SO-DSTTC and SO-STTC at 3 b/s.Hz.
......................................................................................................................................... 76
Figure (5.2): FER performance for 4- and 8-state SO-DSTTC and SOTC-SM at 3 b/s.Hz.
......................................................................................................................................... 77
Figure (5.3): BER performance for 4-state and 8-state SO-DSTTC at 4 b/s.Hz. ........... 78
Figure (5.4): FER performance for 4-state and 8-state SO-DSTTC at 4 b/s.Hz. ........... 78
Figure (5.5): FER performance for 4-state SO-DSTTC, SOSTTC and SOTC-SM at 4
b/s.Hz. .............................................................................................................................. 79
XIII
Figure (5.6): FER performance of SO-DSTTC at 3 and 4 b/s.Hz. ................................. 80
Figure (5.7): FER performance for 4-state SO-DSTTC with and without two-step
decoding. .......................................................................................................................... 81
XIV
List of Abbreviations
AWGN Additive Wight Gaussian Noise
BER Bit Error Rate
BPSK Binary Phase Shift Keying
CGD Coding Gain Distance
CSI Channel State Information
DSTTD Double Space Time Transmit Diversity
ESM Enhanced Spatial Modulation
FER Frame Error Rate
IC Interference Cancellation
ICI Inter Channel Interference
MIMO Multiple Input Multiple Output
ML Maximum Likelihood
MMSE Minimum Mean Square Error
MRRC Maximum Ratio Receiving Combining
MSE Mean Square Error
OFDM Orthogonal Frequency Division Multiplexing
QAM Quadrature Amplitude Modulation
QPSK Quadrature Phase Shift Keying
QSM Quadrature Spatial Modulation
SER Symbol Error Rate
SM Spatial Modulation
SMTC Spatial Modulation with Trellis Coding
SNR Signal to Noise Ration
SO-STBC Super Orthogonal Space Time Block Codes
SO-STTC Super Orthogonal Space Time Trellis Coding
SOTC-SM Super Orthogonal Trellis Coded Spatial Modulation
STBC Space Time Block Coding
STBC-CSM Space-Time Block Coded Spatial with Cyclic Structure
STBC-SM Space Time Block Coded Spatial Modulation
STC Space Time Coding
STTC Space Time Trellis Coding
TCM Trellis Coded Modulation
TCSM Trellis Coded Spatial Modulation
V-BLAST Vertical-Bell Laboratories Layered Space-Time
1
Chapter 1
Introduction
2
Chapter 1
Introduction
1.1 Introduction
Wireless communication systems become one of the most important parts in our
modern life and their applications are almost found in every aspect of life. The demand
on the wireless systems with higher data rates is increasing strongly due to the rapid
technological revolution. Therefore, systems with higher data rates becomes more
appealing to the consumers.
Achieving high data rates is not an easy process in the presence of channel fading
and multipath propagation impacts. Channel effects impact strongly the transmission
process and limits the possibility to reach the optimum capacity limit (Shanon capacity).
Many techniques and research efforts were proposed to enhance the channel
capacity in the presence of multipath fading phenomenon and reach Shanon’s limit. These
efforts include but not limited to Turbo coding, Orthogonal Frequency Division
Multiplexing (OFDM) and Multiple Input Multiple Output (MIMO) technologies
(Vucetic & Yuan, 2003).
MIMO technology offers a good solution for high data rate wireless systems and it
has a key role in the current and future communication systems such as 4G/5G of mobile
communications and WiMAX. It is basically based on the use of multiple antennas in both
the transmitter and the receiver, which results in a significant increase on the transmission
rate and minimization of the bit error rate. While MIMO technology offers a significant
enhancement in the spectral and power efficiencies, the systems become more complex
(Jankiraman, 2004).
The initial work of multiple transceiver antennas was initiated by the marvellous
work of Winter (Winters, June 1987), Foschini (FOSCHINI & GANS, 1998), and Telatar
(Telatar, Nov, 1999). They had predicted remarkable spectral efficiency for MIMO
wireless systems.
3
To enhance the performance of the MIMO systems, an effective and practical
channel-coding technique called Space-Time Coding (STC) is employed. STC is a coding
technique which introduces a correlation between transmitted signals from multiple
antennas in different periods of time (Vucetic & Yuan, 2003). Using this approach, error
rate can be minimized in the channel and enhancement occurs in spectral efficiency
without any increase in the bandwidth.
There are mainly two types of STC: Space-Time Block Coding (STBC) and Space-
Time Trellis Coding (STTC). In STBC, the encoder deals with the input stream as
separated blocks then transmits them over time and space. In contrast, STTC encoder
transmits multiple trellis codes over space and time. STTC can simultaneously offers a
substantial coding gain, spectral efficiency, and diversity improvement on flat fading
channels while STBC offers only full diversity gain. However, STBC offers simplicity at
both transmitter and receiver.
In this thesis, we will introduce a novel technique based on the both STBC and
STTC that increase the spectral efficiency and error performance of the wireless systems
considered.
1.2 Motivations:
Channel capacity and power efficiency are the most important factors in any
communication system. Multipath fading phenomena pose a barrier to increase the
channel capacity in the ordinary schemes. Most of modulation schemes have a poor
performance in multipath fading channels and cannot achieve the demand for high data
rate and high spectral efficiency, whereas STC codes with MIMO systems introduce a
better solution for this problem.
STC codes include different approaches that each one has its own advantages. For
example, STBC schemes can offer full diversity gain with simple decoding algorithm,
while STTC provides coding gain beside the diversity gain. STTC codes use Viterbi
algorithm in decoding process which has a high complexity. A novel transmission scheme
was proposed called Spatial Modulation (SM). In this scheme only one transmitting
4
antenna is active at each time instant. Therefore, Inter-Channel Interference (ICI) and the
need for synchronization in the receiver are avoided, also the receiving algorithm is less
complexity. In addition, SM increases the spectral efficiency by the base-two logarithm
of the total number of transmit antennas (R Mesleh, Haas, Sinanovic, Ahn, & Yun, July
2008).
The combination between these codes, such as the case of Super Orthogonal Trellis
Coded Spatial Modulation (SOTC-SM) and Super Orthogonal Space Time Trellis Code
(SO-STTC), can lead to systems with higher spectral efficiency, high error performance
compared with similar systems.
1.3 Literature Review:
There are many efforts and researches cover the MIMO systems and the
corresponding STCs. Alamouti’s code is the first STBC that was produced to give the full
diversity to MIMO system with 2 transmit antennas (Alamouti, 1998). This scheme was
generalized in (Tarokh, Jafarkhani, & Calderbank, 1999a) to any number of transmit
antennas.
A new approach, called ‘Double Space Time Transmit Diversity’ (DSTTD), was
proposed in (Naguib, Seshadri, & Calderbank, 1998), (Naguib, Seshadri, & Calderbank,
2000). Its system consists of two Alamouti’s STBC at the transmitter and an interferer-
resistance decoder at the receiver. This approach improved the spectral efficiency of the
system and benefit from the diversity gain of the structure of Alamouti’s code. Besides
that, the main disadvantage of DSTTC is the interference which increases the complexity
of the decoder. This disadvantage is mitigated in (Lee & Shieh, 2011) by using a
cancellation technique that separate the two STBC codes and decrease the needed
operations for the decoder.
Another category of STCs, STTC, was first introduced in 1998 by Tarokh, Seshadri
and Calderbank in (Tarokh, Seshadri, & Calderbank, March 1998). This novel technique
provided improved error performance for wireless communication. In (H Jafarkhani &
Seshadri, 2003, April), the authors introduced a new scheme that improved the
5
performance of STTC by more than 2 dB and also provided a systematic method to
maximize the coding gain for a given rate, constellation, and number of states.
In (Hamid Jafarkhani & Seshadri, 2003) a novel scheme was realized by
concatenating the Alamouti’s STBC symbols drawn from Phase Shift Keying (PSK)
constellation scheme with an outer trellis code. This scheme is called ‘Super Orthogonal
Space-Time Trellis Code’ (SO-STTC). This scheme suffers from high number of parallel
branches which negatively impact the performance of the system.
SM concept was first introduced in 2008 by Mesleh in (R. Y. Mesleh, Haas, &
Sinanovic, July 2008) and he also proposed a Trellis Coded Spatial Modulation (TCSM)
in (Raed Mesleh, Stefan, Haas, & Grant, Feb, 2009), (Raed Mesleh, Renzo, Haas, & Grant,
July 2010). In TCSM scheme, the incoming sequence of bits is divided into two groups,
the second group directly enters the SM mapper while the first enters the SM mapper after
being coded by 4-states convolutional encoder. In this scheme, the improvement in
performance occurs only in the correlated channels whereas there is no any error
performance advantage in uncorrelated channels compared to uncoded SM. In (Basar,
Aygulu, Panayirci, & Poor, August 2011), the authors directly combined the trellis coding
and SM by passing all the incoming bits in convolutional encoder then entering SM
mapper. So, this scheme benefits from trellis coding in both correlated and uncorrelated
channels by coding all the incoming bits not partially.
After the introducing of SM concept, the authors of (Raed Mesleh, Ikki, & Aggoune,
June 2015) proposed a new method to enhance the overall spectral efficiency of the SM
technique while retaining all the advantages of that system. The proposed technique,
called ‘Quadrature Spatial Modulation’ QSM, successded in increasing the spectral
efficiency of its systems over what in SM was and improving the error performance
without any increasing in cost or receiving complexity. Another scheme based on SM
called Enhanced Spatial Modulation (ESM) was proposed in (Cheng, Sari, Sezginer, &
Su, June 2015 ). This scheme uses one or two transmit antennas and multiple constellation
sets and the information is conveyed in both the index(es) of the active antenna(s) and the
constellation set.
6
Novel schemes were proposed by gathering the advantages of the STBCs and the
SM concept in the same scheme. In (Basar, Aygolu, Panayirci, & Poor, 2011b), a novel
design, called “Space-Time Block Coded Spatial Modulation” (STBC-SM), was realized
by employing a STBC for SM. In this scheme, both the STBC code and the indices of the
active pair of transmit antennas carry the information. STBC-SM offered improvement on
the error performance over SM and Vertical-Bell Laboratories Layered Space-Time (V-
BLAST) with low-complexity maximum likelihood decoder. An improvement in spectral
efficiency over STBC-SM was proposed in a new scheme called Space Time Block Coded
Spatial with Cyclic structure (STBC-CSM) (Li & Wang, 2014). In this scheme, as in
STBC-SM, both the STBC symbols and the indices of the active antennas carry
information. In addition, the active pair of transmit antennas is chosen circularly along the
total transmit antennas.
A new class of STTC, called ‘Super-Orthogonal Trellis-Coded Spatial Modulation’
(SOTC-SM), was proposed in (Başar et al., 2012). This code applies the set-partitioning
on the super set of STBC-SM, which is proposed in (Basar et al., 2011b). Unlike SO-
STTC, which uses a super set of STBC, SOTC-SM uses a super set of STBC-SM which
results in increasing the distance spectrum of the trellis codes, resulting in an improvement
in the error performance while maintaining the same spectral efficiency. As in SO-STTC,
SOTC-SM suffers from a high number of parallel branches and a high complexity
decoder.
1.4 Problem Statement:
In SO-STBC and SOTC-SM MIMO schemes, as the spectral efficiency in the
system is increasing, the number of the branches that diverge from each state in the trellis
structure is also increasing steadily. This increasing results in degradation in the error
performance at the high data rates and increasing in the decoding complexity.
1.5 Thesis Contribution:
The main contributions of this thesis are summarized as the following:
7
• A new MIMO transmission scheme is proposed that directly combines the
SO-STBC and the trellis coding technique. The new scheme reduces the
number of branches in the trellis structure by using double space diversity
approach. This results in reduction in the decoding complexity and
improvement in the error performance over SO-STTC and SOTC-SM,
particularly at the high data rates.
• Optimize the SO-STBC rotation angles to suite the new scheme and get the
best error performance at the same spectral efficiency.
• Offer some of designs for the new scheme with different number of states at
high data rates.
1.6 Thesis Organization:
This thesis is mainly concerned with the issue of constructing STC scheme that
offers better error performance and lower decoding complexity at high data rates. The
thesis is organised as the follow:
In Chapter 2, a general overview about wireless channels and their properties and
limitations will be presented. In addition, we will give a brief description of STBC, SM
and other related STC. For each, its basics, the encoding process, the decoding process
and the error performance will be discussed
In Chapter 3, the STTC and a set of other STCs that are based on it will be discussed.
In chapter 2 and this chapter, we will focus only on the details that are strongly related to
our developed scheme.
In Chapter 4, the details of the proposed scheme will be shown and the encoding
process, the optimization step of the code, the decoding process and the complexity
calculations for the scheme will be explained. Moreover, the proposed scheme will be
illustrated in various number of states and spectral efficiency values.
8
In Chapter 5, the simulation results of the designed codes will be presented and
compared with similar codes of SO-STTC and SOTC-SM schemes. We will conclude the
thesis in chapter 5 with illustration of possible future work.
9
Chapter 2
Thesis’s Background
(Wireless Channels, MIMO Systems
and Some Related STCs)
10
Chapter 2
Thesis’s Background
(Wireless Channels, MIMO Systems and Some Related STCs)
Wireless channel is an important component in the wireless system and it received
a lot of attention and research due to its effect on the performance of the system. In order
to mitigate the negative impact of it, multiple techniques are created and considered like
MIMO technique.
STC is a coding technique that aims to benefit from the MIMO systems by
introducing a transmit diversity and a coding gain. In the last few years, STC generated a
significant amount of interest in the modern communication researches and many different
schemes of it were proposed.
In this chapter, a brief overview about wireless channel will be presented and the
concept of STBC and SM schemes that are related to our work will be illustrated.
2.1 Wireless Channel Characteristics:
Any transmitted signal in wireless channels is affected by multiple forms of effects
that could cause damage the signal by different ways. These effects can be categorized as
additive white Gaussian noise, phase shift, path loss, shadowing, multipath fading,
interference, and so on. These effects change with many different parameters as
geographical environment, distance, mobility of the source or the receiver, transmitting
frequency and others (Goldsmith, 2005). These effects constitute in their aggregate the
characteristic of the wireless channel.
2.1.1 Additive White Gaussian Noise (AWGN):
AWGN is the main model describes the natural random noise in the channel. This
type of noise has an equal power distribution over the whole spectrum (flat power density),
so it is called (white noise). It is described as an independent source that affects all signals
independently so it is usually added to the effected signal in analysis process.
11
The probability distribution function (PDF) of the Gaussian model is given by (Kim,
2015):
𝑃(𝑥) =1
𝜎√2𝜋𝑒−
1
2(𝑥−𝜇
𝜎)2
(2.1)
where σ and µ are the standard deviation and the mean of the noise distribution.
AWGN affects proportionally on the channel capacity by the term signal-to-noise
ratio. As the noise power is increased, the capacity of the system decreases and the channel
becomes worse.
2.1.2 Large Scale Models:
During the broadcasting of the transmitted signal in the channel, its power decreases
steadily with the distance due to two factors (Kim, 2015):
1. Path loss which results mainly from the power dissipation of the transmitted signal
through the channel.
2. Shadowing: which caused when an obstacle intercepts the path between the
transmitter and the receiver. This interception can affect by absorption, reflection,
scattering and diffraction.
These two effects are called large scale effects since they occur over relatively large
distances. The following figure illustrates the effects of the channel components on the
received power (Goldsmith, 2005).
12
2.1.2.1 Free Space Path Loss:
When the signal travels in the free pace without any obstacles, its power attenuation
relates directly to the distance. This model is called free space model and one of simple
models that represent this state is Friis model (Friis, 1946).
Figure (2.1): Path Loss, Shadowing and Multipath versus Distance
(Goldsmith, 2005).
Figure (2.2): Friis transmission model.
13
This model supposes that the transmitted power spreads out in a sphere and the
received power is related to major parameters as the transmitted power, antennas gain,
transmitted frequency and the distance between the transmitter and receiver (Kim, 2015).
The received power Pr is expressed as the following:
𝑃𝑟 = 𝑃𝑡𝐺𝑡𝐺𝑟 (𝜆
4𝜋𝑅)2
(2.2)
where Pt is the transmitted power, Gt and Gr are the gain of transmit and receive antennas
respectively, λ is the wavelength and R is the distance between the transmitter and
receiver.
From previous equation, we notice that the received power is inversely proportional
to the square of the distance and direct proportional to the wavelength.
2.1.2.2 Two-Ray model
Free space model or Friis Equation deals only with the line of sight (LOS) component
of the transmitted signal, whereas there is another state that there is another wave resulted
from the reflection of the travel wave from the earth. The model that takes in consideration
this state is called two-ray model. The following figure illustrates this model (Goldsmith,
2005).
14
In the two-ray model, the received signal consists from two components: LOS
component and the ground reflected component. The following formula expresses the
model(Kim, 2015):
𝑃𝑟 = 𝑃𝑡𝐺𝑡𝐺𝑟 (ℎ𝑡ℎ𝑟
𝑑2 )2
(2.3)
where ht and hr denote the transmitter antenna height and receiver antenna height,
respectively.
The equation indicates that the received power is affected by the height of the
transmit and receive antennas, also, unlike Friis Equation, it decreases more quickly
according to the distance since it inversely proportion with the fourth power of the distance
(d4).
2.1.2.3 Diffraction and scattering:
In the urban areas, beside the LOS and reflected components there are other
components related to the buildings and the other existing objects. These components are
resulted from reflection, diffraction and scattering.
Figure (2.3): Two-Ray model (Kim, 2015).
15
Diffraction is a phenomenon that describes the binding of the transmitted signal
around an object in its path to the receiver. This phenomenon can occur for many reasons
include the binding shape of the earth, sharp edges of obstacles, irregular terrain and
blocking obstructions between the transmitter and receiver. In general, the LOS and
reflected components are the dominant components due to the high losses of diffraction
and scattering components(Goldsmith, 2005).
Diffraction can be modelled by Fresnel knife edge diffraction model due to its
simplicity. The model is illustrated in the following figure:
From the previous geometry we can show that the signal must travel additional
distance compared to the LOS signal according to h. The travelled distance that the signal
takes is (d+d`) which results in a phase difference equal to 2𝜋(𝑑+𝑑`)
𝜆. From knife-edge
geometry, an improtant parameter is extracted called Fresnel-Kirchoff diffraction
parameter (v) which is expressed as the following:
𝑣 = ℎ√2(𝑑+𝑑`)
𝜆𝑑𝑑` (2.4)
The path loss associated with knife-edge diffraction is a function of (v) and
computing it is more complicated and require using special principles (Goldsmith, 2005).
There are multiple rays in addition to diffracted rays. These rays include rays that
diffracted multiple times and rays are both reflected and diffracted. However, the
attenuation of these rays is large enough to be negligent compared with dominant rays.
Figure (2.4): Knife-Edge model (Goldsmith, 2005).
16
Also, these rays can be modelled in a special model associated with special environments
such as models for diffracted signals from buildings in cellular systems.
Scattering is a phenomenon which is resulted when there are objects that are smaller
than the wavelength of the travelled signal in the way between the transmitter and receiver.
The incident wave will scatter and produce multiple waves which will propagate in many
directions (Jankiraman, 2004).
2.1.2.4 Empirical path loss models:
In complex environment, neither free space path loss model nor ray tracing are
sufficient for accurately predict the received power. A number of models are developed
for this purpose in wireless environment such urban cells and inside buildings. These
models are based on empirical measurements over given conditions but can also be used
in similar environments. There are many empirical models that are applied nowadays such
as Okumura model and Hata model (Goldsmith, 2005).
2.1.3 Multipath Channels:
During the propagation of the signal over the channel, reflection, diffraction and
scattering are occurred and produce multiple copies of the traveling wave. These copies
propagate in different paths and arrive the receiver in different time delays with different
phase shifts and amplitudes. The combination of these copies at the receiver affects on the
recovered signal positively or negatively.
17
The multipath channel can be modelled as a linear time-varying finite impulse
response filter. The impulse response, h(t,τ), of the multipath channel is
ℎ(𝑡, 𝜏) = ∑ 𝑎𝑖(𝑡)𝛿(𝜏 − 𝜏𝑖)𝑁𝑖=1 (2.5)
where ai(t) and δ(τ-τi) denote amplitude of a multipath and the Dirac delta function,
respectively and τ is the time delay (Kim, 2015).
There are many parameters related to the nature of the multipath channel. These
parameters are (Goldsmith, 2005):
- Coherence bandwidth: is a statistical measurement of the bandwidth where the
channel is considered as a flat. This results that any two signals passing through
the channel experience the same amplitude and phase response.
This parameter divides the fading impacts on the channel into the following 2
types:
o Flat fading: when the bandwidth of the signal is smaller than the
coherence bandwidth of the channel.
Figure (2.5): Transmitted signals and its reflected versions (Kim, 2015).
18
o Frequency selective fading: when the bandwidth of the signal is larger
than the coherence bandwidth of the channel.
- Coherence time: is the time interval that the impulse response of the channel is
regarded as not varying.
The fading in the channel is divided into another 2 types due to that parameter:
o Slow fading: when the signal period is smaller than the coherence time of
the channel.
o Fast fading: when the signal period is larger than the coherence time of
the channel.
According to the previous divisions, the channel can be classified into one of the
following categories:
- Flat slow fading.
- Flat fast fading.
- Frequency selective slow fading.
- Frequency selective fast fading.
2.2 MIMO Systems:
Using multiple antennas technique in the modern communication systems is an
essential issue for its advantages. MIMO technique can achieve the increase in the data
rate through multiplexing or diversity. In multiplexing, the independent signalling path is
used to send independent data which resulting in increasing the spectral efficiency, while
in the diversity, the same data is send over different channels experiencing different path
fading (Goldsmith, 2005).
MIMO system model can be expressed as illustrated in the following diagram
(Vucetic & Yuan, 2003). Consider a MIMO system with nT transmit antennas and nR
receive antennas.
19
The transmitted signal in each instant is expressed as an array of 𝑛𝑇 × 1 , such that
each element represents the symbol which will be transmitted from the corresponding
antenna. The channel is represented by an 𝑛𝑇 × 𝑛𝑅 matrix denoted by H. The ij-th
element of the H matrix represents the fading of the path from the ith transmit antenna to
the jth receive antenna. The elements of the H matrix are random values with channel
distribution such as Rayleigh or Racian. The noise of the channel is represented by nR×1
matrix denoted by n where the elements of the matrix are complex zero-mean Gaussian
distributed elements. The received signals are 𝑛𝑅 × 1 matrix where each element
represents the signal received by the corresponding receive antenna. The overall MIMO
system can be represented by the following:
[
𝑦1
⋮𝑦𝑛𝑅
] = [
ℎ11 … ℎ1×𝑛𝑇
⋮ ⋱ ⋮ℎ𝑛𝑅×1 … ℎ𝑛𝑅×𝑛𝑇
] [
𝑠1
⋮𝑠𝑛𝑇
] + [
𝑛1
⋮𝑛𝑛𝑅
] (2.6)
Figure (2.6): MIMO system model (Vucetic & Yuan, 2003).
20
2.3 Space Time Block Codes:
Space time block codes (STBC) is a MIMO technique that is used to transmit
multiple copies of the symbols over multiple time slots. When using STBC scheme, the
incoming data stream is divided into blocks prior to transmission. Then these blocks are
transmitted from the multiple antennas according to the used code. At the receiver side,
the received signals are combined and then sent to the maximum likelihood detector (ML)
where the decision rules are applied.
STBCs are considered to be orthogonal codes in order to maintain the simplicity of
decoding complexity while providing the full diversity specified by the number of transmit
and receive antennas (Santumon & Sujatha, 2012).
A space time block code is usually represented by a coding matrix. In this matrix,
each row represents a time slot and each column represents the transmit antenna’s
symbols, so each element represents one antenna's transmission vector over a time slot.
2.3.1 STBC Encoder:
Figure (2.7) shows the general block diagram of the implementation of STBC. In
general, STBC system can be modeled as an 𝑝 × 𝑛𝑇 transmission matrix X, where 𝑛𝑇
and 𝑝 represent the number of transmit antennas and the number of timeslots used to
transmit the symbols, respectively. The transmission matrix X is given by:
𝑋 = [
𝑠11 𝑠12 ⋯ 𝑠𝑝1
𝑠21 𝑠22 ⋯ 𝑠𝑝2
⋮ ⋱ ⋱ ⋮𝑠𝑝×1 𝑠𝑝×2 ⋯ 𝑠𝑝×𝑛𝑇
] (2.7)
where the element 𝑠𝑖𝑗 represents the transmitted symbol from an antenna i in a time slot j
or its conjugate.
21
In STBC, for each encoded block by the encoder consists from k symbols, there are
p space-time symbols transmitted from each antenna. Hence, the rate of STBC is defined
as the ratio between the number of symbols that the encoder takes as its input and the
number of space-time coded symbols transmitted from each antenna. It is given by
(Vucetic & Yuan, 2003),
𝑅 =𝑘
𝑝 (2.8)
In the orthogonal codes, the transmitted signals from any two antennas are
orthogonal, i.e. the rows of the transmission matrix are orthogonal. The orthogonality of
STBCs enables the codes to achieve the full diversity for the given transmit and receive
antennas and, at the same time, enables the receiver to decouple the received signals and
perform simple maximum likelihood decoding process (Vucetic & Yuan, 2003).
2.3.2 Alamouti’s STBC:
Almouti’s STBC is an orthogonal space-time block code that deals with systems
with two transmit antennas. The encoding block diagram of Alamouti’s STBC is
illustrated in Figure (2.8).
Figure (2.7): The general block diagram for STBC implementation.
22
Alamouti’s code encodes the input signal stream by dividing it into blocks of length
two and transmit each block according to the following transmitting matrix
𝑋 = [𝑠1 𝑠2
−𝑠2∗ 𝑠1
∗] (2.9)
From Equation (2.9), at the timeslot 1, the transmitted signal from the two antennas
are 𝑠1 and 𝑠2, respectively, while at the time slot 2, the transmitted signals are −𝑠2∗
and 𝑠1∗ , respectively.
To ensure that the code achieves the full diversity, the rank of the difference matrix
between any two different transmitted matrices should equal 2. The difference matrix is
expressed as
𝐷(𝑋, 𝑋′) = 𝑋 − 𝑋′ = [𝑠1 − 𝑠1
′ 𝑠2 − 𝑠2′
𝑠2′∗ − 𝑠2
∗ 𝑠1∗ − 𝑠1
′∗] , 𝑋 ≠ 𝑋′ (2.10)
For the decoding process of the Alamouti’s STBC, assume that the receiver has one
receive antenna and the path gains from transmit antennas 1 and 2 are h1 and h2,
respectively. The received signals at time slot 1 and 2 are r1 and r2; where
𝑟1 = ℎ1𝑠1 + ℎ2𝑠2 + 𝑛1,
𝑟2 = −ℎ1𝑠2∗ + ℎ2𝑠1
∗ + 𝑛1. (2.11)
Figure (2.8): The encoding block diagram of Alamouti’s STBC.
23
The maximum-likelihood (ML) decoder checks all possible pairs of the
constellation signals (s1, s2) that minimize the decision metric in the following metric:
|𝑟1 − ℎ1𝑠1 − ℎ2𝑠2| + |𝑟2+ℎ1𝑠2∗ − ℎ2𝑠1
∗| (2.12)
The metric in Equation (2.12) requires a full search over all possible values of
(s1, s2) which increases the complexity of the receiver significantly as the transmit antenna
number increases. Due to the orthogonality of STBC, one can expand Equation (2.12) and
convert it to the two following separated equations after removing the common term
|r1|2 + |r2|
2:
|𝑠1|2 ∑ |ℎ𝑛|22
𝑛=1 − [𝑟1ℎ1∗𝑠1
∗ + 𝑟1∗ℎ1𝑠1 + 𝑟2ℎ2
∗𝑠1 + 𝑟2∗ℎ2𝑠1
∗] (2.13)
|𝑠2|2 ∑ |ℎ𝑛|22
𝑛=1 − [𝑟1ℎ2∗𝑠2
∗ + 𝑟1∗ℎ2𝑠2 − 𝑟2ℎ1
∗𝑠2 − 𝑟2∗ℎ1𝑠2
∗] (2.14)
where Equation (2.13) is a function of s1 only and Equation (2.14) is a function of s2 only.
Therefore, instead of search over all possible of (s1,s2), one can simultaneously minimize
Equation (2.13) over all possible s1 only and minimize Equation (2.14) over all possible
s2 only (Tarokh, Jafarkhani, & Calderbank, 1999b).
The performance of Alamouti’s code in a quasi-static Rayleigh fading channel is
illustrated in Figure (2.9). The system uses QPSK modulation scheme and one antenna at
the receiver. This Figure shows that the Alamouti’s code improved the symbol error rate
(SER) of the uncoded system by about 11 dB at SER of 10−3 .
24
2.3.3 Super Orthogonal Space-Time Block Codes (SO-STBC):
Multiple orthogonal matrices can be generated from known orthogonal one by
multiplying it by a unitary matrix. The resulting matrix is a rotated version from the
original and has the same properties of it.
The unitary generator matrix, U is expressed as
𝑈 = [𝑒𝑗𝜃 00 1
] (2.15)
Figure (2.9): Symbol error probability of Alamouti’s STBC with QPSK symbols
and one receive antenna (Hamid Jafarkhani, 2005).
25
The corresponding orthogonal matrix which is resulted from multiplying an
Alamouti’s STBC with the unitary matrix is expressed as (Hamid Jafarkhani & Seshadri,
2003),
𝒪(𝑥1, 𝑥2, 𝜃) = 𝒪(𝑥1, 𝑥2). 𝑈 = [𝑥1𝑒
𝑗𝜃 𝑥2
−𝑥2∗𝑒𝑗𝜃 𝑥1
∗] (2.16)
The union of multiple orthogonal matrices is called the ‘super set’ of orthogonal
matrices. The main advantage of the super-orthogonal STBC is the ability to design full
rate and full diversity trellis codes with it (Hamid Jafarkhani, 2005).
2.4 Spatial Modulation (SM):
SM, was first introduced by Mesleh in (R. Y. Mesleh et al., 2008), is a novel MIMO
transmission scheme that uses the indices of the multiple transmit antennas to convey extra
information bits in addition to the symbol constellation. In that scheme, only one transmit
antenna is available at each transmit instant while the others do not transmit. Therefore,
ICI at the receiver and the need to the synchronization with the transmit antennas can be
avoided (Raed Mesleh, Ikki, & Aggoune, 2015).
2.4.1 Spatial Modulation coding:
The SM system model is shown in Figure (2.10).
26
𝑄(𝑘) is a symbol which will be transmitted through the channel at time instant k. SM
mapper maps 𝑄(𝑘) into another symbol 𝑋(𝑘).
To illustrate the concept of SM, the following example is introduced. Consider we
have a MIMO system with 4 transmit antennas and QPSK modulation scheme. The
following table maps each binary stream (4 bits) into a QPSK symbol and the index of a
transmit antenna from the available four transmit antennas (R. Y. Mesleh et al., 2008).
Table (2.1): SM mapping table (R. Y. Mesleh et al., 2008).
Input bits Transmit
antenna
Transmit
symbol Input bits
Transmit
antenna
Transmit
symbol
0000 1 +1+ j 1000 3 +1+ j
0001 1 -1+ j 1001 3 -1+ j
0010 1 -1- j 1010 3 -1- j
0011 1 +1- j 1011 3 +1- j
0100 2 +1+ j 1100 4 +1+ j
0101 2 -1+ j 1101 4 -1+ j
0110 2 -1- j 1110 4 -1- j
0111 2 +1- j 1111 4 +1- j
Figure (2.10): SM system model.
27
In general, the total number of bits that can be transmitted in each symbol after the
mapping is
𝑚 = log2 𝑀 + log2 𝑛𝑇 (2.17)
where M is the constellation size of the modulated symbol and 𝑛𝑇 denotes the number of
transmit antennas.
From Equation (2.17), it can be noted that SM can increase the spectral efficiency
by base two logarithm of the total number of transmit antennas.
2.4.2 Spatial modulation decoding and performance:
For the receiver of SM, a low complexity Maximum-Likelihood decoder (ML) and
Maximum Ratio Receiver Combining (MRRC) decoder can be used (R. Y. Mesleh et al.,
2008). Figure (2.11) demonstrates the performance of SM over ideal channel with
6 b/s.Hz.
Figure (2.11): The BER of SM over ideal channel with 6 bits/s.Hz (R. Y.
Mesleh, Haas, Sinanovic, Ahn, & Yun, 2008)
28
From the Figure (2.11), we can note that SM technique achieved improvement in
the Bit Error Rate (BER) over V-BLAST and Almouti’s code.
2.5 Space-Time Block Coded Spatial Modulation (STBC-SM):
STBC-SM is a new MIMO transmission scheme that employs spatial modulation
for STBC. In this scheme, both the STBC and the transmit antenna indices convey
information. Combining STBC with SM in this technique can improve the overall
efficiency by diversity gain (Başar et al., 2012). This concept was first introduced in
(Basar et al., 2011b).
2.5.1 STBC-SM coding:
In STBC-SM, each of the transmitted symbols corresponding to the selected STBC
and the transmit antennas indices are carrying information. In this scheme, Alamouti’s
STBC is chosen as the core STBC due to its advantages.
STBC-SM expands Alamouti’s STBC matrix over antenna domain. For example,
for a MIMO system with four transmit antennas; one of the following four STBC-SM
codewords will be transmitted:
𝑋1 = {𝑋11, 𝑋12} = {(𝑥1 𝑥2 0 0
−𝑥2∗ 𝑥1
∗ 0 0) , (
0 0 𝑥1 𝑥2
0 0 −𝑥2∗ 𝑥1
∗)}
𝑋2 = {𝑋21, 𝑋22} = {(0 𝑥1 𝑥2 00 −𝑥2
∗ 𝑥1∗ 0
) , (𝑥1 0 0 𝑥2
−𝑥2∗ 0 0 𝑥1
∗)} 𝑒𝑗𝜃 (2.18)
where 𝑋𝑖 , 𝑖 = 1, 2 are STBC-SM codebooks. Each of them contains two STBC-SM
codewords that don’t interfere to each other. θ in Equation (2.18) is a rotating angle which
must be optimized to ensure achieving the optimal diversity and coding gain. Note that, if
θ is not considered, the overlapping columns from the two codebooks will reduce the
diversity order (Basar et al., 2011b).
Table (2.2) illustrates the mapping rule for 2 b/s.Hz spectral efficiency and BPSK
modulation scheme based on the codebooks of Equations in (2.18).
29
Table (2.2): The mapping rule for 2 b/s.Hz and BPSK modulation (Basar et al., 2011b).
Input Bits Transmission
matrix Input Bits Transmission matrix
0000 (1 1 0 0
−1 1 0 0) 1000 (
0 1 1 00 −1 1 0
) 𝑒𝑗𝜃
0001 (1 −1 0 01 1 0 0
) 1001 (0 1 −1 00 1 1 0
) 𝑒𝑗𝜃
0010 (−1 1 0 0−1 −1 0 0
) 1010 (0 −1 1 00 −1 −1 0
) 𝑒𝑗𝜃
0011 (−1 −1 0 01 −1 0 0
) 1011 (0 −1 −1 00 1 −1 0
) 𝑒𝑗𝜃
0100 (0 0 1 10 0 −1 1
) 1100 (1 0 0 1
−1 0 0 1) 𝑒𝑗𝜃
0101 (0 0 1 −10 0 1 1
) 1101 (1 0 0 −11 0 0 1
) 𝑒𝑗𝜃
0110 (0 0 −1 10 0 −1 −1
) 1110 (−1 0 0 1−1 0 0 −1
) 𝑒𝑗𝜃
0111 (0 0 −1 −10 0 1 −1
) 1111 (−1 0 0 −11 0 0 −1
) 𝑒𝑗𝜃
2.6 Double Space-Time Transmit Diversity (DSTTD):
The Double Space-Time Transmit Diversity (DSTTD) approach consists of two
Alamouti’s STBCs at the transmitter and an interference-resistant detector at the receiver.
It was proposed in (Naguib et al., 1998) and (Naguib et al., 2000).
In this scheme, each of STBC and the dual structure are compromised. This
technique provides the transmit diversity from the STBC and an improvement for data
throughput (Zheng & Tse, 2003). The main disadvantage of this scheme is the high
complexity for the decoding process at the receiver due to the occurred interference.
2.6.1 DSTTD model:
In DSTTD system with 4 transmit antennas and 𝑛𝑟 ≥ 2, receive antennas, the
incoming data is demultiplexed into two streams, each is encoded by independent
30
Alamouti’s STBC. The result transmission matrix for the four antennas is expressed as
(Lee & Shieh, 2011)
𝑋 = [𝑠1 𝑠2 𝑠3 𝑠4
−𝑠2∗ 𝑠1
∗ −𝑠4∗ 𝑠3
∗]𝑇
(2.19)
The received signal matrix over flat fading channel is
𝑌 = 𝐻𝑋 + 𝑍, (2.20)
where,
𝑌 = [𝑦11 𝑦21 ⋯ 𝑦𝑛𝑟1
𝑦12 𝑦22 ⋯ 𝑦𝑛𝑟2]𝑇
(2.21)
𝑦𝑛𝑘 denotes the received signal by the 𝑁𝑡ℎ receive antenna at timeslot k (in Alamouti’s
STBC, k = 1,2).
𝐻 = [
ℎ11 ℎ12 ℎ13 ℎ14
ℎ21 ℎ22 ℎ23 ℎ24
⋮ ⋮ ⋮ ⋮ℎ𝑛𝑟1 ℎ𝑛𝑟2 ℎ𝑛𝑟3 ℎ𝑛𝑟4
] (2.22)
where ℎ𝑛𝑚 denotes the channel coefficient between the 𝑚𝑡ℎ transmit antenna and the 𝑛𝑡ℎ
receive antenna.
𝑍 = [𝑧11 𝑧21 … 𝑧𝑛𝑟1
𝑧12 𝑧22 … 𝑧𝑛𝑟2]𝑇
(2.23)
where 𝑧𝑛𝑘 represents the noise element in the 𝑛𝑡ℎ receive antenna at timeslot k.
31
2.6.2 Minimum-mean square error (MMSE) interference cancellation for DSTTD:
As was shown in the previous section, DSTTD has two transmit terminals, each is
equipped with 2 transmit antennas. The first is formed by s1 and s2, the other is formed by
s3 and s4. The contribution from one terminal to the other can be eliminated using
Minimum-Mean Square Error (MMSE) interference cancellation algorithm which is
described in (Naguib et al., 1998).
First of all, we need to rewrite the system model in Equation (2.20) to the following
equivalent model (Paulraj, Nabar, & Gore, 2003)
𝑦 =
[ 𝑦11
𝑦12∗
⋮𝑦𝑁1
𝑦𝑁2∗ ]
= 𝐻𝑒𝑥 + 𝑛 (2.24)
where,
𝐻𝑒 =
[ ℎ11 ℎ12 ℎ13 ℎ14
ℎ12∗ −ℎ11
∗ ℎ14∗ −ℎ13
∗
⋮ ⋮ ⋮ ⋮ℎ𝑁1 ℎ𝑁2 ℎ𝑁3 ℎ𝑁4
ℎ𝑁2∗ −ℎ𝑁1
∗ ℎ𝑁4∗ −ℎ𝑁3
∗ ]
, 𝑥 = [
𝑠1
𝑠2
𝑠3
𝑠4
]
For the first terminal, the decoder can eliminate the contribution from the
transmitted symbols from the second terminal, s3 and s4, by using the following scheme
(Naguib et al., 1998)
(𝑠1̃, 𝑠2̃) = 𝑎𝑟𝑔 min{‖𝛼1𝐻𝑦 − 𝑠1‖
2 + ‖𝛼2𝐻𝑦 − 𝑠2‖
2} (2.25)
where,
𝛼1 = 𝑀−1ℎ1 , 𝛼2 = 𝑀−1ℎ2 (2.26)
𝑀 = 𝐻𝑒𝐻𝑒𝐻 +
1
𝜌𝐼2𝑁 , (2.27)
32
where ℎ𝑖 in Equation (2.26) is the ith column of 𝐻𝑒, ρ is the Signal to Noise Ratio (SNR)
and 𝐼𝑀𝑇 represents an identity matrix of size 𝑀𝑇 × 𝑀𝑇.
Using the above process, we can detect (𝑠1, 𝑠2) by minimizing the Mean Square
Error (MSE) described in Equation (2.25). Once we have detected (𝑠1, 𝑠2) correctly, the
contribution of them can be perfectly canceled using the following process
𝑦𝑐 = 𝑦 − 𝐻𝑒1�̃� (2.28)
where 𝑦𝑐 denotes the received signal corresponds to (𝑠3, 𝑠4) after canceling the
contribution of (𝑠1, 𝑠2). 𝐻𝑒1 and �̃� are
𝐻𝑒1 =
[ ℎ11 ℎ12
ℎ12∗ −ℎ11
∗
⋮ ⋮ℎ𝑁1 ℎ𝑁2
ℎ𝑁2∗ −ℎ𝑁1
∗ ]
, �̃� = [𝑠1̃
𝑠2̃]
After the cancellation, the symbols (𝑠3, 𝑠4) can be decoded using ML decoder as
described in Section (2.1.2) (Jung & Lee, 2009).
A two-step MMSE-IC can be performed as the following:
• First step: decode (𝑠1, 𝑠2) firstly using Equation (2.25) then decode (𝑠3, 𝑠4) later
after canceling the contribution of (𝑠1, 𝑠2). Then, the receiver repeats the process
but, in this time, by decoding (𝑠3, 𝑠4) first using Equation (2.25) then decode
(𝑠1, 𝑠2) later using ML decoder.
• Second step: for each case of step one, compute the sum of MSE of the decoded
symbols, which are denoted by Δ0 and Δ1. Then, compare these values and choose
the symbols corresponds to the lowest (𝑠1, 𝑠2, 𝑠3, 𝑠4)0 if Δ0 < Δ1 or (𝑠1, 𝑠2, 𝑠3, 𝑠4)1 if
(Δ0 > Δ1) (Naguib et al., 1998).
33
2.7 Conclusion:
The channel of the wireless system is an essential component that affects on the
performance of the system. MIMO technique is one of the important efforts that aims to
mitigate the negative impact of the wireless channel by benefit from the spatial diversity
occurred due to the using of multiple antennas in the transmitting and receiving.
STCs is a coding technique that aims to benefit from the MIMO systems by
introducing a transmit diversity. In this chapter, multiple STC schemes are reviewed like
STBC, SM and others that are based on them. Each scheme has its own advantage and the
degree of the its receiver complexity.
34
Chapter 3
Space-Time Trellis Coding
Schemes
35
Chapter 3
Space-Time Trellis Coding Schemes
In the previous chapter, we presented the basics of STBC and SM schemes and we
have shown how can STBC offer a full diversity scheme with low complexity decoding
receiver. In this chapter, we will review the concept of STTC and some of other STCs
which they were based on it.
3.1 Trellis coded Modulation (TCM):
Trellis diagram is a technique that represents the coding process graphically. In this
diagram, each path represents a codeword of a convolutional code. Combining this
technique with Viterbi decoding algorithm makes it possible to decode convolutional
codes with reduced complexity. Trellis diagram was first introduced by Forney (Forney,
1973) in 1973.
Coded modulation schemes are techniques that combine both the coding and the
modulation to achieve coding gain without any increase or expansion in the bandwidth.
Trellis Coded Modulation (TCM) is a coded modulation based on convolutional coding
that combines a convolutional code with rate R = (k / k + 1) with M-ary modulation scheme
where M = k + 1 (G Ungerboeck & Csajka, 1976). By this method, we can achieve codes
with spectral efficiency similar to the uncoded scheme. For example, a convolutional code
with a rate R = 2/3 combined with 8-PSK modulation has the same spectral efficiency of
4-QAM modulation scheme which is 2 bits/s (Lin & Castello, 2004). Hence, TCM
maintains the spectral efficiency of the uncoded code by expansion the constellation set
of the modulation scheme. This expansion forces the constellation points to be closer
which means lower Euclidean distance. However, this issue can be treated by a good
design and proper selection of the code and the modulation mapping together.
The concept of TCM is based on designing the code and the signal mapping jointly
to maximize the minimum free Euclidean distance between the sequences. This joint
design is done using set partitioning technique (Ungerboek, January 1982). Set
partitioning is a technique which partitions the total set into smaller subsets with equal
36
size, then also partitioning every subset into smaller subsets, thereby a tree structure of
k + 1 levels is constructed. Subsets labelling must be done in such a way that maximize
the minimum Euclidean distance between the subsets in the same level (Lin & Castello,
2004) .
The following example shows the set- partitioning of 8-PSK:
After perform the partitioning of the overall set into small subsets have the possible
maximum Euclidean distance, the next step is to assign each subset to each of the trellis
branches. Each state has 2b branches leaving it and another incoming to it, where b denotes
the spectral efficiency.
The main criteria in TCM design process is summarized in the following (Gottfried
Ungerboeck, 1982):
• All subsets should be used an equal number of times in the trellis.
• Transitions originating from the same state or merging into the same state in the
trellis should be assigned subsets that are separated by the largest Euclidean
distance.
Figure (3.1): Set partitioning of 8-PSK constellation (Hamid Jafarkhani, 2005).
37
• Parallel paths, if they occur, should be assigned signal points separated by the
largest Euclidean distances.
Figure (3.2) illustrates a trellis structure for the set-partitioning in Figure (3.1)
3.2 Space-Time Trellis Codes (STTC):
As we have seen in the previous section, TCM combines the coding and modulation
together in order to enhance the error performance of the system. Also, Space-Time Trellis
Codes (STTCs) combine the modulation and the coding to send the coded data over
multiple channels and enhance the error performance of MIMO system.
STTCs can simultaneously offer the coding gain beside the diversity gain and the
spectral efficiency. However, the complexity degree of the decoder is relatively high
(Vucetic & Yuan, 2003).
3.2.1 STTC Encoding:
For STTC that sends b b/s.Hz, number of 2b branches leave each state of the trellis
structure and the encoder assigns the transmitted symbols for each branch. So, the
Figure (3.2): The trellis structure for the set-partitioning in Figure
(3.1) (Hamid Jafarkhani, 2005).
38
incoming data bits are mapped into space time symbols distributed by the trellis diagram.
Let us consider the stream of bits that will be encoded is
𝑐 = {𝑐0, 𝑐1, 𝑐2, … , 𝑐𝑡} (3.1)
where t denotes the time instant. The encoder maps the input stream into stream of
symbols x where x is described as the following
𝒙 = {𝒙0, 𝒙1, 𝒙𝟐, … , 𝒙𝒕} (3.2)
where xt denotes the space-time symbol and is given by
𝒙𝒕 = {𝑥𝑡1, 𝑥𝑡
2, 𝑥𝑡3, … , 𝑥𝑡
𝑛𝑡 } (3.3)
where nt denotes the number of transmit antennas. The modulated signals xt are
transmitted simultaneously through the nt transmit antennas (Vucetic & Yuan, 2003).
Figure (3.3) shows an example for a trellis structure for a 4-state space-time coded
QPSK with 2 transmit antennas.
As shown in Figure (3.3), at each time instant, every antenna transmits a symbol
according to the input bits and hence the active branch. The state of the system also
changes every time according to the input. For example, if the current state of the system
Figure (3.3): Trellis diagram for 4-state STTC with QPSK symbols
and 2 transmit antennas.
39
is state 0 and the input binary is (01), the next will be 1 and the transmitted symbols from
the two transmit antennas are 0, 1, respectively.
The performance of the code depends mainly on the Coding Gain Distance (CGD)
between each valid two transmitted codewords in the system. In STTC, the valid
codeword is defined as any codeword that starts at state zero and ends also at state zero
(Hamid Jafarkhani, 2005).
The CGD of the codes is expressed as the following (Tarokh et al., 1998)
𝐵(𝑒, 𝑐) =
[ 𝑒1
1 − 𝑐11 𝑒2
1 − 𝑐21 ⋯ ⋯ 𝑒𝑙
1 − 𝑐𝑙1
𝑒12 − 𝑐1
2 𝑒22 − 𝑐2
2 ⋯ ⋯ 𝑒𝑙2 − 𝑐𝑙
2
𝑒13 − 𝑐1
3 𝑒23 − 𝑐2
3 ⋯ ⋯ 𝑒𝑙3 − 𝑐𝑙
3
⋮ ⋮ ⋱ ⋱ ⋮𝑒1
𝑛 − 𝑐1𝑛 𝑒2
𝑛 − 𝑐2𝑛 ⋯ ⋯ 𝑒𝑙
𝑛 − 𝑐𝑙𝑛]
(3.4)
Based on the matrix in Equation (3.4), there are two criteria in the design process of
STTC (Tarokh et al., 1998):
• The Rank Criterion: In order to achieve the maximum diversity mn, the matrix
B(e,c) has to be full rank for any codewords e and c . If B(e,c) has minimum rank
r over the set of two tuples of distinct codewords, then a diversity of rm is achieved.
• The Determinant Criterion: suppose that the target is achieving a diversity benefit
by rm. The minimum of rth roots of the sum of determinants of all 𝑟 × 𝑟 principal
cofactors of 𝐴(𝑒, 𝑐) = 𝐵(𝑒, 𝑐)𝐵∗(𝑒, 𝑐) taken over all pairs of distinct codewords e
and c corresponds to the coding advantage, where r is the rank of A(e,c).
3.2.2 STTC Decoding:
Similar to TCM, STTC receivers use the Viterbi algorithm in the decoding process
of the STTCs. Also, ML decoding is applied by the Viterbi algorithm to find the most-
likely valid codeword that starts from state zero and ends with state zero after a specific
frame length.
40
If a branch of a trellis structure transmits symbols s1 and s2 from antennas one and
two respectively, the corresponding branch metric is given by
∑ |𝑟𝑡,𝑚 − ℎ1,𝑚𝑠1 − ℎ2,𝑚𝑠2|2𝑀
𝑚=1 (3.5)
where rt,m is the received symbol at instant t from the receive antenna m and α1,m and α2,m
are the channels gain form transmit antennas 1 and 2 to receive antenna m respectively.
The path metric of a valid code is the sum of all branch metrics that form that path. Finally,
the most-likely path is the one that has the minimum path metric as described in the
following minimization problem (Hamid Jafarkhani, 2005):
𝑚𝑖𝑛𝑐1,1,𝑐1,2,𝑐2,1,𝑐2,2,…,𝑐𝐿,1,,𝑐𝐿,2= ∑ ∑ |𝑟𝑡,𝑚 − ℎ1,𝑚𝑐𝑡,1 − ℎ2,𝑚𝑐𝑡,2|2𝑀
𝑚=1𝐿𝑡=1 (3.6)
Hence, the used Viterbi algorithm in the STTC decoding process uses the path metric in
make a decision instead of the Euclidian distance as in TCM.
Figures (3.5) and (3.6) show the Frame Error Rate (FER) of STTC for 4-PSK using
two transmit antennas and two receive antennas with rates 2 bits/s.Hz and 3 bits/s.Hz,
respectively. These figures show that STTC offers an improvement in the FER. In STTC,
as the number of states increases, the error performance also increases and the decoder
become more complexity.
41
Figure (3.4): FER of STTC for 4-PSK using two transmit antennas and two
receive antennas with rate 2 b/s.Hz (Tarokh, Seshadri, & Calderbank, 1998).
Figure (3.5): FER of STTC for 4-PSK using two transmit antennas and two receive
antennas with rate 3 b/s.Hz (Tarokh et al., 1998).
42
3.3 Super-Orthogonal Space-Time Trellis Coding (SO-STTC):
As was discussed in Section (2.3), STBCs can offer a full diversity without a coding
gain. Whereas, the concatenating of the trellis structure with STBCs can offer additional
performance improvement to the system due to the resulted coding gain (Hamid
Jafarkhani & Seshadri, 2003). However, this mixing yields to a loss in the system rate
since the constituent signal constellation size does not increase.
To alleviate this problem and benefit from the advantages of mixing STBCs with
the outer trellis structure, extended coding matrices, named as Super-Orthogonal STBCs
(SO-STBCs), are used instead of mere STBC matrices. Super-Orthogonal STTCs (SO-
STTCs) can provide maximum diversity and rate. In addition, they achieve coding gains
higher than STTCs (Hamid Jafarkhani, 2005).
As shown in Section (2.3.3), multiple orthogonal STBCs can be derived from
Alamouti’s STBC by multiplying the original code by a unitary generator matrix, U as
shown in Equation (2.16). To design SO-STTC, firstly, set partitioning of the SO-STBCs
is applied then assign every branch in the trellis structure with a code according to the
result of the partitioning.
3.3.1 Set partitioning of SO-STBCs:
The set partitioning of SO-STBCs is similar to that is used in TCM in (Gottfried
Ungerboeck, 1982). In the case of the set-partitioning of STBCs, the used metric is the
CGD between each two codewords (code matrices) (Hamid Jafarkhani & Seshadri, 2003).
The difference matrix between transmission matrices ci and cj is denoted by D(ci,cj) where
𝐷(𝑐𝑖, 𝑐𝑗) = 𝑐𝑖 − 𝑐𝑗 𝑖 ≠ 𝑗 (3.7)
and
𝐴(𝑐𝑖, 𝑐𝑗) = 𝐷(𝑐𝑖, 𝑐𝑗)𝐻𝐷(𝑐𝑖, 𝑐𝑗) (3.8)
43
For a full-diversity code, the coding gain is the minimum of the determinant of the
matrix A(ci,cj) over all possible pairs of distinct codewords ci and cj. So, the CGD between
codewords ci and cj is expressed as
𝑑 = det (𝐴(𝑐𝑖, 𝑐𝑗)), (3.9)
where det(A(ci, cj )) is the determinant of matrix A .
At each level of the set partitioning, the codes are chosen to maximize the minimum
CGD among all possible distinct codes.
The set partitioning of SO-STBCs ensures that maximize the coding gain without
sacrificing the rate by utilizing the rotating angle to generate other orthogonal codes.
Figures (3.6), (3.7) and (3.8) illustrate the set partitioning of SO-STBCs for BPSK with
θ = (0, π), the trellis structure for 4-state SO-STTC with r = 2 bits/s.Hz using QPSK codes
and the trellis structure for 4-state SO-STTC with r = 3 bits/s.Hz using 8-PSK codes,
respectively.
Figure (3.6): The set-partitioning of SO-STBCs for BPSK with θ = (0, π) (Hamid
Jafarkhani, 2005).
44
Figure (3.7): The trellis structure for 4-state SO-STTC with
r = 2 b/s.Hz using QPSK codes (Hamid Jafarkhani, 2005).
Figure (3.8): The trellis structure for 4-state SO-STTC with r = 3 b/s.Hz
using 8-PSK codes (Hamid Jafarkhani, 2005).
45
Figure (3.9) illustrates the performance of SO-STTCs for 2 b/s.Hz with two transmit
antennas and two receive antennas. From the figure, it can be observed that the 4-state
SO-STTC improved the FER by about 1.5 dB over 4-state STTC (Hamid Jafarkhani,
2005).
Figure (3.10) shows the performance of SO-STTCs for spectral efficiency of
3 b/s.Hz with two transmit antennas and two receive antennas. An 8-state code outperform
a 4-state code but the decoding complexity becomes more (Hamid Jafarkhani, 2005).
Figure (3.9): FER of SO-STTCs for 2 b/s.Hz with two transmit antennas and
two receive antennas (Hamid Jafarkhani, 2005).
46
3.4 Spatial Modulation with trellis coding (SMTC):
Spatial modulation with trellis coding (SMTC) is a new MIMO transmission
technique that directly combines the trellis coding and SM to take advantage of the
benefits of both. This concept was first introduced in (Raed Mesleh, Di Renzo, Haas, &
Grant, 2010) and (Basar et al., 2011a).
3.4.1 SMTC coding:
The system model of SMTC is illustrated in Figure (3.11). Assume that the system
has 𝑛𝑇 × 𝑛𝑅 MIMO system. Firstly, the incoming binary stream, u is encoded by the trellis
encoder of rate (k /n). Then, the SM mapper maps the encoded data v, the output from
trellis encoder, into SM symbols by choosing the appropriate indices for the transmit
antennas and the symbol which will be transmitted.
Figure (3.10): FER of SO-STTCs for 3 bits/s.Hz with two transmit antennas
and two receive antennas (Hamid Jafarkhani, 2005).
47
The final output signal from the SM mapper is 𝑥 = (𝑖, 𝑠) where 𝑠 is the data symbol
transmitted over the antenna labelled by 𝑖 ∈{1, 2, ⋅⋅⋅, 𝑛𝑇}. So, the output from SMTC
system is an 1×𝑛𝑇 vector with all elements are zeros except the ith entry which corresponds
to the selected transmit antenna (Basar et al., 2011a).
For an SMTC system with nT = 4, k = 2/4 and QPSK modulation scheme, the
corresponding trellis diagram is shown in Figure (3.12). Each branch is labeled by (i, s)
symbol which denotes the s symbol which will be transmitted over the ith antenna. For
further classification, if the system was in the state (0) and the input binary was (0,1), the
system state transitions to the state (1) and the symbol (2) is transmitted from the 1st
antenna.
Figure (3.11): SMTC system model.
Figure (3.12): The trellis structure for 4-state SMTC with 4 transmit
antennas (Basar, Aygolu, Panayirci, & Poor, 2011a).
48
3.4.2 SMTC decoding and performance:
At the receiver, a soft decision Viterbi decoder is used to perform ML algorithm.
The BER performance of SM-TCs with 4, 8 and 16 states at 2 b/s.Hz and 8 and 16 states
at 3 b/s.Hz are illustrated in Figures (3.13) and (3.14), respectively.
In Figure (3.13), the SM-TC achieved an improvement in BER over STTC in 8-
and 16-state. This improvement can be explained by the optimized spectral distance of
SM-TC scheme. In Figure (3.14) the BER of the SM-TC scheme is improved over STTC
and the error performance gap between them became more than that of the 2 b/s.Hz, since
in 3 b/s.Hz the SM-TC employees 8 transmit antennas and the spectral distance between
the codes becomes more.
Figure (3.13): The BER performance of SM-TC with 4, 8 and 16 states at
2 b/s.Hz (Basar et al., 2011a).
49
3.5 Super-Orthogonal trellis Coded Spatial Modulation (SOTC-SM):
It was shown in Section (3.3) that SO-STBC is combined with trellis coding.
Similarly, the SOTC-SM is a novel technique that also combines the STBC-SM with
trellis coding. This scheme is introduced in (Başar et al., 2012).
3.5.1 Construction of SOTC-SM codebooks:
As shown in Equation (2.18), the set of X1 and X2 is called ‘super set’ of STBC-SM.
The backbone of SOTC-SM code construction is the set partitioning of the orthogonal
STBC-SM codewords to find subsets that achieve maximum CGD as was described in
SO-STTC. Figure (3.15) shows the set partitioning of STBC-SM codewords for QPSK,
8-PSK and 16-PSK.
Figure (3.14): The BER performance of SM-TC with 8 and 16 states at 3 b/s.Hz
(Basar et al., 2011a).
50
During SOTC-SM construction, each state of the trellis structure is assigned with
different STBC-SM code, which not only guarantees the transmit diversity of the STBC,
but also avoids the catastrophic of the encoder (Başar et al., 2012). For k b/s.Hz, the trellis
structure has 2kT branches diverge from each state where T denotes the number of timeslots
used in STBC. In particular, in the case of Alamouti’s STBC, we have 22k branches diverge
from each state.
Figure (3.15): The set partitioning of STBC-SM codewords for QPSK, 8-PSK and
16-QAM (Başar et al., 2012).
51
Table (3.1) shows the trellis state transition matrices for SOTC-SM schemes where
the submatrix at row i and column j is corresponding to the subset that is assigned to
parallel transition diverging from state i and merging to state j. A zero matrix denotes that
is no transition between the state i and state j and Xa, Xb, … , Xh represent STBC-SM
codewords with different transmit antennas for each (Başar et al., 2012).
Figure (3.16): The trellis diagram for 4-state SOTC-SM using QPSK for 2 bits/s.Hz
or 8-PSK for 3 b/s.Hz or 16-QAM for 4 b/s.Hz (Başar et al., 2012).
52
3.5.2 SOTC-SM decoding and performance:
Viterbi algorithm is used to perform the ML decoding which intends to find the
most-likely transmitted path, with minimum branch metric among all states. In this
scheme, the decoder benefits from the orthogonality of the core STBC codes to reduce the
total number of the required calculations.
The high number of parallel transitions at each state increases the complexity of the
decoding process. For example, for a SOTC-SM code with 4 b/s.Hz, 4-state and 16-QAM,
Table (3.1): The trellis state transition matrices for SOTC-SM (Başar, Aygölü,
Panayırcı, & Poor, 2012).
53
the total number of orthogonal codes that diverge from each state is 256 and the number
of parallel transitions is 64. In an ordinary case, without any simplification, the total
number of metric calculation that must be performed in the decoder is 256, but the
proposed decoding technique in SO-STTC (Hamid Jafarkhani, 2005) and SOTC-SM
(Başar et al., 2012) reduced this complexity significantly.
Figure (3.17) shows the FER performance of SOTC-SM code with 2, 4 and 8-state
at 2 b/s.Hz while Figure (3.18) shows the FER performance of SOTC-SM codes with 2, 4
and 8-state at 3 b/s.Hz compared with that of SO-STTC. In Figure (3.18), the 4-state
SOTC-SM FER is improved over SO-STTC by about 2.2 and 1.6 dB for nR =1 and 2,
respectively, whereas the 8-state-I SOTC-SM achieved SNR gains of 2.1 and 1.7 dB for
nR = 1 and 2, respectively.
Figure (3.17): FER performance of SOTC-SM codes with 2, 4 and
8-state at 2 bits/s.Hz (Başar et al., 2012).
54
3.6 Conclusion:
In this chapter, some of the important schemes that are based on the trellis coding
are presented. These schemes include SO-STTC and STBC-SM. The basic idea in these
schemes is designing the super-set of Alamouti’s STBC and the STBC-SM over the trellis
coding. The main advantage of these codes is the high error performance due to the
combining between both the diversity and the coding gain. However, These codes suffer
from the high complexity decoding and the degradation of the error performance at high
data rates.
Figure (3.18): FER performance of SOTC-SM codes with 2,
4 and 8-state at 3 bits/s.Hz (Başar et al., 2012).
55
Chapter 4
Super Orthogonal Double
Space-Time Trellis Coding
(SO-DSTTC)
56
Chapter 4
Super Orthogonal Double Space-Time Trellis Coding
(SO-DSTTC)
Super Orthogonal Double Space-Time Trellis Coding (SO-DSTTC) is a novel
technique that aims to introduce a MIMO transmission scheme that achieves high data
rates with a low complexity decoder. It mainly benefits from the coding and diversity
gains in SO-STTCs and then increasing the performance and decreasing the receiving
complexity by dividing the overall encoding system into two symmetrical independent
SO-STTC with half of the rate for each. Each system employs a different pair of transmit
antennas.
High number of parallel branches in trellis code has a negative impact on the error
performance of the system. The parallel branching problems become worse when higher
data code is desired and/or lower complexity code is designed by reducing the number of
trellis code states. The division of the encoding system into two separated SO-STTCs
with half of the rate for each reduces the number of the parallel branches in each state in
the code. At the same time, it reduces the complexity of the maximum-likelihood decoder.
To elaborate the idea of the new scheme, assume that we have a 4-state MIMO
system with spectral efficiency 3 b/s.Hz. In SO-STTC, there are 64 transitions diverge
from each state and merge into the next states and thus the number of parallel branches is
16. While in SO-DSTTC, there are two systems with 1.5 b/s.Hz for each. For each state
in both systems, there are 8 transitions diverge from it and there are only two parallel
branches. This significant decreasing in the number of overall transitions from each state
and the resultant number of the parallel branches enhance the error performance of the
system, especially in the high data rate systems such as 4 b/s.Hz, and also in reducing the
complexity of the ML decoder.
57
4.1 SO-DSTTC Encoding:
For generality, consider a MIMO system with 𝑁𝑇 transmit antennas, 𝑁𝑅 receive
antennas and 𝑘 b/s.Hz spectral efficiency. As shown in the block diagram of SO-DSTTC
encoder in Figure (4.1), we firstly construct two symmetrical 𝑁𝑇 × 𝑁𝑅 SO-STTC systems
each with 𝑘 2⁄ b/s.Hz spectral efficiency . Each system employs different pair of transmit
antennas, i.e. the first system employs the first and the second transmit antennas, while
the second employs the third and the forth.
The incoming data stream is divided into two streams. For each system, 2k bits are
encoded by SO-STTC and produce an Alamouti’s STBC according to the trellis structure
of the employed code. The number of leaving branches from each state is 2k and the
number of the parallel branches is equal to (2k/number of merging states).
Now, Consider a 4×2 SO-DSTTC MIMO system. The transmitted matrix is
𝑋 = [𝑠1𝑒
𝑗𝜃11 𝑠2𝑒𝑗𝜃12 𝑠3𝑒
𝑗𝜃21 𝑠4𝑒𝑗𝜃22
−𝑠2∗𝑒−𝑗𝜃12 𝑠1
∗𝑒−𝑗𝜃11 −𝑠4∗𝑒−𝑗𝜃22 𝑠3
∗𝑒−𝑗𝜃21]
𝑇
(4.1)
where (𝑠1, 𝑠2) are the transmitted symbols from the first antenna group and (𝑠3, 𝑠4) are
the transmitted symbols from the second antenna group. The transmitted symbols
De- m
ultip
lexer
SO-STTC
Encoder 1
De-M
UX
1
x1, x2 Stream 1
SO-STTC
Encoder 2
Stream 2
Data In
x3, x4
De-M
UX
2
Figure (4.1): SO-DSTTC encoder’s block diagram.
58
𝑠𝑖, 𝑖 = 0, 1, … , 4 are drawn from M-PSK/QAM with phase rotations of {𝜃11, 𝜃12} for
(𝑠1, 𝑠2) and {𝜃21, 𝜃22} for (𝑠3, 𝑠4) , respectively. In the proposed scheme, the rotating
angles of the other sets of the constellation points were optimized to ensure maximum
diversity and coding gain.
The received signal matrix over flat fading channel during two-time intervals can
be expressed as
𝑌 = 𝐻𝑋 + 𝑍 (4.2)
where,
𝑌 = [𝑦11 𝑦21 ⋯ 𝑦𝑁1
𝑦12 𝑦22 ⋯ 𝑦𝑁2]𝑇
(4.3)
𝑦𝑛𝑘 denotes the received signal by the 𝑁𝑡ℎ receive antenna at timeslot k (in Alamouti’s
STBC, k = 1,2).
𝐻 = [
ℎ11 ℎ12 ℎ13 ℎ14
ℎ21 ℎ22 ℎ23 ℎ24
⋮ ⋮ ⋮ ⋮ℎ𝑁1 ℎ𝑁2 ℎ𝑁3 ℎ𝑁4
] (4.4)
where ℎ𝑛𝑚 denotes the channel coefficient between the 𝑚𝑡ℎ transmit antenna and the 𝑛𝑡ℎ
receive antenna.
𝑍 = [𝑧11 𝑧21 … 𝑧𝑁1
𝑧12 𝑧22 … 𝑧𝑁2]𝑇
(4.5)
where 𝑧𝑛𝑘 represents the noise element in the 𝑛𝑡ℎ receive antenna at timeslot k.
The system model in Equation (4.2) can be changed to the following equivalent
form:
59
𝑦 =
[ 𝑦11
𝑦12∗
⋮𝑦𝑁1
𝑦𝑁2∗ ]
= 𝐻𝑒𝑥 + 𝑛 (4.6)
where,
𝐻𝑒 =
[ ℎ11 ℎ12 ℎ13 ℎ14
ℎ12∗ −ℎ11
∗ ℎ14∗ −ℎ13
∗
⋮ ⋮ ⋮ ⋮ℎ𝑁1 ℎ𝑁2 ℎ𝑁3 ℎ𝑁4
ℎ𝑁2∗ −ℎ𝑁1
∗ ℎ𝑁4∗ −ℎ𝑁3
∗ ]
, 𝑥 =
[ 𝑠1𝑒
𝑗𝜃11
𝑠2𝑒𝑗𝜃12
𝑠3𝑒𝑗𝜃21
𝑠4𝑒𝑗𝜃21 ]
(4.7)
4.2 Set partitioning of the super-set of STBCs:
As was shown in Section (3.3), the set-partitioning of the super-set of Alamouti’s
code is performed to ensure that the constructed trellis structure achieves the needed
coding gain. The set-partitioning of these codes is based on the CGD metric, which is
expressed as:
𝑑 = det (𝐴(𝑐𝑖, 𝑐𝑗)), (4.8)
where:
𝐴(𝑐𝑖, 𝑐𝑗) = 𝐷(𝑐𝑖, 𝑐𝑗)𝐻𝐷(𝑐𝑖, 𝑐𝑗) (4.9)
and D is the difference matrix between transmission matrices ci and cj and expressed as:
𝐷(𝑐𝑖, 𝑐𝑗) = 𝑐𝑖 − 𝑐𝑗 , 𝑖 ≠ 𝑗 (4.10)
The set partitioning of STBC codewords for 8-PSK is illustrated in Figure (4.2) and
the set partitioning of STBC codewords for QPSK is illustrated in Figure (4.3), while the
60
set partitioning of STBC codewords for 16-QAM is based on the following criteria (Wang
& Xia, 2007):
The first step is to construct an offset array for 24-QAM (𝑂4), which are used to
generate all subsets at each partitioning level. The offset array is illustrated in Table (4.1):
Table (4.1): The offset array of O4 for 16QAM:
k 1 2 3 4 5 6 7 8
𝑶𝟒(𝒌) (0,1) (1,1) (0,2) (2,2) (0,4) (4,4) (0,8) (8,8)
When the offset array O4 is generated, the set partitioning for a 16-QAM can be
done as the following:
• Let the set S0000 = (0, 0).
• For i = 0, 1, …, 3:
o Construct another subset at (2𝑀 − 𝑖)𝑡ℎ partition level as 𝑆0…1⏟4−𝑖
= 𝑆0…0⏟4−𝑖
⊕
𝑂4(4 − 𝑖), where ⊕ is modulo 24 addition.
o Generate 𝑆 0…0⏟4−𝑖−1
, which is a subset at (2𝑀 − 𝑖 − 1)𝑡ℎ partition level, by
combining 𝑆0…0⏟4−𝑖
and 𝑆0…1⏟4−𝑖
, i.e., 𝑆 0…0⏟4−𝑖−1
= 𝑆0…0⏟4−𝑖
∪ 𝑆0…1⏟4−𝑖
61
Figure (4.3): The set partitioning of STBC codewords for 8-PSK.
Figure (4.2): The set-partitioning of STBC codewords for QPSK.
62
4.3 SO-DSTTC Trellis structure for different states:
After performing the set-partitioning of the super-set of STBC codewords, the trellis
structure for the code can be constructed by assigning different STBC codewords for
transitions originating from every state.
Figures (4.4 - 4.6) demonstrate examples of the new SO-DSTTC scheme. In these
figures, 𝐶(𝑠1, 𝑠2, 𝜃1, 𝜃2) represents the particular codewords from the set-partitioning for
the state with rotating angles θ1 and θ2 for the symbols s1 and s2, respectively. As
symmetric codes are used, each example shows one of the parallel codes trellis structure.
Figure (4.4) shows a 4-state example with a rate of 3 b/s.Hz. In this example, we use
QPSK and the corresponding set-partitioning in Figure (4.2). In our new code, each state
has 8 branches departing from it, while in similar system in SO-STTC and SOTC-SM,
they use an 8-PSK and each state has 64 branches diverge from it. In this example, only 2
pairs of optimized rotating angles are used. 𝐶(𝑠1, 𝑠2, 0,0) is assigned for the first two states
and 𝐶(𝑠1, 𝑠2, 𝜃1, 𝜃2) is assigned for the last two states in order to increase the coding gain.
Figure (4.5) shows an 8-state SO-DSTTC example with a rate of 3 b/s.Hz using
QPSK and the corresponding set-partitioning in Figure (4.2). In this example, the number
Figure (4.4): A 4-state SO-DSTTC with r = 3 b/s.Hz and QPSK (the first code
trellis structure).
63
of branches originating from each state is equal to 8 and these branches merge into 4 states
only, so there are 2 parallel branches in each state. In this example, we use two pairs of
optimized rotating angles only.
In Figure (4.6), an example of 8-state SO-DSTTC is illustrated. This example also
uses a QPSK modulation scheme and the corresponding set-partitioning in Figure (4.2)
with a rate of 3 b/s.Hz. Every state in this code has 8 diverging branches that merge into
the next eight states. Hence, in this code, there are no parallel branches in any state. A four
pairs of optimized rotating angles are used in this example to ensure achieving the
maximum coding gain.
Figure (4.5): An 8-state SO-DSTTC with r = 3 b/s.Hz and QPSK (the first code
trellis structure).
64
Figure (4.7) illustrates an example of 4-state SO-DSTTC for a rate of 4 b/s.Hz using
QPSK modulation scheme. In this example, each state has 16 diverging branches. A four
pairs of optimized rotating angles are used to ensure achieving the maximum coding gain.
Figure (4.6): An 8-state SO-DSTTC with r = 3 b/s.Hz and QPSK (the first code
trellis structure).
65
4.4 Rotating angles optimization:
Rotating angles pairs {𝜃1, 𝜃2} are considered to be optimized in our design to ensure
maximum coding and diversity gain. These angles are related directly to the minimum
CGD, so this optimization is performed to maximize the minimum CGD of codewords
that will be assigned to the different states of the code.
In this work, the optimized rotating angles pairs are calculated by a linear
optimization algorithm with a cost function that maximize the min CGD and the results
are recorded in Table (4.2). In Table (4.2), the symbols are assigned according to Figures
(4.4) – (4.7) where 𝜃 ∈ {−𝜋, 𝜋}.
Table (4.2): The optimized rotating angles of SO-DSTTC in Figures (4.4) - (4.7)
Figure
Spectral
efficiency
(b/s.Hz)
Num. of
states
Num. of
rotating
angle pairs
θk1 (rad) θk2 (rad)
4.4 3 4 2 0 0
2.0944 -0.5236
4.5 3 8-I 2 0 0
Figure (4.7): A 4-state SO-DSTTC with r = 4 b/s.Hz and QPSK (the first
structure only).
66
2.8274 0.7854
4.6 3 8-II 4
0 0
-1.5708 2.618
-2.618 -2.618
2.0944 3.1416
4.7 4 4 4
0 0
0.9163 -2.4871
-1.4399 -0.9163
-2.7489 -1.4399
4.5 ML decoding with Interference Cancellation (IC) for SO-DSTTC
scheme:
SO-DSTTC receiver uses the Viterbi algorithm to perform a soft ML decoding
process and find the most likely valid path for a specific frame length. In general, the
decoding process starts by cancelling the interference between the two systems using IC
algorithm such as MMSE, zero nulling, …, etc. Then, the output of the previous step is
processed to decode the output from the first system. Finally, the output from the second
system can be decoded after eliminating the impact from the first.
The SO-DSTTC decoding process passes through the following stages:
1) Calculate the weights (𝜶𝟏, 𝜶𝟐)for MMSE-IC:
The weights 𝛼1 and 𝛼2 are used in the interference canceller that minimize
the MSE which is used in the decoding process of (𝑠1, 𝑠2) , the transmitted symbols
from the first structure. According to the system model in Equation (4.6), 𝛼1 and
𝛼2 can be calculated as the following:
67
𝑀 = 𝐻𝑒𝐻𝑒𝐻 +
2.5
𝜌𝐼2𝑁 (4.11)
𝛼1 = 𝑀−1ℎ1 , 𝛼2 = 𝑀−1ℎ2 (4.12)
where ℎ𝑖 in Equation (4.12) is the 𝑖𝑡ℎ column of 𝐻𝑒 in Equation (4.7), ρ is the SNR
and 𝐼𝑀𝑇 represents an identity matrix of size 𝑀𝑇 × 𝑀𝑇 .
2) First structure decoding (𝒔𝟏, 𝒔𝟐):
The Viterbi algorithm is used to perform the MMSE decoder to find the most
likely path. The metric used in the Viterbi process is MMSE-IC based on the
weights of 𝛼1 and 𝛼2, which are calculated in the previous step.
At each state, we should find the best transition among all transitions. Then,
we used the best transition to calculate the path metric in the Viterbi process.
According to the system model in Equation (4.6), the branch metric used in
the Viterbi algorithm is
𝐽(𝑠1, 𝑠2) = ‖𝛼1𝐻𝑦 − 𝑠1𝑒
𝑗𝜃1‖2+ ‖𝛼2
𝐻𝑦 − 𝑠2𝑒𝑗𝜃2‖
2 (4.13)
Due to the orthogonality of Alamouti’s STBC, the previous metric can be
decomposed into two separated metrics where
𝐽(𝑠1, 𝑠2) = 𝐽1(𝑠1) + 𝐽2(𝑠2) (4.14)
and
𝐽1(𝑠1) = ‖𝛼1𝐻𝑦 − 𝑠1𝑒
𝑗𝜃1‖2 (4.15)
𝐽2(𝑠2) = ‖𝛼2𝐻𝑦 − 𝑠2𝑒
𝑗𝜃2‖2 (4.16)
J1 is a function of s1 only and J2 is a function of s2 only. This separation
simplified the search for the branch with the minimum metric among all branches.
68
Unlike the orthogonal STBC, not all pairs of the constellation symbols are allowed
for each trellis transition. So, the STBC symbols are not independent and therefore
we cannot perform the separated decoding process. For explanation, if we find the
symbols (𝑠1) that minimize 𝐽1 and the symbol (𝑠2) that minimize 𝐽2 , the pair
(𝑠1, 𝑠2) may be not a valid pair for the specific transition. In order to utilize the
reduced complexity, the set-partitioning of the super-set of STBC must be merged
with the separate decoding (Hamid Jafarkhani, 2005).
The reduced complexity decoder can be performed by dividing the set of all
merging STBC codewords to subsets for which the symbols (𝑠1, 𝑠2) are
independent. Then, we find the symbols (𝑠1, 𝑠2) for each subset that minimize 𝐽1
and 𝐽2 independently. After that, we compare the resulted pairs in each subset and
choose the one with the minimum branch metric (𝐽1 + 𝐽2) (Hamid Jafarkhani &
Seshadri, 2003).
Note that, if the state has all the subsets of the set-partitioning, then there is
no need to perform the previous procedure since it has all the pairs of (𝑠1, 𝑠2).
3) Second structure decoding (s3, s4):
After decoding (𝑠1, 𝑠2) for the whole frame, we can eliminate the impact of
the first system using Equation (2.28). Now, the decoding process can be
performed as the first structure with modification on the branch metric. The used
branch metric after canceling the first system contribution is
𝐽(𝑠3, 𝑠4) = ∑ |�̃�𝑚1 − ℎ𝑚3𝑠3𝑒𝑗𝜃1 − ℎ𝑚4𝑠4𝑒
𝑗𝜃2|2+ |�̃�𝑚2
∗ + ℎ𝑚3∗ 𝑠4𝑒
𝑗𝜃2 − ℎ𝑚4∗ 𝑠3𝑒
𝑗𝜃1|2𝑁
𝑚=1 (4.17)
where �̃� represents the received vector after cancelling the contribution of the first
system. By expanding Equation (4.17) and removing the constant terms, the
branch metric results in the following:
69
𝐽(𝑠3, 𝑠4) = ∑ 2ℜ{�̃�𝑚2∗ ℎ𝑚3𝑠4𝑒
−𝑗𝜃2 − �̃�𝑚2∗ ℎ𝑚4𝑠3𝑒
−𝑗𝜃1 − �̃�𝑚1ℎ𝑚3∗ 𝑠3𝑒
−𝑗𝜃1 −𝑁𝑚=1
�̃�𝑚1ℎ4∗𝑠4𝑒
−𝑗𝜃2} (4.18)
Now, Equation (4.18) can be rewritten as two separated functions
𝐽(𝑠3, 𝑠4) = 𝐽1(𝑠3) + 𝐽2(𝑠4) (4.19)
where,
𝐽1(𝑠3) = −ℜ{[�̃�𝑚2∗ ℎ𝑚4 − �̃�𝑚1ℎ𝑚3
∗ ]𝑠3𝑒−𝑗𝜃1} (4.20)
𝐽2(𝑠4) = ℜ{[�̃�𝑚2∗ ℎ𝑚3 − �̃�𝑚1ℎ4
∗]𝑠4𝑒−𝑗𝜃2} (4.21)
Note that J1 is a function of s3 only and J2 is a function of s4 only. The
simplified ML decoder can be done now as was done with the first system.
4) Two-step interference cancellation with ML:
In this work, the two-step decoding stage is performed to enhance the overall
performance of the system. In the first step we get the decoded vector 𝑑0 by
decoding (𝑠1, 𝑠2) first and (𝑠3, 𝑠4) later. In the second step, we assume decoding
(𝑠3, 𝑠4) first and then (𝑠1, 𝑠2) after the cancellation. The decoded vector 𝑑1 is
obtained now. For each step, we calculate the sum of MSE of the decoded vectors
which are denoted by Δ0 and Δ1 as respectively. The receiver chooses 𝑑0 if
Δ0 < Δ1 or 𝑑1 if Δ0 > Δ1.
4.6 Complexity of SO-DSTTC decoder:
Based on the illustrated decoding criteria in previous section, one can estimate the
degree of the complexity for the new scheme. SO-STTC decoding complexity and
calculations are explained in (Hamid Jafarkhani, 2005) and based on this calculations we
will illustrate the new scheme complexity.
70
In the following example, we will elaborate the complexity degree of the decoding
algorithm by needed calculations in the step of finding the best branch among all parallel
branches. Suppose that we have the 4-state trellis structure shown in Figure (4.4) with a
rate of 1.5 b/s.Hz. The system uses a QPSK modulation with the set-partitioning in
Figure (4.2).
We can divide the needed calculations into stages:
1) Calculate the weights (𝜶𝟏, 𝜶𝟐):
Calculating the weights (𝛼1, 𝛼2) requires 128 real multiplications and 135
real additions (Jung & Lee, 2009). But, this step is calculated once at each frame,
so the complexity of this stage is divided by the frame length.
2) ML decoding calculations:
By the same criteria that is used in calculating the branch metric in SO-STTC
(Hamid Jafarkhani, 2005), this step requires 24 real multiplications and 16 real
additions for a transition that includes the transmission of two symbols.
3) The two-step decoding:
The previous step is repeated two times to perform the two-step MMSE.
P00 P01
P10 P11
P01 P00
P11 P10
Figure (4.8): A 4-state SO-DSTTC with r = 3 b/s.Hz using QPSK.
71
Table (4.3) tabulates the stages of the branch metric and the corresponding
calculations in each step for a rate of 3 b/s.Hz, while Table (4.4) tabulates the same
calculations for a rate of 4 b/s.Hz.
Table (4.3): Number of operations required by the stages of the branch metric for a rate
of 3 b/s.Hz
stage Number of
multiplications
Number of
additions
Calculate the weights (𝛼1, 𝛼2) 6 7
First system ML decoding 24 16
second system ML decoding 24 16
Repeat the first system ML decoding 24 16
two-step decoding 88 60
Total 166 115
Table (4.4): Number of operations required by the stages of the branch metric for a rate
of 4 b/s.Hz
stage Number of
multiplications
Number of
additions
Calculate the weights (𝛼1, 𝛼2) 6 7
First system ML decoding 32 24
second system ML decoding 32 24
Repeat the first system ML decoding 32 24
two-step decoding (optional) 112 84
Total 214 163
72
Table (4.5) presents the total number of the required operations for SO-STTC and
SOTC-SM simplified ML decoder (Başar et al., 2012).
Table (4.5): Number of operations required by SO-STTC and SOTC-SM ML decoder:
3 b/s.Hz (8-PSK)
4-state 8-state
SO-STTC
184 RM
104 RA
376 RM
216 RA
SOTC-SM 192 RM
112 RA
360 RM
308 RA
In general, we observe that the complexity of the new scheme is slightly lower than
in SO-STTC and SOTC-SM at schemes with a rate of 3 b/s.Hz. But in SO-DSTTC with a
rate of 4 b/s.Hz, the complexity becomes much less than the other schemes.
73
4.7 Conclusion:
SO-DSTTC is a novel technique based on dividing the overall system into two
identical SO-STTC systems with a half of the total rate for each. This technique improves
the error performance and decreases the decoding complexity especially when high data
rate is required.
SO-DSTTC can be designed systematically by design a single SO-STTC for half of
the rate and optimize the rotating angles. Throughout the chapter, multiple schemes are
designed for various number of states and rates.
Dividing the full rate trellis structure into two similar structures with half of the rate
for each helped in decreasing the number of needed codes for the design, the number of
parallel branches and the complexity of the encoding and decoding. In general, this
technique contributes in increasing the error performance of the system, especially in the
high data rate, and, at the same time, decreases the complexity of the system.
However, due to the using of double structure of the trellis code, the interference
between the two system impacts on the performance of the overall system and needs
interference-cancellation algorithm to eliminate it. Furthermore, the constellation space
used in the design is increased due to using rotating angles other than 𝑛𝜋
2 rad.
74
Chapter 5
Simulation Results
75
Chapter 5
Simulation Results
In the previous chapter, the design criteria for the new scheme was illustrated. In
this chapter, the simulation results for the proposed SO-DSTTC are demonstrated using
four transmit antennas and two receive antennas. The error performance of the new
scheme is compared with that of SO-STTC and SOTC-SM schemes. The FERs of these
schemes are evaluated using Monto Carlo simulation for various spectral efficiencies and
number of trellis states. In all cases, the simulation is done using a frame length of 40k
bits for a spectral efficiency of k b/s.Hz. All simulations are evaluated in MATLAB
simulation environment.
We assume a quasi-static flat Rayleigh fading model for the channel. Therefore, the
path gains are independent complex Gaussian random variables and fixed during the
transmission of one frame. In addition, we assume that the perfect Channel State
Information (CSI) is available at the receiver and the transmitter.
5.1 Results for spectral efficiency of 3 b/s.Hz:
Figure (5.1) shows the frame error rates for 4- and 8-state SO-DSTTC at 3 b/s.Hz,
which are illustrated in Figures (4.4), (4.5) and (4.6). The rotation angles are provided in
Table (4.2) for each code. For comparison, we also provided the results for SO-STTCs
with the same configurations and spectral efficiencies.
The FER performance of a SO-DSTTC is better than that of the corresponding SO-
STTC at lower SNR (< 15 dB), but at higher SNR, the FER of SO-DSSTC is worse than
SO-STTC. This behavior at higher SNR is related to the occurred interference between
the two systems. However, the decoding complexity of SO-DSTTC is lower than the
decoding complexity of SO-STTC.
76
Figure (5.2) shows the FER for the proposed scheme at 3 b/s.Hz compared with the
results from SOTC-SM at the same rate. In this figure, we can notice that the error
performance of the new scheme is worse than that of the SOTC-SM, but any way, it has
a lower decoding complexity compared with it.
Figure (5.1): FER performance for 4- and 8-state SO-DSTTC and SO-
STTC at 3 b/s.Hz.
77
5.2 Results for spectral efficiency of 4 b/s.Hz:
Figures (5.3) and (5.4) shows the BER and FER for 4- and 8-state SO-DSTTC
scheme at 4 b/s.Hz, respectively.
Figure (5.2): FER performance for 4- and 8-state SO-DSTTC and SOTC-
SM at 3 b/s.Hz.
78
Figure (5.3): FER performance for 4-state and 8-state SO-DSTTC at 4 b/s.Hz.
Figure (5.4): BER performance for 4-state and 8-state SO-DSTTC at 4 b/s.Hz.
79
Figure (5.5) shows the FER of the simulation results for SO-DSTTC scheme at
4 b/s.Hz compared with the results from SOTC-SM and SO-STTC schemes at the same
rate. In this case, the FER performance of the 4-state SO-DSTTC is better than that of a
4-state SOTC-SM and SO-STTC by about 1 dB. Also, the decoding complexity of
a SO-DSTTC is lower than that of a SOTC-SM and SO-STTC with similar number of
states, as shown in Section (4.6).
Figure (5.5): FER performance for 4-state SO-DSTTC, SOSTTC and SOTC-SM
at 4 b/s.Hz.
80
Figure (5.6) shows the FER of the 4- and 8-state of the proposed scheme at 3 and
4 b/s.Hz, respectively.
5.3 Comparison between using two-step MMSI-IC and using only one-step:
Figure (5.7) shows the comparison between using two-step MMSE-IC and one-step
in the decoding process of SO-DSTTC. In that figure, we perform the comparison on the
results from 4-state SO-DSTTC at 3, 4 b/s.Hz, respectively. Using two-step MMSE
improves its results over the results of one-step by about 2 dB for 3, 4 b/s.Hz. However,
performing MMSE over two-step increases the complexity of the receiver.
Figure (5.6): FER performance of SO-DSTTC at 3 and 4 b/s.Hz.
81
Figure (5.7): FER performance for 4-state SO-DSTTC with and without two-step
decoding.
82
5.4 Conclusion:
In this chapter, the simulation results for the proposed scheme with 4- and 8-states
at 3 and 4 b/s.Hz were represented. Also, they were compared with the results from SO-
STTC and SOTC-SM.
The comparison shows that the new scheme at 3 b/s.Hz achieves an error
performance improvement over SO-STTC at the same rate by about 0.5 dB in the lower
SNR (<15 dB), while it becomes worse than that of SO-STTC at the higher SNR due to
the occurred interference between the two systems. Also at 3 b/s.Hz, the error performance
of the proposed scheme is worse than that of SOTC-SM.
At 4 b/s.Hz, the FER performance of the 4- and 8-state SO-DSTTC is better than
that of a 4- and 8-state SOTC-SM and SO-STTC by about 1 dB.
As was shown in this chapter, the new scheme offers a good design for high data
rate systems. It has better error performance compared with similar systems and has a low
complexity decoder.
83
Chapter 6
Conclusion and Future
Works
84
Chapter 6
Conclusion and Future Works
6.1 Conclusion:
STCs is a coding technique that aims to benefit from the MIMO systems by
introducing a correlation between the transmitted signals. Multiple STC schemes are
proposed like STBC, STTC and SM codes. Each scheme has its own advantage like the
achieved gain (diversity, coding or the both) and the degree of the receiver complexity.
Other STC schemes are also introduced based on other schemes to benefit from their
advantages like SO-STTC which merged between STBC and STTC to achieve a coding
gain beside the diversity gain at full rate. Also, SOTC-SM was designed based on the
merging between STBC-SM and STTC.
In this thesis, a novel MIMO transmission scheme was proposed based on three
main concepts:
1. Constructing super orthogonal codes from Alamouti’s STBC. This concept has a
key role in increasing the space of the available codes and therefore the ability of
designing a full rate trellis structure with SO-STBC. Also, using STBCs in the
scheme gives it the diversity gain.
2. Trellis coding which gives the scheme the coding gain advantage.
3. Double space time scheme which reduces the number of the overall branches in
the trellis structure and hence, improving the error performance of the system and
decreasing the complexity of the decoder.
By mixing these concepts, the super orthogonal double space-time trellis coding
scheme is proposed. The new scheme is based on dividing the overall system into two
identical SO-STTC systems with a half of the total rate for each. By this way, the number
of the needed codes for designing the trellis structure and the number of parallel branches
is decreased.
85
The first step in designing SO-DSTTC is to generate super-set from Alamouti’s
STBC. The rotating angles used in this step must be optimized to ensure maximizing the
minimum CGD of the codes. Then, set partitioning is performed over the generated super-
set. After that, the trellis structure can be designed by assign every branch with the
appropriate code from the set partitioning.
The new scheme achieved an error performance improvement over SO-STTC and
SOTC-SM in the high data rate systems (4 b/s.Hz). From the results, it is clear that the
performance of the 4- and 8-state SO-DSTTC at 4 b/s.Hz is better than that of a 4- and 8-
state SOTC-SM and SO-STTC by about 1 dB.
The decoding complexity of the new scheme is reduced due to the lower number of
leaving branches in the trellis structure. In the decoding process, a two-step MMSE with
interference cancellation was used to decode the four symbols. The complexity
calculations for SO-STTC, SOTC-SM and the new scheme show that the new scheme is
slightly lower complexity than the others at spectral efficiency of 3 b/s.Hz, while at 4
b/s.Hz, it becomes less complexity.
However, due to the using of double structure of the trellis code, the interference
between the two system impacts on the performance of the overall system and needs
interference-cancellation algorithm to eliminate it. Furthermore, the constellation space
used in the design is expanded due to the using of rotating angles other than 𝑛𝜋
2 rad in the
super-set generating step.
86
6.2 Future Works:
1. For the proposed scheme, apply the mutual Viterbi detection for the two structure
and check the performance and the complexity of the new scheme.
2. Check the performance of the new scheme over higher data rates (spectral
efficiency > 4 b/s.Hz).
3. Apply the same criteria for the STBC-SM instead of SO-STBC.
87
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