carrier aggregation intermodulation distortions in 4g and

VRIJE UNIVERSITEIT BRUSSELDepartment of Fundamental Electricity and Instrumentation (ELEC)

Carrier aggregation intermodulation distortions in 4G and 5Gmobile networks

Thesis submitted in fulfilment of the requirements for the degree of Doctor in Engineering(Doctor in de Ingenieurswetenschappen)

byLeonidas NIYONKURU

Promoter: Prof. Dr. ir Gerd VANDERSTEEN

Co-Promoter: Prof. Dr. ir Leo VAN BIESEN

Members of the jury:

Prof. dr. ir. STEENHAUT KRIS (President)

Vrije Universiteit Brussel, Belgium

Prof. dr. VOUNCKX ROGER (Vice President)


Prof. dr. ir. OTTEVAERE HEIDI (Secretary)


Prof. dr. ir. TIBERGHIEN JACQUES


Prof. dr. ir. LAY-EKUAKILLE Aime

University of Salento, Italy

Prof. dr. NGENDAKUMANA GASPARD

University of Burundi, Burundi

March, 2020

Abstract

This PhD thesis analyses the interferences caused by carrier aggregation intermodulationin 4G and 5G mobile networks. Many research works have mentioned the issue of carrieraggregation intermodulation without a systematic analysis of how often this may happenin mobile networks. In the first part of this work, a method for the calculation of frequen-cies, shapes and magnitudes of intermodulation distortions is elaborated. Based on it andusing the list of aggregated bands as elaborated by 3GPP (Third Generation PartnershipProject), an algorithm is developed for finding the intermodulation frequencies, the in-terference cases for any order and for any number of aggregated bands, be it in uplink ordownlink transmission. A predistortion structure is also suggested for which each carrieruses his one I/Q modulator, opposite to the suggested in the literature topology for whichone I/Q modulator is used for all the carriers. The advantage of the suggested structureis that it can be used for interband carrier aggregation intermodulation cancellation forfrequency bands remote to each other. The second part of this PhD thesis focuses onthe design of digital intermodulation synthesizer to be used in the suggested predistortionstructure. The digital technology was chosen for easy integration with the digital phaselocked loop. Measurements performed on the designed device showed that the idea ofdigital intermodulation synthesizer is viable, however more efforts are needed to mitigatespurs at the output signal.

iii

Dedication

To my spouse Gaudence NDUWIMANA and my children Guy Fleury NISHIMWE, SamuelNDAYISHIMIYE, Moise MUGISHA, David MUCO and Levy Dior NGABIRE.

v

Declaration

I declare that this thesis is my own, original work.

vii

Acknowledgements

Many people and organizations have contributed to the realisation of this PhD thesis.Those who are not mentioned on this page may know that I am thankful to them also.

• I would like to thank Prof. Dr. ir. Gerd VANDERSTEEN and Prof. Dr. ir.Leo VAN BIESEN, respectively promoter and copromoter of this work. By theirknowledge and patience, they have helped me to reach this final destination. I justwant to say: thank you!!!

• Many thanks to all the staff of department ELEC. They have created a friendlyenvironment for my research.

• I would like to thank also the VLIR-UOS project and ELEC Department for theirfinancial support.

• Prof. Dr.ir. BATURURIMI Leonard, through the Project-5 ofVLIR-UOS withUniversity of Burundi, has played a very important role for the accomplishment ofthis work. Many thanks to him.

ix

Contents

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx

List of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii

General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

I Interference due to carrier aggregation nonlinear distor-tions 3

1 Carrier aggregation in 4G and 5G mobile networks 5

1.1 Brief review of mobile networks . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 LTE, LTE-Advanced and 5G mobile networks . . . . . . . . . . . . . . . . 6

1.2.1 Long Term Evolution (LTE) . . . . . . . . . . . . . . . . . . . . . . 6

1.2.2 LTE Advanced (LTE-A) . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.3 Fifth generation (5G) . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Carrier aggregation in 4G and 5G . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.1 The concept of carrier aggregation . . . . . . . . . . . . . . . . . . 12

1.3.2 Transmitter architectures for carrier aggregation . . . . . . . . . . . 12

1.3.2.1 Single-band RF transmitter . . . . . . . . . . . . . . . . . 12

1.3.2.2 Multiple branch transmitter . . . . . . . . . . . . . . . . . 14

1.3.2.3 Multiple branch transmitter with multiband RF filter andantenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.2.4 Multiband transmitter architecture . . . . . . . . . . . . . 14

1.3.2.5 Delta-sigma-based CA transmitter architecture . . . . . . 14

2 Intermodulation distortions due to carrier aggregation in 4G and 5Gmobile networks 15

2.1 Linear and nonlinear system . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Polynomial model of a nonlinear element . . . . . . . . . . . . . . . . . . . 16

2.3 Total Harmonic Distortion(THD) . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Intermodulation power calculation . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Intercept point concept . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Power of the second order intermodulation distortions (IM2) . . . . 20

2.4.3 Power of third order intermodulation distortions (IM3) . . . . . . . 22

2.5 Carrier aggregation intermodulation distortion in 4G and 5G networks . . 23

2.5.1 The convolution and the support frequency band . . . . . . . . . . 24

xi

CONTENTS

2.5.2 Example of calculation of the second and third order intermodula-tion of carrier aggregation of band 17 with band 4 . . . . . . . . . . 26

2.6 Carrier aggregation intermodulation issues in 4G and 5G mobile network . 272.6.1 Carrier aggregation intermodulation in 4G and 5G mobile networks

and receiver desensitization . . . . . . . . . . . . . . . . . . . . . . 272.7 Calculation of IMD and interference frequencies . . . . . . . . . . . . . . . 34

2.7.1 Calculation of IMD and harmonics . . . . . . . . . . . . . . . . . . 342.7.2 Interference calculation . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.8 IMDs and Interference in 4G and 5G mobile networks . . . . . . . . . . . . 372.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3 Predistortion 433.1 Classification of predistortion methods . . . . . . . . . . . . . . . . . . . . 433.2 State-of-the art and suggestion of a new structure . . . . . . . . . . . . . . 45

II Frequency synthesis of the intermodulator carrier 47

4 The digital multiplier 514.1 Design methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2 The theory of the suggested mixer . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.1 90phase shift with D flip-flop . . . . . . . . . . . . . . . . . . . . . 534.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4 Hardware implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.5 Measurement results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.6 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.7 The multiplier model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.7.1 The no spurs condition . . . . . . . . . . . . . . . . . . . . . . . . . 624.7.2 The spectrum of the output of the multiplier . . . . . . . . . . . . . 62

4.8 Spurs attenuation using frequency multiplication and division . . . . . . . 664.9 Generalization of frequency division as a down conversion process . . . . . 74

5 Power spectrum measurement of high frequency angle modulated digitalsignal from output power spectrum of a digital divider 755.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.2 Description of the method . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.4 Results discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6 Overview of Phase Locked Loop 816.1 The phase locked loop (PLL) . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.1.2 The structure of the PLL . . . . . . . . . . . . . . . . . . . . . . . . 81

6.2 Introductory theory for a PLL . . . . . . . . . . . . . . . . . . . . . . . . . 826.3 Type and order of a PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.3.1 General definition of the loop gain K . . . . . . . . . . . . . . . . . 836.3.2 Type I PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

xii

CONTENTS

6.3.2.1 First order PLL . . . . . . . . . . . . . . . . . . . . . . . . 846.3.2.2 Second-Order PLL with lag-lead Filter . . . . . . . . . . . 84

6.3.3 Type II PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.3.3.1 Integrator-Only Loop Filter . . . . . . . . . . . . . . . . . 856.3.3.2 Third-Order Type II PLL . . . . . . . . . . . . . . . . . . 85

6.4 Second order type I PLL parameters . . . . . . . . . . . . . . . . . . . . 866.5 Charge-pump phase-lock loop . . . . . . . . . . . . . . . . . . . . . . . . . 87

7 Design of intermodulator carrier using a multiplier and a PLL 897.1 The CD74HC4046A chip . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.1.1 Overview of overall operation of the PLL chip CD74HC4046 . . . . 897.1.1.1 The voltage controlled oscillator (VCO) . . . . . . . . . . 897.1.1.2 The phase comparators of the CD74HC4046 . . . . . . . . 917.1.1.3 The CD74HC4046 charge pump . . . . . . . . . . . . . . . 91

7.1.2 The VCO frequency . . . . . . . . . . . . . . . . . . . . . . . . . . 967.1.3 The VCO gain Ko and the phase detector gain Kd . . . . . . . . . 97

7.2 The PLL calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.2.1 Phase comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.2.2 The PLL voltage controlled oscillator . . . . . . . . . . . . . . . . . 977.2.3 Spurs mitigation with PLL used as passband filter . . . . . . . . . . 987.2.4 Spurs mitigation with multiplier inserted in the PLL loop . . . . . . 99

7.3 Realization of a frequency multiplier . . . . . . . . . . . . . . . . . . . . . 1047.4 Measurement results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Conclusion 111

A Code mathematica for intermodulation calculation in case of harmonicinputs 113

B Code matlab pour le calcul des intermodulations 115

C code Maxima for IMD and harmonics plotting 121

D Counter CD74hc4059 123

xiii

CONTENTS

xiv

List of Figures

1.1 Intraband contiguous carrier aggregation . . . . . . . . . . . . . . . . . . . 12

1.2 Intraband non-contiguous carrier aggregation . . . . . . . . . . . . . . . . . 12

1.3 Interband carrier aggregation . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4 Candidate transmitter architectures for CA in LTE-advanced systems:(a) Single-band RF transmitter,(b) Multiple branch transmitter,(c) Multi-ple branch transmitter with multiband RF filter and antenna, (d)Multibandtransmitter architecture and (e)Delta-sigma-based CA transmitter archi-tecture [52] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 Intermodulations of harmonics with frequencies close to each other, theIMD products are grouped around DC, ω1 = 1850 rad/s, ω2 = 1900 rad/s,ω3 = 1950 rad/s and their harmonics . . . . . . . . . . . . . . . . . . . . . 18

2.2 Intermodulations of harmonics with frequencies not close to each other,ω1 = 1500 rad/s, ω2 = 1950 rad/s and ω3 = 2300 rad/s the IMD productsare scattered on frequency axis . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Example of third order output intercept point OIP3i and third order inputintercept point IIP3i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Convolution of 2 bands S1 and S2 . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Illustration of the second order harmonics and intermodulation obtainedby graphical method of convolution . . . . . . . . . . . . . . . . . . . . . . 26

2.6 Assumed power vs frequency of the input signals B4 and B17 to a nonlinearpower amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.7 Second order harmonics of B17 . . . . . . . . . . . . . . . . . . . . . . . . 29

2.8 Intermodulation second order I4 17 . . . . . . . . . . . . . . . . . . . . . . 30

2.9 Third order harmonic of Band 17 I17 17 17 . . . . . . . . . . . . . . . . . . 30

2.10 Third order harmonic of Band 4 . . . . . . . . . . . . . . . . . . . . . . . . 31

2.11 Third order intermodulation distortion of Band 4 and band 17 I4 4 17 . . . 31

2.12 Third order intermodulation of band 17 and Band 4 I17 17 4 . . . . . . . . 32

2.13 Receiver desensitization of band 4 by band 17 third order harmonic . . . . 33

2.14 Algorithm for IMD and harmonics calculation . . . . . . . . . . . . . . . . 35

2.15 Algorithm for interference calculation of IMD with a given band . . . . . . 35

2.16 interference of 2 bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.17 The percentage interference is 100% as B17 receiving band is entirely insidethe IMD frequency band . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.18 The percentage interference is 100% as B17 receiving band is entirely insidethe IMD frequency band . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

xv

LIST OF FIGURES

3.1 Predistortion concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2 Simplified functional diagram of a transmitter with ARFPD . . . . . . . . 443.3 Simplified functional diagram of a transmitter with DPD . . . . . . . . . . 443.4 Example of DPD using a carrier whose frequency is a linear combination

of main signals carrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.5 Suggested structure for the subband distortion, with I/Q modulator for

each signal (2 mains signals and the third order intermodulation . . . . . . 46A Structure where the PLL loop is used as passband filter . . . . . . . . . . . 49B Structure where the multiplier is inserted in the PLL loop . . . . . . . . . 50

4.1 90phase shifting using D flip flop . . . . . . . . . . . . . . . . . . . . . . . 534.2 Example showing how frequency division leads to phase division . . . . . . 544.3 Time diagram showing 90phase shift by D flip flop . . . . . . . . . . . . . 544.4 Digital mixer with digital logic . . . . . . . . . . . . . . . . . . . . . . . . . 554.5 Simulation model using Simulink . . . . . . . . . . . . . . . . . . . . . . . 554.6 Inputs and Output RS flip flop (figure 4.5): the output remains in the same

state if the inputs have a different value . . . . . . . . . . . . . . . . . . . . 564.7 Output power spectrum f1=1530 Hz, f2=3060Hz, fout=765 Hz. There is no

spurs as f1 = n|f1− f2|

2is verified, only fundamental and harmonic . . . 56

4.8 Output power spectrum f1=1530 Hz, f2=3500 Hz, fout=985 Hz. There are


2is not verified . . . . . . . . . . . . . . . . . . . . 57

4.9 RS flip flop implementation using NOR gate . . . . . . . . . . . . . . . . . 574.10 The digital multiplier schematic . . . . . . . . . . . . . . . . . . . . . . . . 584.11 Photo of the digital multiplier . . . . . . . . . . . . . . . . . . . . . . . . . 594.12 Output digital multiplier spectral density f1=30000 Hz f2=10000 Hz fout=1/2(f1−

f2)=10000 Hz. There is slowly moving from left to right spur. The causeremains unknown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.13 Output digital multiplier spectral density f1=30001 Hz f2=10000 Hz fout=1/2(f1-f2)=10000.5 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.14 Output digital multiplier spectral density f1=30005Hz f2=10000 Hz fout=1/2(f1-f2)=10002.5 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.15 Multiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.16 f1=13527 Hz, m=4, f2 =m

m− 2f1 = 27054Hz, fout =

|f1− f2|2

=

6764Hz In principle there is no spurs, but a slowly moving componentfrom left to right. The origin is unknown. . . . . . . . . . . . . . . . . . . . 64

4.17 f1 = 13527Hz, m=5, m/(m-2)=5/3,f2 =m

m− 2f1 = 22545Hz , fout =

|f1− f2|2

= 4509Hz. The fundamental and 6 harmonics of plotted, show-

ing that there are no spurs. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.18 f1=13527 Hz, m=6, f2 =m

m− 2f1 = 20291Hz , fout =

|f1− f2|2

=

3382Hz, fundamentals and 6 harmonics are shown, no spurs observed. . . 664.19 Spectrum for m=5, no spurs as m is integer . . . . . . . . . . . . . . . . . 674.20 Spectrum for m=5.5,one spur dividing band from fo to 3fo by 1

0.5= 2 . . 68

4.21 Spectrum for m=5.25, 3 spurs dividing band from fo to 3fo by 10.25

= 4 . . 69

xvi

LIST OF FIGURES

4.22 Spectrum for m=5.125, 7 spurs dividing band from fo to 3fo by 10.125

= 8 . 704.23 Spectrum for m=5.0625, 15 spurs dividing band from fo to 3fo by 1

0.0625= 16 71

4.24 The functional diagram for attenuating spurs using multiplier and divider . 714.25 Measured and theoretical values of the spurs power at the divider output

as a function of division ratio N . . . . . . . . . . . . . . . . . . . . . . . . 724.26 Spurs attenuation by multiplication and division by N: N=8, N=16, N=32

and N=64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.1 Down conversion of high frequency angle modulated digital signal usingdigital divider before the low frequency spectrum analyzer . . . . . . . . . 76

5.2 Divider with angle modulated signal at his input . . . . . . . . . . . . . . . 765.3 Input (top curve) and output power spectra for division ratio of 3,4,5,6,12,25,39

(from top to bottom) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.4 Output power as function of division ratio for the fundamentals and differ-

ents spurs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.1 Functional diagram of PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . 826.2 The PLL basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826.3 Example of filter for second order type I PLL . . . . . . . . . . . . . . . . 866.4 Phase frequency detector followed by a charge pump . . . . . . . . . . . . 87

7.1 Chip CD74HC4046 diagram [87] . . . . . . . . . . . . . . . . . . . . . . . . 907.2 74HC4046 VCO operation [87] . . . . . . . . . . . . . . . . . . . . . . . . . 907.3 Typical Waveforms for PLL With PC1 [87] . . . . . . . . . . . . . . . . . . 927.4 PC1 Average Output Voltage as a Function of Input Phase Difference [87] 927.5 Typical Waveforms for PLL With PC2 [87] . . . . . . . . . . . . . . . . . . 937.6 PC2 Average Output Voltage as a Function of Input Phase Difference [87] 937.7 Typical Waveforms for PLL With PC3 [87] . . . . . . . . . . . . . . . . . . 947.8 PC3 Average Output Voltage as a Function of Input Phase Difference [87] 947.9 Charge and discharge of the capacitor C1 and the output VCO voltage [87] 957.10 Thevenin-Norton transformation . . . . . . . . . . . . . . . . . . . . . . . . 957.11 RC low passfilter with damping resistor . . . . . . . . . . . . . . . . . . . . 987.12 Transfer function of the calculated filter.The role of damping resistor R4

(for preventing gainpeak) is also shown. However the filtering is relativelypoor for high frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.13 Effect of filtering using a PLL: at multiplier input f1 = 56464Hz andf2 = 37918Hz, at PLL output fout = |f1−f2|

2= 9273Hz . . . . . . . . . . 100

7.14 Spurs mitigation with the multiplier inserted in the loop of the PLL . . . . 1017.15 Spurs mitigation with PLL used as pass band filter . . . . . . . . . . . . . 1027.16 Comparison of the 2 structures: multiplier inserted in the PLL loop (yellow

color) and PLL used as passband filter (gray color). The design with themultiplier inserted in the PLL loop performs better. . . . . . . . . . . . . . 103

7.17 A reduction of spurs by 13 dB (from -54 dBm to -67 dBm ) is achieved byincreasing C3 from 10 pF(yellow line) to 100 pF(red line), but this pushesparameter b = 1 + C

C3from 11 to 2 which is the stability boundary . . . . . 103

7.18 Schematic of the multiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.21 Spectral density of input signal . . . . . . . . . . . . . . . . . . . . . . . . 1067.22 Output spectral density of out signal for a multiplication factor N=3 . . . 106

xvii

LIST OF FIGURES

7.23 Output spectral density of out signal for a multiplication factor N=4 . . . 1077.24 Output spectral density of out signal for a multiplication factor N=5 . . . 1077.19 photo of the frequency multiplier: The PLL based on CD744046A and the

counter Cd74HC4059 in the loop . . . . . . . . . . . . . . . . . . . . . . . 1087.20 View of the counter CD74HC4059 mounted in the loop of the PLL . . . . . 109

D.1 Chip CD74HC4059 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

xviii

List of Tables

1.1 LTE frequency bands [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Frequency range for 5G mobile network . . . . . . . . . . . . . . . . . . . 10

1.3 NR operating bands in FR1 [50] . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 NR operating bands in FR1 (continued) [50] . . . . . . . . . . . . . . . . . 11

1.5 NR operating bands in FR2 [50] . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Expression of intermodulation products in frequency domain, convolutionis noted by * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Multiplication in time and convolution in frequency domain . . . . . . . . 24

2.3 Example of carrier aggregated frequency bands . . . . . . . . . . . . . . . . 27

2.4 frequency bands of band 4 and band 17 . . . . . . . . . . . . . . . . . . 37

2.5 Result of the command percent interference CA([4 17], up, down, 3)showing the IMDs that cause interferences, the perturbated bands (bandsthat can be potentially desensitized) and percentage of interference . . . . 37

2.6 List of carrier aggregation of 2 bands [50] . . . . . . . . . . . . . . . . . . . 40

2.7 List of carrier aggregation of 3 bands, 4 bands and 5 bands [50] . . . . . . 41

2.8 Number of carrier aggregations for which there is a potential risk of desen-sitization for uplink transmission . . . . . . . . . . . . . . . . . . . . . . . 42

2.9 Number of carrier aggregations for which there is a potential risk of desen-sitization for downlink transmission . . . . . . . . . . . . . . . . . . . . . . 42

4.1 Arithmetic addition of 2 digital signals . . . . . . . . . . . . . . . . . . . . 53

4.2 Example of set of frequencies f1 and f2 without spurs. f1 = 17316 and f2is calculated according to equation4.10 . . . . . . . . . . . . . . . . . . . . 63

4.3 f2 = 10000Hz,, f1 = 20001Hz, fo = 12|f1−f2|, ∆f =fspurs-f0, Pspurs=measured

spurs power, Pfo=Measured first harmonics power . . . . . . . . . . . . . 67

4.4 Spurs attenuation by multiplying the input multiplier signal by N anddividing by N the obtained signal at the multiplier output f2 = 10000Hz,,f1 = 20002Hz, fo = 1

2|f1 − f2|, ∆f =fspurs-f0, Pspurs=measured spurs

power, Pfo=Measured first harmonics power . . . . . . . . . . . . . . . . 68

4.5 Spurs attenuation by multiplying the input multiplier signal by N anddividing by N the obtained signal at the multiplier output f2 = 10000Hz,,f1 = 20003Hz, fo = 1

2|f1 − f2|, ∆f =fspurs-f0, Pspurs=measured spurs

power, Pfo=Measured first harmonics power . . . . . . . . . . . . . . . . 68

xix

LIST OF TABLES

4.6 Spurs attenuation by multiplying the input multiplier signal by N anddividing by N the obtained signal at the multiplier output f2 = 10000Hz,f1 = 30001Hz, fo = 1

2|f1−f2|, ∆f = fspurs-f0, Pspurs = measured spurs

power, Pfo = Measured first harmonics power . . . . . . . . . . . . . . . 694.7 Spurs attenuation by multiplying the input multiplier signal by N and

dividing by N the obtained signal at the multiplier output f2 = 10000Hz,f1 = 30002Hz, fo = 1


power, Pfo = Measured first harmonics power . . . . . . . . . . . . . . . 694.8 Spurs attenuation by multiplying the input multiplier signal by N and

dividing by N the obtained signal at the multiplier output f2 = 10000Hz,,f1 = 30003Hz, fo = 1


power, Pfo = Measured first harmonics power . . . . . . . . . . . . . . . 704.9 Theoretical values of spurs power after multiplication and division by N . . 724.10 Standart deviation for each N . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.1 Samples of measurement at some peaks in figure 5.3 [dBm] . . . . . . . . 795.2 Relative attenuation of angle modulated signal due to digital divider at

different frequencies compared with 20 logN [dB] . . . . . . . . . . . . . . . 79

7.1 Detection range and gain of different phase detectors of the chip CD74HC4046A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

xx

List of abbreviations

3GPP Third Generation Partnership Project4G Fourth Generation5G Fifth GenerationADC Analogue-to-Digital ConverterAMPS Advanced Mobile Phone ServiceARFPD Analogue Radio Frequency PredistortionBS Base StationBSC Base Station ControllerCA Carrier AggregationCDMA Code Division Multiple AccessDAC Digital-to-Analogue ConverterDL Down LinkDPD Digital PredistortionDSP Digital Signal processingEDGE Enhanced Data Rates for GSM EvolutionETSI European Telecommunications Standards InstituteFDD Frequency Division DuplexFR Frequency RangeGPRS General Packet Radio ServiceGSM Global System for Mobile CommunicationI/Q In-Phase and QuadratureIIP Input Intercept PointIMD Intermodulation DistortionITU International telecommunication UnionLPF Low Pass FilterLTE Long Term EvolutionLTE-A Long Term Evolution AdvancedM2M Machine-To-Machine CommunicationMIMO Multiple Input Multiple OutputMPR Maximum Power ReductionN/A Not ApplicableNFV Network Function VirtualizationNMT Nordic Mobile TelephoneNR New RadioOFDM Orthogonal Frequency Division MultiplexingOIP Output intercept PointPA Power Amplifier

xxi

List of abbreviations

PAPR Peak-to-Average-Power-RatioPC Phase ComparatorPFD Phase Frequency DetectorPLL Phase Locked LoopRF Radio FrequencyRMS Root Mean SquareRNC Radio Network ControllerSUD Supplementary DownlinkSUL Supplementary UplinkTACS Total Access Communication SystemTDD Time Division DuplexUE User EquipmentUL Up LinkUMTS Universal Mobile Telecommunication SystemVCO Voltage Controlled OscillatorZB zettabyte

xxii

General introduction

The volume of data to be transmitted over communication channels increases every yearand no end to this phenomenon is expected for the near future. According to CISCO,total traffic will increase up to 4.8 ZB per year in 2020, which is an increase of 300 %compared to 1.5 ZB (zettabyte= 1021 bytes) annual traffic in 2017 [1]. 71% of those datawill be on mobile wireless network whereas 29 % will be exchanged on wired network.A shift in terminals used is expected: the traffic on smart device will grow from 19 %in 2018, to 44 % in 2022 whereas the traffic on personal computer will decline from 41% to 19 % at the same period [1]. It is then clear that mobile networks will play amajor role in data transmission. However, increasing data throughput on mobile net-works brings new challenges to mobile network technology in terms of access technologyand used equipments; be it user equipments or network side ones. Intense research is car-ried out around the world to meet that growing traffic specially by using mobile networks.

Increasing the data throughput is generally the target of any telecommunication sys-tem. Carrier aggregation (CA) and Multiple-Input Multiple- Output(MIMO) are the twoimportant technical innovations added in LTE-Advanced to increase the transmission datarate [2]. Carrier aggregation is a technique by which more than one carrier is assigned toone user, in uplink and/or in downlink transmission. MIMO is, in turn, a technique ofusing multiple antennas on one device, be it in downlink / uplink transmission direction.MIMO is used for the following reasons:

• Increasing the quality of the signal and hence the signal-to-noise ratio. In this case,the same data is transmitted through all the antenna [3];

• Increasing the transmission rate by segmenting the input data and transmit eachsegment using each individual antenna [4];

• Beamforming: steer the transmitted energy in wanted direction by changing thephase of the transmitted signal [5],[6].

Carrier aggregation is used for the following reasons:

• Increasing the throughput. It is known that to increase the channel capacity, thefrequency bandwidth has to be increased. However, the needed frequency band isnot always available as a contiguous resource [7],[8] ;

• Efficiency use of the frequency resources. Carrier aggregation allows using all thefrequency resources [9].

1

General introduction

Power amplifier operates in nonlinear mode for efficiency reason [10]. Therefore, usingmultiple frequency bands leads inevitably to IMD distortions in the power amplifier,especially in non-contiguous transmission scheme. Generated IMD can be very “harmful”as they can fall in the receiver band of one of used frequency bands, causing receiverdesensitization. Many works aiming IMD attenuation have been published [11]-[12].

For many of the used IMD cancellation methods, it is necessary to generate linearcombinations of the used frequency carriers[13]. In the first part of this work, we willanswer to the following questions:

• How to calculate the frequencies occupied by IMD of a given order and for a givencarrier aggregation?

• What are the carrier aggregations for which IMD distortions of a given order fall inone or more receiver bands of the used frequency bands?

• What is the power of the generated IMD ?

• What is the percentage of interference of the given IMD with the receiver band?

• What are the main methods used for IMD cancellation and attenuation?

Nonlinear IMD predistortion exists for contiguous CA [13] but this requires that thebands (the two original bands + the IMD band) need to be in the same frequency rangesuch that they can make use of a single IQ modulator stage. The question now is: howto do this IMD compensation if the 3 bands (2 bands + their IMD) need to make use ofindividual IQ modulator?

The second part of this work therefore focuses on the generation of the carriers whosefrequencies are the linear combination of the frequencies of the carrier components. Wewill name such device intermodulator carrier. It has 3 main modules:

• The frequency multipliers which generate the multiple of the input frequencies;

• The multiplier which generate the differences of frequencies at his input;

• The filter for attenuation of the frequency spurs

The frequency multiplier and the filter are based on the same phase locked loop (PLL)chip. For the multiplier, a divider is included in the feedback path of the PLL. For thepass band filter, a special attention is given to the filter design.

2

Part I

Interference due to carrieraggregation nonlinear distortions

3

Chapter 1

Carrier aggregation in 4G and 5Gmobile networks

Carrier aggregation is a relatively new technology which is implemented from 3GPP Re-lease 10. To understand its utility, it is important to review how the performance of thenetwork generation is tightly related, among other thinks, to the bandwidth assigned toeach user. In the following section, we will review 1G, 2G and 3G mobile networks. TheLTE, LTE-advanced and 5G are discussed in a separate sections due to their close rela-tion to carrier aggregation. The third section introduces the concept of carrier aggregationtogether with the transmitter architecture used for that technology.

1.1 Brief review of mobile networks

Starting from 1980s, there has been a new generation of mobile cellular networks everydecade [14]. The first generation was commercially launched in 1981. It consisted of ana-logue system supporting only voice transmission. There have been different incompatiblesystems [15]:

• Nordic Mobile Telephone (NMT),

• Advanced Mobile Phone Service(AMPS),

• Total Access Communications System (TACS),

• C-Netz,

• Radiocom2000.

The description of the mentioned systems as well as the countries in which they wereadopted can be found in [15].

The second generation was digital and launched in 1991. It was the first fully digitalsystem. There are 2 standards: GSM which was developed in Europe by ETSI and CDMAdesigned in North America. CDMA has been adopted in North America and South Koreawhile GSM has been deployed in the rest of the world. GSM and CDMA were designedfor providing mainly voice services. However, limited transmission data rate (around 10Kbps) was possible [16]. Second generation mobile network allowed roaming betweenoperators of different countries. The bandwidth per user in GSM is 200 KHz. There have

5

1.2. LTE, LTE-Advanced and 5G mobile networks

been 2 improvements of GSM to support data transmission. The first improvement wasGPRS, referred to as 2.5G, which increases data transmission upto 140 Kbps and thesecond, referred to as 2.75G was EDGE. It allows data transmission up to 340 Kbps [17].The throughput increase is due to the following technical innovations:

• In GSM, a single time slot was assigned to a user, while in GPRS and EDGE oneuser could use all the available time slots, that is up to 8.

• Different coding schemes were introduced. GPRS uses 5 coding schemes, whileEDGE 9. Coding schemes are introduced to enhance error correction. The mainidea is to transmit less bits for error correction if the quality of the signal is goodand more bits when the signal quality is degrading.

Compared to GPRS, EDGE introduces more faster modulation schemes. GSM, GPRSand EDGE are still in use today especially in rural regions, where there is no 3G or 4Gcoverage [18]. The GSM voice service has a good quality.

The third generation was launched in 2000 and was targeting to support 1Mbps asthe minimum speed data transmission. There are 2 implementations of 3G:

• Universal Mobile Telecommunication System (UMTS): Its core network was heritedfrom GPRS but its radio access technology was based on WCDMA (Wide CodeDivision Multiple Access). The bandwidth per user is 5 MHz, but many user canshare the same frequency band by using different codes [15]. UMTS was adoptedall over the world except in North America. UMTS was developed by 3GPP (ThirdGeneration Partnership Project).

• CDMA2000 was developed in North America and was a successor of IS-95. It usedalso CDMA technology but only a bandwidth of 1.25 MHz was assigned to eachuser.

There has been subsequent upgrade of those standard to improve their features [15].

1.2 LTE, LTE-Advanced and 5G mobile networks

1.2.1 Long Term Evolution (LTE)

Long Term Evolution (of UMTS) was designed by 3GPP as the successor of UMTS.Compared to its predecessors, LTE uses many frequency bands as it is seen in table 1.1[19]. LTE was introduced in 3GPP Release 8. It was required to deliver 100 Mbps indownlink and 50 Mbps in uplink whereas the requirement for 3G was 14 Mbps in downlinkand 5.7 Mbps in Uplink [20]

E-UTRAOperatingBand

Uplink (UL)operating bandBS receive/ UE transmit

Downlink (DL)operating bandBS transmit / UE receive

Duplex Mode

FUL low – FUL high[MHz] FDL low – FDL high[MHz]1 1920 – 1980 2110 – 2170 FDD2 1850 – 1910 1930 – 1990 FDD3 1710 – 1785 1805 – 1880 FDD

6

Chapter 1. Carrier aggregation in 4G and 5G mobile networks

E-UTRAOperatingBand



Duplex Mode

FUL low – FUL high[MHz] FDL low – FDL high[MHz]4 1710 – 1755 2110 – 2155 FDD5 824 – 849 869 – 894 FDD6 830 – 840 875 – 885 FDD7 2500 – 2570 2620 – 2690 FDD8 880 – 915 925 – 960 FDD9 1749.9 – 1784.9 1844.9 – 1879.9 FDD10 1710 – 1770 2110 – 2170 FDD11 1427.9 – 1447.9 1475.9 – 1495.9 FDD12 699 – 716 729 – 746 FDD13 777 – 787 746 – 756 FDD14 788 – 798 758 – 768 FDD15 Reserved Reserved FDD16 Reserved Reserved FDD17 704 – 716 734 – 746 FDD18 815 – 830 860 – 875 FDD19 830 – 845 875 – 890 FDD20 832 – 862 791 – 821 FDD21 1447.9 – 1462.9 1495.9 – 1510.9 FDD22 3410 – 3490 3510 – 3590 FDD23 2000 – 2020 2180 – 2200 FDD24 1626.5 – 1660.5 1525 – 1559 FDD25 1850 – 1915 1930 – 1995 FDD26 814 – 849 859 – 894 FDD27 807 – 824 852 – 869 FDD28 703 – 748 758 – 803 FDD29 N/A 717 – 728 FDD30 2305 – 2315 2350 – 2360 FDD31 452.5 – 457.5 462.5 – 467.5 FDD32 N/A 1452 – 1496 FDD33 1900 – 1920 1900 – 1920 TDD34 2010 – 2025 2010 – 2025 TDD35 1850 – 1910 1850 – 1910 TDD36 1930 – 1990 1930 – 1990 TDD37 1910 – 1930 1910 – 1930 TDD38 2570 – 2620 2570 – 2620 TDD39 1880 – 1920 1880 – 1920 TDD40 2300 – 2400 2300 – 2400 TDD41 2496 – 2690 2496 – 2690 TDD42 3400 – 3600 3400 – 3600 TDD43 3600 – 3800 3600 – 3800 TDD44 703 – 803 703 – 803 TDD

7


E-UTRAOperatingBand



Duplex Mode

FUL low – FUL high[MHz] FDL low – FDL high[MHz]45 1447 – 1467 1447 – 1467 TDD46 5150 – 5925 5150 – 5925 TDD47 5855 – 5925 5855 – 5925 TDD48 3550 – 3700 3550 – 3700 TDD49 3550 – 3700 3550 – 3700 TDD50 1432 - 1517 1432 - 1517 TDD51 1427 - 1432 1427 - 1432 TDD52 3300 - 3400 3300 - 3400 TDD53 2483.5 - 2495 2483.5 - 2495 TDD65 1920 – 2010 2110 – 2200 FDD66 1710 – 1780 2110 – 2200 FDD67 N/A 738 – 758 FDD68 698 – 728 753 – 783 FDD69 N/A 2570 – 2620 FDD70 1695 – 1710 1995 – 2020 FDD71 663 – 698 617 – 652 FDD72 451 – 456 461 – 466 FDD73 450 – 455 460 – 465 FDD74 1427 – 1470 1475 – 1518 FDD75 N/A 1432 – 1517 FDD76 N/A 1427 – 1432 FDD85 698 – 716 728 – 746 FDD87 410 – 415 420 – 425 FDD88 412 – 417 422 – 427 FDD

Table 1.1: LTE frequency bands [19]

LTE is different from UMTS both from the radio access technology side and the corenetwork side [21]:

• LTE uses OFDM (Orthogonal Frequency Division Multiplexing) modulation, whichallows mitigation of inter-symbol interferences and flexible assignment of the band-width to the users. In LTE, the following bandwidth are used per user: 1.4, 3, 5,10, 15 and 20 MHz.

• In the LTE architecture, there is no equivalent to RNC (Radio Network Controller)in UMTS or BSC (Base Station Controller) in GSM in the network structure.

• The circuit switched core network was suppressed in the core network. The voicehas to be considered as data.

• Multiple antenna techniques were introduced.

Operators suggested LTE as 4G networks but it did not meet the 4 G requirements byIMT, that is a data rate transmission of 100 Mbps. However, due to commercial pressureLTE has been “accredited” as 4G.

8


1.2.2 LTE Advanced (LTE-A)

LTE-Advanced (LTE-A) was introduced in 3GPP Release 10 in 2009 [22] and is an im-provement of LTE as one can guess from its name. LTE-A uses the same frequency bandsand the same waveform as LTE. LTE-A was developed to meet the requirements of IMT-Advanced by ITU (International Telecommunication Union). Those requirements were,among other things, a data throughput of 600 Mbps in downlink and 270 Mbps in uplinkon a bandwidth of 40 MHz. New features were introduced as well as improvements ofexisting ones [23]:

• Carrier aggregation was introduced. It consists in using many frequency band intransmission between base station and the user, be it in downlink or in uplink[24]-[25].

• Multiple antenna techniques were improved [26]-[27] .

Indeed, LTE-A was designed to deliver 1000 Mbps in downlink and 500 Mbps in uplink ona bandwidth of 40 MHz (two components carriers) using 8 layers antenna for downlink and4 layers antenna in uplink. The use of 5 carrier components of 20 MHz each should increasethat throughput up to 3000 Mbps ad 1500 Mbps in downlink and uplink respectively.Therefore LTE-A is compliant with ITU IMT-Advanced requirement (data throughput of600 Mbps in downlink and 270 Mbps in uplink on a bandwidth of 40 MHz).

1.2.3 Fifth generation (5G)

The 5G is the last generation mobile network, which is designed for a diversity of usagecases [28] [29]. The main requirements for 5G networks are: high speed, high capacity,high energy efficiency, massive number of connections, ultra-low latency, and ultra-highreliability.

• High speed: peak data rate should be at least 10 Gbps/user.

• Ultra-low latency: the user plan latency should be less than 1 ms [30]-[31].

• Massive number of connections: 10000 devices/cell [32].

To achieve the mentioned above requirements, 5G uses the following technologies:

• Carrier aggregation [33],[34].

• Use of millimeter waves (above 6 GHz up to 100 GHz). This provides 5G withwide bandwidth necessary for high throughput. In case of carrier aggregation thebandwidth per user can reach 32 GHz [35].

• Hyperdense small cells deployment. This is possible due to the short range propa-gation of the millimeter wave [36].

• Multi-antenna technologies [37]-[38]. It is a use of multiple antennas on one device,for increasing throughput or beam steering. The use of millimeter wave will reducethe antenna dimensions, and therefore will ease physical implementation of multipleantenna on one device.

9


Frequencyrange designa-tion

Corresponding frequencyrange

FR1 410 MHz – 7125 MHzFR2 24250 MHz – 52600 MHz

Table 1.2: Frequency range for 5G mobile network

NRoperatingband

Uplink (UL)operating bandBS receiveUE transmitFUL low – FUL high[MHz]

Downlink (DL)operating bandBS transmit / UE receiveFDL low – FDL high[MHz]

Duplex Mode

n1 1920 – 1980 2110 – 2170 FDDn2 1850 – 1910 1930 – 1990 FDDn3 1710 – 1785 1805 – 1880 FDDn5 824 – 849 869 – 894 FDDn7 2500 – 2570 2620 – 2690 FDDn8 880 – 915 925 – 960 FDDn12 699 – 716 729 – 746 FDDn20 832 – 862 791 – 821 FDDn25 1850 – 1915 1930 – 1995 FDDn28 703 – 748 758 – 803 FDDn34 2010 – 2025 2010 – 2025 TDDn38 2570 – 2620 2570 – 2620 TDD

Table 1.3: NR operating bands in FR1 [50]

• Self-Organising Network (SON) [39]-[40]. The mobile operators are no longer ableto maintain all the base stations due to hyperdense small cells deployment. Thenetwork should be able to configure itself.

• Machine-Type Communications [41] , [42]. It is an automated data communicationamong devices, also referred to M2M (Machine-To-Machine) communications [43].

• Network Function Virtualization [44]-[45]. It is an implementation of network func-tions in software [46]. NFV allows creation of many logically independent networkson a unique physical network [47].

• Energy efficiency [48]-[49]. Massive number of connections requires low power con-sumption for each connected device.

The table 1.3 shows the frequency bands used for 5G [50].

10


NRoperatingband

Uplink (UL)operating bandBS receiveUE transmitFUL low–FUL high [MHz]

Downlink (DL)operating bandBS transmit / UE receiveFDL low–FDL high [MHz]

Duplex Mode

n39 1880 – 1920 1880 – 1920 TDDn40 2300 – 2400 2300 – 2400 TDDn41 2496 – 2690 2496 – 2690 TDDn50 1432 – 1517 1432 – 1517 TDD1n51 1427 – 1432 1427 – 1432 TDDn66 1710 – 1780 2110 – 2200 FDDn70 1695 – 1710 1995 – 2020 FDDn71 663 – 698 617 – 652 FDDn74 1427 – 1470 1475 – 1518 FDDn75 N/A 1432 – 1517 SDLn76 N/A 1427 – 1432 SDLn77 3300 – 4200 3300 – 4200 TDDn78 3300 – 3800 3300 – 3800 TDDn79 4400 – 5000 4400 – 5000 TDDn80 1710 – 1785 N/A SULn81 880 – 915 N/A SULn82 832 – 862 N/A SULn83 703 – 748 N/A SULn84 1920 – 1980 N/A SULn86 1710 – 1780 N/A SUL

Table 1.4: NR operating bands in FR1 (continued) [50]

NRoperatingband

Uplink (UL)operating bandBS receiveUE transmitFUL low–FUL high [MHz]

Downlink (DL)operating bandBS transmit / UE receiveFDL low–FDL high [MHz]

Duplex Mode

n257 26500 – 29500 26500 – 29500 TDDn258 24250 – 27500 24250 – 27500 TDDn260 37000 – 40000 37000 – 40000 TDDn261 27500 – 28350 27500 – 28350 TDD

Table 1.5: NR operating bands in FR2 [50]

11

1.3. Carrier aggregation in 4G and 5G

1.3 Carrier aggregation in 4G and 5G

1.3.1 The concept of carrier aggregation

Carrier aggregation consists in the assignment of multiple bands to one user. Those bandscan be contiguous or non-contiguous. 3GPP Release 10 allows up to 5 carriers combina-tions for LTE-A increasing the single user bandwidth to 100 MHz. Carrier aggregationcan be subdivided in inband and interband carrier aggregation [51]. Figure 1.1 showsintraband contiguous carrier aggregation. Figure 1.2 shows non-contiguous intrabandcarrier aggregation, while Figure 1.3 shows interband carrier aggregation.

Figure 1.1: Intraband contiguous carrier aggregation

Figure 1.2: Intraband non-contiguous carrier aggregation

Figure 1.3: Interband carrier aggregation

1.3.2 Transmitter architectures for carrier aggregation

Transmitter architectures for carrier aggregation has been extensively discussed in [52].The main modules of the transmitter are: the baseband processing module, the DAC(Digital to Analog Converter) converter module, the upper-conversion module, the poweramplifier module and the RF filter module.

The following topologies were discussed by the authors in [52] and are shown on figure1.4.

1.3.2.1 Single-band RF transmitter

The single-band RF transmitter is shown on figure 1.4(a). It can be used in case of con-tiguous or non-contiguous intraband carrier aggregation. The advantage of such topologyis the simplicity of the design, realization and packaging. The main disadvantage is itslimitation as it can not be used for interband carrier aggregation, when the bands areremote to each other, due to the necessary high sampling rate for DAC in this case.

12


Basebandprocessing DAC Up-conversion

Unit PARF Filter

DAC Up-conversionUnit PA

RF Filter


RF Filter



DAC Up-conversionUnit

DAC Up-conversionUnit

RFmultiplexer

BasebandProcessing

BasebandProcessing

BasebandProcessing

BasebandProcessing

BasebandProcessing

BasebandProcessing

PowerCombiner

MultibandPA

MultibandRF Filter

Baseband processing

I1

Q1

2f1

2f1

1 0 -1 0 @ 4f1

1 0 -1 0 @ 4f1

Baseband processing

Delta-SigmaModultor

Delta-SigmaModultor

I2

Q2

2f2 1 0 -1 0 @ 4f2

1 0 -1 0 @ 4f22f2

Dual-bandPA

Dual-bandRF Filter

(a)

(b)

(c)

(d)

(e)

Digital Combiner

Delta-SigmaModulator

Delta-SigmaModulator

MultibandRF Filter

Figure 1.4: Candidate transmitter architectures for CA in LTE-advanced systems:(a) Single-band RF transmitter,(b) Multiple branch transmitter,(c) Multiple branch trans-mitter with multiband RF filter and antenna, (d)Multiband transmitter architecture and(e)Delta-sigma-based CA transmitter architecture [52]

13

1.3. Carrier aggregation in 4G and 5G

1.3.2.2 Multiple branch transmitter

For the figure 1.4(b), the CA transmitter is composed by independent transmitter(orchannel) for each carrier component. There is no common module between channels. Theadvantage of such topology is that it is easy to design and can be used for intraband andinterband carrier aggregation. The disaventage is that the device will be bulky and withlow energy efficiency.

1.3.2.3 Multiple branch transmitter with multiband RF filter and antenna

The multiple branch transmitter shown in figure 1.4(c) is about the CA transmitter topol-ogy for which there is an amplifier for each component carrier but the structure uses aRF multiplexer to feed the signal to the common multiband RF filter before the com-mon antenna. This topology has the advantage of being less bulky than the one in thefigure 1.4(b). However the energy efficiency is low due to the insertion loss of the mul-tiplexer (around 1.5 dB) and the isolator(0.5 dB). Furthermore, the linearization shouldbe achieved for each power amplifier.

1.3.2.4 Multiband transmitter architecture

The multiband transmitter architecture is shown in figure 1.4(d). Common power ampli-fier is used for all the component carriers. The topology leads to a less bulky device dueto the reuse of most of RF components by the two component carriers. The linearizationwill be done for one power amplifier.

1.3.2.5 Delta-sigma-based CA transmitter architecture

The delta-sigma-based CA transmitter architecture is shown on figure 1.4(e) [53]. Thedelta-sigma modulators produce a 2-level signals which implies that digital multiplexerscan be used for feeding the signal to power amplifier. Furthermore, the possibility of usinga swithcing power amplifier will increase energy efficiency. However the main challenge ofthis topology is the mitigation of the noise generated by delta-sigma modulators, so thatit may not interfere with the main signals [54].The multiband transmitter architecture will be assumed for the rest of this work.

14

Chapter 2

Intermodulation distortions due tocarrier aggregation in 4G and 5Gmobile networks

Carrier aggregation is a smart solution for increasing the user bandwidth, be it for down-link or uplink transmission. However, the use of many bands for a single user leads tononlinear intermodulation distortions, especially when a single power amplifier must beused in a nonlinear mode and when the signal has a high PAPR (peak-to-average powerratio).

2.1 Linear and nonlinear system

In most general terms, a system can be defined as a set of functionally interconnectedelements. In this work, the systems will be analyzed through their input-output behaviour.The relation between system inputs and system outputs allow the classification in linearand nonlinear systems. The linear systems obey the superposition principle whereasnonlinear don’t. The superposition principle can be summarised as the one for which thereaction of the sum equals to the sum of the reactions. For a linear system S with signalsa1x1(t) and a2x2(t) at his input, we will have

S(α1x1(t) + α2x2(t)) = α1S(x1(t)) + α2S(x2(t)) (2.1)

with α1 and α2 constant coefficients.Sytems not obeying this superposition principle are called nonlinear.Efficient mathematical tools for linear system analysis have been developed. . Opposedto this, analyzing nonlinear systems is a great challenge for a scientist. That is why mostof the nonlinear systems are often approximated to linear systems.In this thesis, we will deal with nonlinearity of radiofrequency front end devices of 4G and5G mobile networks. The power amplifier is one of the nonlinear front end elements of atransceiver, when used in nonlinear regime. The use of power amplifier in nonlinear modeis dictated by the energy efficiency in that mode as explained in [55]. Nonlinear systemscan also be classified in systems with memory and system without memory (memoryless).A system has memory if his output not only depends on its current inputs but also on itspast inputs. A system is memoryless if the output solely depends on the current inputs. A

15

2.2. Polynomial model of a nonlinear element

system with memory contains reactive elements which store energy. A sufficient conditionfor a system to be memoryless is having a transfer function which does not depend on thefrequency. In practice, for a frequency band larger than 10 MHz, memory effect should beconsidered. Weakly nonlinear systems with memory are generally described with Volterraseries and harmonic balance can be used to compute the response of strong nonlinearsystems. System without memory are often approximated with polynomials.In this work, even if the system which we deal with has a bandwidth larger than 10 MHz,we will use a polynomials to model nonlinearity. We first begin with the harmonic inputsand use a third order polynomial to determine the nonlinear response.

Some intermodulation products are more harmful than others: those that fall in thereceiver band are especially harmful. In LTE Advanced systems, this can happen in theuser equipment as well as in the base station (enode B). However, the intermodulationsin the user equipment are more difficult to deal with, for mainly 2 reasons:

• The power efficiency requirement is more tough as user equipment (mainly handset)are working on battery.

• The processing capability on handset for intermodulation attenuation is limited.

In this chapter we will find answers to the following questions:

• What are the frequencies of intermodulation distortions ?

• Can transmission intermodulation products fall in the reception frequencies of con-sidered bands?

2.2 Polynomial model of a nonlinear element

Suppose a device for which input and output are linked by the following expression:y(t) = α1x(t) + α2x

2(t) + α3x3(t)

with x(t) and y(t) being the input and the output signal respectivelyIf x(t) = A1cos(ω1t) + A2cos(ω2t)then

y(t) =1

2α2(A

21 + A2

2) + (A1α1 +3

4A3

1α3 +3

2A1A

22α3)cos(ω1t)+

(A2α1 +3

4A3

2α3 +3

2A2

1A1α3)cos(ω2t) +1

2A2

1α2cos(2ω1t)

+1

2A2

2α2cos(2ω2t) + A1A2α2cos(ω1 − ω2)t+ A1A2α2cos(ω1 + ω2)t+

3

4A2

1A2α3cos(2ω1 − ω2)t+3

4A1A

22α3cos(ω1 − 2ω2)t+

3

4A2

1A2α3cos(2ω1 + ω2)t+

3

4A1A

22α3cos(ω1 + 2ω2)t+

1

4A3

1α3cos(3ω1t) +1

4A3

2α3cos(3ω2t)

(2.2)

The terms of equation 2.2 can be classified in the following groups:

• DC components : 12α2(A

21 + A2

2). This components will change the DC offset pointof the amplifier.

16

Chapter 2. Intermodulation distortions due to carrier aggregation in 4G and 5G mobilenetworks

• Components proportional to the input signals: A1α1cos(ω1t) + A2α1cos(ω2t). Thisis the useful signal as the output is proportional to the input.

• Components whose frequency is the same as the input but whose amplitude is notproportional to input amplitude: (3

4A3

1α3+32A1A

22α3)cos(ω1t)+(3

4A3

2α3+32A2

2α3)cos(ω2t).

• Components with sum of frequencies: 12A2

1α2cos(2ω1t)+12A2

2α2cos(2ω2t)+A1A2α2cos(ω1+ω2)t . Usually they are not considered to be harmful as they are far from the usefulsignals and can be removed by filtering. However in 4G and 5G mobile network,they can disturb neighbouring frequency bands.

• Components with the difference of the frequencies of the input: A1A2α2cos(ω1−ω2)t.This is supposed to be low frequency components under the assumption that ω1 isclose to ω2, and so again these fall out of the considered frequency bands.

• Components with the difference of the double of one frequency and another fre-quency: 3

4A2

1A2α3cos(2ω1−ω2)t+34A1A

22α3cos(ω1−2ω2)t. If ω1 is close to ω2, those

components can generate in band or out-of-band distortions.

• Components with the sum of the double of the frequency of one signal and thefrequency of another: 3

4A2

1A2α3cos(2ω1 + ω2)t+34A1A

22α3cos(ω1 + 2ω2)t + 1

4A3

1α3cos(3ω1t) + 14A3

2α3cos(3ω2t). They can cause highfrequent out-of-band distortion.

The systematic way for IMD calculation was suggested in [56]. We will explain brieflythe suggested method in the mentioned document before we extend it to modulated signal.Consider that x(t) can be written as:

x(t) = A1cos(ω1t) + A2cos(ω2t) =A1

2(e−iω1t + eiω1t) +

A2

2(e−iω2t + eiω2t) (2.3)

In general, for a sum of Q cosinusoidal functions, x(t) can be written as:

x(t) =

Q∑q=1

Aqcos(ωqt) =1

2

Q∑q=−Qq 6=0

Aqeiωqt (2.4)

where Q is the number of harmonics and Aq and ωq are respectively the amplitude andthe frequency of the q component.The nth power of the signal will be [56]

xn(t) = (1

2

Q∑q=−Qq 6=0

Aqeiωqt)n =

1

2n

Q∑q1=−Q

Aq1eiωq1t

Q∑q2=−Q

Aq2eiωq2t

Q∑q3=−Q

Aq3eiωq3t...

Q∑qn=−Q

Aqneiωqnt

(2.5)

or

xn(t) =1

2n

Q∑q1=−Q

Q∑q2=−Q

Q∑q3=−Q

....

Q∑qn=−Q

Aq1Aq2Aq3...Aqnei(ωq1+ωq2+ωq3+...+ωqn)t (2.6)

17

2.2. Polynomial model of a nonlinear element

Figure 2.1: Intermodulations of harmonics with frequencies close to each other, the IMDproducts are grouped around DC, ω1 = 1850 rad/s, ω2 = 1900 rad/s, ω3 = 1950 rad/sand their harmonics

The output component frequency is a combination of input components frequencies:

ωn,v = ωq1 +ωq2 +ωq3 + ...+ωqn = m−Qω−Q + ...+m−1ω−1 +m1ω1 + ...+mQωQ (2.7)

where v = [m−Q...m−1m1...mQ] is the nth order mixing vector which must verify

Q∑q=−Q

mq = m−Q + ...+m−1 +m1 + ...+mQ = n (2.8)

Each mixing vector can be generated differently by arrangement of different tones. Thenumber of those arrangements is given by [56]:

tn,v =n!

m−Q!...m−1!m1!...mQ

(2.9)

and the amplitude of each mixing product will be [56]

A =tn,v2n−1

, (2.10)

except for DC, where A = tn,v

2n.

The complexity of the above calculation increases rapidly with the increases of the num-ber of the input harmonics and the degree of the polynomial used to approximate thenonlinearity.For this reason, a script was written in mathematica for the above task and is provided inAppendix A. The script allows to plot the spectrum of the IMD. The figures 2.1 and 2.2show spectra when ω1 is and ω2 are close to each other and when ω1 and ω2 are remoteto each other respectively.

18


Figure 2.2: Intermodulations of harmonics with frequencies not close to each other, ω1 =1500 rad/s, ω2 = 1950 rad/s and ω3 = 2300 rad/s the IMD products are scattered onfrequency axis

If ω1 and ω2 are close to each other, the intermodulation products are grouped aroundDC, ω1 and ω2 and their harmonics, as can be seen on figure 2.1. If ω1 and ω2 are remoteto each other, the intermodulation products are scattered on the frequency axis as canbe seen on figure 2.2. Carrier aggregation in 4G and 5G networks involves, most of thetime, the use of carrier frequencies which are not close to each other.

2.3 Total Harmonic Distortion(THD)

THD is a measure of nonlinear distortion of a signal at the output of a nonlinear device.Suppose we have a nonlinear device with the following static nonlinearity:

y(t) = α1x(t) + α2x2(t) + α3x

3(t) (2.11)

where y(t) and x(t) are the input and the output signals respectively.If x(t) = A cosωt, then:

y(t) =α2A

2

2+ (α1A+

3

4α3A

3) cosωt+α2A

2

2cos 2ωt+

α3A3

4cos 3ωt (2.12)

The THD is the ratio between the RMS of the sum of harmonics and the RMS of thefundamental:

THD =

√12(α2A2

2)2 + 1

2(α3A3

4)2√

12(α1A+ 3

4α3A3)2

(2.13)

2.4 Intermodulation power calculation

The expression 2.2 shows the frequencies of the intermodulation products. The next ques-tion is: How can we calculate the power of those intermodulations for a given amplifier

19

2.4. Intermodulation power calculation

and a given inputs power for frequency ω1 and ω2? The following parameters are generallygiven for the amplifier:-gain (G) in dB,-intercept point (OIP2 and OIP3: second and third order, input or output interceptpoint),-1 dB compression point.

2.4.1 Intercept point concept

In this subsection, we will introduce the intercept point concept which will be usedfor intermodulation power calculation. The intercept point is one of the parameters usedto characterize the device nonlinearity. The equation 2.2 shows the output of nonlinearelement when the input is a sum of 2 tones. There are input intercept point (IIP) andoutput intercept point (OIP). The output intercept point n-order is the power level atwhich the output power of intermodulation n-order would be equal to the output power ofone of the main tone if there was no saturation of the device. The output intercept pointis therefore a fictive power. The n-order input intercept point (IIP) is the input powercorresponding to the n-order output intercept point (OIP). As an example, the figure 2.3shows the third order output intercept point and the third order input intercept point.In the same manner, intercept point can also be defined for n-order harmonic.

2.4.2 Power of the second order intermodulation distortions(IM2)

Let’s apply the introduced intercept point concept to the calculation of the power ofthe second order intermodulation component for a given OIP2 of a device and a giveninput power of 2 harmonics at ω1 and ω2 . From equation 2.2, the two second orderintermodulation components are A1A2α2cos(ω1 − ω2)t and A1A2α2cos(ω1 + ω2). Theyhave the same amplitude, therefore they have the same power.

As explained in previous subsection, the second order output intercept point is thelevel at which the power of one of fundamental signal is equal to the power of one ofsecond order intermodulation component.Therefore, from equation 2.2 we have:

OIP2 =(α1A1)

2

2=

(α2A1A2)2

2(2.14)

where(α1A1)

2

2is the output power of the component at frequency ω1 and

(α2A1A2)2

2is

the power of one of the intermodulation product second order.The characterization (the determination) of OIP2 is done with equal-amplitude test [56].Therefore, from 2.14 we will have

A1 = A2 =α1

α2

(2.15)

20


Figure 2.3: Example of third order output intercept point OIP3i and third order inputintercept point IIP3i

21

2.4. Intermodulation power calculation

The substitution of A1 =α1

α2

in(α1A1)

2

2= OIP2 gives:

α22 =

α41

2OIP2

(2.16)

At the other hand, the substitution of α2 in the power of the second order intermodulation

signal(α2A1A2)

2

2gives:

IM2 = (α21A

21

2)(α21A

22

2)

1

OIP2

(2.17)

Or

IM2 =(PA1)(PA2)

OIP2

(2.18)

The power of IM2 expressed in dBm will then be:

IM2(dBm) = PA1(dBm) + PA2(dBm)−OIP2(dBm) (2.19)

PA1(dBm) and PA2(dBm) in expression 2.19 are the output power of the fundamen-tals at frequencies ω1 and ω2 respectively. However, usually the input power is known.The power of IM2, as function of input powers will then be:

IM2(dBm) = G(dB) + PA1in(dBm) +G(dB) + PA2in(dBm)−OIP2(dBm) (2.20)

IM2(dBm) = 2G(dB) + PA1in(dBm) + PA2in(dBm)−OIP2(dBm) (2.21)

Where G is the power amplifier gain.

2.4.3 Power of third order intermodulation distortions (IM3)

The power of the third order intermodulation component can be calculated following thesame method as for the second order in section 2.4.2, where the definition of interceptpoint is used. Using the definition of OIP3, we will determine α3. The third order outputintercept point is the power at which one of the fundamental power equals to the thirdorder intermodulation’s one.

OIP3 =(α1A1)

2

2=

(34α3A

21A2)

2

2(2.22)

Taking into consideration that the OIP3 is measured with equal-amplitude A1 andA2, we have from (2.22) :

A21 =

4

3

α1

α3

(2.23)

22


The substitution of (2.23) in(α1A1)

2

2gives

α3 =2

3α31

1

OIP3

(2.24)

Substituting (2.24) in(34α3A

21A2)

2

2gives:

IM3 =(α2

1A21)

2

4

(α1A2)2

2

1

OIP 23

(2.25)

whic is the same as:

IM3 = (PA1)2PA2

1

OIP 23

(2.26)

Expressed in decibel, the IM3 power will then be:

IM3(dBm) = 2PA1(dBm) + PA2(dBm)− 2OIP3(dBm) (2.27)

Again, PA1(dBm) and PA2(dBm) in expression 2.27 are the output power of the fun-damentals with frequency ω1 and ω2 respectively. However, it better to express 2.27 asfunction of input power and gain G.

Therefore:

IM3(dBm) = 2(G(dB) + PA1in(dBm)) + (G(dB) + PA2in(dBm))− 2OIP3(dBm)

= 3G(dB) + 2PA1in(dBm) + PA2in(dBm)− 2OIP3(dBm)

(2.28)

where PA1in and PA2in are input power of the useful signals at frequencies ω1 and ω2

The above result means that we can know the power of IMD whenever input powerof differents bands and the intercept point are given.

2.5 Carrier aggregation intermodulation distortion in

4G and 5G networks

In section 2.2, we have described the input-output relationship for a sum of harmonicinputs. However, the signal carrying information are not harmonics, but has non zerobandwidth. In this section, we will analyze the input-output relationship for such signals.

Suppose that x(t) = s1(t) + s2(t) is applied to a third order static nonlinearityy(t) = α1x(t) + α2x

2(t) + α3x3(t)

y(t) = α1(s1(t) + s2(t)) + α2(s1(t) + s2(t))2 + α3(s1(t) + s2(t))

3

= α1s1(t) + α1s2(t) + α2s21(t) + α2s

22(t) + 2α2s1(t)s2(t)+

α3s31(t) + 3α3s

21(t)s2(t) + 3α3s1(t)s

22(t) + α3s

32(t)

(2.29)

23

2.5. Carrier aggregation intermodulation distortion in 4G and 5G networks

Table 2.1: Expression of intermodulation products in frequency domain, convolution isnoted by *

time domain frequency domain2α2s1(t)s2(t) 2α2(S1(f) ∗ S2(f))α2s

21(t) = α2s1(t)s1(t) α2(S1(f) ∗ S1(f))

α2s22(t) = α2s2(t)s1(t) α2(S2(f) ∗ S2(f))

3α3s21(t)s2(t) 3α3((S1(f) ∗ S2(f)) ∗ S2(f)

3α3s1(t)s22(t) 3α3((S2(f) ∗ S2(f)) ∗ S1(f)

α3s31(t) α3((S1(f) ∗ S1(f)) ∗ S1(f)

α3s32(t) α3((S2(f) ∗ S2(f)) ∗ S2(f)

Table 2.2: Multiplication in time and convolution in frequency domain

• α1s1(t), α1s2(t): main signals,

• 2α2s1(t)s2(t): intermodulation distortions second order,

• α2s21(t), α2s

22(t) : harmonics second order,

• 3α3s21(t)s2(t), 3α3s1(t)s

22(t): intermodulation distortions third order,

• α3s31(t), α3s

32(t): harmonics third order.

Let’s suppose, for simplicity, that each signal has a constant power spectral density inits frequency band. It is well known that multiplication in time domain is equivalent toconvolution in frequency domain. If S1(f) and S2(f) represent the power spectra of s1(t)and s2(t), the expressions for the output spectra of the differents nonlinear componentsare shown in the table 2.2.

The coefficients α2 and α3 can be calculated for a given device following the methoddescribed in subsection 2.4.2 and 2.4.3 while the coefficient α1 is given by the gain of thedevice.

The figures 2.7, 2.9 and 2.11 show the power spectra of the different harmonics andintermodulations.The calculation was done using the programme in Appendix C

2.5.1 The convolution and the support frequency band

In this paragraph, we will call the ”the support frequency band”, the band for which thepower spectrum is non-zero.Suppose that:

• S1 is a signal with support frequency bands [−f1p,−f1] and [f1, f1p].

• S2 is a signal with support frequency bands [−f2p,−f2] and [f2, f2p].

We will show (graphically) that the support frequency bands of the convolution S1(f) ∗S2(f) is [−f1p − f2p,−f1 − f2], [f1 − f2p, f1p − f2], [f2 − f1p, f2p − f1] and [f1 +f2, f1p+ f2p].

24


Figure 2.4: Convolution of 2 bands S1 and S2

The convolution S1(f) ∗ S2(f) is expressed as:

S1(f) ∗ S2(f) =

∫ ∞−∞

S1(τ)S2(f − τ)dτ (2.30)

Figure 2.4 explains how the convolution is graphically achieved:

1. mirror of S2(f): S2(−f);

2. Shift of mirror S2(−f): S2(−f + fshift);

3. Sum the product S1(f) and shifted S2(−f + fshift).

fshift varies from −∞ to +∞.Indeed it is as if S2(−f + fshift) is ”travelling” from −∞ to +∞.

From the above steps, as illustrated on figure 2.5 it is clear that:

1. The convolution will be different from zero starting from the frequency at whichthe product is different from zero, namely at f2p + fshift = −f1p or fshift =−f1p− f2p.

25

2.5. Carrier aggregation intermodulation distortion in 4G and 5G networks

Figure 2.5: Illustration of the second order harmonics and intermodulation obtained bygraphical method of convolution

2. The product remains non- zero until f2 + fshift = −f1 or fshift = −f1− f2.

3. Therefore, the first support frequency band of the convolutionS1(f)∗S2(f) is[−f1p−f2p,−f1− f2].

4. By further shifting S2(f), we can find the following support frequency bands:[f1−f2p, f1p− f2], [f2− f1p, f2p− f1] and [f1 + f2, f1p+ f2p].

Suppose now that the signals S1(f) and S2(f) are at the input of nonlinear device,the second order intermodulation and harmonics will be2α2(S1(f) ∗ S2(f)), α2(S1(f) ∗ S1(f) and α2(S2(f) ∗ S2(f))The figure 2.5 shows the graphics of those convolution

In particular:

1. Harmonics are the convolution of the signal with itself. Therefore the second orderharmonic of S1(f) will have [−2× f1p , −2× f1] and [2× f1 , 2× f1p] as supportfrequency. It means that the frequency band of order n harmonic will be n timesthe frequency band of the initial signal. Furthermore the second order harmonicshave the triangular PSD form.

2. Second order intermodulations have trapezoidal shape.

2.5.2 Example of calculation of the second and third order in-termodulation of carrier aggregation of band 17 with band4

In this subsection, we will analyze the intermodulation and harmonics of carrier aggrega-tion of band 4 and band 17 with the frequency bands showed in table 2.3. Consider the

26


Table 2.3: Example of carrier aggregated frequency bands

frequencybandnumber

uplinkfrequencyband[MHz]

Downlinkfrequencyband3[MHz]

4 1710-1755 2110-215517 704-716 734-716

amplifier PHA-11+ from Mini-Circuit System with the following features [57]:

• IP3 of +44 dBm and IP2 of 72 dBm at 0.8 GHz in push-pul configuration;• Gain of 16 dB typ. at 0.8 GHz

The maximum output power for a user equipment operating in carrier aggregation modeis 23 dBm [58]. The power at the input is

Pin = Pout−Gain = 23 dBm− 16 dB = 7 dBm (2.31)

We can suppose, for simplicity, that the power density is uniformly distributed in thetotal frequency bands. From the table 2.3, the total uplink frequency bandwidth for the2 bands is 45MHz + 12MHz = 57MHz. The power density at the input is then

Ain[dBm/MHz] = Pin− 10 ∗ log(totalbandwidth[MHz]) (2.32)

Ain[dBm/MHz] = ((7− 10log(57)) dBm/MHz = −10.56 dBm/MHz

Ain[mW/MHz] = 0.088mW/MHzFrom the other side, the RMS is the square root of the power

RMS =√P (2.33)

Therefore the effective value distribution in our case isAineff [mV ] =

√0.088mW/MHz = 0.3mV/MHz

The intermodulation and the harmonic components can be calculated as describedin subsection 2.5.1 using the obtained effective signal distribution. Figure 2.6 show thespectra of B4 and B17 at the input of the amplifier.

For simplicity, only some intermodulations and harmonics at the output are calculatedand shown on figure 2.7, 2.8, 2.9 and 2.11. The script used to obtain the graphics is givenin Appendix C.

2.6 Carrier aggregation intermodulation issues in 4G

and 5G mobile network

2.6.1 Carrier aggregation intermodulation in 4G and 5G mobilenetworks and receiver desensitization

The receiver desensitization is the main concern in this thesis. We will analyze in thisparagraph the desensitization risk for 4G and 5G mobile networks.

27

2.6. Carrier aggregation intermodulation issues in 4G and 5G mobile network

(a) Amplitude B4

(b) Amplitude B17

Figure 2.6: Assumed power vs frequency of the input signals B4 and B17 to a nonlinearpower amplifier

28


(a) second order harmonic B4

(b) second order harmonic B17

Figure 2.7: Second order harmonics of B17

29


Figure 2.8: Intermodulation second order I4 17

Figure 2.9: Third order harmonic of Band 17 I17 17 17

30


Figure 2.10: Third order harmonic of Band 4

Figure 2.11: Third order intermodulation distortion of Band 4 and band 17 I4 4 17

31


Figure 2.12: Third order intermodulation of band 17 and Band 4 I17 17 4

One refers to the receiver desensitization when a strong interfering signal deteriorates thereceiver performance upto blocking it. In 4G and 5G, the desensitization is more harmfuldue to carrier aggregation as the intermodulation products from the transmitter can fallin one of the receiving bands.We will proceed as follows:

• For a given carrier aggregation, we will calculate the intermodulation or harmoniccomponent potentially causing the receiver desensitization;

• We will assume isolation of transmission and reception of 60 dB , which is the stateof the art [59];

• We will then compare the power of intermodulation in the receiver band with theblocking power of the LTE receiver;

• Under these assumptions, we can judge how harmful the IMD is.

Let’s take again an example of aggregation of band 4 and band 17. The uplink trans-mission frequency band for band 17 is [704, 716]MHz . The band 17 third harmonic willhave frequency band [704 ∗ 3, 716 ∗ 3]MHz = [2112, 2148]MHz. This component falls inthe band 4 receiver frequency band which is [2110, 2155]MHz. Therefore it can causereceiver desensitization.

The power of the third order band 17 can be found by integrating the power spec-trum densite I17 17 17(f) on figure 2.9. However, the power should be calculated in the

32


Figure 2.13: Receiver desensitization of band 4 by band 17 third order harmonic

frequency bandwidth for which the spurious component will cause interference. The fig-ure 2.13 shows an example, in which band 17 third harmonic will interfer with 20 MHzreceiver band of band 4.

PowerI17 17 17(f) =

∫ 2140

2110

I17 17 17(f)df = 0.273 mW = −5.6 dBm (2.34)

whereI17 17 17(f) is the power density of Band 17 third harmonic. The calculation ofI17 17 17(f) is explained in subsection 2.5.1.

The blocking power is the interference power which causes receiver desensitization. In4G and 5G network, the blocking power is equal to the reference sensitivity + specificvalue for each channel bandwidth [58]. For 20 MHz channel bandwidth, the blockingpower equals reference receiver desensitization + 7 dBm:−94 dBm+ 7 dBm = −87 dBm.An isolation of −5.6 dBm− (−87 dBm) = 81.4 dB is therefore necessary to prevent band17 third order harmonic from blocking the 20 MHz receiver band at 2130 MHz. As

33

2.7. Calculation of IMD and interference frequencies

providing such isolation may be difficult, the amplifier linearization is mandatory.

2.7 Calculation of IMD and interference frequencies

It is obvious that a tool is needed to compute the frequencies for the nonlinear products.In this paragraph, we will describe how such tool was developed.

2.7.1 Calculation of IMD and harmonics

The starting data are the number of frequency band, the direction of transmission (up/down),and the order of intermodulation to which the nonlinear product will be calculated. Forthe second order IMDs and harmonics, calculation follows the same principle as explainedin the subsection 2.5.1. For orders higher than 2, the nonlinear products are calculatedfollowing the same principles from the second order nonlinear products but by using oneband and one of the second order product. The algorithm described in figure 2.14 showsthe different steps for the IMD calculation:

1. At the input, there are the aggregated bands CA, the transmission direction andthe order of IMD to be considered;

2. For each frequency band number, its lower and upper frequencies are selected to en-able the above described calculation principle. Additionally, the negative frequenciesof the concerned band are added;

3. The IMD and harmonics of second order are calculated;

4. Using the second order nonlinear products, higher order nonlinear products arecalculated.

.

2.7.2 Interference calculation

The interference calculation, i.e the interference of nonlinear products with a given band,is determined as follows:

1. If f1 and f1p are the low and high frequencies of band A1, and f2 and f2p are thelow and high frequencies of A2, we will say that A1 and A2 interfer if their supportfrequencies intersect;

2. For a given carrier aggregation CA, the transmit direction determines the frequencybands of intermodulation products and harmonics of a given order. Using the prin-ciple above, each frequency band of a nonlinear product is checked for interferenceband with the transmitted or the received signal. The case of the interference withthe received signal is the most harmful as the received signal has usually less powerwhich possibly leads to desensitization.

34


Figure 2.14: Algorithm for IMD and harmonics calculation

Figure 2.15: Algorithm for interference calculation of IMD with a given band

35

2.7. Calculation of IMD and interference frequencies

Figure 2.16: interference of 2 bands

The above steps are shown on figure 2.15. It has been mentioned above that wheneverwe have intersection of IMD or harmonics with ”useful” band, we will affirm that thereis interference. However being able to determine the percentage of the interference canclarify further the degree of the later. Let’s take as previously the 2 bands A1 with f1and f1p the low and high frequency respectively, and A2 with low and high frequencyf2 and f2p respectively. The percentage of interference will then be defined as the ra-tio of the interfered frequency range with the total band of that useful signal. Thereforeif A1 and A2 are interfering, we will have one of the following cases as shown in figure 2.16:

(a) f1 < f2 < f1p < f2p. The percentage of interference will be P = (f1p−f2)/(f2p−f2) ∗ 100%;

(b) f2 > f1 and f2p < f1p. the percentage of interference will be: P = 100%;

(c) f2 < f1 < f2p < f1p. The percentage of interference will be:(f2p − f1)/(f2p −f2) ∗ 100%;

(d) f2 < f1 and f2p > f1p. The percentage of interference will be:(f1p− f1)/(f2p−f2) ∗ 100%.

In the example below, we will give an illustration of the concepts explained aboveusing the designed toolSuppose we want to know, for the carrier aggregation of band 4 and band 17 , the IMDs

36


Table 2.4: frequency bands of band 4 and band 17

frequencybandnumber

uplinkfrequencyband[MHz]

Downlinkfrequencyband[MHz]

4 1710-1755 2110-215517 704-716 734-716

CA interfering IMD[MHz]

IMD order interferes withfrequency band[MHz]

band num-ber

percentage

[ 4 17] [ 659 , 761] 3 [734 , 746] 17 100[ 4 17 ] [ 2112 , 2148] 3 [2110 , 2155] 4 80

Table 2.5: Result of the command percent interference CA([4 17], up, down, 3)showing the IMDs that cause interferences, the perturbated bands (bands that can bepotentially desensitized) and percentage of interference

and harmonics which will fall in one of the receiving bands. The signature of the function(the command) elaborated for this task is:

percent interference CA(CA,TransmitDirection,InterferenceDirection,n).

• percent interference CA is the name of the function;

• CA is the carrier aggregation. It contains the number of the aggregated bands;

• TransmitDirection is the direction of transmission: it can be uplink or downlink;

• InterferenceDirection is the direction in which we are looking for interference.For receiver desensitization, it is opposite to TransmitDirection;

• n is the order of nonlinearity upto which we will consider the intermodulationsdistortions.

The command will be percent interference CA([4 17], up, down, 3).The table 2.4 shows the frequencies of band 4 and 17, repeated here for convenience.

The result of the command is shown in table 2.5.Figures 2.17 and 2.18 illustrate the meaning of the interference percentage.

2.8 IMDs and Interference in 4G and 5G mobile net-

works

In subsection 2.7.1 we elaborated a calculation method of IMDs and harmonics frequenciesand in 2.7.2 a calculation method of interferences for a given carrier aggregation. In thissection, we will apply this techniques on the whole list of carrier aggregation as provided by

37

2.8. IMDs and Interference in 4G and 5G mobile networks

Figure 2.17: The percentage interference is 100% as B17 receiving band is entirely insidethe IMD frequency band

38


Figure 2.18: The percentage interference is 100% as B17 receiving band is entirely insidethe IMD frequency band

39

2.8. IMDs and Interference in 4G and 5G mobile networks

number ofaggregatedbands

List of combination of bands

2 [1 3],[1 5], [1 7], [1 28], [1 8], [1 11], [1 18], [1 19], [1 20], [1 21],[1 26],[1 28], [1 32],[1 38],[1 40], [1 41], [1 42],[1 43], [1 46], [2 4], [2 5],[2 7],[212],[2 29],[2 12],[2 13],[2 14],[2 17],[2 28],[2 29],[2 30],[2 46],[2 48], [2 49],[266],[2 71],[3 5],[3 7],[3 8],[3 11],[3 18],[3 19],[3 20],[3 21],[3 28], [3 41],[342],[3 26],[3 27],[3 31],[3 32],[3 38],[3 40],[3 43],[3 46],[3 69],[4 5], [4 7],[412],[4 13],[4 17],[4 27],[4 28],[4 29],[4 30],[4 46],[4 48],[4 71],[5 40], [5 41],[5 46],[5 48],[5 66],[7 8],[7 12], [7 20],[7 22],[7 26],[7 28],[7 30],[7 32], [740],[7 42],[7 46],[7 66],[8 11], [8 20],[8 27],[8 28],[8 32],[8 38],[8 38],[8 38],[8 39],[8 40],[8 41],[8 42],[8 46],[11 18],[11 26],[11 28],[11 41],[11 42],[1146], [12 25],[12 30],[12 46],[12 48],[12 66],[13 46 ],[12 48],[13 66],[14 66],[14 30], [18 28],[19 21], [19 28],[19 42],[19 46],[20 28],[20 31],[20 32],[2038],[20 40], [20 42],[20 43],[20 67],[20 75],[20 76],[21 28],[20 46],[21 28],[2142], [21 46],[23 29], [25 26], [25 41], [25 46], [23 29],[25 26], [25 41],[2546], [26 41],[26 46], [26 46],[26 48],[28 38],[28 40],[28 41],[28 42],[28 46],[2930], [29 66],[29 70],[30 66],[32 42],[32 43],[34 39],[34 41],[38 40],[39 41],[3940],[39 42], [39 46],[40 41],[40 42],[40 43],[40 43],[40 46],[41 42],[41 46],[4148],[42 43],[42 46], [46 48], [46 66],[46 70],[46 71],[48 66],[48 71],[66 70],[6671],[70 71]

Table 2.6: List of carrier aggregation of 2 bands [50]

3GPP [50]. The purpose is to find, among all the carrier aggregation combinations, whichones has the risk of self desensitization, it means which ones has the intermodulationsor harmonics in own receiving bands. For convenience, we will first give the list of allcarriers aggregations as defined by 3 GPP TS 36.101 in paragraph 5.5A [50]

We will answer to the following questions:in the whole list of carrier aggregations,how many carrier aggregations has a potential risk of desensitization for a given order ofIMDs? The answer is provided by obtained results in table 2.8 and 2.9.

The results in table 2.8 for uplink transmission mean that:

• For 2 components carrier aggregations, in the uplink transmission, there are 15carrier combinations, out of a total of 158, whose nonlinear products fall in oneof the receiver band if second order IMDs are considered. The number of carrieraggregations with potential risk of desensitization increases upto 54 if we considerIMDs upto third order, and up to 160 if consider IMDs upto to fourth order,etc;

• For 3 components carrier aggregations, there are 54 carrier aggregations, out ofa total of 183, in the uplink transmission in which may happen desensitization ifIMDs second order are considered. For IMDs third order, there are 160 carriercombinations etc .

The same interpretation holds for the results in table 2.9 for downlink transmission.From tables 2.8 and 2.9, it is seen that the number of carrier combinations with a riskof desensitization increases with the order of considered IMDs and with the number ofcomponents in carrier aggregation.

40


numberof ag-gre-gatedbands

List of combination of bands

3 [1 3 5], [1 3 7],[1 3 8],[1 3 43],[1 3 11],[1 3 18],[1 3 19],[1 3 20],[1 3 21],[1 3 26],[1 3 28], [1 3 32], [1 3 38], [1 3 40], [1 3 41], [1 3 43], [1 5 7], [1 5 40], [1 5 41],[15 46], [1 7 8], [1 7 20], [1 7 26], [1 7 28], [1 7 32], [1 7 40], [1 7 42], [1 7 46], [18 11], [1 8 20],[1 8 28],[1 8 38],[1 8 40],[1 11 18], [1 11 28],[1 18 28],[1 19 21],[119 28], [1 19 42], [1 20 28],[1 20 32],[1 20 42],[1 20 43],[1 21 28],[1 21 42],[1 2842],[1 32 42], [1 32 43], [1 41 42],[1 42 42], [1 42 43], [2 4 5], [2 4 12],[2 5 12],[25 30],[2 5 46],[2 5 66], [2 12 30], [2 12 66],[2 13 66],[2 14 66],[2 30 66],[2 4 7],[24 12],[2 5 66],[2 4 13],[2 4 28],[2 4 29],[2 4 30], [2 4 71],[2 5 7],[2 5 12],[2 4 13],[2 4 28],[2 4 29],[2 4 30],[2 4 71],[2 5 7],[2 5 12], [2 5 13], [2 5 28], [2 5 29], [2 530], [2 5 46],[2 5 66],[2 7 12],[2 7 12],[2 7 28],[2 7 30],[2 7 66], [2 12 30], [2 1266], [2 13 46], [2 13 48],[2 13 66],[2 14 30],[2 14 66],[2 29 30],[2 29 66],[2 30 66],[2 46 48],[2 46 66],[2 48 66],[2 66 71],[3 5 7], [3 5 40],[3 5 41],[3 7 8],[3 7 20],[37 26],[3 7 32], [3 7 38], [3 7 40], [3 7 42], [3 7 46], [3 8 11], [3 8 20],[3 8 28],[3 832],[3 8 38],[3 8 40],[3 11 18], [3 11 26], [3 11 28 ],[3 11 26],[3 11 28],[3 19 21],[319 42],[3 20 28],[3 20 32],[3 20 42],[3 32 42],[3 32 43 ], [3 42 43],[4 5 12], [4 513],[4 5 29],[4 5 30],[4 7 12 ],[4 7 28],[4 12 30],[4 29 30],[5 7 28], [5 7 46],[5 1246],[5 12 48],[5 12 66],[5 30 66],[5 40 41],[5 46 66],[7 8 20],[7 8 38],[7 8 40],[712 66], [7 20 28],[7 20 32],[7 20 38],[7 20 42],[7 28 38],[7 30 66],[7 46 66],[8 1128],[8 20 28],[8 28 41],[8 39 41], [12 30 66],[13 46 66],[13 48 66],[14 30 66],[1921 42],[20 32 42],[20 32 43],[20 38 40],[25 26 41], [20 38 40],[21 28 42],[29 3066],[29 46 66],[29 66 70],[32 42 30],[46 48 66],[46 48 66],[46 48 71],[66 70 71]

4 [1 3 5 7],[1 3 5 40],[1 3 5 41],[1 3 7 26],[1 3 7 8],[1 3 7 20],[1 3 7 28],[1 3 7 32],[13 7 40], [1 3 7 42],[1 3 8 11],[1 3 8 20],[1 3 8 28],[1 3 8 38],[1 3 11 28],[1 3 840],[1 3 19 21],[1 3 19 42], [1 3 20 28 ],[1 3 20 32],[1 3 21 28],[1 3 21 42],[1 328 42],[1 3 32 42],[1 3 32 43],[1 3 42 43], [1 5 7 46],[1 7 8 20],[1 7 8 40],[1 7 2028],[1 7 20 32],[1 7 20 42],[1 8 11 28],[1 8 20 28], [1 19 21 42],[1 20 32 42],[1 2032 43],[1 21 28 42],[1 32 42 43],[2 5 12 66],[2 5 30 66],[2 7 12 66], [2 12 30 66],[214 30 66],[2 4 5 12], [2 4 5 29],[2 4 5 30],[2 4 7 12],[2 4 12 30],[2 4 29 30],[2 5 728], [2 5 12 66], [2 5 30 66],[2 7 12 66],[2 7 46 66],[2 12 30 66],[2 13 48 66],[2 1430 66], [2 29 30 66],[2 46 48 66 ],[3 7 8 20],[3 7 8 38],[3 7 8 40],[3 7 20 28],[3 720 32],[3 7 20 42], [3 7 28 38],[3 8 11 28],[3 8 20 28],[3 19 21 42],[3 20 32 42],[320 32 43],[3 21 28 42],[3 28 41 42], [3 32 42 43]

5 [1 3 7 20 28],[1 3 7 20 42],[1 3 8 11 28]

Table 2.7: List of carrier aggregation of 3 bands, 4 bands and 5 bands [50]

41

2.9. Conclusion

Order of IMD and harmonics

Number of bands in each CA 2 3 42 15 141 1603 54 160 1604 55 70 705 3 3 3

Table 2.8: Number of carrier aggregations for which there is a potential risk of desensiti-zation for uplink transmission

Order of IMD and harmonics

Number of bands in each CA 2 3 42 18 140 1593 51 160 1604 55 70 705 3 3 3

Table 2.9: Number of carrier aggregations for which there is a potential risk of desensiti-zation for downlink transmission

2.9 Conclusion

The occurrence of desensitization risk is high: for the uplink transmission, already for thethird order IMDs and for 2 components carrier aggregations, the occurrence is 54out ofa total of 158, and for 3 components carrier aggregation, if IMDs upto to third order areconsidered, the occurrence is 160 out of 183 CAs. The comparable results are observedin downlink transmission. This chapter shows that the linearization is mandatory.

42

Chapter 3

Predistortion

Predistortion is a technique used to remedy the nonlinearity of a power amplifier. Itconsists of preprocessing the input signal of the power amplifier, in such a way that thenonlinearities (inband distortions, out-of-band distortions, harmonics and intermodulationdistortions) at the output of the power amplifier are compensated [60]. It is also calledprecompensation.As it has been mentioned in section 2.2, the nonlinearity of the power amplifier leads toharmonics and intermodulation distortions, when the power amplifier is used in nonlinearmode [61]. The power amplifier is normally used in its nonlinear regime for efficiencyreasons. At the other hand, modern telecommunication systems use complex modulationssystems, with higher peak-to-average power ratios (PAPR) [62],[63] which requires highlinearity. An example of such modulation is OFDM( Orthogonal Frequency DivisionMultiplexing) which is used in LTE, LTE-A and 5G mobile networks [64]. One of thesolutions to this problem is to reduce the transmitted power, in such a way that theamplifier operates in the linear mode. However, this will reduce the power efficiency.This method of backing power off is refered to as Maximum Power Reduction (MPR).The linearity requirement has become more stringent with the use of carrier aggregation inLTE-Advanced and 5G mobile networks [65],[66]. The non-contiguous carrier aggregation,in case of FDD (Frequency Division Duplex) leads to nonlinear products which can evendesensitize the receiver part of the equipment in use [67].The following section gives an overview of different predistortion methods.

The predistortion concept is shown on the figure 3.1. This chapter gives first anoverview of the predistortion methods, and after the analysis of the state-of-the-art, another predistortion method is suggested, which is suitable both for intraband and inter-band carrier aggregations.

3.1 Classification of predistortion methods

Depending on which module performs the predistortion of the transmitter, the predistor-tions can be classified in Analog Radio Frequency Predistortion (ARFPD) or in DigitalPredistortion (DPD) [68]. ARFPD is done in the RF module just before the power ampli-fier, while DPD is performed in the digital base band. Figures 3.2 and 3.3 show examplesof functional diagram of the transmitter with ARFPD and DPD predistortion respectivily.

DPD relies heavily on digital signal processing and take all advantages from this field:

43

3.1. Classification of predistortion methods

Figure 3.1: Predistortion concept

Figure 3.2: Simplified functional diagram of a transmitter with ARFPD

Figure 3.3: Simplified functional diagram of a transmitter with DPD

44

Chapter 3. Predistortion

• Progress in miniatirization and hence in power consumption;

• low cost of processing.

However, DPD has the following disadvantages:

A wide bandwidth is required in the whole transmission channel from baseband topower amplifier. This will pose more problems as more and more wide bandwidths willbe used especially for 5G networks. Furthermore, spurious products to be mitigated(which are the main concerns in this thesis) even increase the necessary bandwidth. Widebandwidth signals will require high sampling rate for digital to analogue conversion.

Depending on whether memory effect is taken in account or not, predistortions aredivided in memory-aware and memory-unaware. Both ARFPD and DPD can be eithermemory-unaware or memory-aware. In general, memory effects need to be taken in con-sideration for wide bandwidth signal. Memory effects can be considered rather easily inDPD.

In this thesis we will focus on DPD, to which we aim to contribute by suggesting anew structure and by designing a digital intermodulator synthesizer which can be used inmodulation of a signal which will compensate the IMD in the suggested structure.

In the mitigation of spurious emission, one can consider full band attenuation orsubband attenuation. In full-band DPD, the linearization is focused on the whole signalcomposite, while in subband DPD, linearization is focused to a given spurious component,for example an intermodulation distortion of a given order [69]. Predistortion of thetargeted frequency band releases the requirements on processing resources as the bandwithbecomes smaller.

3.2 State-of-the art and suggestion of a new structure

It has been emphasized in chapter 2 that the spurs of nolinear effect in LTE-A and 5Gnetworks are specifically harmfull due to the use of carrier aggregation in those network.The subband predistortion is one of the used method for mitigation of such spurs [69].The figure 3.4 shows an example of subband distortion mitigation of the IM3, i.e theintermodulation 3rd order is attenuated [69]. This structure use one I/Q modulator forall the 2 components carrier and the compensating signal. However, the use of one I/Qmodulator requires the two modulating signals to be close in frequency domain, so thatthey may be covered with one equivalent base band signal in digital domain. Otherwisethe sampling rate will be high. However, the frequency bands are often remote from eachother in case of interband CA, which implies a need for an other structure

We suggest a predistortion method which use an I/Q modulator for each componentcarrier and compensating signal (figure 3.5). In this method, the compensation is done infrequency domain. Therefore the relation between the carriers and the intermodulationcarrier is important.

In the second part of this thesis, we will focus on synthesis of the carrier signal whosefrequency is a linear combination of input carriers.

45

3.2. State-of-the art and suggestion of a new structure

Figure 3.4: Example of DPD using a carrier whose frequency is a linear combination ofmain signals carrier

Figure 3.5: Suggested structure for the subband distortion, with I/Q modulator for eachsignal (2 mains signals and the third order intermodulation

46

Part II

Frequency synthesis of theintermodulator carrier

47

Digital intermodulator synthesiserdesign methodology

In the first part of this thesis, we have suggested a structure for subband predistortionin case of two bands which are remote from each other. The proposed method carry outcompensation on modulated signal. This cancellation can take place only if there is arelationship between the phase of cancelling signal carrier and the phase of the each ofmain signals carriers.

In this second part of the thesis, we design a digital intermodulator carrier from themain signals carriers. The digital technology is preferred as it can be easily integratedwith the digital PLL CD74HC4046A. We l use two structures (topologies):

• The first topology use a PLL as passband, at the output of the multiplier.

Figure A shows the functional diagram of the suggested mixer. It has the followingmain nodes:

– 1 and 2 are signal generators not necessary derived from the same referenceclock;

– 3 and 4 are frequency multipliers. The output of the frequency multiplier isthe multiple of the frequency at the input;

– 5 is a signal multiplier which takes the 2 signals at its input such that the outputfrequency is the difference of the 2 frequencies of the input. It is generally calledthe mixer and will be designed using the logic elements;

– 6 is the PLL based frequency filter. It’s role is to filter nonlinear distortion atthe output of the digital multiplier;

Figure A: Structure where the PLL loop is used as passband filter

1,2: Signal generator for f1 et f23,4: PLL based frequency multiplier

49

5: Signal multiplier6: PLL based filter

• The second topology uses the multiplier in the PLL loop as shown in the figures B.This topology is inspired by the mixer design with the analogue components wherethe analogue mixer is inserted in the PLL loop.

Figure B: Structure where the multiplier is inserted in the PLL loop

The details of each module are given in the following chapters:

• Chapter 4 describes the design of the digital multiplier. It is designed based on theprinciple of its analogue equivalent;

• Chapter 5 is about releasing frequency requirements of spectrum analyzer by down-converting the digital signal to be measured using a frequency divider;

• Chapter 6 gives an overview of the PLL: the structure, the type and the order ofthe phase locked loop are introduced;

• Chapter 7 treats the realization of the intermodulator carrier filter and the frequencymultiplier. The frequency multiplier is a circuit whose output signal frequency is amultiple of input frequency signal. It is used for generating the harmonics of themain signal carriers. In our case, it is realized by inserting a divider in the loopof the PLL. The role of the filter is, at its turn, mitigating spurs from the digitalmultiplier.

50

Chapter 4

The digital multiplier

This chapter is based on [70]. A mixer is a device whose output signal is the product ofinput signals . With f1 and f2 as input frequencies, the output frequency is f1 + f2 or|f1 − f2|. The mixer is generally an analogue device. In this work, we suggest a digitalmixer, designed and implemented using digital logic. A phase locked loop is added atthe output of the mixer acting as a pass band filter. The digital nature of the input andoutput signals implies that there is no conversion loss.Frequency mixers are widely used in communications systems for signals up or downconversion.. Digital mixers have been proposed in the literature. EXOR gates are usedfor multiplication of the input signals [71] and some of the intermodulation spurs werecancelled through multi-phasing of the input signals [72]. However multiple phases (upto 7 phases in the example given in [72]) were necessary to obtain satisfactory results.In [73] a nonlinear Digital-to-Analog Conversion was used in addition to multi-phasing.This nonlinear DAC adds more complexity to the method. An FPGA implementation ofa frequency mixer was also proposed in [4], in which VLSI (Very Large Scale Integration)is used for frequency conversion. The last method appears to be very complex in view ofhardware involved. We suggest a simple digital mixer whose operation theory is based ontrigonometric identity (1). The novelties of the method are the following:

• The use of the model of trigonometric identity for intermodulation cancelation ofhalf of the intermodulations spurs,

• The use of digital logic for the operation “addition” of two square waves signals asshown in section 4.2

• Obtaining a square wave at the output of the frequency mixer. The method usedin [73] and [72] leads to a sinusoidal signal.

• The suggested mixer does not need any calculation as in [73] and [72] and, therefore,can be used for high frequencies.

The limitation of the proposed method is the presence of spurs which could not be re-moved by the filter as they are near the fundamentals and the harmonics of the squarewave. The proposed mixer is digital in the sense that only digital logic gates and digitalsignals are used instead of analogue components and analogue signals. Section 4.1 de-scribes the design methodology, which is based on mathematical trigonometric identity.The simulation and a hardware implementation will be shown in 4.3 and 4.4. From the

51

4.1. Design methodology

simulation, the hardware implementation and the measurements that have been made, itwill be shown, that a pass band filter at the output is necessary for the attenuation ofspurious components.

4.1 Design methodology

The digital mixer operation theory is elaborated based on the following trigonometricidentity:

cos(ω1t) cos(ω2t) + sin(ω1t) sin(ω2t) = cos((ω1 − ω2)t) (4.1)

where ω1 and ω2 are the input signals pulsations.

Square wave signals are used as digital inputs while ADDITION and MULTIPLICA-TION are replaced by digital logic. Simulation is done using Simulink and hardwareimplementation is achieved using High Speed CMOS logic gates.

4.2 The theory of the suggested mixer

We will focus on digital mixer with the difference frequency at the output. However, theproposed methodology can be equally applied to get the sum frequency at the output, ifrequired.An ideal analogue mixer with the difference frequency at the output can be expressed bythe identity 4.1, or

cos(ω1t) cos(ω2t) + cos

(ω1t−

π

2

)cos

(ω2t−

π

2

)= cos((ω1 − ω2)t) (4.2)

A simple multiplication of two cosines would have given:

cos(ω1t) cos(ω2t) =1

2

(cos((ω1 − ω2)t) + cos((ω1 + ω2)t)) (4.3)

We will use the same principle for the digital mixer, with the difference that the signalsat the input are digital square waves now and that the ADDITION and MULTIPLICA-TION in the analogue domain are replaced by their equivalent in the digital domain. It iswell known that MULTIPLICATION in that case is equivalent to XOR. In this paragraph,we explain how the ADDITION is implemented. Let A and B be the inputs to the digitalmixer and let 1 and -1 be the low and high signal level respectively. The “ADDITIONA+B” is shown on table 4.1.

A and B are 2-level square wave signals while A+B is a 3-level signal. Based on table4.1, A+B can be implemented using digital logic. The first row in the table 4.1 will betransformed in the low level, while the last row will be transformed into the high level.The first row is “NEITHER A nor B (logic NOR)” and it will reset the RS trigger whilethe last row “A and B (AND)” will set the RS trigger. The RS flip-flop makes sure thatthe output remains in the same state if A and B have different value. Figure 4.4 showsthe digital mixer based on the above mentioned principle. Therefore, equation 4.1 canbe implemented by the digital circuit represented in figure 4.4 provided a 90shift is donebefore the signal is fed to XOR gate.

52

Chapter 4. The digital multiplier

A B A+B-1 -1 -2-1 1 01 -1 01 1 +2

Table 4.1: Arithmetic addition of 2 digital signals

Figure 4.1: 90phase shifting using D flip flop

4.2.1 90phase shift with D flip-flop

This section is about 90phase shift implementation for digital signal using D flip flop.Consider the figure 4.1, the gate NOT introduces a shift of 180 and the flip flop dividethe frequency by 2, implying a division of the initial 180 phase shift introduced by NOTgate by 2 as can been seen on an example on figure 4.2. The 90 phase shift resultingfrom the schematic 4.1 is shown in figure 4.3

4.3 Simulation

Figure 4.5 shows the simulation model using Simulink. The digital mixer is fed with twoclock signals with frequencies f1 and f2. Each D flip flop divides by 2 the frequency of thesignal at its input. The gate NOT shifts the input signal by 180. This results in a 90shiftbetween the signals at the output of “D flip flop” and “D flip flop1”. The same 90shifttakes place between the “D flip flop2” and “D flip flop3” outputs. Due to the divisionby 2 when using D flip flops, the output of mixer is |f1 − f2|/2. Simulation showed

that whenever the relation f1 = n|f1− f2|

2(figure 4.7), the mixer works perfectly while

spurious components appear whenever this is not the case (figure 4.8) as it is discussedin subsection 4.7.1. An output filter is therefore necessary, as early mentioned.

53

4.3. Simulation

Figure 4.2: Example showing how frequency division leads to phase division

Figure 4.3: Time diagram showing 90phase shift by D flip flop

54


Figure 4.4: Digital mixer with digital logic

Figure 4.5: Simulation model using Simulink

55

4.3. Simulation

Figure 4.6: Inputs and Output RS flip flop (figure 4.5): the output remains in the samestate if the inputs have a different value

Figure 4.7: Output power spectrum f1=1530 Hz, f2=3060Hz, fout=765 Hz. There is no


2is verified, only fundamental and harmonic

56


Figure 4.8: Output power spectrum f1=1530 Hz, f2=3500 Hz, fout=985 Hz. There are


2is not verified

Figure 4.9: RS flip flop implementation using NOR gate

4.4 Hardware implementation

The hardware implementation is straightforward from simulation functional diagramshown on figure 4.5 by replacing different blocks with corresponding logic gates. Thefollowing integrated circuits were used: D flip flop CD74HC74E, NOT gate CD74HC04E,XOR gate CD74HC86E, NOR gate CD74HC02E and AND gate CD74HC08EE4. TheRS flip flop was implemented using two NOR gates as shown in the figure 4.9. Figures4.10 and 4.11 show the schematic of the digital multiplier and the photo of the designedmultiplier respectively

57

4.4. Hardware implementation

Figure 4.10: The digital multiplier schematic58


Figure 4.11: Photo of the digital multiplier

4.5 Measurement results

This section shows the measurement results. The multiplier output when the inputs aref1=3000 Hz and f2=1000 Hz is shown on the figure 4.12. There is slowly moving from leftto right spur. The cause remains unknown. A change of 1Hz from f1=3000 Hz to f1=3001Hz leads to appearance of spurs as shown on figure 4.13. A further further increase of f1to f1=3005 Hz causes appearance of more spurs as illustrated on figure 4.14.

4.6 Results and discussion

The signal output frequency is the difference of input frequencies. However, appearanceof spurs is observed except in some f1 and f2 relationship and will be discussed in nextsection. Both the simulation and hardware implementation show that the suggestedmethod for the digital frequency mixer is viable. However, the measurement show thatmore effort is needed for spurs attenuation. The chapter 7 discuss the spurs attenuationusing a PLL (pase locked loop) based filter. Its main advantage, compared to its analogueequivalent, is that there is no conversion loss and that good isolation of the output frominputs is assured.

4.7 The multiplier model

In this section we will establish the operation of the multiplier based solely on experiments

59

4.7. The multiplier model

Figure 4.12: Output digital multiplier spectral density f1=30000 Hz f2=10000 Hzfout=1/2(f1 − f2)=10000 Hz. There is slowly moving from left to right spur. The causeremains unknown

For

f1 = m ∗ |f1− f2|/2 (4.4)

and

f2 = n ∗ |f1− f2|/2 (4.5)

If m is integer than n is also integerProof:From 4.5

n =2f2

f1− f2(4.6)

Substitution of f1 from 4.4 in 4.6 gives:

n =2f2

mnf2− f2

(4.7)

Or

n =2

mn− 1

(4.8)

and finaly

m− n = 2 (4.9)

Therefore if m is integer, than n is also integer.Furthermore, the decimal part of m is equal to the decimal part of n.

60


Figure 4.13: Output digital multiplier spectral density f1=30001 Hz f2=10000 Hzfout=1/2(f1-f2)=10000.5 Hz

Figure 4.14: Output digital multiplier spectral density f1=30005Hz f2=10000 Hzfout=1/2(f1-f2)=10002.5 Hz

61


Figure 4.15: Multiplier

4.7.1 The no spurs condition

It has been observed that for m and n integer, there are no spurs at the output of thedigital multiplier

Note: f1 = m ∗ |f1− f2|/2 implies f2 = n ∗ |f1− f2|/2Therefore it is enough to verify one of the 2 conditions:f2 = m ∗ |f1− f2|/22 ∗ f2/m = |f1− f2|if f1 < f2,2 ∗ f2/m = f2− f1f1 = f2 ∗ (1− 2/m) = f2 ∗ (m− 2)/m

f2 =m

m− 2f1 (4.10)

There are no spurs if f1 and f2 verify equation 4.10

Given the frequency f1, we can calculate the frequencies f2 for which there will be nospurs at the output of the multiplier. An example are given in table 4.2 . It is clear fromformula 4.10 that m=1 and m=2 are not applicable, as those values will lead to negativefrequencies.

Calculation examplef1=17316 Hz. The set of f2 for which there are no spurs is given in table 4.2

The figures 4.16, 4.17 and 4.18 show some spectrum samples of the signal at the outputof the multiplier, showing the absence of spurs.

4.7.2 The spectrum of the output of the multiplier

This subsection is a attempt to predict the spectrum of the multiplier output signal. Weaffirm that the spectrum depends solely on the parameters m or n with:

f1 =m|f1− f2|

2(4.11)

Or

f2 =m|f1− f2|

2(4.12)

Section 4.7.1 was dealing with m and n integer, in which case there are no spurs. In thissection we will do the analysis for non integer m and n.

62


mm

m− 2f2 =

m

m− 2f1

[Hz]

fout =|f1− f2|

2[Hz]

3 3 51948 173164 2 34632 86585 5/3 28860 57726 3/2 25974 43297 7/5 24242,4 34638 4/3 23088 28869 9/7 22263,43 247410 5/4 21645 216511 11/9 21164 192412 6/5 20779,2 173213 6/5 20464,36 157414 7/6 20202 144315 8/7 19980 133216 8/7 19789,71 123717 9/8 19624,8 115418 9/8 19480,5 108219 9/8 19353,18 101920 10/9 19240 96221 10/9 19138,74 911

Table 4.2: Example of set of frequencies f1 and f2 without spurs. f1 = 17316 and f2 iscalculated according to equation4.10

63


Figure 4.16: f1=13527 Hz, m=4, f2 =m

m− 2f1 = 27054Hz, fout =

|f1− f2|2

=

6764Hz In principle there is no spurs, but a slowly moving component from left to right.The origin is unknown.

64


Figure 4.17: f1 = 13527Hz, m=5, m/(m-2)=5/3,f2 =m

m− 2f1 = 22545Hz , fout =

|f1− f2|2

= 4509Hz. The fundamental and 6 harmonics of plotted, showing that thereare no spurs.

65

4.8. Spurs attenuation using frequency multiplication and division

Figure 4.18: f1=13527 Hz, m=6, f2 =m

m− 2f1 = 20291Hz , fout =

|f1− f2|2

=

3382Hz, fundamentals and 6 harmonics are shown, no spurs observed.

Affirmation:If m has non nil fractional part, the spurs are enterily determined by that fractional part.If the fractional part of m is d, the spurs are determined by:

• If d <= 0.5 , then x = 1d

determines the numbers of spurs. If the x is an integer,then the band of frequency between the main component fo and the third harmonic3fo will be divided by spurs in x interval.

• If d > 0.5, then x = 11−d determines the spectrum as in case above

The figures 4.19 to 4.23 show the spectrum for differents m.

4.8 Spurs attenuation using frequency multiplica-

tion and division

In this section we will show how the frequency multiplication and division can be used forattenuating spurs. Suppose that we have a digital multiplier which gives the difference offrequencies of the input signals f1 and f2, as shown on figure ??.

The signals f1 and f2 are from function generator. The multiplier has also spurs atits output that we aim to mitigate. For that purpose, we will multiply the input signalsf1 and f2 by n, which means that we will take n ∗ f1 and n ∗ f2 from the functiongenerators. We will use a frequency divider at the multiplier output to recover |f1− f2|.

66


Figure 4.19: Spectrum for m=5, no spurs as m is integer

N 64 32 16 12 10 8N*f1(Hz) 1280064 640032 320016 240012 200010 160008N*f2(Hz) 640000 320000 160000 120000 100000 80000∆f(Hz) 125 62.5 31.5 24 20 16Pspurs(dBm) -55.6 -49.7 -43.7 -41.2 -39.0 -37.8

Table 4.3: f2 = 10000Hz,, f1 = 20001Hz, fo = 12|f1 − f2|, ∆f =fspurs-f0,

Pspurs=measured spurs power, Pfo=Measured first harmonics power

The figure 4.24 illustrates the above explained principle.

Measurements show that multiplication of N by 2 increases ∆f by 2 and decreasethe spurs power by 6dB. In general, a multiplication of N by n increase ∆f by n anddecrease the spurs power by 20 log n. For example, for f2 = 10000Hz and f1 = 30003Hz,for N = 16, ∆f = 49, and Pspurs = −41.2dBm

for N = 32 = 16∗2, ∆f = 96 = 49∗2 and Pspurs = −47.3dBm ≈ −41.2dBm−6dBm

Not only does the spurs power decrease but the fact that ∆f is multiplied by N meansthat the spurs will be distant from the useful signal and from each other(figure 4.26). Ashas been shown in subsection 4.7.2, that the spectrum depends upon the decimal of m,m = 2f1

|f1−f2| .If for example m = 3.3333, the decimal part is 0.3333 which means the the interval3fo−fo is divided by 3. by multipliying and dividing by N = 3, there will be no spurs!!!.

67


Figure 4.20: Spectrum for m=5.5,one spur dividing band from fo to 3fo by 10.5

= 2

N 64 32 16 12 10 8N*f1(Hz) 1280128 640064 320032 240024 200020 160016N*f2(Hz) 640000 320000 160000 120000 100000 80000∆f(Hz) 254 128 65 48 40.5 32.5Pspurs(dBm) -55.7 -49.7 -43.7 -41.5 -39.6 -37.8

Table 4.4: Spurs attenuation by multiplying the input multiplier signal by N and dividingby N the obtained signal at the multiplier output f2 = 10000Hz,, f1 = 20002Hz, fo =12|f1−f2|, ∆f =fspurs-f0, Pspurs=measured spurs power, Pfo=Measured first harmonics

power

N 64 32 16 12 10 8N*f1(Hz) 1280192 640096 320048 240036 200030 160024N*f2(Hz) 640000 320000 160000 120000 100000 80000∆f(Hz) 254 128 65 48 40.5 32.5Pspurs(dBm) -55.7 -49.7 -43.7 -41.3 -39.7 -37.8

Table 4.5: Spurs attenuation by multiplying the input multiplier signal by N and dividingby N the obtained signal at the multiplier output f2 = 10000Hz,, f1 = 20003Hz, fo =12|f1−f2|, ∆f =fspurs-f0, Pspurs=measured spurs power, Pfo=Measured first harmonics

power

68


Figure 4.21: Spectrum for m=5.25, 3 spurs dividing band from fo to 3fo by 10.25

= 4

N 64 32 16 8N*f1(Hz) 192064 960032 480016 240008N*f2(Hz) 640000 320000 160000 80000∆f(Hz) 62 31.5 16 8Pspurs(dBm) -53.3 -47.3 -41.5 -35.4

Table 4.6: Spurs attenuation by multiplying the input multiplier signal by N and dividingby N the obtained signal at the multiplier output f2 = 10000Hz, f1 = 30001Hz, fo =12|f1 − f2|, ∆f = fspurs-f0, Pspurs = measured spurs power, Pfo = Measured first

harmonics power

N 64 32 16 8N*f1(Hz) 1920128 960064 480032 240016N*f2(Hz) 640000 320000 160000 80000∆f(Hz) 127 64 32.5 16.8Pspurs(dBm) -53.3 -47.4 -41.2 -35.3

Table 4.7: Spurs attenuation by multiplying the input multiplier signal by N and dividingby N the obtained signal at the multiplier output f2 = 10000Hz, f1 = 30002Hz, fo =12|f1 − f2|, ∆f = fspurs-f0, Pspurs = measured spurs power, Pfo = Measured first

harmonics power

69



= 8

N 64 32 16 8N*f1(Hz) 1920192 960096 480048 240024N*f2(Hz) 640000 320000 160000 80000∆f(Hz) 191 96 49 25.5Pspurs(dBm) -53.1 -47.3 -41.2 -35.3

Table 4.8: Spurs attenuation by multiplying the input multiplier signal by N and dividingby N the obtained signal at the multiplier output f2 = 10000Hz,, f1 = 30003Hz,fo = 1

2|f1− f2|, ∆f = fspurs-f0, Pspurs = measured spurs power, Pfo = Measured first

harmonics power

70



= 16

Figure 4.24: The functional diagram for attenuating spurs using multiplier and divider

Starting from N=8, we can predict the power of the spurs based on the above expla-nation. The calculation results are shown in table 4.9.

Figure 4.25 represents the measured spurs powers and the theoretical values. Themeasured spurs power is the average of the measured spurs power from table 4.3, 4.4 and4.5. The average was done for each N from the measurements done in each mentionnedtable.The standard deviation for each N is shown in the table 4.10. The riple observed ongraphic 4.25 and corresponding to the difference of measured power and theoritical powerin the table 4.9 for N = 10 is due to an error in measurement as shows the standarddeviation for N = 10, compared to the standard deviation for other values of N in thetable 4.10.

We can see that the power attenuation after multiplication and division by N is pre-dictable.

Discussion: It has been explained in section 4.7.1 that the spectrum at the output of

71


N 64 32 16 12 10 8Pspurs(theoritical)(dBm)

-55.8 -49.8 -43.8 -41.3 -39.7 -37.8

Pspurs(measured average)(dBm)

-55.7 -49.7 -43.7 -41.3 -39.4 -37.8

Difference(Theoritical and mea-sured)(dBm)

0.1 0.1 0.1 -0.2 0.3 0

Table 4.9: Theoretical values of spurs power after multiplication and division by N

N 64 32 16 12 10 8Standart de-viation

0.04714 0 0 0.12472 0.30912 0

Table 4.10: Standart deviation for each N

Figure 4.25: Measured and theoretical values of the spurs power at the divider output asa function of division ratio N

72


Figure 4.26: Spurs attenuation by multiplication and division by N: N=8, N=16, N=32and N=64

73

4.9. Generalization of frequency division as a down conversion process

the multiplier is determined by m defined as:

f1 = m|f1− f2|

2(4.13)

or

m = 2|f1− f2|

f1(4.14)

Multiplication of f1 and f2 by N will lead to:

Nf1 = m|Nf1−Nf2|

2(4.15)

or

Nf1 = mN|f1− f2|

2(4.16)

So at the output of the multiplier the spurs will be at Nd from the main componentswhere d is the decimal part of m as previously. The main question is why does the dividerby N at the output of the multiplier does not reduce back the frequency distance Nd tod? In section 5.2 on page 76, it has been shown that in case of digital angle modulatedsignal, the division by N will down convert the spectrum. Intuitively, one can understandthat this principle is applicable to other type of continuous modulation.

4.9 Generalization of frequency division as a down

conversion process

In this section, we will show that a frequency divider, both digital and analogue, will downcovert a modulated signal (continuous modulation). Let’s begin with the oldest modu-lation: AM modulation. The mathematical expression of conventional AM modulatedsignal is :

A(t) = (Ac+ Sm(t)) cos(ωct) (4.17)

where A(t) - modulated signalAc - amplitude of the carrierSm(t) modulating signalThe frequency divider N will lead to:

A(t) = (Ac+ Sm(t)) cos(ωcNt)

(4.18)

Therefore only the frequency of the carrier will change, not the spectrum around thecarrier.

Conclusion

Design and implementation of a digital frequency difference generator has been achievedin this chapter. The suggested scheme use digital logic(digital gates). However, there arespurs at the output of the designed device. The spurs mitigation using a frequency mul-tiplier before the frequency difference generator and a divider at it’s output is described.An other mitigation method using a PLL will be described in chapter 7.

74

Chapter 5

Power spectrum measurement ofhigh frequency angle modulateddigital signal from output powerspectrum of a digital divider

This chapter is based on [74].It shows how to measure the power spectrum of high fre-quency angle modulated digital signals using a relatively low frequency spectrum analyzerand a digital frequency divider. The mathematical proof is based on comparison of thesignal spectrum before and after the frequency divider. The spectral scaling of an anglemodulated digital signal by the divider is predictable mathematically implying that thepower spectrum at the input of the divider can be deduced from the power spectrum atthe digital output of the frequency divider. The proposed method has been confirmed bymeasurement.

5.1 Introduction

High frequency spectrum analyzers can be expensive and are not always available to theexperimenter [75]. Down converting the high frequency signal to be measured enablesthe usage of lower frequency spectrum analyzers [76]. A first, classical possibility is toperform a frequency down conversion using analogue mixers and a stable high-frequencysource [77]. This chapter develops an alternative method to measure the power spectrumof a high frequency angle modulated digital signal using a frequency divider. Figure 5.1shows the functional scheme of that method in which the digital divider do not containany analogue components (e.g. analog mixer or oscillator). The programmability of suchdigital frequency dividers leads to a high flexibility [78] [79]. For angle modulated digitalsignals, we show that a digital frequency divider can be used to down convert the powerspectrum of an angle modulated signal to a lower frequency band which can be moreconvenient from measurement point of view. The mathematical proof of the proposedmethod is based on the analysis of the angle modulated signal at the input and theoutput of the digital divider. This mathematical framework is afterwards confirmed usingmeasurements of an angle modulated digital signal power spectrum at the input and adigital divider with a variable division factor (N=3,4,5,6,12,25,39). Finally, we compare

75

5.2. Description of the method

Figure 5.1: Down conversion of high frequency angle modulated digital signal using digitaldivider before the low frequency spectrum analyzer

Figure 5.2: Divider with angle modulated signal at his input

the input and output spectra for various division factors N.1. High frequency angle modulated digital signal

2. Lower frequency angle modulated digital signal3. Digital frequency divider4. Lower frequency spectrum analyzerThe above principle is illustrated in figure 5.1. The module 3 is a digital frequency dividerwhich is fed with a high frequency angle modulated digital signal. The signal 2 is a lowfrequency angle modulated signal suitable for the mesurement by the lower frequencyspectrum analyzer (module 4)

5.2 Description of the method

This paragraph gives the mathematical description of the angle modulated digital signalthat is down converted using a digital frequency divider. The mathematical descriptionstarts by first decomposing the digital (square wave) signal in its fundamental and itsharmonic components. The power spectrum at the output of the frequency divider willbe measured around a single carrier. Consider an angle modulated signal, A(t), at theinput of the frequency divider by integer N and let Ad(t) be the signal at the output ofthe mentioned divider.

The general expression of an angle modulated signal can be written as:

A(t) = A cos(ωot+mS(t)) (5.1)

with A the carrier amplitude, ωo the carrier frequency, m the modulation index, and S(t)the phase modulating of the signal. For the ease of analyze, suppose that

S(t) = sin(ωmt) (5.2)

Expression then becomes

A(t) = A cos(ωot+m sin(ωmt)) (5.3)

76

Chapter 5. Power spectrum measurement of high frequency angle modulated digitalsignal from output power spectrum of a digital divider

The instantaneous (radial) frequency, which equals the derivative of the phase, is givenby

ωo +mωm cos(ωmt). (5.4)

The output frequency at frequency divider by N then yield a frequency

ωoN

+(mωm)

Ncos(ωmt) (5.5)

The modulated signal at the divider output therefore equals

Ad(t) = Ad cos

(∫ t

0

(ωoN

+mωmN

cos(ωmt))dt+ φ0

)(5.6)

and hence

Ad(t) = Ad cos(ωoNt+

m

Nsin[(ωmt)] + φ0

)(5.7)

Expression 5.3 and 5.7 are quite similar, except that both the carrier amplitude andthe modulation index have changed. Note that the modulation frequency ωm, i.e. themodulation frequency around the carrier, remains constant in both expressions. Expres-sions 5.3 and 5.7 can be written as

A(t) = A∞∑

n=−∞

Jn(m) cos(ωo − nωm)t (5.8)

and

Ad(t) = Ad

∞∑n=∞

Jn(m

N) cos

(ωoN− nωm

)t (5.9)

where Jn(m) and Jn(mN

) are the first kind Bessel functions, m and mN

the modulationindex of the signal at the input and output of the frequency divider respectively.Obviously, A(t) and Ad(t) have similar spectral components. The relative amplitude ofcomponents at nωm frequency will be scaled by Jn(m

N)/Jn(m) which can be approximated

by 1N

for a small modulation index m. The relative power will therefore decrease by20logN . Hence, measuring the angle modulated signal spectrum with small modulationindex at the output of the divider enables us to calculate the signal’s input power spec-trum. The above analyses can be extended to digital signals, which can be considered asa sum of sinusoidal signals. The next section provides the experimental validation of theproposed method.

5.3 Measurements

A divider based on the CD74HC4059 frequency divider chip with an integer division factorN between 3 and 15999 was used . Measurements will be shown for N=3,4,5,6,12,25 and39. While the frequency divider is fed with an angle modulated digital signal, the powerspectrum is measured of the output of the digital divider. The input signal spectrum and

77

5.4. Results discussion

Figure 5.3: Input (top curve) and output power spectra for division ratio of3,4,5,6,12,25,39 (from top to bottom)

the output spectra for different division ratio N=3,4,5,6,12,25 and 39 are shown on figure5.3. For each division ratio, the graph is plotted at a relative frequency from the carrierfrequency taken as reference. The spectrum was measured for a frequency band of 1kHzaround the carrier for every division ration N. The top curve in Fig. 6 is the spectrum ofthe input signal while the others represent the output signal spectrum for N=3,4,5,6,12,25and 39 (from top to bottom)

5.4 Results discussion

Figure 5.3 shows that the measured spectrum with different division factor N are quitesimilar and that they follow a relative attenuation of 20logN as predicted in the previoussection for small modulation indexes. Table 5.1 shows the measurements at the frequencieswhere peaks are observed. The first row represents the input spectra, while the otherrows represent the output spectra of the divider for different division ratio N. To comparedifferent outputs, the following calculations were preformed: for each frequency in Table5.1 and for each division factor N, we take the difference of power (in dB) at the inputand the output of the divider and subtract the difference of carrier power at input andoutput. The carrier power is at frequency zero (see 5.3). The calculation result is shownin Table5.2. Example: for the division factor N=3 and relative frequency -250 Hz, theoutput power of the divider is -42.28 dBm and the input power is -32.00 dBm. Thedifference of input and out power is -32.00 dBm- (-42.28 dBm) = 10.28 dB. The differenceof carrier power at input and output for N=3 is -1.64 dBm-(-2.96 dBm) = 1.32 dB. Hence,

78

Chapter 5. Power spectrum measurement of high frequency angle modulated digitalsignal from output power spectrum of a digital divider

frequency

Division factor N -250 -150 0 150 250Input -32.00 -34.12 -1.64 -33.42 -31.623 -42.28 -44.68 -2.96 -44.68 -42.354 -46.80 –48.48 -4.73 –48.99 -46.745 -50.53 -52.56 -6.33 -51.94 -50.176 -53.39 -55.22 -7.72 -55.36 -53.1112 -64.25 -66.49 -13.10 -66.22 64.1025 -77.03 -79.93 -19.27 -78.54 -77.0539 -86.82 -88.00 -24.27 -86.90 -85.05

Table 5.1: Samples of measurement at some peaks in figure 5.3 [dBm]

frequency

Division factor N -250 -150 150 250 20logN [dB]3 8.96 9.24 9.94 9.41 9.544 11.71 11.27 12.48 12.03 12.045 13.84 13.75 13.83 13.86 13.986 15.31 15.02 15.86 15.41 15.5612 20.79 20.91 21.34 21.17 21.5825 27.4 28.18 27.49 27.8 27.9539 32.19 31.25 30.85 30.8 31.82

Table 5.2: Relative attenuation of angle modulated signal due to digital divider at differentfrequencies compared with 20 logN [dB]

the relative difference is 10.28 dB - 1.32 dB = 8.96 dB (shown in Table5.2). This resultis to be compared with 20logN=20log3=9.54 dB shown in last column. Note that theattenuation of 20logN is valid only for small modulation index m and m/N. For largermodulation index, the value of Bessel function for each components n determines theoutput amplitude.

The table 5.2 shows that the attenuation by the digital divider for each frequency andfor each division ratio N was comparable to 20logN. The digital frequency divider can beused to down convert the frequency of an angle modulated digital signal and can thereforebe used for its spectrum measurement using a lower frequent spectrum analyzer.

5.5 Conclusion

This chapter shows the possibility to measure the power spectrum of an angle modulateddigital signal using a digital frequency divider and a spectral measurement using a lowerfrequency spectrum analyzer. The method is based on the fact that the frequency andamplitude at the divider’s output are predictable and hence by measuring the divideroutput spectrum, we can deduce the input spectrum. Finally, the results were supportedand demonstrated through measurements.

79

5.5. Conclusion

Figure 5.4: Output power as function of division ratio for the fundamentals and differentsspurs.

80

Chapter 6

Overview of Phase Locked Loop

6.1 The phase locked loop (PLL)

6.1.1 Introduction

A phase locked loop is a device that keeps the input and the output phases in lock. Itwas invented in 1932 by Henri de Bellescize [80]. The PLL is widely used in electronics[81], computers [81], telecommunications [82] etc. In this section we will give the generaldescription of the PLL. The structure, the type and the order of a PLL are explained.

6.1.2 The structure of the PLL

The PLL is made up of 3 main parts: a phase frequency detector, a low pass filter and avoltage controlled oscillator. Figure 6.1 illustrates those parts and their relationship.

• The block 1 is the source of the reference signal. The aim of the PLL is to lock thephase of the block 1 to the phase of the output signal of the block 4.

• The block 2 is the phase detector, called also phase comparator. Modern PLLs use aphase frequency detector (PFD). Its output is an electric signal proportional to thephase difference of the input signals. Different types of phase/frequency detectorsare described in [83].

• The block 3 represents the low pass filter. Its output signal controls the frequency ofthe VCO. The main role of the filter is the dynamic control of the PLL [84]. Indeedmost of the PLL parameters (locktime, lockrange, etc) are controlled by the filter.Its design is one of the main tasks in the PLL engineering.

• The block 4 is the voltage controlled oscillator, the output signal phase of whichis compared (is locked) to the input phase signal either directly or divided by thefrequency divider.

• The block 5 represents the frequency divider, the role of which is indeed the outputfrequency control. Using the frequency divider, a signal whose frequency is the mul-tiple of the input one can be generated. That principle is widely used in frequencysynthesis.

81

6.2. Introductory theory for a PLL

Figure 6.1: Functional diagram of PLL

Figure 6.2: The PLL basics

6.2 Introductory theory for a PLL

In this section, we will present a short theory of PLL so that we may justify the expressionsused for calculation. This section is higly inspired by [84] and [83]. For the beginning, wewill analyse the PLL without the frequency divider. Figure 6.2 illustre the basic of a PLL.We are interested in the phase of the input signal θi(t) and in the phase of the outputsignal θo(t). The output of the detector is a signal the voltage of which is proportional tothe difference of the phases of input signals.

Vd(t) = Kd(θi(t)− θo(t)) (6.1)

where θi(t) and θo(t) are the phase of the input and the output of the VCO signals respec-tively. The signal Vd(t) is filtered by the low pass filter and gives the signal Vc(t). Theoutput frequency of the VCO is proportional to the input signal voltage Vc(t). However,we are interested in phase θo(t) which is given by the integral of the frequency:

θo(t) =

∫KoVc(t)dt (6.2)

We can apply the Laplace transform to the above expressions, resulting in:

Vd(s) = Kd(θo(s)− θi(s)) (6.3)

82

Chapter 6. Overview of Phase Locked Loop

and

θo(s) =1

sKoVc(s) (6.4)

The open loop transfer function can be written as

θo(s)

θe(s)=

1

sKoKdF (s) = G(s) (6.5)

with F(s) the transfer function of the filter.The closed loop transfer function will then be:

θo(s)

θi(s)= H(s) =

G(s)

1 +G(s)(6.6)

The error transfer function will be:

θe(s)

θi(s)=θi(s)− θo(s)

θi(s)= 1−H(s) =

1

1 +G(s)(6.7)

In the sequel, we will maintain the above notations:G(s): open loop transfer functionH(s): closed loop transfer functionE(s): error transfer function

6.3 Type and order of a PLL

The denomiator 1 +G(s) of the equation 6.6 is called characteristic equation. Its zeros ,itmeans the roots of the equation 1 +G(s) = 0, are called the poles of the transfer functionH(s). The zeros of the numerator G(s) are called zeros of the transfer function H(s).Thetype refers to the number of the poles at the origin whereas the order refers to the highestorder of the denominator or the numerator. From this definition, it is clear that the ordercan not be less than the type, as each pole is a root of the denominator.

6.3.1 General definition of the loop gain K

The transfer function of the loop filter F (s) can be divided into two sections [84]:

F (s) = Fp+i(s)Fhf (s) (6.8)

where ”p+i” represents ”proportional plus integral” and ”hf” represents ”high frequency”.Fhf (0) must be finite and non zero.The expression Fp+i(s) can be written as:

Fp+i(s) = K1 +K2

s+K3

s2+ ... (6.9)

83

6.3. Type and order of a PLL

The open loop transfer function G(s) is therefore

G(s) =KdKoFp+iFhf (s)

s=KdKo

s(K1 +

K2

s+K3

s2+ ...)Fhf (s)

=KdKoK1Fhf (0)

s(1 +

K2

K1s+

K3

K1s2+ ...)

Fhf (s)

Fhf (0)

=K

s(1 +

K2

K1s+

K3

K1s2+ ...)

Fhf (s)

Fhf (o)

(6.10)

The general definition of K is then:

K = KdKoK1Fhf (o) rad/sec (6.11)

6.3.2 Type I PLL

6.3.2.1 First order PLL

The first order PLL, which must be type I as the type can not be greater than the order,has no loop filter: Fpi(s) = K1 and Fhf (s) = 1. We will therefore have:

K = KdKoK1 = KDC rad/sec (6.12)

and

G(s) =K

s

H(s) =K

s+K

E(s) =s

s+K

(6.13)

Loop gain in this case K is equal to ω3dB bandwidth. Large DC gain is opposite to narrowbandwidth.

6.3.2.2 Second-Order PLL with lag-lead Filter

Introduction of lag-lead filter allows setting independently narrow bandwidth and loopgain. The loop filter becomes:

F (s) =sτ2 + 1

sτ1 + 1=τ2τ1

(1 +1τ2− 1

τ1

s+ 1τ1

) (6.14)

where τ1 < τ2. F (s) can be interpreted as a proportional plus non-perfect integratorfilter with K1 = τ2

τ1, K2

K1= 1

τ2− 1

τ1. The loop gain is K = KdKoK1 and the DC gain is

KDC = KdKo. We will than have:

G(s) =K

s(1 +

1τ2− 1

τ1

s+ 1τ1

)

H(s) =K(s+ 1

τ2)

s2 + s(K + 1τ1

) + Kτ2

E(s) =s(s+ 1

τ1)

s2 + s(K + 1τ1

) + Kτ2

(6.15)

84


6.3.3 Type II PLL

The DC gain KDC = ∞ for all PLL type II or higher. Therefore, the trade-off betweenDC gain and bandwidth is only inherent to type I PLL.

6.3.3.1 Integrator-Only Loop Filter

Suppose we have a loop filter with only an integrator: F (s) =K2

s. The loop transfer

functions will then be:

G(s) =KdKoK2

s2

H(s) =KdKoK2

s2 +KdKoK2

E(s) =s2

s2 +KdKoK2

(6.16)

H(s) has no zero and its poles lie on imaginary axes: s = ±j√KdKoK2. The PLL is

therefore at its stability boundary.

6.3.3.2 Third-Order Type II PLL

The third-order PLL can be obtained by adding one pole to the integrator-only PLLanalyzed in section 6.3.3.1. The open-loop transfer function becomes:

G(s) =KdKo

s

sτ2 + 1

sτ1(sτ3 + 1)

=K

s(1 +

1

sτ2)

1

sτ3 + 1

=K

s(1 +

1

sτ2)

1

1 + s τ2b

(6.17)

where s = − 1τ3

is the third pole, K = KdKoτ2τ1

and b = τ2τ3

After some manupilations,

H(s) =Kτ2(sτ2 + 1)

s3τ 32 /b+ s2τ 22 +Ksτ 22 +Kτ2

E(s) =s2τ 22 (sτ2/b+ 1)

s3τ 32 /b+ s2τ 22 +Ksτ 22 +Kτ2

(6.18)

After defining normalised gain and normalized frequency :

K ′ = Kτ2 , p = sτ2 (6.19)

we will have

H(p) =K ′(p+ 1)

p3/b+ p2 +K ′p+K ′

E(p) =p2(p/b+ 1)

p3/b+ p2 +K ′p+K ′

(6.20)

85

6.4. Second order type I PLL parameters

Figure 6.3: Example of filter for second order type I PLL

6.4 Second order type I PLL parameters

In this section, we will discuss 2 parameters applicable for second-order PLL: naturalfrequency ωn and damping factor ζ. In section 6.2, we obtained the following open loopgain

θo(s)

θi(s)=

1

sKoKdF (s) = G(s) (6.21)

Let’s consider the filter on figure 6.3. We will now substitute F(s) by the expression:

F (s) =1 + sR4C2

1 + s(R3 +R4)C2

(6.22)

Replacement of R3C2 and R4C2 by τ1 and τ2 respectively gives:

F (s) =1 + τ2s

1 + s(τ1 + τ2)(6.23)

The substitution of 6.23 in 6.21 gives:

G(s) =KoKd

s

1 + τ2s

1 + s(τ1 + τ2)(6.24)

The closed loop gain was obtained in section 6.2 :

H(s) =G(s)

1 +G(s)(6.25)

and substitution of 6.24 in 6.25 gives:

H(s) =

KdKo(1 + sτ2)

(τ1 + τ2)

s2 +s(1 + τ2KdKo)

τ1 + τ2+

KdKo

τ1 + τ2

(6.26)

We can introduce the following notation:

ωn =

√KdKo

τ1 + τ2(6.27)

86


Figure 6.4: Phase frequency detector followed by a charge pump

and

ζ =1

2ωn(τ2 +

1

KdKo

) (6.28)

to get finally H(s) in the form

H(s) =s(2ζωn − ω2

n

KoKd) + ω2

n

s2 + 2ζωns+ ω2n

(6.29)

ωn is called the natural frequency or undamped natural frequency and ζ is damping factor.The transfer function H(s) in 6.29 includes 2 more coefficients Ko and Kd. KoKd is the

DC gain. In the case of use of active filter, DC gain is infinite and the transfer functionH(s) becomes:

H(s) =2ζωn + ω2

n

s2 + 2ζωns+ ω2n

(6.30)

6.5 Charge-pump phase-lock loop

A charge pump is a circuit that converts the logic state of a PFD (Phase Frequency De-tector) into analog signal suitable for controlling the VCO (Voltage Controlled Oscillator)[85]. In this section, we will give an overview of its operation and pinpoint its advantagecompared to other passive filters. Figure 6.4 shows a charge pump functional diagrammefollowed by a filter. The switches S1 and S2 are controlled by the signals UP and DNrespectively. When UP is HIGH, the switch S1 is closed and the current ICP ”pumps” thecharge in the filter and when S2 is HIGH, the current ICP pumps out the charges fromthe filter. The capacitor C3 is used to reduce ripple. Suppose that the PLL is locked atfrequency ωc rad/s and let the phase error be θi − θo = θe radians. The signal UP or DNwill be HIGH for the time

87

6.5. Charge-pump phase-lock loop

tp =|θe|ωc

(6.31)

for each period 2π/ωc. The average current for one period will then be:

id =IptpTc

=Ipθe2π

amperes (6.32)

where Tc = 2πωc

The phase detector gain is therefore:

Kd =idθe

=Ip2π

A/rad (6.33)

The voltage controlling the VCO will then be, in transform domain :

Vc(s) = Id(s)ZF (s) =Ipθe(s)ZF (s)

2π(6.34)

where ZF (s) is the impedance of the filter.The output signal phase from the VCO is:

θo(s) =KoVc(s)

srad (6.35)

G(s) =θo(s)

θe(s)=KoIpZF (s)

2πs

H(s) =θo(s)

θi(s)=

KoIpZF (s)

2πs+KoIpZF (s)

E(s) =θe(s)

θi(s)= 1−H(s) =

2πs

2πs+KoIpZF (s)

(6.36)

G(s), H(s) and E(s) are the open loop transfer function, the closed loop transfer functionand the error transfer function respectively.If we define b = 1 + C

C3and τ2 = R2C, ZF (s) will be:

ZF (s) =b− 1

b

1 + sτ2

sC(sτ2b

+ 1) (6.37)

The open loop gain is:

K =b− 1

b

KoIpR2

2π(6.38)

Substitution of (6.37) and (6.38) in (6.36) leads to transfer functions (6.17) to (6.20) forthird-order type II PLL. Therefore the studied charge pump with the filter behaves like athird-order type II PLL. The use of charge pump in a PLL has the following advantages :

• The static phase error of a PLL with charge pump is zero. This property which cannot be achieved with passive filter, but only with active filter with infinite DC gain, is achieved by using PLL [84]

• The pull-in rage is unbounded for charge pump PLL second order and high-order[86]

88

Chapter 7

Design of intermodulator carrierusing a multiplier and a PLL

7.1 The CD74HC4046A chip

In this thesis, the PLL chip CD74HC4046 A is used. Its detailed description is given in[87]. In this section we will highlight the main characteristics of that chip.

7.1.1 Overview of overall operation of the PLL chip CD74HC4046

The chip CD74HC4046 contains two parts: The VCO and the phase comparator (PC).There are 3 implementations of the PC from which the user can chose.

7.1.1.1 The voltage controlled oscillator (VCO)

The description of the operation of the VCO is based in figures 7.1 and 7.2. The fre-quency of the VCO is controlled by the input voltage V COin, resistors R1, R2 and thecapacitor C1 in the following way: the charging time of the capacitor C1 depends onthe charging current, which in turn depends on values of R1 and R2, V COin and V CC.The value of the current through R1, I1 is V COin

R1whereas the current through R2 is

(V CC−0.6V )R2

. It is the amplified sum I1 + I2 that charges the capacitor C1. The chargingand discharging mechanism is controlled by invertors G1 and G2 and the JK FLIP FLOP(figure 7.1). When the flip flop output Q is high, the output Q is low and the gate ofG1 connected to Q trough invertor is high. The capacitor C1 is then charged throughPNMOS of G1. The NMOS of G2 discharges the capacitor C1 to −0.7V , the value of theintrinsic NMOS diode. The voltage on K input (J-K flip flop) increase until it reaches1.1V , a sufficient voltage to reverse the flip flop output. The output Q becomes low andthe output Q becomes high. The capacitor C1 is charged through PMOS of G2 and theNMOS of G1 discharges the capacitor C1. The J voltage increases until it reverse the flipflop output. The diode D1 and D2 in the functional diagram 7.2 represent the intrinsicdiode of NMOS of G1 andNMOS of G2 respectively and are not represented in thefigure 7.1.

89

7.1. The CD74HC4046A chip

Figure 7.1: Chip CD74HC4046 diagram [87]

Figure 7.2: 74HC4046 VCO operation [87]

90

Chapter 7. Design of intermodulator carrier using a multiplier and a PLL

Phase detector Detection range Gain

XOR-gate π Kp =VHIGH − VLOW

π

JK flip flop 2π Kp =VHIGH − VLOW

2π

PFD(Phase FrequencyDetector)(three state)

4π Kp =VHIGH − VLOW

4π

Table 7.1: Detection range and gain of different phase detectors of the chip CD74HC4046A

7.1.1.2 The phase comparators of the CD74HC4046

The chip CD74HC4046 has 3 phase comparators (PC), noted PC1, PC2 and PC3 as it isseen on figure 7.1. PC1 is simply a XOR gate, PC2 is three-state phase frequency detectorand PC3 is a two-state phase detector based on the flip flop. The three phase detectorsbelong to 3 types of detectors:

• PC1 belongs to the multiplier detector type. It is a XOR gate.

• PC2 belongs to the phase frequency detector. It is a three state detector.

• PC3 belongs to the flip flop detector type. It is based on JK flip flop and it is a twostate detector.

The typical waveforms for PLL with PC1 is shown on figure 7.3 and it’s average outputvoltage as function of input phase difference in figure 7.4. It is seen that the detectionrange is π. The XOR phase detector has the advantage of high gain, high noise handlingcapability.Figures 7.5 and 7.6 show the the typical waveforms for PLL with PC2 and it’s averageoutput as function of input phase difference respectively. The PC2 is an edge-triggeredJ-K flip-flop, which implies that it’s noise handling capability is lower than the PC1 one,and that the duty cycle of input signals is not important . It has 2 output signals UP andDOWN which drives a charge-pump (described in subsection 7.1.1.3). PC2 has a widedetection range of 4π but above all, it’s main advantage is that it is a phase frequencydetector. It is for this last feature that it was chosen to be used for this thesis.The PC3 operation is shown in figures 7.7 and 7.8 , where typical wave forms and averageoutput voltage describe its main features. It is edge-triggered R-S flip flop, that meansthat the duty cycle is not important but the noise handling capability is lower, comparedto XOR phase detector. It’s detection range is 2π.

7.1.1.3 The CD74HC4046 charge pump

At the output of the phase comparator II (PC2) (Figure 7.1), which is a phase frequencydetector, is implemented a charge pump. The current source is designed as a voltagesource VCC in series with a resistor R4. This shematic is equivalent to a curent sourceaccording to Thevenin-Norton transformation as shown in figure 7.10. The switches arethe PMOS and NMOS controlled by the output of the PFD as described in section 6.5

91


Figure 7.3: Typical Waveforms for PLL With PC1 [87]

Figure 7.4: PC1 Average Output Voltage as a Function of Input Phase Difference [87]

92




93




94


Figure 7.9: Charge and discharge of the capacitor C1 and the output VCO voltage [87]

Figure 7.10: Thevenin-Norton transformation

95


7.1.2 The VCO frequency

The CD74HC4046 VCO operation is explained by the figure 7.2.The VCO frequency is controlled by R1, R2 , C1 and VCOin. The VCO output

frequency is given by:

fosc =1

Tosc=

1

2Tc + 2Tpd(7.1)

with: fosc oscillation frequencyTosc oscillation periodTc charge periodTpd the propagation delay which depends on number of cascaded stages in the flip flop,plus the G1 and G2 switching propagation delay-times.

Tc =[(C1 + Cs)Vramp]

[M1I1 +M2I2](7.2)

with C1 external capacitanceCs stray capacitance from pin 6 to pin 7M1 and M2 multiplier ratios for CMA1 and CMA2 respectivilyCMA: current mirror amplifier

Tc =[(C1 + Cs)Vramp]

[M1V COin

R1+M2

VrefR2

](7.3)

Vramp Voltage rampV COin VCO input voltageVref input bias voltage

The stray capacitance Cs and the time delay Tpd can be neglected

Therefore the equation 7.1 becomes:

fosc =1

Tosc=

1

2Tc(7.4)

with

Tc =[C1Vramp]

[M1V COin

R1+M2

VrefR2

](7.5)

The capacitance C1 can then be calculated as:

C1 =Tc[M1

V COin

R1+M2

VrefR2

]

Vramp(7.6)

96


R2 is the resistance for setting offset frequency, it means the frequency at which willoscillate the VCO if there is no imput voltage.In our case we will not use R2, as we do not need any offset frequency. equation 7.5become

Tc =[C1Vramp]

[M1V COin

R1]

(7.7)

From equation 7.7, three parameters determine the oscillation frequency: C1, R1 andV COin. The V COin voltage can vary from 1.0 V to 0.9VCC. VCC is power supply voltage.

The oscillation frequency fosc is therefore given by:

fosc = 1/(2 ∗ Tc) =1

2

[M1V COin

R1]

[C1Vramp](7.8)

7.1.3 The VCO gain Ko and the phase detector gain Kd

• The VCO is a voltage controlled oscillator module. It means that the output fre-quency is controlled by the input voltage. The VCO gain is the ratio of the outputfrequency by input voltage. From equation 7.8, Ko is :

Ko =dfosc

dV COin=

1

2

M1

R1C1V ramp(7.9)

Ko depends on external elements R1 and C1.

• The phase detector gain is determined by which detector is chosen from the chipCD74HC4046AE. In our case we will choose PC2 with phase detector gain

Kd =V CC

4π(7.10)

7.2 The PLL calculation

7.2.1 Phase comparator

As described above, the chip CD74HC4046A has 3 phase detectors the user can chosefrom. PC2 was chosen for this thesis as it is the only one with phase frequency detection[88], [83] and [84]. It has a charge pump at his output as previously described.

7.2.2 The PLL voltage controlled oscillator

In this section we will calculate the component value of our PLL. The designed PLLshould serve also as frequency multiplier when a divider is inserted between VCO andphase detector. In practice, in case there is a frequency divider in the PLL loop, it hasbeen observed that the loop is closed( there is oscillation at the VCO output) if thecapacitor C1 reaches a value of 33 nF. For capacitor smaller than 33 nF, there was nooscillation. Therefore we will take the value of C1=33 nF.With the VCC=5 V, the central oscillation frequency can be calculated taking VCOin=2.5V.

97

7.2. The PLL calculation

Figure 7.11: RC low passfilter with damping resistor

Vramp=1.8V and M1=7Let’s take for our experiment, a central oscillation frequency of 17 kHz. There is no needfor an offset frequency, therefore there is no R2. R1 can be calculated from 7.8.

R1 =M1 ∗ V COin

(2 ∗ C1 ∗ V ramp ∗ fosc)= 8665Ω (7.11)

We can take the close nominal value of 8.6kΩ and the oscillation frequency becomes17125Hz.The VCO gain is, from expression (7.9)Ko = 1

2M1

R1C1V ramp= 1

27

8600∗33∗10−9∗1.8 = 6851 rads.V

7.2.3 Spurs mitigation with PLL used as passband filter

In this subsection, we will design intermodulator carrier according to the topology infigure A. Attention is focused to the design of the low pass filter. Preference is given tothe second-order PLL as it is unconditionally stable.A lag-lead filter is chosen as it has adumping resistor, that prevents gain peaking. Figure 7.11 shows the chosen topology. Theuse of this topology is also in agreement with the fact that the output of the phase detectorPC2 is a charge pump as described in section 7.1.1.3. The resistor R3 is considered asthe resistance R4 in figure 7.10.

The lowpass filter of figure 7.11 has the following transfer function

F (s) =1 + sR4C2

1 + s(R3 +R4)C2

(7.12)

The values of the differents components can calculated as follows:

• We define τ1 = R3C2 and τ2 = R4C2

• We choose the ratioωfωn

= 10 and ωn = 200 rad/s and solve a system of equation

98


Figure 7.12: Transfer function of the calculated filter.The role of damping resistor R4(for preventing gainpeak) is also shown. However the filtering is relatively poor for highfrequencies.

[87]:

ωf =1√

τ 21 + 2τ1τ2 − τ 22 )

ωn =√K/(τ1 + τ2)

(7.13)

where ωf is the bandwidth of the filter and ωn is the natural frequency of the PL.K = KdKo = 4π ∗ 6851 = 2727Then we find R3 = 11KΩ , R4 = 110Ω and C2 = 100µF. The transfer function ofthe loop with the obtained values is shown in figure 7.12. Furthermore, the role ofdamping resistor R4 is also shown (by comparing the bodeplot with and withoutR4). The figure 7.13 shows the effect of filtering, where the measurement are donewith and without the filter.

7.2.4 Spurs mitigation with multiplier inserted in the PLL loop

In this subsection, intermodulator carrier is designed according to figure B, according towhich the digital multiplier is inserted in the loop of the PLL, as shown in the figure 7.14When there is a lock, the frequencies at the input of the PFD (Phase Frequency Detector)

99


Figure 7.13: Effect of filtering using a PLL: at multiplier input f1 = 56464Hz andf2 = 37918Hz, at PLL output fout = |f1−f2|

2= 9273Hz

are equal:

1

2|f2− fvco| = 1

2f1 (7.14)

Or in case of f2 > fvco, fvco = f2− f1.The VCO output frequency is the difference of input frequencies. In the simulation isused a charge-pump PLL as described in the section 6.5 and illustrated by the figure 6.4. The expression of the open loop gain is given by (6.38) , repeated below.

K =b− 1

b

KoIpR2

2π

Suppose we want a VCO output frequency around 2 MHz, and a bandwidth of the PLLof 20 KHz. We may note that this bandwidth is very narrow, compared to the frequencyof the output (frequency of the VCO). The following values give the nedeed bandwidth:C = 100pF, C3 = 10pF, Ko = 2000Hz/V, Ip = 300µA, R = 36kΩFor comparison, the simulation has also been done for the case when the PLL is used aspass band filter, as shown in the figure 7.15. Figure 7.16 shows the obtained results. Thestructure with the multiplier in the PLL loop performs better then the structure with thePLL used as pass band filter.The spurs in the case of difference frequency generator inserted in the loop can be reducedby increasing C3 as shown on the figure 7.17, but this is done at the expense of PLLstability as the parameter b = 1 + C

C3will decrease, the boundary stability being at

b = 2[85]. The chosen value C3 = 10pF corresponds to b=11, wich is a good compromisebetween spurs level and stability.

100


Figure 7.14: Spurs mitigation with the multiplier inserted in the loop of the PLL

101


Figure 7.15: Spurs mitigation with PLL used as pass band filter

102


Figure 7.16: Comparison of the 2 structures: multiplier inserted in the PLL loop (yellowcolor) and PLL used as passband filter (gray color). The design with the multiplier insertedin the PLL loop performs better.

Figure 7.17: A reduction of spurs by 13 dB (from -54 dBm to -67 dBm ) is achievedby increasing C3 from 10 pF(yellow line) to 100 pF(red line), but this pushes parameterb = 1 + C

C3from 11 to 2 which is the stability boundary

103

7.3. Realization of a frequency multiplier

7.3 Realization of a frequency multiplier

This section describes the realization of frequency multiplier (which is different fromthe signal multiplier described in chapter 4). As mentioned in chapter , it is role is tosynthesize a frequency whose value is the multiple of the input frequency. Our design isbased the PLL. By including a frequency divider by N in the feedback of the PLL loop,the frequecy of the output signal of of the VCO will be multiplied by N.More details about design of the PLL used in this work is given in chapter 6.The functional diagram is shown on the diagram on figure 6.1.

The schematic for the frequency multiplier is shown on figure 7.18. The photos hard-ware implementation are shown in figure 7.19 and 7.20

Figure 7.18: Schematic of the multiplier

104


7.4 Measurement results

The figures 7.21, 7.22, 7.23 and 7.24 show a degradation of the output signal whith theincrease of the multiplication factor N. The noise increase with the multiplier factor N.

105

7.4. Measurement results

Figure 7.21: Spectral density of input signal

Figure 7.22: Output spectral density of out signal for amultiplication factor N=3

106




107


Figure 7.19: photo of the frequency multiplier: The PLL based on CD744046A and thecounter Cd74HC4059 in the loop

108


Figure 7.20: View of the counter CD74HC4059 mounted in the loop of the PLL

109


110

General conclusion

Carrier aggregation is one of key enabler technologies for 4G and 5G mobile networks.This work has layed out one of the challenges to be overcome for its implementation:nonlinear distortions. The following has been achieved in this PhD thesis:

• In the literature, receiver desensitization is often mentioned. However no systematicanalysis has been done to show how often this can happen in 4G and 5G. In my work,I suggest a method and a tool for finding all interferences, all receiver desensitizationcases for all the number of aggregated components and for any order of nonlineardistortion. Using that tool, a counting of the risk of desensitization has been donefor all the carrier combinations as suggested by 3GPP.

• A method that can be used both for intraband and interband carrier aggregationsis suggested for intermodulation compensation. Compared to the state-of-the-art,the novelty of the method is that it can be used in case of bands and IMD distanteach other, as a use of I/Q modulator for each of them is proposed. Howeverphase relation between the main signals carriers and the intermodulation carrier isimportant.

• A digital intermodulator carrier is designed in this thesis. ”Digital” means thatdigital gates are used instead of classical analogue components, which leads to aneasy integration with other components. The intermodulation carrier is synthesisedfrom the carriers of the main signals.

However, more works need to be done for the device implementation of the suggestedsolution:

• The work done was mainly a proof of concept. The real device should be designedon one chip, optimized for weight, size and power consumption.

• The device is designed for aggregation of 2 components only, however 4G networksallows aggregation upto 32 components, while 16 components are proposed for 5G.Then, it becomes necessary to design for more aggregated components.

111


112

Appendix A

Code mathematica forintermodulation calculation in caseof harmonic inputs

Remove[”Global‘*”]x = A1 Cos[w1 t] + A2 Cos[w2 t] + A3 Cos[w3 t]y = a1x+ a2x2 + a3x3

TrigExpand[%];TrigReduce[%];Collect[%, Cos[h ]];List @@ %; % /. a Cos[h ] → h, a;% /. h, a → FactorTerms[h], a;f[t ] = Factor[%[[All, 1]]];f = f’[t]; a = Factor[%%%[[All, 2]]];a1 = 0.1a2 = 0.05a3 = 0.01A1 = 1.5A2 = 1.5A3 = 1.5w1 = 1950w2 = 1500w3 = 2300xx = Abs[Evaluate[f]];yy = Evaluate[a];data = Transpose@xx, yyListPlot[data, Filling → Axis,AxesLabel → pulsation[rad/s], ”relative amplitude”]

113

Appendix B

Code matlab pour le calcul desintermodulations

Main-code.mcomment ”FB” is a list of LTE frequency bandsFB=[1 1920 1980 2110 2170; 2 1850 1910 1930 1990; 3 1710 1785 1805 1880; 4 1710 17552110 2155; 5 825 849 869 894; 6 830 840 875 885; 7 2500 2570 2620 2690; 8 880 915925 960; 9 1749.9 1784.9 1844.9 1879.9; 10 1710 1770 2110 2170; 11 1427.9 1452.8 1475.91500.9; 12 698 716 728 746; 13 777 787 746 756; 14 788 798 758 768; 15 1900 1920 26002620; 16 2010 2025 2585 2600; 17 704 716 734 746; 18 815 830 860 875; 19 830 845 875890; 20 832 862 791 821; 21 1447.9 1462.9 1495.9 1510.9; 22 3410 3500 3510 3600; 23 20002020 2180 2200; 24 1625.5 1660.5 1525 1559; 25 1850 1915 1930 19995;... 26 814 849 859894; 27 807 824 852 869; 28 703 748 758 803; 29 717 728 717 728; 30 2305 2315 2350 2360;31 452.5 457.5 462.5 467.5; 32 1452 1496 1452 1496; 33 1900 1920 1900 1920; 34 2010 20252010 2025; 35 1850 1910 1850 1910; 36 1930 1990 1930 1990; 37 1910 1930 1910 1930; 382570 2620 2570 2620; 39 1880 1920 1880 1920; 40 2300 2400 2300 2400; 41 2496 2690 24962690; 42 3400 3600 3400 3600; 43 3600 3800 3600 3800; 44 703 803 703 703; 45 1447 14671447 1467; 46 51150 5925 51150 5925; 47 5855 5925 5855 5925; 48 3550 3700 3550 3700;49 3550 3700 3550 3700; 50 1432 1517 1432 1517; 51 1427 1432 1427 1432; 52 3300 34003300 3400; 65 1920 2010 2110 2200; 66 1710 1780 2110 2200; 67 738 758 738 758; 68 698728 753 783; 69 2570 2620 2570 2620; 70 1695 1710 1995 2020; 71 663 698 617 652; 72451 456 461 466; 73 450 455 460 465; 74 1427 1470 1475 1518; 75 1432 1517 1432 1517;76 1427 1432 1427 1432; 85 698 716 728 746];up=[FB(:,1),FB(:,2:3)];down=[FB(:,1),FB(:,4:5)];

listCA =[1 3],[1 5], [1 7], [1 28], [1 8], [1 11], [1 18], [1 19], [1 20], [1 21],[1 26], [1 28],[1 32],[1 38],[1 40], [1 41], [1 42],[1 43], [1 46], [2 4], [2 5],[2 7],[2 12],[2 29],[2 13],[2 14],[217],[2 28],[2 30],[2 46],[2 48], [2 49],[2 66],[2 71],[3 5],[3 7],[3 8],[3 11],[3 18],[3 19],[3 20],[321],[3 28], [3 41],[3 42],[3 26],[3 27],[3 31],[3 32],[3 38],[3 40],[3 43],[3 46],[3 69],[4 5], [4 7],[412],[4 13],[4 17],[4 27],[4 28],[4 29],[4 30],[4 46],[4 48],[4 71],[5 40], [5 41], [5 46],[5 48],[566],[7 8],[7 12], [7 20],[7 22],[7 26],[7 28],[7 30],[7 32], [7 40],[7 42],[7 46],[7 66],[8 11], [820],[8 27],[8 28],[8 32],[8 38],[8 38],[8 38], [8 39],[8 40],[8 41],[8 42],[8 46],[11 18],[11 26],[1128],[11 41],[11 42],[11 46], [12 25],[12 30],[12 46],[12 48],[12 66],[13 46 ],[12 48],[13 66],[1466], [14 30], [18 28],[19 21], [19 28],[19 42],[19 46],[20 28],[20 31],[20 32],[20 38],[20 40], [20

115

42],[20 43],[20 67],[20 75],[20 76],[21 28],[20 42],[20 46],[21 28],[21 42], [21 46],[23 29], [2526], [25 41], [25 46], [23 29],[25 26], [25 41],[25 46], [26 41],[26 46], [26 46],[26 48],[28 38],[2840],[28 41],[28 42],[28 46],[29 30], [29 66],[29 70],[30 66],[32 42],[32 43],[34 39],[34 41],[3840],[39 41],[39 40],[39 42], [39 46],[40 41],[40 42],[40 43],[40 43],[40 46],[41 42],[41 46],[4148],[42 43],[42 46], [46 48], [46 66],[46 70],[46 71],[48 66],[48 71],[66 70],[66 71],[70 71], [13 5], [1 3 7],[1 3 8],[1 3 43],[1 3 11],[1 3 18],[1 3 19],[1 3 20],[1 3 21],[1 3 26], [1 3 28], [1 332], [1 3 38], [1 3 40], [1 3 41], [1 3 43], [1 5 7], [1 5 40], [1 5 41],[1 5 46], [1 7 8], [1 7 20],[1 7 26], [1 7 28], [1 7 32], [1 7 40], [1 7 42], [1 7 46], [1 8 11], [1 8 20],[1 8 28],[1 8 38],[1 840],[1 11 18], [1 11 28],[1 18 28],[1 19 21],[1 19 28], [1 19 42], [1 20 28],[1 20 32],[1 20 42],[120 43],[1 21 28],[1 21 42],[1 28 42],[1 32 42], [1 32 43], [1 41 42],[1 42 42], [1 42 43], [2 4 5],[2 4 12],[2 5 12],[2 5 30],[2 5 46],[2 5 66], [2 12 30], [2 12 66],[2 13 66],[2 14 66],[2 30 66],[24 7],[2 4 12],[2 5 66],[2 4 13],[2 4 28],[2 4 29],[2 4 30], [2 4 71],[2 5 7],[2 5 12],[2 4 13], [2 428],[2 4 29],[2 4 30],[2 4 71],[2 5 7],[2 5 12], [2 5 13], [2 5 28], [2 5 29], [2 5 30], [2 5 46],[25 66],[2 7 12],[2 7 28],[2 7 30],[2 7 66], [2 12 30], [2 12 66], [2 13 46], [2 13 48],[2 13 66],[214 30],[2 14 66],[2 29 30],[2 29 66],[2 30 66], [2 46 48],[2 46 66],[2 48 66],[2 66 71],[3 5 7],[3 5 40],[3 5 41],[3 7 8],[3 7 20],[3 7 26],[3 7 32], [3 7 38], [3 7 40], [3 7 42], [3 7 46], [3 811], [3 8 20],[3 8 28],[3 8 32],[3 8 38],[3 8 40],[3 11 18], [3 11 26], [3 11 28 ],[3 11 26],[3 1128],[3 19 21],[3 19 42],[3 20 28],[3 20 32],[3 20 42],[3 32 42],[3 32 43 ], [3 42 43],[4 5 12], [45 13],[4 5 29],[4 5 30],[4 7 12 ],[4 7 28],[4 12 30],[4 29 30],[5 7 28], [5 7 46],[5 12 46],[5 1248],[5 12 66],[5 30 66],[5 40 41],[5 46 66],[7 8 20],[7 8 38],[7 8 40],[7 12 66], [7 20 28],[7 2032],[7 20 38],[7 20 42],[7 28 38],[7 30 66],[7 46 66],[8 11 28],[8 20 28],[8 28 41],[8 39 41], [1230 66],[13 46 66],[13 48 66],[14 30 66],[19 21 42],[20 32 42],[20 32 43],[20 38 40],[25 26 41],[20 38 40],[21 28 42],[29 30 66],[29 46 66],[29 66 70],[32 42 30],[46 48 66],[46 48 66],[46 4871],[66 70 71], [1 3 5 7],[1 3 5 40],[1 3 5 41],[1 3 7 26],[1 3 7 8],[1 3 7 20],[1 3 7 28],[1 3 732],[1 3 7 40], [1 3 7 42],[1 3 8 11],[1 3 8 20],[1 3 8 28],[1 3 8 38],[1 3 11 28],[1 3 8 40],[1 319 21],[1 3 19 42], [1 3 20 28 ],[1 3 20 32],[1 3 21 28],[1 3 21 42],[1 3 28 42],[1 3 32 42],[1 332 43],[1 3 42 43], [1 5 7 46],[1 7 8 20],[1 7 8 40],[1 7 20 28],[1 7 20 32],[1 7 20 42],[1 8 1128],[1 8 20 28], [1 19 21 42],[1 20 32 42],[1 20 32 43],[1 21 28 42],[1 32 42 43],[2 5 12 66],[25 30 66],[2 7 12 66], [2 12 30 66],[2 14 30 66],[2 4 5 12], [2 4 5 29],[2 4 5 30],[2 4 7 12],[2 412 30],[2 4 29 30],[2 5 7 28], [2 5 12 66], [2 5 30 66],[2 7 12 66],[2 7 46 66],[2 12 30 66],[2 1348 66],[2 14 30 66], [2 29 30 66],[2 46 48 66 ],[3 7 8 20],[3 7 8 38],[3 7 8 40],[3 7 20 28],[3 720 32],[3 7 20 42], [3 7 28 38],[3 8 11 28],[3 8 20 28],[3 19 21 42],[3 20 32 42],[3 20 32 43],[321 28 42],[3 28 41 42], [3 32 42 43], [1 3 7 20 28],[1 3 7 20 42],[1 3 8 11 28];

listCA2 =[1 3],[1 5], [1 7], [1 28], [1 8], [1 11], [1 18], [1 19], [1 20], [1 21],[1 26], [1 28],[1 32],[1 38],[1 40], [1 41], [1 42],[1 43], [1 46], [2 4], [2 5],[2 7],[2 12],[2 29],[2 13],[2 14],[217],[2 28],[2 29],[2 30],[2 46],[2 48], [2 49],[2 66],[2 71],[3 5],[3 7],[3 8],[3 11],[3 18],[3 19],[320],[3 21],[3 28], [3 41],[3 42],[3 26],[3 27],[3 31],[3 32],[3 38],[3 40],[3 43],[3 46],[3 69],[4 5],[4 7],[4 12],[4 13],[4 17],[4 27],[4 28],[4 29],[4 30],[4 46],[4 48],[4 71],[5 40], [5 41], [5 46],[548],[5 66],[7 8],[7 12], [7 20],[7 22],[7 26],[7 28],[7 30],[7 32], [7 40],[7 42],[7 46],[7 66],[8 11],[8 20],[8 27],[8 28],[8 32],[8 38], [8 39],[8 40],[8 41],[8 42],[8 46],[11 18],[11 26],[11 28],[1141],[11 42],[11 46], [12 25],[12 30],[12 46],[12 48],[12 66],[13 46 ],[12 48],[13 66],[14 66], [1430], [18 28],[19 21], [19 28],[19 42],[19 46],[20 28],[20 31],[20 32],[20 38],[20 40], [20 42],[2043],[20 67],[20 75],[20 76],[21 28],[20 46],[21 28],[21 42], [21 46],[23 29], [25 26], [25 41], [2546], [23 29],[25 26], [25 41],[25 46], [26 41],[26 48],[28 38],[28 40],[28 41],[28 42],[28 46],[2930], [29 66],[29 70],[30 66], [46 66],[46 70],[46 71],[48 66],[48 71],[66 70],[66 71],[70 71];

listCA3=[1 3 5], [1 3 7],[1 3 8],[1 3 43],[1 3 11],[1 3 18],[1 3 19],[1 3 20],[1 3 21],[1 3 26],[1 3 28], [1 3 32], [1 3 38], [1 3 40], [1 3 41], [1 3 43], [1 5 7], [1 5 40], [1 5 41],[1 5 46], [1

116

Chapter B. Code matlab pour le calcul des intermodulations

7 8], [1 7 20], [1 7 26], [1 7 28], [1 7 32], [1 7 40], [1 7 42], [1 7 46], [1 8 11], [1 8 20],[1 828],[1 8 38],[1 8 40],[1 11 18], [1 11 28],[1 18 28],[1 19 21],[1 19 28], [1 19 42], [1 20 28],[120 32],[1 20 42],[1 20 43],[1 21 28],[1 21 42],[1 28 42],[1 32 42], [1 32 43], [1 41 42],[1 4242], [1 42 43], [2 4 5], [2 4 12],[2 5 12],[2 5 30],[2 5 46],[2 5 66], [2 12 30], [2 12 66],[2 1366],[2 14 66],[2 30 66],[2 4 7],[2 4 12],[2 5 66],[2 4 13],[2 4 28],[2 4 29],[2 4 30], [2 4 71],[25 7],[2 5 12],[2 4 13], [2 4 28],[2 4 29],[2 4 30],[2 4 71],[2 5 7],[2 5 12], [2 5 13], [2 5 28], [25 29], [2 5 30], [2 5 46],[2 5 66],[2 7 12],[2 7 12],[2 7 28],[2 7 30],[2 7 66], [2 12 30], [2 1266], [2 13 46], [2 13 48],[2 13 66],[2 14 30],[2 14 66],[2 29 30],[2 29 66],[2 30 66], [2 46 48],[246 66],[2 48 66],[2 66 71],[3 5 7], [3 5 40],[3 5 41],[3 7 8],[3 7 20],[3 7 26],[3 7 32], [3 7 38],[3 7 40], [3 7 42], [3 7 46], [3 8 11], [3 8 20],[3 8 28],[3 8 32],[3 8 38],[3 8 40],[3 11 18], [311 26], [3 11 28 ],[3 11 26],[3 11 28],[3 19 21],[3 19 42],[3 20 28],[3 20 32],[3 20 42],[3 3242],[3 32 43 ], [3 42 43],[4 5 12], [4 5 13],[4 5 29],[4 5 30],[4 7 12 ],[4 7 28],[4 12 30],[4 2930],[5 7 28], [5 7 46],[5 12 46],[5 12 48],[5 12 66],[5 30 66],[5 40 41],[5 46 66],[7 8 20],[7 838],[7 8 40],[7 12 66], [7 20 28],[7 20 32],[7 20 38],[7 20 42],[7 28 38],[7 30 66],[7 46 66],[8 1128],[8 20 28],[8 28 41],[8 39 41], [12 30 66],[13 46 66],[13 48 66],[14 30 66],[19 21 42],[20 3242],[20 32 43],[20 38 40],[25 26 41], [20 38 40],[21 28 42],[29 30 66],[29 46 66],[29 66 70],[3242 30],[46 48 66],[46 48 71],[66 70 71];

listCA4= [1 3 5 7],[1 3 5 40],[1 3 5 41],[1 3 7 26],[1 3 7 8],[1 3 7 20],[1 3 7 28],[1 3 732],[1 3 7 40], [1 3 7 42],[1 3 8 11],[1 3 8 20],[1 3 8 28],[1 3 8 38],[1 3 11 28],[1 3 8 40],[1 319 21],[1 3 19 42], [1 3 20 28 ],[1 3 20 32],[1 3 21 28],[1 3 21 42],[1 3 28 42],[1 3 32 42],[1 332 43],[1 3 42 43], [1 5 7 46],[1 7 8 20],[1 7 8 40],[1 7 20 28],[1 7 20 32],[1 7 20 42],[1 8 1128],[1 8 20 28], [1 19 21 42],[1 20 32 42],[1 20 32 43],[1 21 28 42],[1 32 42 43],[2 5 12 66],[25 30 66],[2 7 12 66], [2 12 30 66],[2 14 30 66],[2 4 5 12], [2 4 5 29],[2 4 5 30],[2 4 7 12],[2 412 30],[2 4 29 30],[2 5 7 28], [2 5 12 66], [2 5 30 66],[2 7 12 66],[2 7 46 66],[2 12 30 66],[2 1348 66],[2 14 30 66], [2 29 30 66],[2 46 48 66 ],[3 7 8 20],[3 7 8 38],[3 7 8 40],[3 7 20 28],[3 720 32],[3 7 20 42], [3 7 28 38],[3 8 11 28],[3 8 20 28],[3 19 21 42],[3 20 32 42],[3 20 32 43],[321 28 42],[3 28 41 42], [3 32 42 43];

listCA5= [1 3 7 20 28],[1 3 7 20 42],[1 3 8 11 28];———————————————————————————————–

chooseCA.m

function K=chooseCA(CA,direction)K=[];

for i=1:numel(CA)for j=1:numel(direction(:,1))

if CA(i)== direction(j,1)

K=[K;direction(j,:)];end

end

end;———————————————————————————————–fconv.m

117

function fconv=fconv(i,j)fconv=[i(1)+j(1),i(2)+j(2),i(3)+j(3)];—————————————————————————————– fconvCA.m

function M=fconvCA(A,B)M=[ ];for i=1:size(A,1)for j=1:size(B,1)M=[M; fconv(A(i,:),B(j,:))];

endend——————————————————————————————————interfer.m

function I=interfer(A,B)if (((A(1)<= B(1)) && (B(1) <= A(2)))——((B(1)<=A(1)) && (A(1)<= B(2))))I=[A,B];elseI=[];end—————————————————————————————————–file:imd-upto-n.m

function IMD=imd-upto-n(CA,direction,n)ba=chooseCA(CA,direction);bands=[ba(:,2) ba(:,3) ones(size(CA,2),1); -ba(:,3) -ba(:,2) ones(size(CA,2),1)];IMD=[];for i=2:nif i==2IMDv=fconvCA(bands,bands);

elseIMDv=fconvCA(imd-n(CA,direction,i-1),bands);

end ;IMD=[IMD;IMDv];end

—————————————————————————————————interference.m

function Inter=interference(CA,TransmitDirection,InterferenceDirection,n)IMD=imd-upto-n(CA,TransmitDirection,n);ba=chooseCA(CA,InterferenceDirection);bands=[ba(:,2) ba(:,3);-ba(:,3) -ba(:,2)];Interv=[];

118

Chapter B. Code matlab pour le calcul des intermodulations

for i=1:size(IMD,1)for j=1:size(bands,1)if( isempty(interfer(IMD(i,:),bands(j,:))))Interv=[Interv;[CA interfer(IMD(i,:),bands(j,:)) ]];endend

Inter=unique(Interv,’rows’);

end—————————————————————————————————–interference-list-CA.m

function inter-list-CA=interference-list-CA(list-CA,TransmitDirection,InterferenceDirection,n)inter-list-CA=[];CA=[];for i=1:numel(list-CA)Iv= interference(list-CAi,TransmitDirection,InterferenceDirection,n);

for j=1:size(Iv,1)

inter-list-CA=[inter-list-CA; Iv(j,:)percent-interference(Iv(j,end-3:end))];end

end;————————————————————————————————-percent-interference.m

function P=percent-interference(A)

switch 1case A(1,1)<A(1,3) && A(1,3)<A(1,2) && A(1,2)< A(1,4)P= round( (A(1,2)-A(1,3))/(A(1,4)-A(1,3))*100);disp(’1’);case (A(1,1)<A(1,3) && A(1,3)<A(1,2)) && A(1,2)> A(1,4)P= 100;disp(’2’);case A(1,1)>A(1,3) && A(1,1)<A(1,4) && A(1,4)<A(1,2)P= round( (A(1,4)-A(1,1))/(A(1,4)-A(1,3))*100);disp(’3’);case A(1,1)>A(1,3) && A(1,1)<A(1,4) && A(1,4)>A(1,2)P= round((A(1,2)-A(1,1))/(A(1,4)-A(1,3))*100);disp(’4’);case (isempty(A))0;

119

otherwiseP= [];disp(’5’);end——————————————————————————————-percent-interference-listCA.m

function Pv=percent-interference-listCA(listCA,TransmitDirection,InterferenceDirection,n)Pv=[];for i=1:size(listCA,2)Pv = [Pv; percent-interference-CA(listCAi,TransmitDirection,InterferenceDirection,n)];endfor j=1:size(Pv,1)Pvj,1;end——————————————————————————————————print-interference-list-CA.m

function v=print-interference-list-CA(list-CA,TransmitDirection,InterferenceDirection,n)M=interference-list-CA(list-CA,TransmitDirection,InterferenceDirection,n);for j=1:size(M,1)v= Mj,1;end————————————————————————————————–table-percent-interference-CA.mfunction table-percent-interference-CA(CA,TransmitDirection,InterferenceDirection,n)p=percent-interference-CA(CA,TransmitDirection,InterferenceDirection,n);pw=power-interference(CA,TransmitDirection,InterferenceDirection,n);t=table;if ( isempty(p))t.carrier-aggregation= [p(:,1:end-6)];t.intermodulation-distortion=[p(:,end-5:end-3)];t.band-interference=[p(:,end-2) p(:,end-1)];t.percent-interference=p(:,end)end

t.power-inteference=pw;—————————————————————————————————table-percent-interference-listCA.m

function table-percent-interference-listCA(listCA,TransmitDirection,InterferenceDirection,n)for i=1:size(listCA,2)table-percent-interference-CA(listCAi,TransmitDirection,InterferenceDirection,n)end

120

Appendix C

code Maxima for IMD andharmonics plotting

load(pw);load(draw);load(qdraw);Pout:23;Gain:16;

B1:45;B2:12;S1(f):= pw([-inf,0,1710,0.3,1755,0,inf],f,’open);

qdraw(ex ([S1(f)],f,1700,1760),yr(0,0.4), pic(jpg,”B4”),label([ ”Band 4, uplink”, 1705,0.36]), more(xlabel= ”frequency [MHz]” , ylabel=”Powerspectral density [mW/MHz]”) );

S2(f):=pw([-inf,0,704,0.3,716,0,inf],f,’open);

qdraw(ex ([S2(f)],f,700,720),yr(0,0.4), pic(jpg,”B17”),label([ ”Band 17, uplink”, 701,0.36]), more(xlabel=”frequency [MHz]” , ylabel=”Powerspectral density [mW/MHz]”));

I12(f):=0.14*pwint(S1(m)*S2(f-m),m,-inf,inf);

qdraw(ex ([I12(f)],f,2410,2476),yr(0,0.4), pic(jpg,”I4 17”),label([ ”second order Intermodulation of band B4 and band B17, uplink”, 2410,0.36]),more(xlabel=”frequency [MHz]” , ylabel=”Power spectral density [mW/MHz]”));

I11(f):=0.14* pwint(S1(m)*S1(f-m),m,-inf,inf);

qdraw(ex ([I11(f)],f,3400,3550),yr(0,1), pic(jpg,”I4 4”),label([ ”second order harmonic of band B4, uplink”, 3410,0.36]), more(xlabel=”frequency[MHz]” , ylabel=”Power spectral density [mW/MHz]”));

121

I22(f):= 0.14*pwint(S2(m)*S2(f-m),m,-inf,inf);qdraw(ex ([I22(f)],f,1400,1450),yr(0,0.4), pic(jpg,”I17 17”),label([ ”second order harmonic of band B17 , uplink”, 1410,0.36]), more(xlabel=”frequency[MHz]” , ylabel=”Power spectral density [mW/MHz]”));

I222(f):=1.25 * pwint(I22(q)*S2(f-q),q,-inf,inf);

qdraw(ex ([I222(f)],f,2105,2155),yr(0,1), pic(jpg,”I17 17 17”),label([ ”third order harmonic of band B17, uplink”, 2110,0.9]), more(xlabel=”frequency[MHz]” , ylabel=”Power spectral density [mW/MHz]”));

I111(f):= 1.25 *pwint(I11(p)*S1(f-p),p,-inf,inf);

qdraw(ex ([I111(f)],f,5100,5275),yr(0,10), pic(jpg,”I4 4 4”),label([ ”third order harmonic of band B4 , uplink”, 5110,3.6]), more(xlabel=”frequency[MHz]” , ylabel=”Power spectral density [mW/MHz]”));

I112(f):=1.25 * pwint(I11(v)*S2(f-v),v,-inf,inf);qdraw(ex ([I112(f)],f,4100,4230),yr(0,5), pic(jpg,”I4 4 17”), /* 2*B4+ B17 */label([ ”third order intermodulation of band 4 and band 17 , uplink”, 4110,0.85]),more(xlabel=”frequency [MHz]” , ylabel=”Power spectral density [mW/MHz]”));

I221(f):=1.25 * pwint(I22(w)*S1(f-w),w,-inf,inf);qdraw(ex ([I221(f)],f,3100,3200),yr(0,5), pic(jpg,”I17 17 4”), /* 2*B17+B4*/label([ ”third order intermodulation of band 4 and band 17 , uplink”, 3105,0.28]),more(xlabel=”frequency [MHz]” , ylabel=”Power spectral density [mW/MHz]”));

122

Appendix D

Counter CD74hc4059

123

Figure D.1: Chip CD74HC4059

124

List of Publications

• Niyonkuru, L., Vandersteen, G. & Van Biesen, L. ” Power spectrum measurementof high frequency angle modulated digital signal from ouput power spectrum of adigital divider”, 17 Sep 2019, 24nd IMEKO TC4 International Symposium. IMEKO

• Niyonkuru, L., Vandersteen, G. & Van Biesen, L. ”Design and Implementationof a Digital Mixer with Digital Logic”, textitJoint IMEKO TC1-TC7-TC13-TC18Symposium 2019: The future glimmers long before it comes to be - St Petersburg,Russian Federation. Published in ”Journal of Physics: Conference Series, 2019”

• Niyonkuru, L., Vandersteen, G. & Van Biesen, L., ”Issues of carrier aggregationintermodulation distortions in LTE-Advanced System”, 35th BENELUX meeting,2016

• Niyonkuru, L., Vandersteen, G. & Van Biesen, L.,” Les distorsions non lineairescausees par l’aggregation des porteuses dans les reseaux mobiles 4G et 5G”, Conference”Contributions des TIC dans le domaine de l’enseignement et de la Recherche audeveloppement durable”, Bujumbura, october,2019

• Niyonkuru, L., Vandersteen, G. & Van Biesen, L., ”5G networks: expectations andchallenges”, in conference ”Projets du vlir-uos/UB, modele de cooperation univer-sitaire? Bilan de 7 annees d’activites”,Bujumbura, September, 19th 2017

• Niyonkuru, L., Vandersteen, G. & Van Biesen, L., ”Design et realisation d’unmelangeur numerique a base de circuits logiques (portes logiques et bascules)” dansla conference sur le theme “ CONTRIBUTION DES UNIVERSITES AU DEVEL-OPPEMENT DURABLE”, organisee par l’Univeversite du Burundi et VLIR-UOSle 19 octobre 2018

125

Bibliography

[1] C. VNI, Cisco Visual Networking Index: Forecast and Trends, 2017–2022. CISCO,2018.

[2] H. Holma and A. Toskala, “Evolution to LTE-advanced second edition,” LTE forUMTS, p. 559,

[3] L. G. Ordonez, D. P. Palomar, A. Pages-Zamora, and J. Fonollosa, “High-SNR ana-lytical performance of spatial multiplexing MIMO systems with CSI,” IEEE Trans-actions on Signal Processing, vol. 55, no. 11, pp. 5447–5463, Nov. 2007, issn: 1053-587X, 1941-0476. doi: 10.1109/TSP.2007.896109. [Online]. Available: https://ieeexplore.ieee.org/document/4355328/ (visited on 02/22/2020).

[4] B. Clerckx, H. Joudeh, C. Hao, M. Dai, and B. Rassouli, “Rate splitting for MIMOwireless networks: A promising PHY-layer strategy for LTE evolution,” IEEE Com-munications Magazine, vol. 54, no. 5, pp. 98–105, May 2016, issn: 0163-6804. doi:10.1109/MCOM.2016.7470942. [Online]. Available: http://ieeexplore.ieee.org/document/7470942/ (visited on 02/22/2020).

[5] A. F. Molisch, V. V. Ratnam, S. Han, Z. Li, S. L. H. Nguyen, L. Li, and K. Haneda,“Hybrid beamforming for massive MIMO: A survey,” IEEE Communications Mag-azine, vol. 55, no. 9, pp. 134–141, 2017, issn: 0163-6804. doi: 10.1109/MCOM.2017.1600400. [Online]. Available: http://ieeexplore.ieee.org/document/8030501/(visited on 02/22/2020).

[6] D. C. Araujo, T. Maksymyuk, A. L. de Almeida, T. Maciel, J. C. Mota, and M.Jo, “Massive MIMO: Survey and future research topics,” IET Communications,vol. 10, no. 15, pp. 1938–1946, Oct. 13, 2016, issn: 1751-8628, 1751-8636. doi:10.1049/iet-com.2015.1091. [Online]. Available: https://digital-library.theiet . org / content / journals / 10 . 1049 / iet - com . 2015 . 1091 (visited on02/22/2020).

[7] H. Wang, C. Rosa, and K. Pedersen, “Performance analysis of downlink inter-bandcarrier aggregation in LTE-advanced,” in 2011 IEEE Vehicular Technology Con-ference (VTC Fall), San Francisco, CA, USA: IEEE, Sep. 2011, pp. 1–5, isbn:978-1-4244-8327-3 978-1-4244-8328-0 978-1-4244-8325-9 978-1-4244-8326-6. doi: 10.1109/VETECF.2011.6092836. [Online]. Available: http://ieeexplore.ieee.org/document/6092836/ (visited on 02/22/2020).

[8] ——, “Uplink component carrier selection for LTE-advanced systems with carrieraggregation,” in 2011 IEEE International Conference on Communications (ICC),Kyoto, Japan: IEEE, Jun. 2011, pp. 1–5, isbn: 978-1-61284-232-5. doi: 10.1109/icc.2011.5963279. [Online]. Available: http://ieeexplore.ieee.org/document/5963279/ (visited on 02/22/2020).

127

https://doi.org/10.1109/TSP.2007.896109

https://ieeexplore.ieee.org/document/4355328/


https://doi.org/10.1109/MCOM.2016.7470942

http://ieeexplore.ieee.org/document/7470942/





https://doi.org/10.1049/iet-com.2015.1091

https://digital-library.theiet.org/content/journals/10.1049/iet-com.2015.1091

https://digital-library.theiet.org/content/journals/10.1049/iet-com.2015.1091

https://doi.org/10.1109/VETECF.2011.6092836

https://doi.org/10.1109/VETECF.2011.6092836



https://doi.org/10.1109/icc.2011.5963279

https://doi.org/10.1109/icc.2011.5963279



BIBLIOGRAPHY

[9] Z. Khan, H. Ahmadi, E. Hossain, M. Coupechoux, L. A. Dasilva, and J. J. Lehtomaki,“Carrier aggregation/channel bonding in next generation cellular networks: Meth-ods and challenges,” IEEE Network, vol. 28, no. 6, pp. 34–40, Nov. 2014, issn:0890-8044, 1558-156X. doi: 10.1109/MNET.2014.6963802. [Online]. Available:https://ieeexplore.ieee.org/document/6963802/ (visited on 02/22/2020).

[10] S. C. Cripps, RF power amplifiers for wireless communications, 2nd ed, ser. ArtechHouse microwave library. Boston: Artech House, 2006, 456 pp., OCLC: ocm67728816,isbn: 978-1-59693-018-6.

[11] M. Z. Waheed, P. P. Campo, D. Korpi, A. Kiayani, L. Anttila, and M. Valkama,“Digital cancellation of passive intermodulation in FDD transceivers,” in 2018 52ndAsilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA:IEEE, Oct. 2018, pp. 1375–1381, isbn: 978-1-5386-9218-9. doi: 10.1109/ACSSC.2018.8645262. [Online]. Available: https://ieeexplore.ieee.org/document/8645262/ (visited on 02/22/2020).

[12] J. Henrie, A. Christianson, and W. Chappell, “Engineered passive nonlinearities forbroadband passive intermodulation distortion mitigation,” IEEE Microwave andWireless Components Letters, vol. 19, no. 10, pp. 614–616, Oct. 2009, issn: 1531-1309, 1558-1764. doi: 10.1109/LMWC.2009.2029733. [Online]. Available: http://ieeexplore.ieee.org/document/5233752/ (visited on 02/22/2020).

[13] M. Abdelaziz, “Low-complexity subband digital predistortion for spurious emissionsuppression in noncontiguous spectrum access,” IEEE Transactions on MicrowaveTheory and Techniques, vol. 64, no. 11, p. 3501, 2016, issn: 0018-9480.

[14] X. Li, A. Gani, R. Salleh, and O. Zakaria, “The future of mobile wireless commu-nication networks,” in 2009 International Conference on Communication Softwareand Networks, Chengdu Sichuan, China: IEEE, 2009, pp. 554–557, isbn: 978-0-7695-3522-7. doi: 10.1109/ICCSN.2009.105. [Online]. Available: http://ieeexplore.ieee.org/document/5076913/ (visited on 02/02/2020).

[15] J. Korhonen, Introduction to 3G mobile communications, 2nd ed, ser. Artech Housemobile communications series. Boston, MA: Artech House, 2003, 544 pp., isbn:978-1-58053-507-6.

[16] R. van Nobelen, N. Seshadri, J. Whitehead, and S. Timiri, “An adaptive radio linkprotocol with enhanced data rates for GSM evolution,” IEEE Personal Communica-tions, vol. 6, no. 1, pp. 54–64, Feb. 1999, issn: 10709916. doi: 10.1109/98.752788.[Online]. Available: http://ieeexplore.ieee.org/document/752788/ (visited on02/02/2020).

[17] J. Korhonen, O. Aalto, A. Gurtov, and H. Lamanen, “Measured performance ofGSM, HSCSD and GPRS,” in ICC 2001. IEEE International Conference on Com-munications. Conference Record (Cat. No.01CH37240), vol. 5, Helsinki, Finland:IEEE, 2001, pp. 1330–1334. doi: 10.1109/ICC.2001.937138. [Online]. Available:http://ieeexplore.ieee.org/document/937138/ (visited on 02/02/2020).

128

https://doi.org/10.1109/MNET.2014.6963802


https://doi.org/10.1109/ACSSC.2018.8645262

https://doi.org/10.1109/ACSSC.2018.8645262



https://doi.org/10.1109/LMWC.2009.2029733



https://doi.org/10.1109/ICCSN.2009.105



https://doi.org/10.1109/98.752788


https://doi.org/10.1109/ICC.2001.937138


BIBLIOGRAPHY

[18] W. Gerstacker, R. Schober, R. Meyer, F. Obernosterer, M. Ruder, and H. Kalveram,“GSM/EDGE: A mobile communications system determined to stay,” AEU - In-ternational Journal of Electronics and Communications, vol. 65, no. 8, pp. 694–700,Aug. 2011, issn: 14348411. doi: 10.1016/j.aeue.2011.01.010. [Online]. Avail-able: https://linkinghub.elsevier.com/retrieve/pii/S1434841111000161(visited on 02/02/2020).

[19] 3GPP, Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS)radio transmission and reception. 2019.

[20] C. Cox, An introduction to LTE, Second edition. Wiley, 2014.

[21] M. Sauter, “From GSM to LTE-advanced,” p. 458,

[22] 3GPP, RP-191440, Dec. 2009.

[23] C. Cox, “An introduction to LTE: LTE, LTE-advanced, SAE, VoLTE and 4g mobilecommunications,” p. 487,

[24] A. Abdelhadi and C. Clancy, “An optimal resource allocation with joint carrier ag-gregation in 4g-LTE,” in 2015 International Conference on Computing, Networkingand Communications (ICNC), Garden Grove, CA, USA: IEEE, Feb. 2015, pp. 138–142, isbn: 978-1-4799-6959-3. doi: 10.1109/ICCNC.2015.7069330. [Online]. Avail-able: http://ieeexplore.ieee.org/document/7069330/ (visited on 02/18/2020).

[25] L. Liu, M. Li, J. Zhou, X. She, L. Chen, Y. Sagae, and M. Iwamura, “Componentcarrier management for carrier aggregation in LTE-advanced system,” in 2011 IEEE73rd Vehicular Technology Conference (VTC Spring), Budapest, Hungary: IEEE,May 2011, pp. 1–6, isbn: 978-1-4244-8332-7. doi: 10.1109/VETECS.2011.5956228.[Online]. Available: http://ieeexplore.ieee.org/document/5956228/ (visitedon 02/18/2020).

[26] J. Wang, M. Wu, and F. Zheng, “The codebook design for MIMO precoding systemsin LTE and LTE-a,” in 2010 International Conference on Computational Intelligenceand Software Engineering, Chengdu City, China: IEEE, Sep. 2010, pp. 1–4, isbn:978-1-4244-3708-5. doi: 10.1109/WICOM.2010.5600618. [Online]. Available: http://ieeexplore.ieee.org/document/5600618/ (visited on 02/18/2020).

[27] J. Lee, J.-K. Han, and J. Zhang, “MIMO technologies in 3gpp LTE and LTE-advanced,” EURASIP Journal on Wireless Communications and Networking, vol. 2009,no. 1, Dec. 2009, issn: 1687-1499. doi: 10.1155/2009/302092. [Online]. Available:https://jwcn-eurasipjournals.springeropen.com/articles/10.1155/2009/

302092 (visited on 02/18/2020).

[28] A. Osseiran, Ed., 5G mobile and wireless communications technology, United King-dom : New York: Cambridge University Press, 2016, 406 pp., isbn: 978-1-107-13009-8.

[29] A. Osseiran, F. Boccardi, V. Braun, K. Kusume, P. Marsch, M. Maternia, O. Que-seth, M. Schellmann, H. Schotten, H. Taoka, H. Tullberg, M. A. Uusitalo, B. Timus,and M. Fallgren, “Scenarios for 5g mobile and wireless communications: The visionof the METIS project,” IEEE Communications Magazine, vol. 52, no. 5, pp. 26–35,May 2014, issn: 0163-6804. doi: 10.1109/MCOM.2014.6815890. [Online]. Available:http://ieeexplore.ieee.org/document/6815890/ (visited on 02/18/2020).

129

https://doi.org/10.1016/j.aeue.2011.01.010

https://linkinghub.elsevier.com/retrieve/pii/S1434841111000161

https://doi.org/10.1109/ICCNC.2015.7069330


https://doi.org/10.1109/VETECS.2011.5956228


https://doi.org/10.1109/WICOM.2010.5600618



https://doi.org/10.1155/2009/302092

https://jwcn-eurasipjournals.springeropen.com/articles/10.1155/2009/302092

https://jwcn-eurasipjournals.springeropen.com/articles/10.1155/2009/302092



BIBLIOGRAPHY

[30] J. Sachs, G. Wikstrom, T. Dudda, R. Baldemair, and K. Kittichokechai, “5g ra-dio network design for ultra-reliable low-latency communication,” IEEE Network,vol. 32, no. 2, pp. 24–31, Mar. 2018, issn: 0890-8044. doi: 10.1109/MNET.2018.1700232. [Online]. Available: http://ieeexplore.ieee.org/document/8329620/(visited on 02/18/2020).

[31] I. Parvez, A. Rahmati, I. Guvenc, A. I. Sarwat, and H. Dai, “A survey on lowlatency towards 5g: RAN, core network and caching solutions,” IEEE Communi-cations Surveys & Tutorials, vol. 20, no. 4, pp. 3098–3130, 2018, issn: 1553-877X,2373-745X. doi: 10.1109/COMST.2018.2841349. [Online]. Available: https://ieeexplore.ieee.org/document/8367785/ (visited on 02/18/2020).

[32] C. Bockelmann, N. Pratas, H. Nikopour, K. Au, T. Svensson, C. Stefanovic, P.Popovski, and A. Dekorsy, “Massive machine-type communications in 5g: Physicaland MAC-layer solutions,” IEEE Communications Magazine, vol. 54, no. 9, pp. 59–65, Sep. 2016, issn: 0163-6804. doi: 10.1109/MCOM.2016.7565189. [Online]. Avail-able: http://ieeexplore.ieee.org/document/7565189/ (visited on 02/09/2020).

[33] S. Rostami, K. Arshad, and P. Rapajic, “A joint resource allocation and link adapta-tion algorithm with carrier aggregation for 5g LTE-advanced network,” in 2015 22ndInternational Conference on Telecommunications (ICT), Sydney, Australia: IEEE,Apr. 2015, pp. 102–106, isbn: 978-1-4799-8078-9. doi: 10.1109/ICT.2015.7124665.[Online]. Available: http://ieeexplore.ieee.org/document/7124665/ (visitedon 02/18/2020).

[34] E. Chavarria-Reyes, I. F. Akyildiz, and E. Fadel, “Energy-efficient multi-stream car-rier aggregation for heterogeneous networks in 5g wireless systems,” IEEE Trans-actions on Wireless Communications, vol. 15, no. 11, pp. 7432–7443, Nov. 2016,issn: 1536-1276. doi: 10.1109/TWC.2016.2602336. [Online]. Available: http:

//ieeexplore.ieee.org/document/7551237/ (visited on 02/18/2020).

[35] T. S. Rappaport, Shu Sun, R. Mayzus, Hang Zhao, Y. Azar, K. Wang, G. N. Wong,J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter wave mobile communicationsfor 5g cellular: It will work!” IEEE Access, vol. 1, pp. 335–349, 2013, issn: 2169-3536.doi: 10.1109/ACCESS.2013.2260813. [Online]. Available: http://ieeexplore.ieee.org/document/6515173/ (visited on 02/09/2020).

[36] X. Ge, S. Tu, G. Mao, C.-X. Wang, and T. Han, “5g ultra-dense cellular networks,”IEEE Wireless Communications, p. 8, 2016.

[37] V. Jungnickel, K. Manolakis, W. Zirwas, B. Panzner, V. Braun, M. Lossow, M.Sternad, R. Apelfrojd, and T. Svensson, “The role of small cells, coordinated multi-point, and massive MIMO in 5g,” IEEE Communications Magazine, vol. 52, no. 5,pp. 44–51, May 2014, issn: 0163-6804. doi: 10.1109/MCOM.2014.6815892. [On-line]. Available: http://ieeexplore.ieee.org/document/6815892/ (visited on02/18/2020).

[38] K. N. R. S. V. Prasad, E. Hossain, and V. K. Bhargava, “Energy efficiency inmassive MIMO-based 5g networks: Opportunities and challenges,” IEEE WirelessCommunications, vol. 24, no. 3, pp. 86–94, Jun. 2017, issn: 1536-1284. doi: 10.1109/MWC.2016.1500374WC. [Online]. Available: http://ieeexplore.ieee.org/document/7811130/ (visited on 02/18/2020).

130




https://doi.org/10.1109/COMST.2018.2841349





https://doi.org/10.1109/ICT.2015.7124665


https://doi.org/10.1109/TWC.2016.2602336



https://doi.org/10.1109/ACCESS.2013.2260813





https://doi.org/10.1109/MWC.2016.1500374WC

https://doi.org/10.1109/MWC.2016.1500374WC



BIBLIOGRAPHY

[39] D. Chen, J. Schuler, P. Wainio, and J. Salmelin, “5g self-optimizing wireless meshbackhaul,” in 2015 IEEE Conference on Computer Communications Workshops(INFOCOM WKSHPS), Hong Kong, Hong Kong: IEEE, Apr. 2015, pp. 23–24, isbn:978-1-4673-7131-5. doi: 10.1109/INFCOMW.2015.7179324. [Online]. Available:http://ieeexplore.ieee.org/document/7179324/ (visited on 02/18/2020).

[40] J. Xu, J. Yao, L. Wang, K. Wu, L. Chen, and W. Lou, “Revolution of self-organizingnetwork for 5g MmWave small cell management: From reactive to proactive,” IEEEWireless Communications, vol. 25, no. 4, pp. 66–73, Aug. 2018, issn: 1536-1284,1558-0687. doi: 10 . 1109 / MWC . 2018 . 1700420. [Online]. Available: https : / /

ieeexplore.ieee.org/document/8454670/ (visited on 02/18/2020).

[41] I. Jovovic, I. Forenbacher, and M. Perisa, “Massive machine-type communications:An overview and perspectives towards 5g,” presented at the The 3rd InternationalVirtual Research Conference In Technical Disciplines, Nov. 20, 2015, pp. 32–37. doi:10.18638/rcitd.2015.3.1.73. [Online]. Available: https://www.rcitd.com/archive/?vid=1&aid=2&kid=140301-73 (visited on 02/09/2020).

[42] M. R. Palattella, M. Dohler, A. Grieco, G. Rizzo, J. Torsner, T. Engel, and L. Ladid,“Internet of things in the 5g era: Enablers, architecture, and business models,” IEEEJournal on Selected Areas in Communications, vol. 34, no. 3, pp. 510–527, Mar.2016, issn: 0733-8716. doi: 10.1109/JSAC.2016.2525418. [Online]. Available:http://ieeexplore.ieee.org/document/7397856/ (visited on 02/18/2020).

[43] H. Shariatmadari, R. Ratasuk, S. Iraji, A. Laya, T. Taleb, R. Jantti, and A. Ghosh,“Machine-type communications: Current status and future perspectives toward 5gsystems,” IEEE Communications Magazine, vol. 53, no. 9, pp. 10–17, Sep. 2015,issn: 0163-6804. doi: 10.1109/MCOM.2015.7263367. [Online]. Available: http://ieeexplore.ieee.org/document/7263367/ (visited on 02/18/2020).

[44] S. Abdelwahab, B. Hamdaoui, M. Guizani, and T. Znati, “Network function virtu-alization in 5g,” IEEE Communications Magazine, vol. 54, no. 4, pp. 84–91, Apr.2016, issn: 0163-6804. doi: 10.1109/MCOM.2016.7452271. [Online]. Available:http://ieeexplore.ieee.org/document/7452271/ (visited on 02/09/2020).

[45] F. Z. Yousaf, M. Bredel, S. Schaller, and F. Schneider, “NFV and SDN—key technol-ogy enablers for 5g networks,” IEEE Journal on Selected Areas in Communications,vol. 35, no. 11, pp. 2468–2478, Nov. 2017, issn: 0733-8716. doi: 10.1109/JSAC.2017.2760418. [Online]. Available: http://ieeexplore.ieee.org/document/8060513/ (visited on 02/18/2020).

[46] J. Rodriguez, “Fundamentals of 5g mobile networks,” p. 336,

[47] B. Chatras, U. S. Tsang Kwong, and N. Bihannic, “NFV enabling network slicingfor 5g,” in 2017 20th Conference on Innovations in Clouds, Internet and Networks(ICIN), Paris: IEEE, Mar. 2017, pp. 219–225, isbn: 978-1-5090-3672-1. doi: 10.1109/ICIN.2017.7899415. [Online]. Available: http://ieeexplore.ieee.org/document/7899415/ (visited on 02/18/2020).

[48] X. Ge, J. Yang, H. Gharavi, and Y. Sun, “Energy efficiency challenges of 5g smallcell networks,” IEEE Communications Magazine, vol. 55, no. 5, pp. 184–191, May2017, issn: 0163-6804. doi: 10.1109/MCOM.2017.1600788. [Online]. Available:http://ieeexplore.ieee.org/document/7926940/ (visited on 02/18/2020).

131

https://doi.org/10.1109/INFCOMW.2015.7179324


https://doi.org/10.1109/MWC.2018.1700420



https://doi.org/10.18638/rcitd.2015.3.1.73

https://www.rcitd.com/archive/?vid=1&aid=2&kid=140301-73

https://www.rcitd.com/archive/?vid=1&aid=2&kid=140301-73

https://doi.org/10.1109/JSAC.2016.2525418











https://doi.org/10.1109/ICIN.2017.7899415

https://doi.org/10.1109/ICIN.2017.7899415





BIBLIOGRAPHY

[49] C.-L. I, C. Rowell, S. Han, Z. Xu, G. Li, and Z. Pan, “Toward green and soft: A5g perspective,” IEEE Communications Magazine, vol. 52, no. 2, pp. 66–73, Feb.2014, issn: 0163-6804. doi: 10.1109/MCOM.2014.6736745. [Online]. Available:http://ieeexplore.ieee.org/document/6736745/ (visited on 02/18/2020).

[50] 3. T. 1. V14.5, Evolved universal terrestrial radio access (e-UTRA); user equipment(UE) radio transmission and reception (3gpp TS 36.101 version 14.5.0 release 14),Nov. 2017.

[51] M. Iwamura, K. Etemad, M.-h. Fong, R. Nory, and R. Love, “Carrier aggregationframework in 3gpp LTE-advanced [WiMAX/LTE update,” IEEE CommunicationsMagazine, vol. 48, no. 8, pp. 60–67, Aug. 2010, issn: 0163-6804. doi: 10.1109/MCOM.2010.5534588. [Online]. Available: http://ieeexplore.ieee.org/document/5534588/ (visited on 02/18/2020).

[52] S. A. Bassam, W. Chen, M. Helaoui, and F. M. Ghannouchi, “Transmitter architec-ture for CA: Carrier aggregation in LTE-advanced systems,” IEEE Microwave Mag-azine, vol. 14, no. 5, pp. 78–86, Jul. 2013, issn: 1527-3342. doi: 10.1109/MMM.2013.2259399. [Online]. Available: http://ieeexplore.ieee.org/document/6556020/(visited on 06/05/2019).

[53] T. Kitayabu and H. Ishikawa, “Generalized architecture of concurrent dual-bandtransmitter for spectrum aggregation system,” in 21st Annual IEEE InternationalSymposium on Personal, Indoor and Mobile Radio Communications, Istanbul, Turkey:IEEE, Sep. 2010, pp. 111–116, isbn: 978-1-4244-8017-3. doi: 10.1109/PIMRC.2010.5672067. [Online]. Available: http://ieeexplore.ieee.org/document/5672067/(visited on 11/19/2019).

[54] M. M. Ebrahimi, M. Helaoui, and F. M. Ghannouchi, “Delta-sigma-based trans-mitters: Advantages and disadvantages,” IEEE Microwave Magazine, vol. 14, no. 1,pp. 68–78, Jan. 2013, issn: 1527-3342. doi: 10.1109/MMM.2012.2226541. [On-line]. Available: http://ieeexplore.ieee.org/document/6421086/ (visited on01/27/2020).

[55] F. M. Ghannouchi and O. Hammi, “Behavioral modeling and predistortion,” IEEEMicrowave Magazine, vol. 10, no. 7, pp. 52–64, Dec. 2009, issn: 1527-3342. doi:10.1109/MMM.2009.934516. [Online]. Available: http://ieeexplore.ieee.org/document/5259211/ (visited on 01/27/2020).

[56] J. C. Pedro and N. B. Carvalho, Intermodulation distortion in microwave and wire-less circuits, ser. Artech House microwave library. Boston: Artech House, 2003,432 pp., isbn: 978-1-58053-356-0.

[57] Mini-Circuits, Surface mounted dual matched mmic amplifier pha-11+ datasheet.[Online]. Available: https://www.minicircuits.com/pdfs/PHA-11+.pdf.

[58] Evolved universal terrestrial radio access (e-UTRA); user equipment (UE) confor-mance specification; radio transmission and reception; part 1: Conformance testing(3gpp TS 36.521-1 version 15.2.0 release 15), section 6.2.5a.33, 2018.

132







https://doi.org/10.1109/MMM.2013.2259399

https://doi.org/10.1109/MMM.2013.2259399


https://doi.org/10.1109/PIMRC.2010.5672067

https://doi.org/10.1109/PIMRC.2010.5672067


https://doi.org/10.1109/MMM.2012.2226541


https://doi.org/10.1109/MMM.2009.934516



https://www.minicircuits.com/pdfs/PHA-11+.pdf

BIBLIOGRAPHY

[59] B. van Liempd, B. Hershberg, S. Ariumi, K. Raczkowski, K.-F. Bink, U. Karthaus,E. Martens, P. Wambacq, and J. Craninckx, “A +70-dBm IIP3 electrical-balance du-plexer for highly integrated tunable front-ends,” IEEE Transactions on MicrowaveTheory and Techniques, vol. 64, no. 12, pp. 4274–4286, Dec. 2016, issn: 0018-9480, 1557-9670. doi: 10.1109/TMTT.2016.2613039. [Online]. Available: http://ieeexplore.ieee.org/document/7589000/ (visited on 01/29/2020).

[60] L. Guan and A. Zhu, “Green communications: Digital predistortion for widebandRF power amplifiers,” IEEE Microwave Magazine, vol. 15, no. 7, pp. 84–99, Nov.2014, issn: 1527-3342. doi: 10 . 1109 / MMM . 2014 . 2356037. [Online]. Available:http://ieeexplore.ieee.org/document/6954520/ (visited on 01/14/2020).

[61] T. L. JOEL L. DAWSON, Feedback linearization of RF Power Amplifiers. KluwerAcademic Publishers, 2004.

[62] H. Ochiai and H. Imai, “On the distribution of the peak-to-average power ratio inOFDM signals,” IEEE Transactions on Communications, vol. 49, no. 2, pp. 282–289, Feb. 2001, issn: 00906778. doi: 10.1109/26.905885. [Online]. Available:http://ieeexplore.ieee.org/document/905885/ (visited on 02/22/2020).

[63] Seung Hee Han and Jae Hong Lee, “Modulation, coding and signal processing forwireless communications - an overview of peak-to-average power ratio reductiontechniques for multicarrier transmission,” IEEE Wireless Communications, vol. 12,no. 2, pp. 56–65, Apr. 2005, issn: 1536-1284. doi: 10.1109/MWC.2005.1421929.[Online]. Available: http://ieeexplore.ieee.org/document/1421929/ (visitedon 02/22/2020).

[64] M. Rana, M. S. Islam, and A. Z. Kouzani, “Peak to average power ratio analysis forLTE systems,” in 2010 Second International Conference on Communication Soft-ware and Networks, Singapore: IEEE, 2010, pp. 516–520, isbn: 978-1-4244-5726-7.doi: 10.1109/ICCSN.2010.53. [Online]. Available: http://ieeexplore.ieee.org/document/5437721/ (visited on 01/14/2020).

[65] N. Kelly, W. Cao, and A. Zhu, “Preparing linearity and efficiency for 5g: Dig-ital predistortion for dual-band doherty power amplifiers with mixed-mode car-rier aggregation,” IEEE Microwave Magazine, vol. 18, no. 1, pp. 76–84, Jan. 2017,issn: 1527-3342. doi: 10.1109/MMM.2016.2616185. [Online]. Available: http:

//ieeexplore.ieee.org/document/7779295/ (visited on 01/14/2020).

[66] Shanzhi Chen and Jian Zhao, “The requirements, challenges, and technologies for 5gof terrestrial mobile telecommunication,” IEEE Communications Magazine, vol. 52,no. 5, pp. 36–43, May 2014, issn: 0163-6804. doi: 10.1109/MCOM.2014.6815891.[Online]. Available: http://ieeexplore.ieee.org/document/6815891/ (visitedon 01/14/2020).

[67] W. Lei, A. C. K. Soong, L. Jianghua, W. Yong, B. Classon, W. Xiao, D. Mazzarese,Z. Yang, and T. Saboorian, 5G system design: an end to end perspective. 2020,OCLC: 1101277320, isbn: 978-3-030-22235-2.

133

https://doi.org/10.1109/TMTT.2016.2613039



https://doi.org/10.1109/MMM.2014.2356037


https://doi.org/10.1109/26.905885


https://doi.org/10.1109/MWC.2005.1421929


https://doi.org/10.1109/ICCSN.2010.53



https://doi.org/10.1109/MMM.2016.2616185





BIBLIOGRAPHY

[68] C. Yu, J. Jing, H. Shao, Z. H. Jiang, P. Yan, X.-W. Zhu, W. Hong, and A. Zhu,“Full-angle digital predistortion of 5g millimeter-wave massive MIMO transmitters,”IEEE Transactions on Microwave Theory and Techniques, vol. 67, no. 7, pp. 2847–2860, Jul. 2019, issn: 0018-9480, 1557-9670. doi: 10.1109/TMTT.2019.2918450.[Online]. Available: https://ieeexplore.ieee.org/document/8740988/ (visitedon 01/14/2020).

[69] M. Abdelaziz, Z. Fu, L. Anttila, A. M. Wyglinski, and M. Valkama, “Digital pre-distortion for mitigating spurious emissions in spectrally agile radios,” IEEE Com-munications Magazine, vol. 54, no. 3, pp. 60–69, Mar. 2016, issn: 0163-6804. doi:10.1109/MCOM.2016.7432149. [Online]. Available: http://ieeexplore.ieee.org/document/7432149/ (visited on 05/25/2019).

[70] L. Niyonkuru, G. Vandersteen, and L. Van Biesen, “Design and implementation ofa digital mixer with digital logic,” Journal of Physics: Conference Series, vol. 1379,p. 012 067, Nov. 2019, issn: 1742-6588, 1742-6596. doi: 10.1088/1742-6596/1379/1/012067. [Online]. Available: https://iopscience.iop.org/article/10.1088/1742-6596/1379/1/012067 (visited on 05/09/2020).

[71] P. P. Sotiriadis and W. A. Ling, “Multiphase EXOR frequency mixers,” in 2009IEEE Radio and Wireless Symposium, San Diego, CA, USA: IEEE, Jan. 2009,pp. 260–263, isbn: 978-1-4244-2698-0. doi: 10.1109/RWS.2009.4957383. [On-line]. Available: http://ieeexplore.ieee.org/document/4957383/ (visited on03/06/2019).

[72] W. A. Ling and P. P. Sotiriadis, “Almost-digital multiphase frequency mixing,” in2009 IEEE Sarnoff Symposium, Princeton, NJ, USA: IEEE, Mar. 2009, pp. 1–4,isbn: 978-1-4244-3381-0. doi: 10.1109/SARNOF.2009.4850366. [Online]. Available:http://ieeexplore.ieee.org/document/4850366/ (visited on 03/06/2019).

[73] ——, “A nearly all-digital frequency mixer based on nonlinear digital-to-analogconversion and intermodulation cancellation,” IEEE Transactions on Circuits andSystems I: Regular Papers, vol. 58, no. 8, pp. 1695–1704, Aug. 2011, issn: 1549-8328, 1558-0806. doi: 10.1109/TCSI.2011.2106051. [Online]. Available: http://ieeexplore.ieee.org/document/5721761/ (visited on 03/06/2019).

[74] L. Niyonkuru, G. Vandersteen, and L. Van Biesen, “Power spectrum measurementof high frequency angle modulated digital signal from output power spectrum ofa digital divider,” Engineering Village (EI) data base, p. 4, [Online]. Available:https://www.imeko.org/publications/tc4-2019/IMEKO-TC4-2019-040.pdf.

[75] N. Adnani, M. Lamanque, T. Helaly, M. Farhan, T. Hember, and I. Ward, “Versatile20 GHz wideband RF digitizer for test and measurement,” IEEE Instrumentation& Measurement Magazine, vol. 17, no. 4, pp. 6–14, Aug. 2014, issn: 1094-6969. doi:10.1109/MIM.2014.6873723. [Online]. Available: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6873723 (visited on 06/22/2019).

[76] C. Rauscher, “R&s pappband spektrumanal,” p. 221,

134

https://doi.org/10.1109/TMTT.2019.2918450





https://doi.org/10.1088/1742-6596/1379/1/012067

https://doi.org/10.1088/1742-6596/1379/1/012067

https://iopscience.iop.org/article/10.1088/1742-6596/1379/1/012067

https://iopscience.iop.org/article/10.1088/1742-6596/1379/1/012067

https://doi.org/10.1109/RWS.2009.4957383


https://doi.org/10.1109/SARNOF.2009.4850366


https://doi.org/10.1109/TCSI.2011.2106051



https://www.imeko.org/publications/tc4-2019/IMEKO-TC4-2019-040.pdf

https://doi.org/10.1109/MIM.2014.6873723

http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6873723

http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6873723

BIBLIOGRAPHY

[77] M. Bertocco and A. Sona, “On the measurement of power via a superhetero-dyne spectrum analyzer,” IEEE Transactions on Instrumentation and Measure-ment, vol. 55, no. 5, pp. 1494–1501, Oct. 2006, issn: 0018-9456. doi: 10.1109/TIM.2006.880322. [Online]. Available: http://ieeexplore.ieee.org/document/1703891/ (visited on 06/22/2019).

[78] S. B. Sleiman, J. G. Atallah, S. Rodriguez, A. Rusu, and M. Ismail, “Wide-division-range high-speed fully programmable frequency divider,” in 2008 Joint 6th Interna-tional IEEE Northeast Workshop on Circuits and Systems and TAISA Conference,Montreal, QC, Canada: IEEE, Jun. 2008, pp. 17–20, isbn: 978-1-4244-2331-6. doi:10.1109/NEWCAS.2008.4606310. [Online]. Available: http://ieeexplore.ieee.org/document/4606310/ (visited on 06/22/2019).

[79] X. Yu, M. Do, L. Jia, J. Ma, and K. Yeo, “Design of a low power wide-band high res-olution programmable frequency divider,” IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems, vol. 13, no. 9, pp. 1098–1103, Sep. 2005, issn: 1063-8210, 1557-9999. doi: 10.1109/TVLSI.2005.857153. [Online]. Available: http://ieeexplore.ieee.org/document/1525043/ (visited on 06/22/2019).

[80] H. de Bellescize, La reception synchrone. E. Chiron, 1932. [Online]. Available: https://books.google.be/books?id=8UJENwAACAAJ.

[81] W. F. Egan, “Advanced frequency synthesis by phase lock,” p. 297,

[82] B. B. Purkayastha and K. K. Sarma, A Digital Phase Locked Loop based Signal andSymbol Recovery System for Wireless Channel, ser. Signals and CommunicationTechnology. New Delhi: Springer India, 2015, isbn: 978-81-322-2040-4 978-81-322-2041-1. doi: 10.1007/978-81-322-2041-1. [Online]. Available: http://link.springer.com/10.1007/978-81-322-2041-1 (visited on 02/23/2020).

[83] W. D. H., Phase-Locked Loop Circuit Design. Prentice-Hall, 2005.

[84] F. M. Gardner, Phaselock techniques, 3. ed. Hoboken, NJ: Wiley, 2005, 425 pp.,OCLC: 845829014, isbn: 978-0-471-43063-6.

[85] F. Gardner, “Charge-pump phase-lock loops,” IEEE Transactions on Communica-tions, vol. 28, no. 11, pp. 1849–1858, Nov. 1980, issn: 0096-2244. doi: 10.1109/TCOM.1980.1094619. [Online]. Available: http://ieeexplore.ieee.org/document/1094619/ (visited on 01/23/2020).

[86] W. Rhee, “Design of high-performance CMOS charge pumps in phase-locked loops,”in ISCAS’99. Proceedings of the 1999 IEEE International Symposium on Circuitsand Systems VLSI (Cat. No.99CH36349), vol. 2, Orlando, FL, USA: IEEE, 1999,pp. 545–548, isbn: 978-0-7803-5471-5. doi: 10.1109/ISCAS.1999.780807. [On-line]. Available: http://ieeexplore.ieee.org/document/780807/ (visited on01/23/2020).

[87] W. M. Austin, “CMOS phase-locked-loop applications using the CD54/74hc/HCT4046aand CD54/74hc/HCT7046a,” p. 50,

[88] F. U. Dowla, Ed., Handbook of RF and wireless technologies, Amsterdam ; Boston:Newnes, 2004, 515 pp., isbn: 978-0-7506-7695-3.

135

https://doi.org/10.1109/TIM.2006.880322

https://doi.org/10.1109/TIM.2006.880322



https://doi.org/10.1109/NEWCAS.2008.4606310



https://doi.org/10.1109/TVLSI.2005.857153



https://books.google.be/books?id=8UJENwAACAAJ

https://books.google.be/books?id=8UJENwAACAAJ

https://doi.org/10.1007/978-81-322-2041-1

http://link.springer.com/10.1007/978-81-322-2041-1

http://link.springer.com/10.1007/978-81-322-2041-1

https://doi.org/10.1109/TCOM.1980.1094619

https://doi.org/10.1109/TCOM.1980.1094619



https://doi.org/10.1109/ISCAS.1999.780807


carrier aggregation intermodulation distortions in 4g and

Documents