Non-Orthogonal Multiple Access Schemes for Future Cellular...

Non-Orthogonal Multiple Access Schemes forFuture Cellular Systems

Lei Wen

Submitted for the Degree ofDoctor of Philosophy

from theUniversity of Surrey

5G Innovation CentreInstitute for Communication Systems

Faculty of Engineering and Physical SciencesUniversity of Surrey

Guildford, Surrey GU2 7XH, U.K.

March 2016

c⃝ Lei Wen 2016

Abstract

Non-orthogonal multiple access (NOMA) is an emerging technology for future cellularsystems in order to accommodate more users via non-orthogonal resource allocation,especially when the number of users/devices exceeds the available degrees of freedom,resulting in an overloaded condition. To date, low density signature (LDS) and sparsecode multiple access (SCMA) are two promising NOMA techniques. However, researchin this area is still in its infancy and there are still several open issues in the LD-S/SCMA transceiver design. This thesis aims to address some of these challenges. Thecontributions are summarized as follows.

1:-LDS-OFDM and low density parity check (LDPC) codes both can be representedby a bipartite graph. Inspired by their similar structure, we construct a joint sparsegraph combining the single graphs of LDS-OFDM and LDPC codes, namely joint sparsegraph for OFDM (JSG-OFDM). A joint detection and decoding scenario is proposedusing message passing algorithm (MPA). Design guidelines for the joint sparse graphare derived through extrinsic information transfer (EXIT) chart analysis. Simulationresults show that the JSG-OFDM outperforms existing techniques such as GO-MC-CDMA, LDS-OFDM and turbo structured LDS-OFDM.

2:-Due to the higher power and spectral efficiency, the filter-bank multi-carrier (FBMC)technique is a promising alternative to OFDM. We use a low density graph to modelthe weight matrix of intrinsic interference in the isotropic orthogonal transform algo-rithm (IOTA) filtered FBMC system. In addition, such graph is combined with LDSand LDPC codes to form a joint sparse graph for FBMC-IOTA (JSG-IOTA). Basedon MPA, a joint detection and decoding scheme is designed for JSG-IOTA, and thejoint sparse graph is optimized by EXIT chart analysis. Numerical results show thesuperiority of JSG-IOTA to conventional techniques.

3:-In SCMA, the processes of bit to symbol mapping and LDS spreading are com-bined together. We investigate multi-dimensional SCMA codebooks, and the designrules are derived to maximize the constellation shaping gain. Moreover, we propose toconstruct SCMA codebooks by copy-and-permute operation on protographs and three-dimensional (3D) constellation shaping. Simulation results show that SCMA outper-forms LDS with high-order constellations, and the proposed optimization methods canfurther improve the SCMA performance.

Key words: Non-orthogonal Multiple Access, 5G, Low Density Signature, Sparse CodeMultiple Access, Joint Sparse Graph, Joint Receiver, Joint Detection and Decoding

Email: [email protected]

Acknowledgements

First of all, I would like to indicate that it is my great fortune to have pursued myPh.D. study under the supervision of Dr Pei Xiao and Dr Muhammad Ali Imran. Ihave learned greatly from their strong knowledge, out-of-box thinking, and exceptionalinsight opinions on the technical as well as practical area of my work. Many thanks fortheir continuous support and encouragement. I would also thank Prof. Rahim Tafazollifor his useful directions and feedbacks for the improvement of my research work of myPh.D. A very special thanks goes out to my friends and colleagues in 5GIC, RaziehRazavi, Mohammed AL-Imari, Man Su, Chang He, Yuchao Zhou, Gaojie Chen, JieZhong, Lei Zhang, Yinan Qi, Yue Cao, who made my years in the University of Surreyso enjoyable. Furthermore, I would thank my wife, my son and my parents for theirsupport.

List of Acronyms

2G The Second Generation2D Two-dimensional3D Three-dimensional3G The Third Generation3GPP 3rd Generation Partnership Project Access Interference4G The Forth Generation5G The Fifth GenerationAMC Adaptive Modulation And CodingAPP A Posteriori ProbabilityAWGN Additive White Gaussian NoiseBER Bit Error RateBPSK Binary Phase Shift KeyingBS Base StationCDMA Code Division Multiple AccessCND Check Node DetectorCNDD Check Node Detector-DecoderCP Cyclic PrefixCQI Channel Quality IndicatorCSI Channel State InformationDECT Digital Enhanced Cordless TelecommunicationsDFT Discrete Fourier TransformeNB Enhanced NodeBEGC Equal Gain CombiningEGF Extended Gaussian FunctionEXIT Extrinsic Information TransferFBMC Filter-bank Multi-carrierFEC Forward Error CorrectionFFT Fast Fourier TransformGO-MC-CDMA Group Orthogonal Multi-Carrier Code Division Multiple AccessGSM Global System For Mobile CommunicationsICI Intercarrier InterferenceiDEN Integrated Digital Enhanced NetworkIFFT Inverse Fast Fourier Transformi.i.d independently and identically distributedIND Intrinsic-Interference Nodes DecoderIOTA Isotropic Orthogonal Transform Algorithm

v

vi

ISI Intersymbol InterferenceITU International Telecommunication UnionJSG Joint Sparse GraphJSG-OFDM Joint Sparse Graph Orthogonal Frequency Division MultiplexJSG-IOTA Joint Sparse Graph Isotropic Orthogonal Transform AlgorithmLDGM Low Density Generator CheckLDPC Low Density Parity CheckLDS Low Density SignatureLDS-CDMA Low Density Signature Code Division Multiple AccessLDS-OFDM Low Density Signature Orthogonal Frequency Division MultiplexLDWM Low Density Weight MatrixLLR Log-Likelihood RatioLT Luby TransformLTE Long Term EvolutionMAI Multiple Access InterferenceMAP Maximum A PosterioriMC-CDMA Multi-Carrier Code Division Multiple AccessMCS Modulation And Coding SchemeMIMO Multiple-Input Multiple-OutputML Maximum LikelihoodMMSE Minimum Mean-Square ErrorMPA Message Passing AlgorithmMRC Maximum Ratio CombiningMTC Machine Type CommunicationMUD Multiuser DetectionMUI Multiuser InterferenceMUSA Multiuser Shared AccessNOMA Non-orthogonal Multiple AccessOFDM Orthogonal Frequency Division multiplexingOFDMA Orthogonal Frequency Division Multiple AccessOMA Orthogonal Multiple AccessOQPSK Offset Quadrature Phase-shift KeyingPDA Probabilistic Data AssociationPDC Personal Digital CellularPDF Probability Density FunctionPDMA Pattern Division Multiple AccessPIC Parallel Interference CancellationPMF Probability Mass FunctionPND Parity-check Node DecoderPON Passive Optical NetworkPPIC Partial Parallel Interference CancellationP/S Parallel To SerialQAM Quadrature Amplitude ModulationQoS Quality of ServiceQPSK Quadrature Phase Shift KeyingRA Repeat-AccumulateRACH Random-access channel

vii

RB Resource BlockRRM Radio Resource ManagementSCMA Sparse Code Multiple AccessSIC Successive Interference CancellationSIMO Single-input Multiple-outputSISO Soft-Input Soft-OutputSNR Signal to Noise RatioS/P Serial To ParallelTDMA Time Division Multiple AccessVND Variable Node DetectorVNDD Variable Node Detector-DecoderWBE Welch Bound EqualityWiMAX Worldwide Interoperability For Microwave AccessZF Zero Forcing

List of Symbols and Notations

A Transmit power gaincn The nth chip, also represents chip nodedc,lds Number of symbols that are superimposed at one chipdc,ldwm Number of intrinsic-interference nodes connected to one chip nodedi,ldwm Number of chip nodes connected to one intrinsic-interference nodedp,ldpc Number of variable nodes connected to one parity-check nodedv,ldpc Number of parity-check nodes connected to one variable nodedv,lds Number of chips that are spread by one symbolDCND(x) Degree distribution polynomials of chip nodesDCNDD(x) Degree distribution polynomials of chip nodesDIND(x) Degree distribution polynomials of intrinsic-interference nodesDPND(x) Degree distribution polynomials of parity-check nodesDV NDD(x) Degree distribution polynomials of variable nodesEk Channel gain for the kth userH Low density parity-check matrices for LDPC codesHk Parity-check matrix for the kth userIA,CND&PND Mutual information between CND&PND and a priori LLRIA,CNDD&PND Mutual information between CNDD&PND and a priori LLRIA,IND&V NDD Mutual information between IND&VNDD and a priori LLRIA,V NDD Mutual information between VNDD and a priori LLRIE,CND&PND Mutual information between CND&PND and extrinsic LLRIE,CNDD&PND Mutual information between CNDD&PND and extrinsic LLRIE,IND&V NDD Mutual information between IND&VNDD and extrinsic LLRIE,V NDD Mutual information between VNDD and extrinsic LLRJ Number of parity-check equations of LDPC codesK Number of usersLcn→in,u LLR delivered from chip node cn to intrinsic-interference node in,uLcn→vk,m LLR delivered from chip node cn to variable node vk,mLin,u→cn LLR delivered from intrinsic-interference node in,u to chip node cnLpj→vk,m LLR delivered from parity-check node pj to variable node vk,mLvk,m Final estimation of the variable node vk,mLvk,m→cn LLR delivered from variable node vk,m to chip node cnLvk,m→pj LLR delivered from variable node vk,m to parity-check node pjM Data length of each userN Number of chipspk,j The jth parity-check equation of the kth user

viii

ix

r[n] Received vectors that spread on the nth chip

rk,m Received spreading sequence for the symbol m of the kth userrnk,m Received signature gain at the nth chip of the variable node vk,mS Low density spreading signaturesSk Spreading matrix for the kth userv Transmitted vectorvk,m The mth symbol of the kth user, also represents variable nodev̂k,m Estimated value of the variable node vk,mv[n] Transmitted vectors containing the symbols spread on the nth chip

y Received signalyn Received signal corresponding to the nth chipz AWGNzn AWGN on the nth chipσ2A Variance of the noiseκn,k,m Normalization coefficientψn Set of symbols interfered on chip cnψn/(k,m) Set of symbols (excluding vk,m) interfered on chip cnεk,m Set of chips spread by vk,mεk,m/n Set of chips (excluding cn) spread by vk,mϕj Set of symbols connected to parity-check node pk,jϕj/(k,m) Set of symbols (excluding vk,m) connected to parity-check node pk,jωk,m Set of parity-check nodes connected to vk,mωk,m/j Set of parity-check nodes (excluding pk,j) connected to vk,mΓ SCMA codebook set

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Motivations and Research Objectives . . . . . . . . . . . . . . . . . . . . 3

1.3 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Survey on Multiple Access Techniques and Their Receiver Design 13

2.1 Multiple Access Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Time Division Multiple Access (TDMA) . . . . . . . . . . . . . . 14

2.1.2 Code Division Multiple Access (CDMA) . . . . . . . . . . . . . . 15

2.1.3 Orthogonal Frequency-Division Multiple Access (OFDMA) . . . 16

2.1.4 Multi-carrier Code Division Multiple Access (MC-CDMA) . . . . 18

2.1.5 Low Density Signature (LDS) . . . . . . . . . . . . . . . . . . . . 20

2.1.5.1 LDS-CDMA . . . . . . . . . . . . . . . . . . . . . . . . 20

2.1.5.2 LDS-OFDM . . . . . . . . . . . . . . . . . . . . . . . . 23

2.1.6 Sparse Code Multiple Access (SCMA) . . . . . . . . . . . . . . . 25

2.1.7 Multiuser Shared Access (MUSA) . . . . . . . . . . . . . . . . . 27

2.1.8 Pattern Division Multiple Access (PDMA) . . . . . . . . . . . . 28

2.2 Multiuser Detection Techniques . . . . . . . . . . . . . . . . . . . . . . . 29

2.2.1 Optimum Multiuser Detector . . . . . . . . . . . . . . . . . . . . 29

2.2.2 Linear Multiuser Detector . . . . . . . . . . . . . . . . . . . . . . 30

2.2.2.1 Minimum Mean Square Error (MMSE) . . . . . . . . . 31

2.2.2.2 Decorrelator . . . . . . . . . . . . . . . . . . . . . . . . 31

x

Contents xi

2.2.3 Nonlinear Multiuser Detector . . . . . . . . . . . . . . . . . . . . 32

2.2.3.1 Successive Interference Cancellation (SIC) . . . . . . . 32

2.2.3.2 Parallel Interference Cancelation (PIC) . . . . . . . . . 32

2.2.3.3 Probabilistic Data Association (PDA) . . . . . . . . . . 33

2.2.3.4 Message Passing Algorithm (MPA) . . . . . . . . . . . 34

2.3 Receiver Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Joint Sparse Graph for OFDM (JSG-OFDM) System 40

3.1 JSG-OFDM System Model . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 Joint Detection and Decoding for JSG-OFDM . . . . . . . . . . . . . . . 43

3.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.2 Updating of Chip Nodes and Parity-Check Nodes . . . . . . . . . 45

3.2.3 Updating of Variable Nodes . . . . . . . . . . . . . . . . . . . . . 46

3.2.4 Estimation and Syndrome Computing . . . . . . . . . . . . . . . 46

3.3 EXIT Chart Analysis of JSG-OFDM . . . . . . . . . . . . . . . . . . . . 47

3.3.1 Iterative Structure of the Joint Sparse Graph . . . . . . . . . . . 48

3.3.2 EXIT Chart Analysis Over AWGN Channel . . . . . . . . . . . . 49

3.3.2.1 EXIT Curve for VNDD . . . . . . . . . . . . . . . . . . 49

3.3.2.2 EXIT Curve for CND&PND . . . . . . . . . . . . . . . 51

3.3.2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.3.3 EXIT Chart Analysis Over Multipath Fading Channels . . . . . 53

3.4 EXIT Chart Based Design of Joint Sparse Graph . . . . . . . . . . . . . 54

3.4.1 Degree Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.4.2 Short Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5.1 Evaluation Configuration . . . . . . . . . . . . . . . . . . . . . . 60

3.5.2 BER Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5.3 Convergence Behavior . . . . . . . . . . . . . . . . . . . . . . . . 64

3.5.4 Performance of Different Users . . . . . . . . . . . . . . . . . . . 64

3.5.5 Near-far Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.5.6 Multipath Diversity . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.5.7 Comparison with MMSE Detector . . . . . . . . . . . . . . . . . 67

3.5.8 Detection Complexity Comparison . . . . . . . . . . . . . . . . . 67

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

xii Contents

4 Joint Sparse Graph for FBMC-IOTA (JSG-IOTA) System 71

4.1 JSG-IOTA System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Joint Detection and Decoding . . . . . . . . . . . . . . . . . . . . . . . . 75

4.3 EXIT Chart Analysis of JSG-IOTA . . . . . . . . . . . . . . . . . . . . . 83

4.3.1 Iterative Structure of the Joint Sparse Graph . . . . . . . . . . . 83

4.3.2 EXIT Chart Analysis . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3.2.1 EXIT Curve for IND&VNDD . . . . . . . . . . . . . . . 86

4.3.2.2 EXIT Curve for CNDD&PND . . . . . . . . . . . . . . 87

4.3.2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.4 EXIT Chart Assisted Joint Sparse Graph Design . . . . . . . . . . . . . 90

4.4.1 Degree Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.4.2 Short Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.4.3 Maximum Achievable Throughput . . . . . . . . . . . . . . . . . 93

4.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.5.1 BER Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.5.2 Convergence Behavior . . . . . . . . . . . . . . . . . . . . . . . . 97

4.5.3 Performance of Different Users . . . . . . . . . . . . . . . . . . . 98

4.5.4 Dynamic Subcarrier Allocation . . . . . . . . . . . . . . . . . . . 99

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5 Sparse Code Multiple Access (SCMA) 101

5.1 Criteria of SCMA Codebook Design . . . . . . . . . . . . . . . . . . . . 101

5.1.1 SCMA System Model . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.2 Multi-stage Optimization Approach of SCMA Codebooks . . . . 103

5.1.2.1 Low Density Signature . . . . . . . . . . . . . . . . . . 103

5.1.2.2 Constellation Points . . . . . . . . . . . . . . . . . . . . 104

5.1.2.3 Mother Multi-dimensional Constellation . . . . . . . . . 104

5.1.2.4 Constellation Function Operators . . . . . . . . . . . . 109

5.1.3 Performance Comparison with LDS . . . . . . . . . . . . . . . . 110

5.2 Design of SCMA Codebooks Based on Protographs . . . . . . . . . . . . 111

5.2.1 Extension of SCMA Codewords by Copy Operation . . . . . . . 111

Contents xiii

5.2.2 Construction of SCMA Codebooks by Copy-and-permute Oper-ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.2.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . 114

5.3 Design of 3D SCMA Codebooks . . . . . . . . . . . . . . . . . . . . . . . 115

5.3.1 Limitations of 2D SCMA Codebooks . . . . . . . . . . . . . . . . 115

5.3.2 Construction of SCMA codebooks with dv,lds of 3 . . . . . . . . . 116

5.3.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . 116

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6 Conclusions and Future Works 119

6.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

A Appendix 123

Bibliography 125

List of Figures

Fig. 1.1 Throughput (capacity) region in downlink . . . . . . . . . . . . . . 4

Fig. 1.2 Throughput (capacity) region in uplink . . . . . . . . . . . . . . . . 4

Fig. 2.1 LDS-CDMA system . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Fig. 2.2 Illustration of a LDS spreader . . . . . . . . . . . . . . . . . . . . . 22

Fig. 2.3 LDS iterative structure . . . . . . . . . . . . . . . . . . . . . . . . . 22

Fig. 2.4 LDS-OFDM system . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Fig. 2.5 SCMA system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Fig. 2.6 MUSA system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Fig. 2.7 Receiver structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Fig. 3.1 JSG-OFDM system model . . . . . . . . . . . . . . . . . . . . . . . 42

Fig. 3.2 Iterative structure of the joint detection and decoding in JSG-OFDM 48

Fig. 3.3 Folded view of the joint sparse graph . . . . . . . . . . . . . . . . . 49

Fig. 3.4 EXIT chart over AWGN Channel at Eb/N0 = 9 dB . . . . . . . . . 52

Fig. 3.5 EXIT chart over ITU Pedestrian Channel B at Eb/N0 = 13 dB . . 55

Fig. 3.6 BER versus IA,V NDD for the joint sparse graph . . . . . . . . . . . 56

Fig. 3.7 EXIT chart for different degree distributions . . . . . . . . . . . . . 58

Fig. 3.8 EXIT chart for different schemes . . . . . . . . . . . . . . . . . . . . 59

Fig. 3.9 Performance of 100% loaded systems . . . . . . . . . . . . . . . . . 62

Fig. 3.10 Performance of 150% loaded systems . . . . . . . . . . . . . . . . . 62

Fig. 3.11 Maximum effective throughput of JSG-OFDM . . . . . . . . . . . 63

Fig. 3.12 Performance at different iterations for JSG-OFDM . . . . . . . . . 64

Fig. 3.13 Performance of different users in JSG-OFDM . . . . . . . . . . . . 65

Fig. 3.14 Near-far effect of JSG-OFDM . . . . . . . . . . . . . . . . . . . . . 66

xiv

List of Figures xv

Fig. 3.15 Performance of JSG-OFDM over different multipath channels . . . 67

Fig. 3.16 Performance comparison with MMSE detector . . . . . . . . . . . 68

Fig. 4.1 JSG-IOTA transmitter model . . . . . . . . . . . . . . . . . . . . . 72

Fig. 4.2 JSG-IOTA receiver model . . . . . . . . . . . . . . . . . . . . . . . 73

Fig. 4.3 Iterative structure of the joint sparse graph . . . . . . . . . . . . . . 83

Fig. 4.4 Tree structure of the joint sparse graph . . . . . . . . . . . . . . . . 85

Fig. 4.5 Folded view of the joint sparse graph . . . . . . . . . . . . . . . . . 85

Fig. 4.6 EXIT chart at Eb/N0 = 12 dB . . . . . . . . . . . . . . . . . . . . . 89

Fig. 4.7 EXIT chart for different degree distributions . . . . . . . . . . . . . 92

Fig. 4.8 EXIT chart for different schemes . . . . . . . . . . . . . . . . . . . . 93

Fig. 4.9 Maximum effective throughput of the joint sparse graph . . . . . . 94

Fig. 4.10 Performance of different systems with 200% loading . . . . . . . . 96

Fig. 4.11 Performance of different systems with 300% loading . . . . . . . . 96

Fig. 4.12 Performance on different iterations at Eb/N0 = 12 dB . . . . . . . 97

Fig. 4.13 Performance of different users . . . . . . . . . . . . . . . . . . . . . 98

Fig. 4.14 Performance of different subcarrier allocation schemes . . . . . . . 99

Fig. 5.1 Merging of QAM modulator and LDS spreading in a SCMA encoder 102

Fig. 5.2 16-point SCMA constellation for dv,lds = 2 . . . . . . . . . . . . . . 107

Fig. 5.3 16-point SCMA constellation with 9-projection-point for dv,lds = 2 . 108

Fig. 5.4 Performance of 150% loaded LDS and SCMA . . . . . . . . . . . . 110

Fig. 5.5 Extension of SCMA codewords by copy operation . . . . . . . . . . 112

Fig. 5.6 Construction of SCMA codebooks by copy-and-permute operation . 113

Fig. 5.7 Performance of 200% loaded SCMA by different construction methods114

Fig. 5.8 4-point SCMA constellation for dv,lds of 2 . . . . . . . . . . . . . . . 117

Fig. 5.9 4-points SCMA constellation for dv,lds of 3 . . . . . . . . . . . . . . 117

Fig. 5.10 Performance of 200% loaded SCMA by different dv,lds . . . . . . . 118

List of Tables

TABLE 2.1 Comparisons of multiple access techniques . . . . . . . . . . . . 39

TABLE 3.1 System parameters . . . . . . . . . . . . . . . . . . . . . . . . . 52

TABLE 3.2 Degree distribution . . . . . . . . . . . . . . . . . . . . . . . . . 57

TABLE 3.3 JSG-OFDM scenarios . . . . . . . . . . . . . . . . . . . . . . . . 61

TABLE 3.4 Equivalent number of addition operations for detection . . . . . 69

TABLE 4.1 System parameters . . . . . . . . . . . . . . . . . . . . . . . . . 88

TABLE 4.2 Degree distribution . . . . . . . . . . . . . . . . . . . . . . . . . 91

TABLE 4.3 JSG-IOTA scenarios . . . . . . . . . . . . . . . . . . . . . . . . 93

TABLE 5.1 SCMA codewords for 16-point . . . . . . . . . . . . . . . . . . . 107

TABLE 5.2 SCMA codewords for 16-point with 9-projection-point . . . . . 109

TABLE A.1 Summary of the joint detection and decoding . . . . . . . . . . 124

xvi

Chapter 1

Introduction

1.1 Background

The explosive traffic growth in wireless communications has motivated many research

activities in both academic and industrial communities. Following the large-scale com-

mercialization of the forth generation (4G) networks, the fifth generation (5G) of mo-

bile communications, which is expected to be standardlized in 2017 and commercialized

towards year 2020 and beyond, has become a focal point for global research and de-

velopment [1] [2]. To satisfy requirements of future cellular systems, some enhanced

technologies have been recently proposed for 5G, e.g. massive multiple-input multiple-

output (MIMO), millimeter wave communications and ultra dense network. With re-

source demanding applications such as mobile internet and Internet of Things (IoT),

air interface techniques need to be designed to achieve improved spectrum utilization

and resource management [3]. Generally speaking, a new air interface for future cel-

lular systems should consist of building blocks and configuration mechanisms such as

advanced multiple access schemes, powerful forward error correction coding, adaptive

multi-carrier waveforms and so on [4] [5]. With these blocks and mechanisms, 5G wire-

less networks can offer significant improvements in coverage and user experience, and

are able to accommodate the a wide variety of user services, spectrum bands and traffic

levels.

The goal in the design of cellular systems is to be able to accommodate as much traffic

1

2 Chapter 1. Introduction

as possible (this is called capacity in cellular terminology) in a given bandwidth with

some reliability. Multiple access technologies allow multiple sources communicate with

the network simultaneously. In the history of wireless communications from the first

generation (1G) to 4G, multiple access techniques have been the key to distinguish

different wireless systems. It is well known that frequency division multiple access

(FDMA) for the first generation (1G), time division multiple access (TDMA) mostly

for the second generation (2G), code division multiple access (CDMA) for the third

generation (3G), and orthogonal frequency division multiple access (OFDMA) for 4G

are the primary multiple access techniques. In these conventional schemes, different

users are allocated to orthogonal resources in either the time/frequency/code domain

in order to avoid or alleviate interuser interference, thus they can be classified as or-

thogonal multiple access (OMA) techniques. In current mobile communication systems

such as Long-Term Evolution (LTE) and LTE-Advanced, OMA techniques have been

adopted, e.g. OFDMA. Ideally, no interference exists among multiple users due to the

orthogonal resource allocation in OMA, simple detection techniques can thus be used

to separate different users’ signals. In other words, the users in each cell are allocated

the resources exclusively and there is no inter-user interference, hence, low-complexity

detection approaches can be implemented on the receiver side to retrieve the users’

signals.

The fast growth of mobile internet has propelled more than 1000-fold data traffic in-

crease for the cellular netwoks. Therefore, how to maximize the spectral efficiency

becomes one of the key challenges to handle such explosive data traffic. Moreover, due

to the rapid development of IoT, 5G systems need to support the massive connectiv-

ity of users and/or devices to meet the demand for low latency, low-cost devices, and

diverse service types. Theoretically, it is known that OMA cannot always achieve the

sum-rate capacity of multiuser wireless systems. Apart from that, in OMA schemes,

the maximum number of supported users is limited by the degree of freedom and the

scheduling granularity of orthogonal resources. This issue is more prominent when fair-

ness among the users is considered [6]. For convenience, we define the system loading

in Definition 1.1.

Definition 1.1 (system loading). Consider a multiuser system with K users and N

1.2. Motivations and Research Objectives 3

dimensions, where the dimensions mean any available degrees of freedom including

chips, subcarriers, I/Q channels, antennas and polarisation. The system loading is

described as the ratio of the number of supported users to the number of dimensions

and is denoted as ρ = K/N . The system is respectively called in under-loaded, fully-

loaded and overloaded conditions when ρ < 1, ρ = 1, and ρ > 1.

1.2 Motivations and Research Objectives

Recently, non-orthogonal multiple access (NOMA), including power domain NOMA

and code domain NOMA, has been attracting a lot of attention. The main difference

between these two groups of NOMA is whether utilizing the spreading technique. Dif-

ferent from conventional OMA, the NOMA schemes are highly expected to improve the

spectral efficiency and accommodate much more users via non-orthogonal resource al-

location. Basically, NOMA allows controllable interference by non-orthogonal resource

allocation with a tolerable increase in the receiver complexity. Compared to OMA, the

main advantages of NOMA include the following.

• Improved spectral efficiency: Fig. 1.1 shows the throughput (capacity) compar-

ison of OMA and NOMA in downlink [7–10], where two users in the additive

white Gaussian noise (AWGN) channel are considered as an example without

loss of generality. The h1 and h2 are complex channel coefficients of the two user-

s, the N0,1 and N0,2 are the power spectral density of Gaussian noise of the two

users, the ptotal is the sum of the two users’ transmission power. It can be seen

that the maximum total throughput is achieved when all the transmission power

is allocated to user 1 only, which is achieved by both OMA and NOMA. However,

the throughput region of NOMA is much wider than that of OMA. For example,

if we want R2 to be 0.8 b/s, the achievable R1 for NOMA is approximately 2-

fold higher than that for OMA. This is because the throughput of user 1 with a

high ptotal| h1 |2/N0,1 is bandwidth-limited rather than power-limited and super-

position coding with user 2 allows user 1 to use the full bandwidth while being

allocated only a small amount of transmission power because of power sharing


with user 2. Thus, user 1 imparts only a small amount of interference to user 2.

In contrast, OMA has to allocate a significant fraction of bandwidth to user 2

to increase its throughput, and this causes severe degradation in the throughput

of user 1 whose throughput is bandwidth-limited. As for the uplink, Fig. 1.2

shows the throughput (capacity) comparison of OMA and NOMA with two users

in the AWGN channel [7–10]. We can see that the throughput region of NOMA

is also wider than that for OMA. If we want R2 to be 0.8 b/s, the achievable R1

for NOMA is approximately 60% higher than that for OMA. Therefore, in both

downlink and uplink transmissions, NOMA can improve the spectral efficiency

compared to OMA.

Fig. 1.1: Throughput (capacity) region in downlink

Fig. 1.2: Throughput (capacity) region in uplink

• Massive connectivity: In future cellular communications, the number of users or

parallel data streams will inevitably exceeds the available dimensions as the de-

mand for the spectrum is increasing while the bandwidth is fixed. Under such

an overloaded condition, it is impossible to obtain the orthogonality of received

signatures, consequently the performance of the bit error rate (BER), the block

error rate (BLER) and the system throughput are limited by the severe multiuser

interference (MUI). The non-orthogonal resource allocation in NOMA indicates

1.2. Motivations and Research Objectives 5

that the number of supported users or parallel data streams is not strictly limited

by the amount of available dimensions and their scheduling granularity [11, 12].

Therefore, in both downlink and uplink transmissions, NOMA can accommo-

date significantly more users than OMA by using non-orthogonal resource allo-

cation [13–15]. In other words, NOMA can support fully-loaded and overloaded

transmissions. For example, NOMA can achieve a reasonable good performance

when the system loading is 200% [11, 16]. As for the maximum number of non-

orthogonally multiplexed users, it is shown in [10] and [17] that when the system

loading is 200%, the capacity gain of NOMA is significantly better than that of

OMA, i.e., about 60% improvement compared with OMA. However, the further

gain by continually increasing the system loading from 200% to 400% is relatively

small, i.e., approximately 63% improvement compared with OMA. This indicates

that it is sufficient to multiplex non-orthogonally a moderate number of users to

obtain the most from the gain of NOMA.

Although NOMA has above advantages, research in the area, especially in the code

domain NOMA, is still in its infancy and there are several open issues needed to be

figured out.

• Code domain NOMA schemes, including low density signature (LDS), sparse code

multiple access (SCMA), multiuser shared access (MUSA) and pattern division

multiple access (PDMA) [16,18], utilizes a low density signature for the spreading.

However, such low density signature is usually generated without careful design

and optimization. For instance, according to the graph theory, many parameters

such as degree distributions and cycle structures will affect the graph’s perfor-

mance. Nevertheless, these factors has not been studied in detail for the NOMA

schemes, and it is still an open question to design good low density signatures.

• On the receiver side, the message passing algorithm (MPA) is employed on the

low density signature to perform multiuser detection (MUD), and the MUI can

be effectively alleviated. However, the convergence behavior of MPA for NOMA

is not optimal. For example, the iteration number of MPA is relatively high.


In addition, although existing receivers in NOMA utilize Turbo-style iterations

between the multiuser detector and the channel decoder to improve the BER

performance, there is still a large gap to the optimum performance. Therefore, it

is necessary to further improve the receiver structure and the performance.

• The existing NOMA schemes are mainly applied in OFDM systems. In future

cellular networks, more advanced waveforms my be utilized. Hence, it is urgent

to research the combination of NOMA techniques and advanced waveforms other

than OFDM.

• The constellation shaping is an interesting topic to the NOMA technique. Al-

though a constellation shaping gain can be obtained in SCMA, further improve-

ment such as multi-dimensional constellations should be studied.

Given the above analysis, this thesis aims to address the listed problems by designing

and optimizing NOMA schemes (in particular, LDS and SCMA techniques). Due to

the fact that the base station in the uplink can afford a relatively high complexity

of MPA, we only focus on uplink transmissions in the thesis. We start with LDS

based NOMA, and propose a joint sparse graph which combines LDS-OFDM and low

density parity-check (LDPC) codes. A joint receiver performing detection and decoding

simultaneously on the joint sparse graph is designed. Different from a Turbo receiver,

the joint receiver has no additional interleaver/deinterleaver between the detector and

the decoder, and no outer-inner iterations. Messages are propagated in a double-door-

double-open/close manner to perform joint detection and decoding. An analytical and

optimization framework based on extrinsic information (EXIT) chart is also proposed

for the joint sparse graph. Such idea is then extended to waveforms other than OFDM,

i.e., filter-bank multi-carrier (FBMC) with isotropic orthogonal transform algorithm

(IOTA) pulse function. In FBMC, there is no need to insert any guard interval [19,

20], and a frequency well-localized pulse shaping leads to higher power and spectral

efficiency compared with OFDM [21–24]. By combining LDS, LDPC and FBMC-

IOTA, it is justified that code domain NOMA can be applied in conjunction with

more advanced waveforms for future mobile networks. Furthermore, to improve the

BER performance of code domain NOMA by exploiting constellation diversity, LDS

1.3. Research Contributions 7

is enhanced to combine multi-dimensional constellation shaping, which becomes the

SCMA scheme. Protograph based codebook and three-dimensional (3D) constellation

are respectively designed for SCMA. By utilizing constellation shaping gain, SCMA

outperforms LDS with high-order modulation schemes.

Objectives of this thesis can be summarized as follows:

• Conduct literature survey on LDS/SCMA schemes for wireless communications;

• Design LDS/SCMA joint receivers for the uplink with affordable complexity;

• Optimize the transreceivers structure of LDS/SCMA schemes.

1.3 Research Contributions

Throughout the course of this Ph.D. study, the following contributions are made:

Design of joint sparse graph for OFDM systems: JSG-OFDM

• The low density signature of LDS-OFDM is represented as a bipartite graph. As

a capacity-approaching code over AWGN channel [25], LDPC code can also be

expressed by a bipartite graph. According to their graph model, we propose to

construct a joint sparse graph which includes the low density signature of LDS-

OFDM and the low density parity-check matrices of LDPC codes. We refer it

as joint sparse graph for OFDM. Unlike any existing sparse graph that is only

used in one specific field such as LDS-OFDM, LDPC code, low density generator

matrix (LDGM) code, repeat-accumulate (RA) code, Luby transform (LT) code

and Raptor code, our proposed JSG-OFDM is based on a novel joint sparse graph

which combines NOMA and FEC techniques. The idea behind the joint sparse

graph is to change the interference pattern being observed by each user, and limit

the amount of interference occured on each chip.

• To the best of our knowledge, there does not exist a multiple access system in

which detection and decoding are performed simultaneously on one sparse graph.

Based on the MPA and the joint sparse graph, we design a joint receiver for the


JSG-OFDM. A joint detection and decoding scenario, which performs detection

and decoding at the same time on the entire sparse graph, is presented. There are

significant differences between JSG-OFDM and LDS-OFDM. The LDS-OFDM

receiver is a separate receiver, i.e., detection and decoding are performed and op-

timized individually. The turbo structured LDS-OFDM receiver performs detec-

tion and decoding iteratively in a turbo style. An extra interleaver/de-interleaver

and outer-inner iterations are dominant characters to the turbo receiver. Howev-

er, our proposed receiver of JSG-OFDM is a joint receiver, where detection and

decoding are performed jointly on the entire graph. There is no turbo structure

in the JSG-OFDM, but the detection and decoding information can be freely

exchanged, thus the JSG-OFDM is a novel scheme and different from existing

systems such as LDS-OFDM and turbo structured LDS-OFDM.

• Analysis of a joint sparse graph is different from that of a single sparse graph. We

depict the iterative structure for JSG-OFDM receiver in details, and use the EXIT

chart to analyse the convergence behavior of the joint detection and decoding in

the receiver.

• According to the EXIT chart analysis, two important factors which affect the per-

formance of the joint sparse graph are investigated: degree distributions and short

cycles. As a result, design guidelines for the joint sparse graph are derived. With

offline optimization of the joint sparse graph, JSG-OFDM outperforms similar

multiple access systems. In other words, all the optimizations (for a wide range

of parameters) are carried out in advance at the design stage and the receiver can

use the optimum graph directly.

Design of joint sparse graph for FBMC systems with IOTA function based pulse: JSG-

IOTA

• The intrinsic interference from real and imaginary branches in FBMC-IOTA

transmissions is usually discarded in existing systems. In fact, the intrinsic in-

terference can be estimated by a weight matrix which defines neighboring time-

frequency positions around the signal of interest, but such weight matrix has

1.3. Research Contributions 9

never been studied from graphical view. In this thesis, we creatively regard the

weight matrix as a generator matrix, and the intrinsic interference as parity sym-

bols. In addition, we choose the most significant positions around the signal of

interest to estimate the intrinsic interference, consequently the weight matrix can

be modeled as a low density graph which is referred to as low density weight ma-

trix (LDWM). This is essentially the principle of block coding, and the embedded

weight matrix can be exploited to improve the system performance.

• According to the graphical model, we propose to construct a joint sparse graph

which includes the LDWM of intrinsic interference of FBMC-IOTA, the low den-

sity signature of LDS and the low density parity-check matrix of LDPC code. It

is referred to as joint sparse graph for IOTA, and it is a novel scheme which com-

bines multi-carrier modulation (LDWM), NOMA (LDS) and FEC (LDPC codes)

techniques.

• Based on the MPA and the joint sparse graph, we design a joint detection and

decoding algorithm which exploit the redundancy introduced by the intrinsic in-

terference and LDPC codes. In the JSG-IOTA receiver, multiuser detection,

intrinsic interference decoding and channel decoding are jointly performed on one

entire graph. In light of this finding, we investigate how to effectively utilize the

coding nature of the FBMC-IOTA system. To demonstrate the advantages of

JSG-IOTA, we also develop LDS-IOTA and turbo structured LDS-IOTA, both

of which have never been previously studied in the literature. Similar to OFD-

M systems, there are significant differences between the LDS-IOTA, the turbo

structured LDS-IOTA and the JSG-IOTA. There is no turbo structure in the

JSG-IOTA, but the detection and decoding information can be exchanged, thus

the JSG-IOTA receiver is different from that of existing systems.

• We analyse the iterative structure of the joint receiver of JSG-IOTA in details, and

utilize the EXIT chart to predict the convergence behaviour of the joint sparse

graph. By optimizing the joint sparse graph, JSG-IOTA outperforms similar

systems.

Design of sparse code multiple access: SCMA


• The state-of-the-art SCMA codebook sets only cover very short codewords. To

extend the graph size, a copy operation can be performed. However, simple com-

bination of small graphs cannot exhibit advantages of the sparse graph, hence

the performance may not be optimal. In this thesis, we propose to use the pro-

tograph as a basic template of a small SCMA graph, and to construct a larger

SCMA codebook by the copy-and-permute operation. The extra permutation is

designed to obtain interleaving gain and eliminate short cycles. By doing so, the

SCMA system performance can be improved.

• Existing SCMA codebook is strictly designed for two-dimensional (2D) constel-

lation shaping, i.e., dv,lds = 2. For MPA on sparse graphs, the node with only

two edges cannot fully utilize the most of dependable message which comes from

other nodes. To further exploit the shaping gain, we propose to design SCMA

codebooks with 3D constellation shaping, i.e., dv,lds = 3. Simulation results show

that 3D codebooks outperform 2D codebooks.

1.4 Thesis Outline

The remainder of this thesis is organized as follows:

Chapter 2: Survey on Multiple Access Techniques and Their Receiver De-

sign

In this chapter, well-known multiple access techniques are reviewed and discussed. S-

ince MUD is required in multiuser transmissions to detect users’ symbols, different

kinds of MUDs are reviewed and their potential strengths and weaknesses in an over-

loaded condition are investigated. Moreover, for coded systems, three typical receiver

types are introduced.

Chapter 3: Joint Sparse Graph for OFDM (JSG-OFDM) System

In this chapter, a joint sparse graph combining single graphs of LDS-OFDM and LDPC

codes is constructed. Based on the graphical model, a joint detection and decoding

algorithm is presented. The iterative structure of JSG-OFDM receiver is illustrated

and its EXIT chart is researched. In addition, design guidelines for the joint sparse

1.4. Thesis Outline 11

graph are derived through the EXIT chart analysis. By offline optimization of the joint

sparse graph, numerical results show that the JSG-OFDM brings about 1.5 - 1.8 dB

performance improvement at BER of 10−5 over similar well-known systems such as

group-orthogonal multi-carrier code division multiple access (GO-MC-CDMA), LDS-

OFDM, and turbo structured LDS-OFDM.

Chapter 4: Joint Sparse Graph for FBMC-IOTA (JSG-IOTA) System

In this chapter, the idea of the graphical model is extended to FBMC system, and a

single sparse graph is modeled to express the weight matrix which is used to calculate

the intrinsic interference in the IOTA function. Then a joint sparse graph for FBMC-

IOTA system is proposed. Such joint sparse graph combines single graphs of LDWM,

LDS and LDPC codes, which represent multi-carrier modulation, NOMA and FEC

techniques, respectively. By employing MPA, an approach for joint detection and

decoding is presented on the joint sparse graph. The iterative structure of JSG-IOTA

receiver is illustrated, and its EXIT chart is analysed. Moreover, similar to that of JSG-

OFDM, design guidelines for the joint sparse graph of JSG-IOTA are derived through

the EXIT chart analysis. Numerical results show the superiority of JSG-IOTA to

similar systems such as OFDM, FBMC-IOTA, LDS-OFDM, JSG-OFDM, LDS-IOTA

and turbo structured LDS-IOTA.

Chapter 5: Sparse Code Multiple Access (SCMA)

In this chapter, SCMA is investigated and optimized. Different from the joint sparse

graph, SCMA combines LDS and symbol mapping modules. By merging of QAM

modulator and LDS spreading, constellation shaping gain is exploited in the overloaded

transmission. We propose two ways to optimize the SCMA codebooks: copy-and-

permute operation on protographs to form larger codebooks, and 3D constellation

shaping to construct more efficient codebooks. Simulation resutls show that SCMA

outperforms LDS with high-order constellations, and the SCMA performance can be

further improved by the proposed optimization approaches.

Chapter 6: Conclusions and Future Works

This chapter provides a conclusive summary of the insights and findings acquired by

the investigations presented in this thesis. Furthermore, some future work is suggested


to address the open issues related to NOMA schemes. The aim is to make NOMA a

viable solution for future cellular networks.

Throughout this thesis, we use the following notations. Variables and constants are

represented in lowercase and uppercase, respectively. Vectors and matrices are denoted

by lowercase and uppercase, respectively, both in bold case. B and C denote the binary

and the complex field, respectively. All vectors are defined as column vectors. The

superscript T represents transpose of a vector or a matrix. Re {·} (or the superscript

R) and Im {·} (or the superscript I) denote the real and imaginary part of a complex

signal, respectively.

1.5 Publications

L. Wen, R. Razavi, M. A. Imran and P. Xiao, Design of joint sparse graph for OFDM

system, IEEE Transactions on Wireless Communications, vol. 14, no. 4, pp. 1823-

1836, November 2014.

L. Wen, P. Xiao, R. Razavi, M. A. Imran and M. Al-Imari, Joint sparse graph for

FBMC-IOTA system, IEEE Transactions on Signal Processing, 2015, submitted and

under review.

L. Wen, P. Xiao, M. A. Imran and R. Razavi, Fast convergence and reduced complexity

receiver design for LDS-OFDM, in IEEE International Symposium on Personal Indoor

and Mobile Radio Communications (PIMRC), pp. 918-912, September, 2014.

L. Wen, P. Xiao, M. A. Imran and R. Tafazolli, joint sparse graph design for multiple

access systems, Patent, No. 1403382.3, February 2014.

L. Wen, R. Razavi, P. Xiao, M. A. Imran and R. Tafazolli, Novel multi-carrier multiple

access scheme JSG-IOTA, Patent, No. 1506036.1, April 2015.

J. Zhong, P. Xiao, R. Tafazolli, L. Wen and G. Chen, Scalable frequency division

multiplexing (SFBM), Patent, No. 1519102.6, October 2015.

Chapter 2

Survey on Multiple Access

Techniques and Their Receiver

Design

In cellular systems, it is necessary to design efficient multiple access schemes that

enable several multiple users to gain access and communicate simultaneously. There

are a number of requirements that multiple access schemes must be able to meet, such

as ability to handle several users without mutual interference and to maximise the

spectrum efficiency. In this chapter various multiple access techniques together with

their receiver design are presented.

2.1 Multiple Access Techniques

Multiple access techniques is central to the way in which the radio technology of the

cellular system functions. In this section, state-of-the-art multiple access techniques

are presented.

13

14 Chapter 2. Survey on Multiple Access Techniques and Their Receiver Design

2.1.1 Time Division Multiple Access (TDMA)

TDMA allows several users to use the same frequency channel by dividing the sig-

nal into different time slots. The users transmit in rapid succession, one after the

other, each using its own time slot. This allows multiple stations to share the same

transmission medium (e.g. radio frequency channel) while using only a part of its

channel capacity [26]. TDMA is applied to 2G cellular systems, i.e., Global System

for Mobile Communications (GSM), and also used in IS-136, Personal Digital Cellular

(PDC), integrated Digital Enhanced Network (iDEN) and Digital Enhanced Cordless

Telecommunications (DECT) standard for portable phones. It is also used extensively

in satellite systems, combat-net radio systems, and Passive Optical Network (PON) for

upstream traffic from premises to the operator [27].

In TDMA systems, the synchronization is achieved by sending timing advance com-

mands from the base station which instructs the mobile phone to transmit earlier and

by how much. This compensates for the propagation delay resulting from the light

speed velocity of radio waves. The mobile phone is not allowed to transmit for its en-

tire time slot, leaving a guard interval at the end of each time slot. As the transmission

moves into the guard period, the mobile network adjusts the timing advance to syn-

chronize the transmission. Initial synchronization of a phone requires even more care.

Before a mobile transmits there is no way to actually know the offset required in the

system. For this reason, an entire time slot has to be dedicated to mobiles attempting

to contact the network; this is known as the random-access channel (RACH) in GSM

system. The mobile attempts to broadcast at the beginning of the time slot, as received

from the network.

A major advantage of TDMA is that the radio part of the mobile only needs to listen

and broadcast for its own time slot. For the rest of the time, the mobile can carry

out measurements on the network, detecting surrounding transmitters on different fre-

quencies. A disadvantage of TDMA is that it creates interference at a frequency which

is directly connected to the time slot length. This is the buzz which can sometimes

be heard if a phone is left next to a radio or speakers. Another disadvantage is that

the “dead time” between time slots limits the potential bandwidth of a TDMA chan-

2.1. Multiple Access Techniques 15

nel. These are implemented in part because of the difficulty in ensuring that different

terminals transmit at exactly the times required. Handsets that are moving will need

to constantly adjust their timings to ensure their transmission is received at precisely

the right time, because as they move further from the base station, their signal will

take longer to arrive. This also means that TDMA systems have very hard limits on

cell sizes in terms of range, though in practice systems the power levels required to

receive and transmit over distances greater than the supported range would be mostly

impractical anyway.

2.1.2 Code Division Multiple Access (CDMA)

As a dominant technique in 3G cellular systems, CDMA allows many users to access a

given frequency allocation [28] [29]. CDMA is based on spectrum spreading, meaning

that a wider radio spectrum is used than the data rate of each of the transferred bit

streams, and several message signals are transferred simultaneously over the same carri-

er frequency, utilizing different spreading codes. Each symbol is spread by a user-unique

high bandwidth pseudo-noise binary sequence, called chips. The wide bandwidth makes

it possible to send with a very low signal-to-noise ratio, meaning that the transmission

power can be reduced to a level below the level of the noise and co-channel interference

(cross talk) from other message signals sharing the same frequency. Different users

are given access to the system by allocating different spreading codes. The scheme has

been likened to being in a room filled with people all speaking different languages. Even

though the noise level is very high, it is still possible to understand someone speaking

in your own language. The receiver mixes down to baseband and then re-multiplies

with the binary pseudo-noise sequence. This effectively removes the pseudo-noise signal

and what remains (of the desired signal) is just the transmitted data. Signals that use

different spreading codes are not decodable, and are discarded in the process. In other

words, the base station uses one code to receive the signal from one mobile, and another

spreading code to receive the signal from a second mobile. Thus in the presence of a

variety of signals it is possible to receive only the required one.

Most of the existing MUD techniques for CDMA systems perform poorly in highly load-


ed conditions [30] [31]. Therefore, the number of users supported in a CDMA cellular

system is typically less than spreading factor, thus the system is said to be under loaded.

References [32] and [33] show the performance comparison of different MUD techniques.

The Branch and Bound technique has been shown to approach the performance of the

optimum MUD technique with typically lower computational complexity by limiting

the search space. However, in an above 100% loaded condition, the detector complexi-

ty increases exponentially with the number of available users, which is intractable for

practical implementation. Actually by using brute-force search, a complexity order

of O(| X |K

)is required, where X is the constellation alphabet and | X | denotes the

cardinality of the set X. On the other hand, when a conventional signature structure is

employed, from the resultant interference pattern, it is easy to see that, the existence

of a strong interferer affects the performance of all users in the system. Therefore more

affordable alternatives that yield a comparable performance to optimum MUD should

be used. Various signature optimization algorithms have been proposed in order to

overcome this high loaded condition problem from the transmit-end [34–37]. The se-

quences which meet the Welch-bound-equality (WBE) [38–40] are able to minimize the

variance of the MUI for symbol-synchronous memoryless channel. In [41] and [42], a

class of overloaded signature is developed for uncoded CDMA systems, where different

inputs give rise to different outputs. Consequently its sequence alphabets are uniquely

detectable. Nevertheless, with above sequences, each user will experience interference

from all the other users’ data symbols, and the system performance is not ideal under

overloaded conditions.

2.1.3 Orthogonal Frequency-Division Multiple Access (OFDMA)

To meet the need for faster and more reliable data services, multi-carrier techniques

have drawn much attention. Multi-carrier systems using overlapping but orthogonal

subcarriers were investigated since the 1960s. However, the use of such systems at the

time was difficult due to the large number of filters and modulators as well as oscilla-

tors required. A major reduction in the required equipment complexity occurred when

the generation of OFDM signals using the discrete fourier transform (DFT) is present-

ed [43]. With the DFT implementation, frequency division is achieved by baseband


processing instead of bandpass filtering. As one of the most important multi-carrier

techniques, OFDM is based on dividing the transmitted bitstream into multiple sub-

streams and sending these over different orthogonal subcarriers. In OFDM, the data

rate achieved on each subcarrier is considerably less than the total data rate. In ad-

dition, the bandwidth occupied by each subcarrier is much less than the total system

bandwidth. A cyclic prefix (CP) has to be inserted in OFDM to mitigate the intercarri-

er interference (ICI) and the intersymbol interference (ISI). The number of subcarriers

is selected such that each subcarrier has a bandwidth less than the coherence band-

width of the channel, in order for the subcarriers to experience relatively flat fading.

This allows OFDM to efficiently resist the effect of frequency selective fading, and the

rate and power can be adjusted on each subcarrier individually. A large continuous

block of spectrum is not needed for high rate multi-carrier communications, and sev-

eral contiguous blocks of smaller size can be used instead. This provides flexibility in

spectrum allocation and spectrum management.

OFDMA is an efficient extension of the OFDM technique to a multiuser scenario, and

it has been adopted as a core technique in 4G cellular networks, i.e., the 3rd Generation

Partnership Project Long Term Evolution (3GPP-LTE) [44] [45] and the Worldwide

Interoperability for Microwave Access (WiMAX) [46–48]. In OFDMA, the set of or-

thogonal subcarriers is divided into several mutually exclusive subsets and then each

subset is allocated to transmission of a user signal. Different numbers of subcarriers

can be assigned to different users, to support differentiated Quality of Service (QoS),

i.e. to control the data rate and error probability individually for each user. The sys-

tem spectrum of OFDMA is divided into a number of channels; each channel consists

of a cluster of a number of consecutive orthogonal OFDM subcarriers. As subcarriers

are orthogonal, intra-cell interference is significantly reduced. In OFDMA systems, the

transmission rate of a channel is variable based on the user allocated to this channel

due to the use of Adaptive Modulation and Coding (AMC). Each enhanced NodeB

(eNB) collects the Channel Quality Indicator (CQI) reports which are derived from

the downlink received reference signal quality and fed back from the users. The CQI

is then used to determine the Modulation and Coding Scheme (MCS) for a channel.

Same MCS is used for all subcarriers in a resource block (RB) allocated to a given user,


and different MCS can be allocated to different resource blocks. Since different users

perceive different channel qualities, a bad channel (due to deep fading and narrowband

interference) for one user may still be favorable to other users. Thus, OFDMA exploit-

s the multiuser diversity by avoiding assigning bad channels, which is an important

feature in OFDMA [49] [50].

Compared with single-carrier systems, OFDMA provides significant advantages in terms

of high spectrum efficiency, robustness against multipath fading channels, resistance to

multiuser interference, simplified equalization, and so on. In addition, OFDMA is

considered as highly suitable for broadband wireless networks, due to scalability and

MIMO-friendliness, as well as ability to take advantage of channel frequency selectiv-

ity [51]. As in OFDMA user-data symbols are assigned directly to subchannels, the

frequency domain diversity will not be achievable at modulation symbols level. Thus

it is crucial to incorporate properly designed FEC coding and interleaving schemes to

obtain this diversity at a later stage.

2.1.4 Multi-carrier Code Division Multiple Access (MC-CDMA)

The combination of OFDM and CDMA, known as multi-carrier code division multiple

access (MC-CDMA), has gained attention as a powerful transmission technique [52] [53].

The MC-CDMA concept is based on OFDM signaling with spreading in the frequency

domain, so multiple access is thus achieved by using distinct spreading sequences for

different users similar to more conventional CDMA systems based on time domain

spreading. In other words, MC-CDMA applies spreading in the frequency domain by

mapping a different chip of the spreading sequence to an individual OFDM subcarrier,

thus it is essentially equivalent to performing the inverse fast Fourier transform (IFFT)

operation on a CDMA signal [54]. For high user data rates, the data symbols are first

serial-to-parallel (S/P) converted into substreams, and then each substream is spread in

the frequency domain with a signature sequence. After spreading, the signal is passed

through a subcarrier multiplexer, parallel-to-serial (P/S) converted. A guard interval

with cyclic extensions similar to OFDM is inserted between symbols to counter ISI

caused by multipath fading. MC-CDMA scheme transmits in parallel chips of a spread


data symbol on different subcarriers and therefore offers diversity.

Similar to OFDM, the MC-CDMA signal is made up of a series of equal amplitude

subcarriers. Unlike OFDM, where each subcarrier transmits a different symbol, MC-

CDMA transmits the same data symbol over each subcarrier. At the MC-CDMA

receiver a coherent detection method is employed to despread the signal. The received

signal energy can be collected in the frequency domain with moderate complexity even

when the signal bandwidth is large. The received signal, after downconversion and dig-

itization, is first coherently detected with FFT, then multiplied by a gain factor. Equal

gain combining (EGC) and maximum ratio combining (MRC) are standard combin-

ing techniques used in MC-CDMA receivers [55]. The advantage of using combining

techniques is that even though individual branches may not have sufficient SNR, their

combined sum increases the probability of detection by increasing the SNR of a given

signal. In EGC all branches are given equal weight irrespective of signal amplitude, but

the signals from each branch are co-phased to avoid signals arriving at the same time.

In MRC each signal is multiplied by a weight factor depending on the signal strength.

Strong signals are amplified, whereas weak signals are attenuated. Like EGC, MRC

signals are also co-phased to avoid signal cancellations [56].

Similar to CDMA systems, non-orthogonality of received effective signatures in MC-

CDMA causes MUI [57] [58], and implementation of optimum MUDs is not practi-

cal due to their prohibitively high computational complexity. A technique named

group-orthogonal MC-CDMA (GO-MC-CDMA) is proposed to handle the overload-

ed transmission [59] [60]. It partitions the available subcarriers into different groups

and distributes users among these groups, then each group behaves as an independent

MC-CDMA system with a smaller number of users. In [61], an iterative interference

cancellation approach is developed for an overloaded Walsh-Hadamard-spread MC-

CDMA system. However, these techniques fail to achieve good performance under

highly-overloaded conditions.


2.1.5 Low Density Signature (LDS)

Wireless cellular technologies are continuously evolving to meet the increasing demands

for the massive connectivity. For conventional multiple access techniques via code do-

main multiplexing, each user spreads the original data using a given spreading sequence,

where elements of the spreading sequence usually take nonzero values, which are opti-

mized under certain criteria, e.g., good auto- and/or cross-correlation properties. These

spreading sequences are orthogonal to each other to avoid MUI, and naturally have high

density, which means majority chips have nonzero values. The drawback is that, each

user will see the interference coming from all other users at the chip level, and it can-

not easily achieve satisfactory performance under overloaded conditions. To deal with

these problems, a multiple access technique named low density signature has been pro-

posed. Several milestones in this area have been achieved, leading to a flurry of further

research.

2.1.5.1 LDS-CDMA

The LDS concept is first proposed for CDMA systems [62–66]. Fig. 2.1 (a) shows the

block diagram of the LDS-CDMA transreceivers with K users and N chips. We can

see that after FEC encoding and symbol mapping, the data are sent to a specially de-

signed spreader. Instead of optimizing the N -chips sequences, the scheme intentionally

arranges each user to spread its data, vk,m, over very limited chips, cn. More explicitly,

the spreading sequences have small number of nonzero values and the rest chips are

zero valued, hence the resultant signature matrix becomes very sparse. Basic principles

of LDS are i) changing the interference pattern being seen by each user; ii) limiting

the amount of interference occurred on each user.


cN

AW

GN

cN

xv

1,1

v1

,2

v1,M

c1

c2

use

r 1

FE

C

enco

der

sym

bo

l

map

per

rad

io

chan

nel

xv

K,1

vK

,M

c1

c2

use

r K

FE

C

enco

der

sym

bo

l

map

per

rad

io

chan

nel

vK

,2

use

r 1

use

r K

FE

C

dec

od

er

FE

C

dec

od

er

SIS

O

iter

ativ

e

det

ecto

r

Fig.2.1:LDS-C

DMA

system


Fig. 2.2 illustrates the LDS principle by using a simple exemplary system with 5 chips

and 10 data symbols, where chip nodes and variable nodes respectively represent chips

and data symbols. It can be seen that each symbol is spread over 2 chips. Each chip is

used by 4 symbols that may belong to different users.

chip nodes

variable nodes x x x x x x x x xx

Fig. 2.2: Illustration of a LDS spreader

To elaborate the LDS structure more clearly, the sets of chip nodes and variable nodes

are associated with chip node detector (CND) and variable node detector (VND), re-

spectively. The iterative structure in the receiver is depicted in Fig. 2.3 and it closely

follows the LDS in Fig. 2.2. CND and VND can be expressed by mathematical func-

tions, and exchange soft messages through the edge interleave. It has been proved that

LDS-CDMA significantly outperforms conventional CDMA systems under overloaded

conditions [64].

CND 1

To FEC decoder

VND

From OFDM demodulator

-

-

Interleaving (edges)

Key:

CND: Chip node detector (corresponding to the chip nodes)

VND: Variable node detector (corresponding to the user nodes)

Fig. 2.3: LDS iterative structure


2.1.5.2 LDS-OFDM

As an extension, LDS is applied to OFDM systems [17,67–69]. Reference [70] extends

LDS to a rateless scenario, i.e., the low density signature is a dynamic graph when

data are transmitted. By doing so, the system spectral efficiency is improved, but the

receiver complexity is higher than a fixed rate LDS. Fig. 2.4 (a) shows the block diagram

of the LDS-OFDM transreceiver. It is similar to conventional MC-CDMA systems.

In MC-CDMA, after FEC encoding and symbol mapping, each modulated symbol

is multiplied with a N -chips spreading sequence which is subsequently transmitted

over orthogonal subcarriers in IFFT module. Cyclic prefix (CP) has to be inserted to

eliminate ISI and ICI. The IFFT and CP insertion comprise the OFDM modulator.

Compared with conventional MC-CDMA transmitter, the main difference in Fig. 2.4

(a) is that the spreading signature has low density. Due to the LDS structure, each data

symbol is spread over very limited chips. Each chip is transmitted over an orthogonal

subcarrier, and each subcarrier is only used by a limited number of data symbols

that may belong to different users. Each user, transmitting on given subcarriers, will

experience interference from only a small number of other users’ data symbols. In other

words, the number of users symbols that are superimposed on each chip is much less

than the total number of data symbols. Meanwhile, the number of chips that are spread

by each symbol is much less than the total number of chips.

The philosophy of LDS is that if a fraction of signal of some user is superimposed

by a fraction of signals coming from a relatively small number of interferers, then the

search-space should be moderate, thus detection technique with affordable complexity

can be used to recover the corrupted signal. Moreover, apart from being practical for

implementation, the LDS structure also benefits from having the intrinsic interference

diversity by avoiding strong interferers to corrupt all chips of a user. Therefore, LDS

is an effective technique for fully-loaded and overloaded transmissions. The drawback

of LDS is that its performance degrades with high order constellations.


cN

AW

GN

cN

xv

1,1

v1

,2

v1,M

c1

c2

use

r 1

FE

C

enco

der

sym

bo

l

map

per

OF

DM

mo

du

lato

r

rad

io

chan

nel

xv

K,1

vK

,M

c1

c2

use

r K

FE

C

enco

der

sym

bo

l

map

per

OF

DM

mo

du

lato

r

rad

io

chan

nel

vK

,2

OF

DM

dem

od

ula

tor

use

r 1

use

r K

FE

C

dec

od

er

FE

C

dec

od

er

SIS

O

iter

ativ

e

det

ecto

r

Fig.2.4:LDS-O

FDM

system


2.1.6 Sparse Code Multiple Access (SCMA)

The recently proposed SCMA is an enhanced version of LDS-OFDM [71–73]. In LDS-

OFDM, a LDS spreader expands a QAM symbol to a sequence of complex symbols by

using a given low density signature. Hence, a LDS spreader can be seen as a process in

which a number of coded bits are mapped to a sequence of complex symbols. From this

point of view, the QAM mapper block and the LDS spreader can be merged together to

directly map a set of bits to a complex vector so called a SCMA codeword. With this

interpretation, a simple LDS spreading action is generalized to a coding process which

in turn raises a new problem in terms of complex multidimensional codeword design

rather than a relatively simple low density signature design. The SCMA characters can

be summarized as follows:

1) Binary domain data are directly encoded to multidimensional complex domain code-

word selected from a predefined codebook set.

2) Multiple access is achievable by generating multiple codebooks, one for each layer

or user.

3) Codeword of the codebook is sparse such that MPA multiuser detection technique

is applicable to detect the multiplexed codeword with a moderate complexity.

4) Like LDS-OFDM, SCMA can be overloaded such that the number of multiplexed

layers can be more than the spreading factor.

Fig. 2.5 shows a SCMA with 6 users where each user has a predefined codebook. All

codewords in the same codebook contain zeros in the same two dimensions, and the

positions of zeros in different codebooks are distinct to facilitate the collision avoidance

of any two users. For each user, two bits are mapped to a complex codeword. Code-

words for all users are multiplexed over four shared orthogonal resources (e.g., OFDM

subcarriers).

The main difference between LDS-OFDM and SCMA is that a multi-dimensional con-

stellation is designed for SCMA to generate codebooks, which brings the shaping gain

that is not possible for LDS-OFDM [74]. Here, shaping gain is the gain in the average

symbol energy when the shape of a constellation is changed. For the concatenated


Fig. 2.5: SCMA system

approach with high-order constellations, the multi-dimensional constellation can be

optimized to obtain shaping gain, then codebooks are generated based on the multi-

dimensional constellation. The design criteria of multi-dimensional constellations in-

clude [74]: i) minimization of the average energy per constellation point; ii) maxi-

mization of the diversity order; iii) maximization of the minimum product distance;

iv) minimization of the product kissing number for the product distance. The SCMA

codebook design is a complicated problem, since different layers are multiplexed with

different codebooks. As the appropriate design criterion and specific solution to the

multi-dimensional problem are still unknown, a multi-stage approach has been pro-

posed to realize a suboptimal solution. Specifically, a complex constellation which is

called the mother constellation is first optimized to improve the shaping gain, and then

some codebook-specific operations are performed to the mother constellation to gener-

ate the constellation for each codebook. Three typical operations are phase rotation,

complex conjugate, and dimensional shuffling of the constellation. In the generated

constellations after codebook-specific operations, each constellation point is multiplied

with a low density matrix to generate a codeword. In this way, SCMA codebooks can

be obtained.

Other work on SCMA includes the blind detection for uplink grant-free multiple access

[75] and irregular SCMA schemes [76]. Although SCMA performs better than LDS,

the codebooks still need to be improved by the means of graph optimization and the

constellation design.


2.1.7 Multiuser Shared Access (MUSA)

MUSA is another NOMA technique via code domain multiplexing, and it is suitable

for overloaded transmissions [77]. Fig. 2.6 shows the MUSA system. Multiple spread-

ing sequences constitute a pool from which each user can randomly pick one of the

sequences. Note that for the same user, different spreading sequences may also be

used for different symbols, which may further improve the performance via interference

averaging. Then all spreading symbols are transmitted over the same time-frequency

resources. The spreading sequences should have low cross-correlation and can be M -

ary. MUSA differs from MC-CDMA in that it is basically synchronous transmission

mechanism when users signals arrive at the base station, while MC-CDMA doesn’t

have this kind of synchronism requirement in the uplink. In addition, MUSA uses non-

binary spreading sequences, while binary spreading sequences are usually considered in

classical MC-CDMA systems.

Fig. 2.6: MUSA system

In downlink MUSA, users are separated into different groups. In each group, different

users’ symbols are mapped to different constellations in a way to ensure Gray mapping


in the combined constellation of superposed signals. The combined constellation is

determined not only by the modulation order of each user, but also by the transmit

power partition among multiplexed users. Orthogonal sequences can be used to spread

the superposed symbols to obtain time or frequency diversity gain. Gray mapping of

the combined constellation reduces the reliance on advanced receivers, therefore less

processing-intensive receivers such as symbol-level SIC can be used.

2.1.8 Pattern Division Multiple Access (PDMA)

PDMA is a NOMA scheme that can be realized in multiple domains [78]. At the

transmitter, PDMA uses non-orthogonal patterns which are designed to maximize the

diversity and minimize the overlaps of multiple users. Then, multiplexing can be real-

ized in code domain, power domain, space domain or their combinations. Multiplexing

in code domain is similar to that in LDS, but the number of subcarriers connected

to the same symbols in the factor graph can be different. At the receiver, MPA is

performed for interference cancellation. In the case of multiplexing in power domain,

power allocation needs to be carefully considered under the total power constraint.

SIC can be also used at the receiver according to SNR difference among multiplexed

users. Multiplexing in space domain, i.e., spatial PDMA, can be combined with the

multiple-antenna technique. The advantage of spatial PDMA compared with multiuser

MIMO is that PDMA doesn’t require joint precoding to realize spatial orthogonality,

which significantly reduces system complexity. In addition, multiple domains can be

combined in PDMA to make full use of various available wireless resources. The system

model of code domain PDMA is similar to that of MUSA, but the spreading matrix in

MUSA is designed with the following principles:

1) The number of groups with different number of nonzero elements in the spreading

sequence should be maximized.

2) The number of the overlapped spreading sequences which have the same number of

nonzero elements should be minimized.

MPA is used at the receiver to separate different users’ signals. The design principle

for spreading matrices in code domain PDMA is to facilitate interference cancellation.

2.2. Multiuser Detection Techniques 29

2.2 Multiuser Detection Techniques

Interference, which originates from channel distortion and from out-of-cell interference,

is unavoidable in wireless systems, even when using orthogonal multiplexing techniques

such as CDMA or OFDMA. Multiuser detection (MUD) deals with demodulation of

the mutually interfering digital streams of information that occur in wireless communi-

cations, and is also investigated for demodulation in low-power inter-chip and intra-chip

communications [79] [80]. Multiuser detection encompasses both receiver technologies

devoted to joint detection of all the interfering signals or to single-user receivers which

are designed to recover only one user but are robustified against multiuser interference

in addition to background noise. By exploiting the structure of the interfering signals,

multiuser detection is an effective way to eliminate the MUI, and can increase spectral

efficiency, receiver sensitivity, and the number of users the system can sustain. Main

performance metrics for MUD techniques include BER performance and near-far effect.

In the following, different multiuser detection techniques are discussed.

2.2.1 Optimum Multiuser Detector

Amaximum likelihood (ML) sequence estimator for a digital pulse-amplitude-modulated

sequence in the presence of finite ISI and white Gaussian noise is studied in [81] and [82].

Such an ML estimator comprises a sampled linear filter and a recursive nonlinear pro-

cessor which utilizes the Viterbi algorithm. The optimal ML receiver for multiuser de-

tection is formulated, e.g., in [83]. It shows an improvement over conventional decoder

by orders of magnitude and achieves the best performance in terms of the probability

of errors. Using the ML detection, the optimal solution can be expressed as

v̂ = arg maxv∈XK

p(y|v) (2.1)

where K, v, y and X represent the user number, the transmitted symbol, the received

signal and the constellation alphabet, respectively.

The ML MUD is optimum in terms of minimizing the block error probability, when the

transmitted data is independently and identically distributed (i.i.d). Therefore, inte-

grating a priori knowledge into the ML function leads to maximum a posteriori (MAP)


detection. MAP detector is implemented by applying two strategies: individually and

jointly optimum detection.

The jointly optimum MAP detection maximizes the joint a posteriori probability mass

function (PMF) of the transmitted symbols v, i.e., p(v|y), while the individually op-

timum MAP detection maximizes the a posteriori PMF, p(vk|y), of the transmitted

symbol for the k-th user by evaluating y. The estimation of vk with individual MAP

detection can be written as

v̂k = argmaxvk∈X

p(vk|y) (2.2)

A posteriori PMF for vk can be found by calculating the marginal of the joint a pos-

teriori PMF, therefore, in order to minimize the symbol error probability, (2.2) can be

written as

v̂k = argmaxvk∈X

∑v ∈

vkXK

p(v|y) (2.3)

Let Pk(vk) be the priori probability of symbol vk, k = 1, ...,K, then according to Bayes’

rule we have

p(v|y) ∝ p(y|v)P (v) (2.4)

where,

P (v) =

K∏k=1

Pk(vk) (2.5)

is the joint a priori PMF of all users’ symbols assuming that they are independent to

each other. Hence, the estimation function can be modified to

v̂k = argmaxvk∈X

∑v ∈

vkXK

p(y|v)K∏l=1

Pl(vl) (2.6)

The optimum MUD’s computational complexity increase exponentially with the user

number K. This high complexity is one of the reasons that optimum MUD is not a

popular choice in practical systems.

2.2.2 Linear Multiuser Detector

Linear detectors, which apply a linear operator or filter to the output of the matched

filter or the received signal, have been well-studied in the literature because of their


efficiency and simplicity [84]. These detectors have much lower complexity compared

to the optimal detector. The most common linear detectors are the minimum mean

square error (MMSE) detector and the decorrelator.

2.2.2.1 Minimum Mean Square Error (MMSE)

The MMSE detector implements the linear mapping which minimises the mean square

error between the actual data symbols and the soft outputs of the detector, and it

provides good performance with much lower complexity compared to the optimum

detector [85]. Considering that this type of MUD detect the actual data symbols based

on both noise statistics and the received signal powers, better BER performance is

expected compared to the decorrelator detector. However, as the performance of linear

MMSE detector depends on the received power of the interfering users, there is some

performance degradation due to the near-far effect problem [86]. It has been discussed

in [87] that the MAI-plus-noise is approximately Gaussian distribution. This property

is particularly useful in the performance analysis of multiuser communication systems

involving the MMSE detector. The limitations of the linear MMSE detector have been

investigated in [88]. It is reported that the MMSE detector is not able to handle the

highly loaded and overloaded conditions, or in other words, the error dose not vanish

as SNR increases.

2.2.2.2 Decorrelator

The decorrelator inverts the channel matrix leaving the received signal without inter-

ference but by doing so also enhances the noise [89]. The advantage of the decorrelator

is that no knowledge of the receive power is necessary and its performance is indepen-

dent of the power of interfering users so that the near-far problem is avoided. Both

MMSE detector and decorrelator handle near-far situations equally well. Indeed, as

the interference powers tend to infinity, the MMSE detector converges to the decorre-

lator. Like the MMSE detector, the decorrelator fails to perform satisfactorily under

overloaded conditions as the desired as well as the interferers’ signal subspace become

rank-deficient.


2.2.3 Nonlinear Multiuser Detector

Nonlinear detectors can achieve better performance than linear detectors. The popular

nonlinear MUD techniques include the successive interference cancellation (SIC), the

parallel interference cancelation (PIC), the probabilistic data association (PDA), the

message passing algorithm (MPA) and so on.

2.2.3.1 Successive Interference Cancellation (SIC)

SIC is an intuitive approach to joint detection of the received symbols from differ-

ent users in multiuser systems [90–92]. It is applied to a multiuser system that its

transmissions are not orthogonal and all the users share the available time and fre-

quency degrees of freedom. In this scheme the effect of estimated symbol of each user

is removed from the observation used for estimating other users’ symbols. It results

in fewer number of interferers seen by other users if the decision is correct, however,

an incorrect decision will result in doubling the interference [93]. In other words, the

first user is affected by all the interferes, whereas the user in succession experience less

interference as the interference cancellation progresses. Therefore, in order to utilize

this scheme, the user ordering mechanism should be incorporated. The SIC process

should start by estimating the signal that can be detected with highest certainty. All

subsequent detections will subtract the contribution of already estimated symbols from

the received aggregate signal before detecting other signals. This cancels the effect of

detected symbols from all subsequent detections. This process continues iteratively for

all received signals from different users.

2.2.3.2 Parallel Interference Cancelation (PIC)

As discussed earlier, a SIC receiver cancels the MAI user by user in each stage such

that the remaining users see less and less MAI, while a PIC scheme cancels the MAI

for all the users simultaneously at each decision stage [94]. As a result, PIC takes a

multi-stage structure and has shorter processing delay, compared to SIC. Also, there

is no need for user ordering since all users will receive the same treatment in removing


their respective MAI. Generally, PIC uses hard decision, and in some cases, fails to

guarantee performance improvements as the iterative process goes on, due to erroneous

interference estimates in cancellation. This is because a poor estimation of the MAI at

early stages will not lead to performance improvement at later stages, therefore it is not

wise to completely use that information to estimate the MAI. To solve this problem,

partial parallel interference cancellation (PPIC) is proposed [95] [96]. PPIC alleviates

the performance degradation by weight method and acquires performance superior

to the conventional PIC with no increase in implementation complexity. Therefore,

PPIC alleviates the above-mentioned problem by introducing a weight in each stage

to mitigate the effect of error propagation. In [97], an adaptive least-mean-squares

PIC (LMS-PIC) structure is proposed, where for each stage the weights are obtained

by minimizing the mean-squared error between the received signal and its estimate

through the LMS algorithm. Their results show a substantial performance improvement

over the brute-force PIC and the conventional PPIC schemes. The performance of SIC

and PIC schemes is highly dependent on the first estimate being fed to the interference

cancelation detector, and at a heavy system load, the update of user symbol estimations

becomes unreliable and may degrade the performance significantly.

2.2.3.3 Probabilistic Data Association (PDA)

The PDA filter introduced in [98] is a highly successful approach to target tracking

in the case that measurements are unlabeled and may be spurious. Since then, it has

been applied in many different areas, including digital communications. In the area of

digital communications, the PDA algorithm is a reduced complexity alternative to the

ML detector. Near-optimal results are demonstrated for a PDA-based MUD for CDMA

systems [99]. Since the computational complexity of an optimal MUD is prohibitive,

this suboptimal solution is proposed to provide reliable decisions with relatively low

complexity. However it should be noted that as concluded in [100] PDA performs well

only for low order modulation schemes, i.e. Binary Phase Shift Keying (BPSK) and

Quadrature Phase Shift Keying (QPSK), and not for higher order modulations.

The PDA detector is based on approximating the MAI component by a Gaussian


random variable. Therefore, considering that the thermal noise is also Gaussian random

variable, the total effective noise can be modeled as Gaussian random variable too.

Furthermore, PDA algorithm is applied sequentially and is performed repeatedly in

every iteration stage. Therefore, similar to SIC, this algorithm is also sensitive to the

order of detected users because PDA algorithm works successively from one user to

another. However, this technique uses soft values instead of hard values, the effect

of error propagation is expected to be less severe. In [99], it is suggested that if the

users are appropriately sorted a performance improvement can be achieved. Again, the

PDA’s performance degrades rapidly under overloaded conditions.

2.2.3.4 Message Passing Algorithm (MPA)

The algorithm iteratively computes the distribution of variables in graph-based models

and comes under different names, depending on the context. These names include:

the sum-product algorithm (SPA), the belief propagation algorithm (BPA), and the

message passing algorithm (MPA). The term “message passing” usually refers to all

such iterative algorithms, including SPA, BPA and their approximations [101–105].

MPA is very efficient for belief propagation on sparse graphs [106, 107], thus we give

some definitions about graphical models [108].

Definition 2.1 (sparse graph). A bipartite graph is a graph (nodes connected by edges)

whose nodes may be separated into two types, and edges only connect two nodes of

different types. If the number of edges in a graph is close to the maximal number of

edges (almost fully connect), it is a dense graph. On the contrary, a graph with only a

few edges, is a sparse graph. The distinction between dense and sparse graphs is the

number of edges.

Definition 2.2 (degree distribution). Degree of a node is the number of edges the

node connected to other kinds of nodes, while degree distribution is the probability

distribution of these degrees in a graphical model. If the degrees are constant values,

the graph is a regular graph. Otherwise, it is an irregular graph.

Definition 2.3 (cycle and girth). A cycle in a graph refers to a finite set of connected

edges, the edge starts and ends at the same node, and it satisfies the condition that no


node (except the initial and final node) appears more than once. Girth of a graph is

the length of the shortest cycle. Apparently, girth should be equal to or greater than

4, and length-4 cycles manifest themselves in the corresponding matrix as four 1’s that

lie on the corners of a sub-matrix.

As for the bipartite graph shown in Fig. 2.2, degrees of chip nodes and variable nodes

are 4 and 2, respectively. Hence it is a regular graph. Bold lines in the figure represent

the shortest cycle of length-6, meaning that the girth of such graph is 6. MPA calculates

the marginal distribution for each node on a sparse graph [109] [110]. The key points

of a clear presentation of MPA are the use of a tensorial representation of the messages

along the edges in the graphical model, and transformations of the graph so that MPA

can be written as equations involving the message updating between different types of

nodes via edges. In a typical run, each node of the graph calculates iteratively from the

previous values of the neighbouring information (two nodes are said to be neighbours

if they are connected by an edge). The information exchanged is the soft value that

represents the reliability of the symbol related to an edge. Degree distributions and

short cycles affect the performance of MPA on sparse graphs significantly [111–113].

On a acyclic (without cycle) graph, the estimated marginal distribution converges to

the true value in a finite number of iterations. Nevertheless, graphs inevitably contain

cycles. It is known that the graph containing length-4 cycles will converge in most cases,

but the probabilities obtained might be incorrect. These graphs may fail to converge,

or oscillate between multiple states over repeated iterations. To analyse and predict

the convergence behavior of MPA on the graphical model, different mathematical tools,

such as the density evolution (DE) [114] [115], the Gaussian approximation (GA) [116]

and the extrinsic information transfer (EXIT) chart [117–122], were developed. In

particular, EXIT chart is a useful tool to analyse the transfer of information between the

soft-input soft-output (SISO) constituents, and it provides an approximate visualization

of the process of belief propagation. In this thesis, we mainly use the EXIT chart to

analyse the MPA on sparse graphs, hence it is necessary to give some definitions of

entropy and mutual information about the EXIT chart [123].

Definition 2.4 (entropy). The entropy H(x) of a continuous random variable x ∈ χ


with probability density function p(x) is defined as

H(x) = −∫χp(x) log p(x)dx (2.7)

Definition 2.5 (conditional entropy). The conditional entropy H(y|x) of a pair of

continuous random variables (x, y) ∈ χ2 is defined as

H(y|x) = −∫χp(x)

∫χp(y|x) log p(y|x)dxdy

= −∫χ

∫χp(x, y) log p(y|x)dxdy

(2.8)

where p(x, y) is the joint probability density function of x and y, p(y|x) is the probability

density function of y conditioned on x.

Definition 2.6 (mutual information). The mutual information I(x, y) between two

continuous random variables x and y is defined as

I(x, y) = −∫χ

∫χp(x, y) log

p(x, y)

p(x)p(y)dxdy

= −∫χ

∫χp(x, y) log

p(x|y)p(x)

dxdy

= −∫χ

∫χp(x, y) log p(x)dxdy −

(−∫χ

∫χp(x, y) log p(x|y)dxdy

)= H(x)−H(x|y)

(2.9)

Intuitively, according to Shannon’s information theory, the entropy gives a measure

of the uncertainty of the random variable, while the mutual information of two ran-

dom variables is a quantity that measures the mutual dependence of the two random

variables and it is the basis of the channel capacity.

MPA has been successfully applied to decoding of sparse graph codes such as LDPC

codes [124–126], low density generator matrix (LDGM) codes [127], repeat-accumulate

(RA) codes [128], Luby transform (LT) codes [129], Raptor codes [130] [131] and so

on. In addition, MPA also has been applied to LDPC coded large-MIMO systems [132]

[133]. For MUD, it is inefficient to apply MPA for detection in conventional multiple

access systems, as their spreading signatures are dense graphs, consequently leading

to prohibitive computational complexity. Unlike conventional systems, LDS-CDMA,

LDS-OFDM and SCMA are based on the sparse graphical model, thus iterative MPA

becomes feasible and can attain satisfactory performance at a relatively low complexity.

2.3. Receiver Structures 37

2.3 Receiver Structures

At the receiver, MUD and FEC decoding are performed to combat MUI and fading

effects as well as the channel noise. As shown in Fig. 2.7, a receiver that performs

detection and decoding i) jointly (optimal) is referred to as Type-A receiver, ii) in-

dependently is referred to as Type-B receiver, and iii) iteratively (between detection

and decoding) is referred to as Type-C receiver [134–136]. The separate detection and

decoding (Type-B receiver) has the lowest complexity, but its performance is subopti-

mal. Turbo equalization that performs detection and decoding in an iterative manner

(Type-C receiver) is known to achieve better performance than the Type-B receiver,

and its computational complexity is several times higher than that of the Type-B re-

ceiver [137] [138]. Although the information is exchanged between the detector and the

decoder in a turbo receiver, it cannot perform the joint detection and decoding as is

the case of the optimal Type-A receiver. In the literature, a Type-A receiver, which

takes into account the knowledge of channels, the FEC decoding, the de-spreading and

the de-interleaving, usually becomes infeasible in practical systems, as it amounts to

essentially trying to fit all possible sequences of transmitted bits to the received data

− a task of prohibitive complexity. Therefore, the goal in this research is to design

a joint receiver which achieve near-optimum performance of the Type-A receiver with

affordable computational costs.

2.4 Summary

In this chapter, we have presented different multiple access techniques, including T-

DMA, CDMA, OFDMA, MC-CDMA, LDS-CDMA, LDS-OFDM, SCMA, MUSA and

PDMA. Advantages and drawbacks of these multiple access techniques are discussed.

Considering that non-orthogonal multiple access systems require MUD, we have pre-

sented several popular MUD techniques. The complexity of the optimum MUD grows

exponentially with the number of users which make it practically prohibitive. Although

linear MUD techniques are among the most popular ones, their performance is not op-

timal. Nonlinear detectors such as SIC, PIC, and PDA cannot achieve satisfactory


(b) Type-B

Detector

Deinterleaver

Decoder

(a) Type-A

Joint receiver

(c) Type-C

Detector

Decoder

Deinterleaver Interleaver

Fig. 2.7: Receiver structures

performance in overloaded conditions. In this regard the application of MPA to sparse

graphical based NOMA schemes such as LDS-CDMA, LDS-OFDM and SCMA can

enable NOMA schemes to obtain good performance under overloaded conditions. TA-

BLE 2.1 summarizes different multiple access techniques and their comparisons. It is

an open issue to design joint receivers for NOMA to achieve near-optimum performance

with affordable computational complexity.

2.4. Summary 39

TABLE

2.1:Compariso

nsofmultiple

access

tech

niques

TDMA

CDMA

OFMDA

MC-C

DMA

LDS-C

DMA

LDS-O

FDM

SCMA

MUSA

PDMA

Multi-carrier

No

No

Yes

Yes

No

Yes

Yes

Yes

Yes

Spreading

No

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

Non

-binary

chips

No

No

No

No

No

No

No

Yes

No

Con

stellationshap

ing

No

No

No

No

No

No

Yes

No

No

Sparsestructure

No

No

No

No

Yes

Yes

Yes

Yes

Yes

Han

dle

overload

ing

No

No

No

No

Yes

Yes

Yes

Yes

Yes

Receiver

MMSE

Rake

MMSE

MMSE

MPA

MPA

MPA

SIC

MPA

NOMA

No

No

No

No

Yes

Yes

Yes

Yes

Yes

Chapter 3

Joint Sparse Graph for OFDM

(JSG-OFDM) System

LDS-OFDM and LDPC codes are NOMA and FEC techniques, respectively. Both

of them can be expressed by a bipartite graph. In this chapter, we construct a joint

sparse graph combining LDS-OFDM and LDPC codes, namely JSG-OFDM. A joint

detection and decoding is presented. The iterative structure of JSG-OFDM receiver is

illustrated, and its EXIT chart is researched. Furthermore, design guidelines for the

joint sparse graph are derived through the EXIT chart analysis. By offline optimization

of the joint sparse graph, JSG-OFDM outperforms similar well-known systems such as

GO-MC-CDMA, LDS-OFDM and turbo structured LDS-OFDM.

3.1 JSG-OFDM System Model

Consider the uplink communications withK users transmitting to the same base station

where the base station and each user are equipped with a single antenna. The block

diagram of JSG-OFDM system is shown in Fig. 3.1. Let the processing gain to be

N , and each user has a data vector consisting of M data symbols. Let J be the

number of parity-check equations in LDPC code. Perfect channel state information

(CSI) is available at the receiver. We assume that the system is applied in machine type

communication (MTC) network (where MTC devices transmit short-burst messages,

40

3.1. JSG-OFDM System Model 41

such as temperature, meter reading, etc.), thus binary phase shift keying (BPSK) is

used in the transmission.

At the transmitter in Fig. 3.1, the functional blocks are similar to a MC-CDMA

system. In conventional MC-CDMA, after FEC encoding and symbol mapping, data

symbols are multiplied with a spreading signature (a random sequence of chips) and

subsequently OFDM modulation is arranged to modulate the chips onto respective

subcarrier frequencies. The main difference in JSG-OFDM transmitter is that the

spreading signature has low density by the use of zero padding, which means a large

number of chips in the sequence are zeros. Due to the low density signature, each

symbol is only spread over a limited number of chips. Each user’s generated chip

is transmitted over an orthogonal subcarrier, and each subcarrier is only used by a

limited number of symbols that may belong to different users. Each user, transmitting

on given subcarriers, will experience interference from only a small number of other

users’ data symbols. More explicitly, the number of symbols that are superimposed

on each chip is much less than the total number of symbols, dc,lds ≪ (K ×M), where

dc,lds is the number of symbols that are superimposed at one chip. Meanwhile, the

number of chips that are spread by each symbol is much less than the total number of

chips, dv,lds ≪ N , where dv,lds is the number of chips that are spread by one symbol.

In other words, the spreading sequences have a maximum of dv,lds nonzero values and

N − dv,lds zero values, then they are interleaved uniquely for each user such that the

resultant signature matrix becomes very sparse. The interleaving process is designed

so that at each received chip there exists a contribution of, instead of all users, only a

small number of users. Consequently, the interference pattern being seen by each user

is different.

As for the receiver in Fig. 3.1, there are three types of nodes: chip nodes cn(n ∈ [1, N ]),

variable nodes vk,m(k ∈ [1,K],m ∈ [1,M ]) and parity-check nodes pk,j(k ∈ [1,K], j ∈

[1, J ]), representing the nth chip, themth data symbol and the jth parity-check equation

of the kth user, respectively. A single graph, as labelled with LDS in the receiver,

represents the low density signature due to LDS-OFDM [68] [17]. The other single

graphs, as labelled with LDPC in the receiver, represent the low density parity-check

matrices due to LDPC codes [124]. These two types of single graphs belong to the

42 Chapter 3. Joint Sparse Graph for OFDM (JSG-OFDM) System

parity-check nodes variable nodes chip nodes

LDPC LDS

OFDM

demodulator

v1,1

v1,2

vK,1

vK,2

v1,M

vK,M

user 1

user K

p1,J

p1,1

pK,J

pK,1

c1

c2

cN

JSG

AWGN

user 1 LDPC

encoder

symbol

mapper

OFDM

modulator

radio

channel

user K LDPC

encoder

symbol

mapper

OFDM

modulator

radio

channel

spreading

spreading

zero

padding

zero

padding

Block diagram for JSG-OFDM transmitter

Block diagram for JSG-OFDM receiver

Fig. 3.1: JSG-OFDM system model

3.2. Joint Detection and Decoding for JSG-OFDM 43

techniques of NOMA and FEC coding, respectively. In our proposal, variable nodes

are used to connect the other two types of nodes (chip nodes and parity-check nodes)

through low density edges. Therefore, the receiver becomes a joint sparse graph labelled

with JSG in the figure. As such, the LDS structure and the LDPC codes are perfectly

linked together. In the joint sparse graph, users’ signals that are using the same chip

will be superimposed, and the number of symbols that interfere with each other at

one chip is much less than the total number of symbols, so the system can perform

well in overloaded conditions. The joint sparse graph is arranged to process the chips

from the received signals to reconstitute the transmitted data. It is noteworthy that

applying MPA on the joint sparse graph performs not only detection, but also decoding

at the same time. Furthermore, the receiver of JSG-OFDM (Type-A receiver in Fig.

2.7) is different from that of the turbo structured LDS-OFDM (Type-C receiver in

Fig. 2.7) [17], as there is no outer-inner turbo style iteration here. Hence, the JSG-

OFDM is based on a joint sparse graph which combines NOMA and sparse graph coding

techniques. To fit the stream format of practical communications, we can extend the

data length, such that one frame contains multiple other than one OFDM symbol. In

the next section, joint detection and decoding on such graph will be described.

3.2 Joint Detection and Decoding for JSG-OFDM

Based on the system model introduced in Section 3.1, we present the joint detection

and decoding on the joint sparse graph.

Let sk,m = [s1k,m, ..., sNk,m]

T ∈ CN×1 be the spreading sequence for the the mth symbol

of the kth user, and hk,j = [h1k,j , ..., hMk,j ]

T ∈ BM×1 be the coefficients for the jth parity-

check equation of the kth user. The spreading signature and the parity-check matrix

for the kth user are Sk = [sk,1, ..., sk,M ] ∈ CN×M and Hk = [hk,1, ...,hk,J ] ∈ BM×J ,

respectively. As for the multi-user scenario, let S = [S1, ...,SK ] ∈ CN×MK and H =

[H1, ...,HK ] ∈ BM×JK be the spreading signatures and the parity-check matrices of

LDPC codes, respectively. We also define A = diag(a1, ..., aK) ∈ CK×K as the transmit

amplitude of users, and Ek = diag(ek,1, ..., ek,N ) ∈ CN×N as the corresponding channel

gain for the kth user, where ak and ek,n are both scalars. Moreover, ψn = {(k,m) :


snk,m ̸= 0} and εk,m = {n : snk,m ̸= 0} are the set of data symbols (which may belong

to different users) that interfere on chip cn and the set of chips that vk,m is spread on,

respectively; ϕk,j = {(k,m) : hmk,j ̸= 0} and ωk,m = {(k, j) : hmk,j ̸= 0} are the set of

data symbols that connect to parity-check node pk,j and the set of parity-check nodes

that connect to vk,m, respectively.

In JSG-OFDM, each user’s chip will be transmitted over an orthogonal subcarrier.

Therefore, the received spreading sequence for the mth symbol of the kth user can be

represented by rk,m = akEksk,m. In particular, the received signature gain at the nth

chip of the variable node vk,m is rnk,m = akek,nsnk,m. For the uplink MC-CDMA, the

received signal corresponding to the nth chip (subcarrier) is written as

yn =

K∑k=1

M∑m=1

rnk,mvk,m + zn (3.1)

where zn is the AWGN with variance σ2A and mean zero. Considering that in JSG-

OFDM, the signature has a limited number of non-zero positions, we can express the

received signal at the nth chip (subcarrier) as

yn =∑

(k,m)∈ψn

rnk,mvk,m + zn (3.2)

Let Lvk,m→cn and Lvk,m→pk,j be the log-likelihood ratio (LLR) delivered from the vari-

able node vk,m to the chip node cn and the parity-check node pk,j , respectively. The

LLR delivered from the chip node cn and the parity-check node pk,j to the variable node

vk,m are given by Lcn→vk,m and Lpk,j→vk,m , respectively. Lvk,m is the final estimation

of the variable node vk,m. In a typical run, each message will be updated iteratively

from the previous values of the neighboring LLR. The joint detection and decoding can

be presented as messages updating between different types of nodes via edges, which is

explained as follows.

3.2.1 Initialization

Assuming there is no a priori probability available, initial LLRs are set to zeros.

Lvk,m→cn = 0, ∀k, ∀m, ∀n (3.3)

Lvk,m→pk,j = 0, ∀k, ∀m,∀j (3.4)

3.2. Joint Detection and Decoding for JSG-OFDM 45

3.2.2 Updating of Chip Nodes and Parity-Check Nodes

LLRs of the chip nodes and the parity-check nodes are calculated at the same time.

For the chip nodes,

Lcn→vk,m = f(vk,m|yn, Lvk′,m′→cn , (k′,m′) ∈ ψn \ (k,m)) (3.5)

where ψn \ (k,m) is the set of data symbols (excluding vk,m) that interfere on the chip

cn. In order to approximate the maximum a posteriori (MAP) probability detector,

the right hand side of (3.5) represents marginalization function, which is based on (3.2),

and can be written as

f(vk,m|yn, Lvk′,m′→cn , (k′,m′) ∈ ψn \ (k,m))

= log(

N∑n=1

p(yn|v)pn(v|vk,m))

= log(

N∑n=1

p(yn|v)∏

(k′,m′)∈ψn\(k,m)

pn(vk′,m′))

(3.6)

where v is the transmitted vector, the conditional probability density function p(yn|v)

and a priori probability pn(vk′,m′) are given as

p(yn|v) =1√2πσA

exp(− 1

2σ2A∥ yn − rT[n]v[n] ∥2) (3.7)

pn(vk′,m′) = exp(Lvk′,m′→cn) (3.8)

where v[n] and r[n] denote the vector containing the symbols transmitted by every

user that spread its data on the nth chip and their corresponding effective received

signature values, respectively. As can be seen from (3.6), based on the received chip

yn and a priori input information pn(vk′,m′), extrinsic values are calculated for all the

constituent bits involved in (3.2). Substituting (3.7) and (3.8) into (3.6), the message

update becomes

Lcn→vk,m = κn,k,mmaxv[n]

∗(∑

(k′,m′)∈ψn\(k,m)

Lvk′,m′→cn − 1

2σ2A∥ yn − rT[n]v[n] ∥2) (3.9)

where κn,k,m denotes the normalization coefficient and

max∗(a, b) , log(ea + eb) = max(a, b) + log(1 + e−|a−b|) (3.10)


The LLR of the parity-check nodes is updated as

Lpk,j→vk,m = α−1(∑

(k′,m′)∈ϕk,j\(k,m)

α(Lvk′,m′→pk,j )) (3.11)

where ϕk,j \ (k,m) is the set of data symbols (excluding vk,m) that connect to the

parity-check node pk,j , and

α(x) = sign(x)× (− log tan| x |2

) (3.12)

where sign(x) represents the sign of x, and the inverse of α(x) is

α−1(x) = (−1)sign(x) × (− log tan| x |2

) (3.13)

3.2.3 Updating of Variable Nodes

In the single graph case, variable nodes only gather information from one type of nodes

(chip nodes or parity-check nodes) [64] [126]. However, in the joint sparse graph, the

updating of Lvk,m→cn not only receives chip nodes information, but also ultilizes the

information that comes from parity-check nodes.

Lvk,m→cn =∑

n′∈εk,m\n

Lcn′→vk,m +∑

j∈ωk,m

Lpk,j→vk,m (3.14)

where εk,m \ n is the set of chips (excluding cn) that vk,m is spread on.

Similarly, calculation of Lvk,m→pk,j also involves the information from both sides, i.e.

Lvk,m→pk,j =∑

j′∈ωk,m\j

Lpk,j′→vk,m +∑

n∈εk,m

Lcn→vk,m (3.15)

where ωk,m \ j is the set of parity-check nodes (excluding pk,j) that connect to the

variable node vk,m.

3.2.4 Estimation and Syndrome Computing

In the single graph case of LDS-OFDM, a posteriori probability of the transmitted

symbol can only be calculated after a fixed number of iterations, as there is no criterion

to determine whether the iterative message has converged [66]. Fortunately, in the

3.3. EXIT Chart Analysis of JSG-OFDM 47

joint sparse graph, parity-check nodes are available, thus it is possible to terminate the

joint detection and decoding by syndrome computing. A posteriori probability of the

transmitted symbol vk,m is calculated as

Lvk,m =∑

n∈εk,m

Lcn→vk,m +∑

j∈ωk,m

Lpk,j→vk,m (3.16)

The estimated value of the variable node vk,m is obtained by making a hard decision,

v̂k,m = argmaxvk,m

Lvk,m (3.17)

If the syndrome computing for each user equals to zero, or the maximum iteration

number is reached, the process is terminated. Otherwise, the iteration goes on.

The implementation algorithm of the joint detection and decoding is summarized in

TABLE A.1. The key features of the joint detection and decoding include: i) there

is no additional interleaver/de-interleaver between the detector and the decoder; ii)

there is no outer-inner Turbo-fashion iterations; and iii) the messages are propagated

in a double-door-double-open/close manner which means that chip nodes and parity-

check nodes update at the same time while variable update at another time. The extra

interleaver/de-interleaver and outer-inner iterations are dominant characters of a Turbo

receiver, and the double-door-double-open/close updating strategy is different in the

way that a Turbo receiver works. Therefore, the JSG-OFDM joint receiver is different

from a Turbo-type receiver. One of the advantages of the iterative receiver for JSG-

OFDM is its ability to support high loads while maintaining satisfactory performance

and affordable complexity. In the next section, we carry out theoretical analysis of the

joint sparse graph using EXIT chart.

3.3 EXIT Chart Analysis of JSG-OFDM

EXIT chart is a useful tool to analyse the transfer of information between SISO con-

stituents, and it provides an approximate visualization of the process of belief prop-

agation [117–122]. However, EXIT chart has not been applied to any joint sparse

graph. In this section, we shall explain how EXIT charts can be utilized to analyse the

convergence behavior of the joint receiver of JSG-OFDM.


3.3.1 Iterative Structure of the Joint Sparse Graph

Before applying EXIT charts to the JSG-OFDM, we depict the iterative structure of

the joint sparse graph. According to the joint detection and decoding presented in Sec-

tion 3.2, variable nodes calculate the extrinsic messages to chip nodes using a priori

information which they receive from other connected chip nodes and parity-check n-

odes. Meanwhile, based on the received a priori information, variable nodes calculate

the extrinsic messages to parity-check nodes. The same rule applies to the extrinsic

messages that the chip nodes and parity-check nodes send to variable nodes. To e-

valuate the transformation of extrinsic information in the joint sparse graph, the sets

of chip nodes, variable nodes and parity-check nodes are referred to as chip nodes de-

tector (CND), variable node detector-decoder (VNDD) and parity-check node decoder

(PND), respectively. Fig. 3.2 shows the structure of the iterative detector and decoder

in JSG-OFDM. As depicted in the figure, the extrinsic LLR that has been passed on

are considered as a priori information by the other detector or decoder. The edge

interleavers connect the different type of nodes, each of which represents a sparse sig-

nature or matrix. It is worth noting that such iterative structure is more complicated

than any previous single graph which only has the left part labelled as LDS [64] or the

right part labelled as LDPC [126] in this figure.

Chip Node

Detector 1

ld s

ld s

Parity Check Node

Decoder

1

ld p c

ld p c

To receiver

Variable Node

Detector & Decoder

From OFDM demodulator

-

-

-

-

LDS LDPC

Fig. 3.2: Iterative structure of the joint detection and decoding in JSG-OFDM

Additionally, Fig. 3.3 shows a folded view of the joint sparse graph. Based on the joint

detection and decoding, chip nodes and parity check nodes update their messages at the

same time, then variable nodes calculate the LLR delivered to chip nodes and parity

check nodes simultaneously. Therefore, it is reasonable to place chip nodes (rectangles)

and parity-check nodes (triangles) on one side, while to draw variable nodes (circles)


on the other side. The chip nodes are used to be spread on for the variable nodes

through low density edges, which are represented by bold lines. The parity-check

nodes, belonging to different users, are connected to corresponding groups of variable

nodes through sparse edges, which are represented by independent groups of dash lines.

Multiple access, FEC coding and the combination of several single sparse graphs, are

clearly depicted in the figure. This provides a basis for the following analysis.

p1, J

p1, 1

c1

c2

cN

v1, 1

v1, 2

vK, 1

vK, 2

v1, M

vK, M

chip nodes

of user 1

of user K

PK, J

PK, 1

of user 1

variable nodes

of user K

parity check nodes

parity check nodes

variable nodes

Fig. 3.3: Folded view of the joint sparse graph

3.3.2 EXIT Chart Analysis Over AWGN Channel

3.3.2.1 EXIT Curve for VNDD

In this thesis, IA,V NDD refers to the average mutual information between the bits on

the VNDD edges and the a priori LLR, IE,V NDD is the average mutual information

between the bits on the VNDD edges and the extrinsic LLR. In order to compute

an EXIT curve for variable nodes, Lcn→vk,m and Lpk,j→vk,m are modelled as the soft

output of an AWGN channel when the inputs are interleaved bits. Then the mutual


information between the variable node’s extrinsic messages and actual values of symbols

on the edges is calculated. A priori LLR can be calculated by

A = µAx+ zn (3.18)

where zn is an independent Gaussian random variable with variance σ2A and mean zero;

x is the original bits on the graph edge. Furthermore, we have

µA =σ2A2

(3.19)

The mutual information IA,V NDD = I(X;A) can be calculated by [123]

IA,V NDD =1

2

∑x=−1,1

∫ +∞

−∞pA(β|X = x) log2

2pA(β|X = x)

pA(β|X = −1) + pA(β|X = 1)dβ

(3.20)

Since the conditional probability density function pA(β|X = x) depends on LLR of A,

we can write

IA,V NDD(σA) =1−∫ +∞

−∞

exp(−((β − σ2A/2)2/2σ2A))√

2πσAlog2(1 + e−β)dβ (3.21)

For abbreviation we define

B(σ) , IA,V NDD(σA = σ) (3.22)

with

limσ→0

B(σ) = 0 (3.23)

limσ→∞

B(σ) = 1 (3.24)

where σ ≥ 0. Considering (3.14) and (3.15) together with the fact that the sum of

two normally distributed random variables is also normally distributed with the mean

and variance equal to the sum of theirs, the EXIT function of a variable node can be

expressed as

IE,V NDD(IA,V NDD, dv,lds, dv,ldpc) = B(√

(dv,lds + dv,ldpc − 1)(B−1(IA,V NDD))2)

(3.25)

where dv,lds is the effective spreading factor and dv,ldpc is the number of parity-check

nodes connected to one variable node. Therefore, unlike single sparse graph where only

one type of node is considered [64] [124], both LDS and LDPC nodes affect the VNDD

performance.


3.3.2.2 EXIT Curve for CND&PND

Let IA,CND&PND refers to the average mutual information between the bits on the

CND&PND edges and the a priori LLR, IE,CND&PND is the average mutual informa-

tion between the bits on the CND&PND edges and the extrinsic LLR. A chip node

has incoming messages from the connected variable nodes and the OFDM demodula-

tor, whereas a parity-check node only has messages coming from neighbored variable

nodes. The output LLR of chip nodes and parity-check nodes are calculated by (3.9)

and (3.11), respectively. We model Lvk,m→cn and Lvk,m→pk,j as the output of an AWGN

channel that the input is the corresponding transmitted bit, and then calculate the mu-

tual information of the output with regards to the actual value on the edges. Due to the

complexity of the calculation in chip nodes and parity-check nodes, their EXIT curves

are computed by simulations over AWGN channel. The probability density function

for extrinsic information is determined by Monte Carlo simulation with histogram mea-

surements [120], the mutual information between the extrinsic information and the bits

on the joint graph edges, is subsequently calculated.

3.3.2.3 Analysis

System parameters are listed in TABLE 3.1 for the following EXIT chart analysis.

The number of chip nodes is less than that of FFT size, and the unused subcarriers

serve as the guard band. Considering the effective transmitted bits, there are 120 chips

available, where each subcarrier can transmit at least 2 bits due to I/Q channels. As

BPSK is used, each variable node represents a 1-bit symbol. Thus the system loading

is calculated as: number of variable nodes / (number of chip nodes × I/Q channels),

i.e., 240/(120 × 2) = 100%. The number of users or variable nodes is related to the

system loading. The effective spreading factor is set to 3 in order to achieve a good

trade-off between frequency diversity and complexity [17]. Fig. 3.4 shows the EXIT

charts over AWGN channel at Eb/N0 = 9 dB. For comparisons, we also plot curves

of LDS-OFDM system, where there are only two sets of nodes in the single graph of

LDS-OFDM: chip node detector (CND) and variable node detector (VND). According

to Fig. 3.4, we can concluded:


TABLE 3.1: System parameters

Number of users 6

Number of chip nodes 120

Number of variable nodes 240

Number of parity-check nodes 120

FFT size 128

System loading 100%

Number of variable nodes connected to each chip node dc,lds = 6

Effective spreading factor dv,lds = 3

Number of parity-check nodes connected to each variable node dv,ldpc = 3

Number of variable nodes connected to each parity-check node dp,ldpc = 6

Modulation BPSK

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CND&PND

& IE,VNDD

I E,C

ND

&P

ND

& I A

,VN

DD

VND in LDS−OFDMCND in LDS−OFDMVNDD in JSG−OFDMCND&PND in JSG−OFDMJMUDD trajectory in JSG−OFDM

Fig. 3.4: EXIT chart over AWGN Channel at Eb/N0 = 9 dB


1) The curve of VND in LDS-OFDM is higher than that of VNDD in JSG-OFDM. This

is because the edge numbers connecting to variable nodes are different between single

graph of LDS-OFDM and joint graph of JSG-OFDM, which has seen illustrated in Fig.

3.2 and Fig. 3.3. As a result, according to (3.25), these two curves are different.

2) The curve of CND in LDS-OFDM is higher than that of CND&PND in JSG-OFDM

when IA,CND&PND ≤ 0.95. This follows from the fact that the CND could receive

information from both OFDM demodulator and neighbored variable nodes, but the

PND only uses the information from the connected variable nodes (shown in Fig. 3.1).

Hence, the PND pulls down the average extrinsic information of CND&PND in JSG-

OFDM at the first few iterations.

3) The intersection point of VNDD and CND&PND in JSG-OFDM, is higher than that

of VND and CND in LDS-OFDM. This phenomenon implies that the JSG-OFDM has

better ability to eliminate the MUI than LDS-OFDM.

4) The simulation trajectory of the joint detection and decoding in JSG-OFDM is

also plotted in Fig. 3.4, which is marked by the dotted line and labelled by JMUDD

which means joint multiuser detection and decoding. We can see that the iterative

process starts with IA,CND&PND = 0 since no prior information is available for the

CND&PND in the beginning. In the following steps, the output LLR is exchanged

between the two solid curves. The trajectory approximately follows the transfer curves

of the components in JSG-OFDM, which indicates that the EXIT charts analysis is

valid for the joint sparse graph. The minor discrepancy is due to the finite size of edge

interleaver in the joint sparse graph.

3.3.3 EXIT Chart Analysis Over Multipath Fading Channels

As OFDM is used to combat the negative effect of multipath, we analyse the EXIT chart

over multipath fading channels in the sequel. Note that the EXIT chart technique is not

limited to the AWGN channel, it can also be applied to multipath fading channels when

perfect channel state information is available at the receiver [117] [118]. An EXIT chart

assumes that the probability density function of the exchanged messages approaches a

Gaussian-like distribution with increasing number of iterations. Consequently, it can


be applied to multipath fading channels as long as the trajectory follows the curves of

the receiver components.

Similar to the analysis for the AWGN channel, the EXIT function of a variable node

is the same as (3.25), which means the fading does not have any effect on the perfor-

mance of VNDD, however its effect will be on the CND&PND because it calculates

its messages based on the received signal from the fading channel. Due to the com-

plexity of calculation in (3.9) and (3.11), their EXIT curves are drawn by simulations.

Considering that ITU Pedestrian Channel B is adopted in 3GPP and is a typical mul-

tipath fading channel model, Fig. 3.5 illustrates the EXIT charts for LDS-OFDM and

JSG-OFDM over ITU Pedestrian Channel B at Eb/N0 = 13 dB [139]. As shown in

the figure, JSG-OFDM has a higher intersection point than LDS-OFDM. Fig. 3.5 also

shows the simulation trajectory of the joint detection and decoding of JSG-OFDM,

which is marked by the dotted line. Thus the EIXT chart analysis is verified and visu-

alized by the simulated trajectory, and the actual trajectory is well predicted at various

iterations with only a marginal difference. This validates the EXIT chart analysis for

multipath fading channels, and it will be further confirmed in Section 3.5.

3.4 EXIT Chart Based Design of Joint Sparse Graph

According to graph theory, there are different parameters affecting the performance

of a sparse graph. Two important factors are degree distribution of nodes and short

cycle [108, 111, 112]. In this section, EXIT charts are used for the optimization of the

joint sparse graph.

3.4.1 Degree Distribution

The degree of a node is equal to the number of edges connecting that node to other

nodes in the graph, while degree distribution is the probability distribution of the

degree. For the joint sparse graph, let DCND(x), DPND(x) and DV NDD(x) denote the

degree distribution polynomials of chip nodes, parity-check nodes and variable nodes,

3.4. EXIT Chart Based Design of Joint Sparse Graph 55

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CND&PND

& IE,VNDD

I E,C

ND

&P

ND

& I A

,VN

DD

VND in LDS−OFDMCND in LDS−OFDMVNDD in JSG−OFDMCND&PND in JSG−OFDMJMUDD trajectory in JSG−OFDM

Fig. 3.5: EXIT chart over ITU Pedestrian Channel B at Eb/N0 = 13 dB

respectively. They are defined as

DCND(x) =

dc,lds∑d=1

PCND(d)xd−1 (3.26)

DPND(x) =

dp,ldpc∑d=1

PPND(d)xd−1 (3.27)

DV NDD(x) =

dv,lds+dv,ldpc∑d=1

PV NDD(d)xd−1 (3.28)

where PCND(d), PPND(d) and PV NDD(d) are fractions of edges related to corresponding

nodes. As 3 is suitable for the effective spreading factor, we fix dv,lds = 3. However,

other degree distributions need to be optimized.

In the information theory, the mutual information is a measure of the variables’ mu-

tual dependence [120]. Ideally, in order to the exchange extrinsic information be-

tween the components to a convergence point such that an arbitrarily low BER can be

achieved, the EXIT curves should not intersect before reaching the (IA, IE) = (1, 1)

point [117–119]. This implies that given IA = 1, we have IE = 1 and provided that


this condition is satisfied, a so-called open-convergence tunnel appears in the EXIT

chart. If however, the two curves intersect at a point lower than the (1, 1) point, it

forms a semi-convergence tunnel, ant it will yield a higher BER than the scheme with

an intersection at the (1, 1) point. In order to investigate how the position of the

intersection point in the EXIT chart affects the BER performance, Fig. 3.6 shows the

achievable BER as a function of the average mutual information IA,V NDD for the joint

sparse graph presented in TABLE 3.1 over ITU Pedestrian Channel B. This figure gives

an indication of the minimum required IA,V NDD in order to achieve a target BER. For

example, to achieve the BER of 10−3/10−4/10−5, the point of intersection should be at

least at IA,V NDD = 0.86/0.93/0.96. Hence, to reach the maximum dependence between

detected symbols and their real values, the goal of an iterative system is to approach

the (1, 1) point in the EXIT chart.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

−6

10−5

10−4

10−3

10−2

10−1

100

IA,VNDD

BE

R

Fig. 3.6: BER versus IA,V NDD for the joint sparse graph

The joint sparse graph presented in TABLE 3.1 is a regular graph. Although its

intersection point is higher than that of LDS-OFDM, which is shown in Fig. 3.4

and Fig. 3.5, the average level of CND&PND in JSG-OFDM is much lower than that

of CND in LDS-OFDM. Our approach is based on invoking EXIT chart analysis for

optimizing the shape of the EXIT curve in order to achieve the (1, 1) point while


keeping the tunnel open. As can be seen from (3.9), the information coming from

the OFDM demodulator serves as input source of the joint sparse graph, and it is

fed into chip nodes in each iteration of the joint detection and decoding. According

to Section 3.2, chip nodes could receive information from both OFDM demodulator

and neighbouring variable nodes, while parity-check nodes only uses the information

from the connected variable nodes excluding any direct channel knowledge, thus the

PND pulls down the average extrinsic information of CND&PND in JSG-OFDM at

the first few iterations. As mentioned previously, the mutual information determines

the dependence between detected symbols and their exact values, thus the EXIT curve

level has to be considered. If the proportion of the edges related to PND is reduced

properly, the curve of CND&PND can be lifted up, and the adjusted curves of the

EXIT chart enable us to create a near-capacity scheme. As a further benefit, we are

able to shift the EXIT functions close to the (1, 1) point in order to obtain a lower

BER. Based on the above analysis, several schemes of degree distribution are shown in

TABLE 3.2, where Dega is the case of a regular joint sparse graph presented in TABLE

3.1, other schemes are for irregular joint sparse graphs. We can see that compared to

Dega, Degc and Degd slightly decrease the degree of PND, then the polynomials of

VNDD are altered accordingly. On the contrary, Degb increases the density of edges of

PND.

TABLE 3.2: Degree distribution

Scheme DCND(x) DPND(x) DV NDD(x)

Dega x5 x5 x5

Degb 0.15x4 + 0.7x5 + 0.15x6 0.09x5 + 0.91x6 0.5x5 + 0.5x6

Degc 0.05x4 + 0.9x5 + 0.05x6 0.4x3 + 0.6x4 0.7x4 + 0.3x5

Degd 0.03x4 + 0.94x5 + 0.03x6 0.8x3 + 0.2x4 0.9x4 + 0.1x5

Fig. 3.7 shows EXIT charts of different degree distributions over ITU Pedestrian Chan-

nel B at Eb/N0 = 13 dB. ForDegc andDegd, the proportion of the edges related to PND

is reduced, consequently, as seen in Fig. 3.7, the average mutual information between

the bits and the extrinsic values of CND&PND are both increased. More important-


ly, their intersection point becomes higher and closer to the (1, 1) point than that of

Dega, which means better performance can be achieved. By contrast, Degb increases

the density of edges of PND, but its average mutual information and intersection point

are both dropped. Thus the degree distribution is a key factor to the JSG-OFDM

performance. Although the curves of Degc and Degd almost overlap, Degd is a more

suitable choice since it has lower density.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CND&PND

& IE,VNDD

I E,C

ND

&P

ND

& I A

,VN

DD

VNDD of Dega

CND&PND of Dega

VNDD of Degb

CND&PND of Degb

VNDD of Degc

CND&PND of Degc

VNDD of Degd

CND&PND of Degd

Fig. 3.7: EXIT chart for different degree distributions

3.4.2 Short Cycles

Usually, short cycles are only considered and avoided in single graphs such as LDPC

codes and LDS-OFDM. Nevertheless, in the joint sparse graph, length-4 cycles are

easy to be regenerated without careful design. The results presented in Fig. 3.7 do not

consider the impact of cycles, therefore, their girths equal to 4.

Fig. 3.8 shows EXIT charts for different girths of the joint sparse graph, over ITU

Pedestrian Channel B at Eb/N0 = 13 dB. It should be emphasized that the restriction

of the girth is applied to the joint graph rather than any single graph. We choose the

optimal Degd to be the degree distribution. In the case when the girth equals to 6, it is

not difficult to remove length-4 cycles by computer search. When the girth equals to 8,


the computer search is time-consuming to eliminate length-4 and length-6 cycles, and

some degrees need to be modified marginally (labelled by Deg′d): DCND(x) is 0.027x4+

0.946x5+0.027x6, DPND(x) is 0.83x3+0.17x4 and DV NDD(x) is 0.915x

4+0.085x5. It

can be seen from this figure that curves of matrices with girth of 4 and 6 are very close

to each other, whereas matrix with girth of 8 outperforms others. This is due to the

same degree distribution adopted by matrices with girth of 4 and 6, while the degree

distribution of matrix with girth of 8 is slightly different. Although the EXIT chart

only depends on the degree distribution, in order to improve system performance, we

suggest to remove cycles of length of 4 and 6 when constructing a joint sparse graph, as

short cycles may lead to failure of message convergence or oscillation between multiple

states over repeat iterations. Ideally, in a cycle-free graph, the belief will converge to

the exact a posteriori probability after a finite number of iterations. Nevertheless,

cycles cannot be avoided, and the propagated information may lead to inaccurate a

posteriori probability. Therefore, degree distribution and short cycle both affect the

JSG-OFDM performance.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CND&PND

& IE,VNDD

I E,C

ND

&P

ND

&I A

,VN

DD

VNDDCND&PND, girth = 4CND&PND, girth = 6CND&PND, girth = 8

Fig. 3.8: EXIT chart for different schemes


3.5 Performance Evaluation

In this section, the JSG-OFDM schemes are simulated and compared with other well-

known systems.

3.5.1 Evaluation Configuration

JSG-OFDM are evaluated and compared with existing well-known multiple access sys-

tems such as GO-MC-CDMA, LDS-OFDM and turbo structured LDS-OFDM. The

simulations are conducted over ITU Pedestrian Channel B, and the system parameters

are listed in TABLE 3.1. For fair comparisons, a half rate quasi-cyclic LDPC code is

adopted by all the systems [125]. For GO-MC-CDMA, Welch-bound-equality (WBE)

is used, and the spreading codes are constructed by algorithms developed in [34]. For

GO-MC-CDMA, the number of subcarriers per group is set to 4 and maximum likeli-

hood detection is employed per group [60]. For LDS-OFDM, the LDS is optimized by

EXIT chart, and an iterative detector is used [68]. For turbo structured LDS-OFDM,

there are six outer-inner turbo iterations between the detector and the decoder, and

the turbo structure is optimized by the EXIT chart in [17]. For JSG-OFDM, based on

the analysis of Section 3.4, three scenarios of the joint sparse graph that have different

degree distribution and girth are given in TABLE 3.3. The maximum iterations are

limited to six for LDS-OFDM and JSG-OFDM. Moreover, in the case when only one

user is active in the uplink transmission, the theoretical single user bound can be ob-

tained by the matched filter which optimally combines the transmitted symbol from all

the paths, similar to a maximum ratio combiner, to maximize the SNR, and thereby

minimizes error probability. All the investigated systems are compared to the optimal

single user bound.

3.5.2 BER Comparison

Fig. 3.9 shows BER results for systems with a load of 100%. As we can see from this

figure, performance of LDS-OFDM is inferior to that of GO-MC-CDMA and turbo

structured LDS-OFDM. Meanwhile, JSG-OFDM outperforms all the other systems.

3.5. Performance Evaluation 61

TABLE 3.3: JSG-OFDM scenarios

Scenario Degree distribution Girth

scenario− 1 Dega 6

scenario− 2 Degb 4

scenario− 3 Deg′d 8

Due to the inherent advantage of the joint sparse graph, JSG-OFDM achieves better

performance than turbo structured LDS-OFDM. With the optimized degree distribu-

tion (Deg′d) and cycle structure (girth of 8), JSG-OFDM scenario − 3 achieves the

best performance. Its performance improvements at BER of 10−5 are: 0.6 dB over

JSG-OFDM scenario − 1, 1.1 dB over JSG-OFDM scenario − 2, 1.5 dB over turbo

structured LDS-OFDM, 1.6 dB over GO-MC-CDMA and 1.8 dB over LDS-OFDM,

respectively. Note that even if JSG-OFDM scenario− 3 is adopted, there is still a gap

to the optimal single user bound. Moreover, for JSG-OFDM scenario − 3, physical

layer framing is adopted and tested, i.e., 10 OFDM symbols constitute a frame. As

its curve outperforms that of JSG-OFDM scenario− 3, the joint sparse graph can be

extended to fit the data length in practical systems.

In addition, the performance for systems with a load of 150% is also evaluated and

shown in Fig. 3.10. It can be seen that the BER results of 150% loading are inferior

to that of 100% loading. For a load of 150%, JSG-OFDM still outperforms other

systems, and the scenario−3 of JSG-OFDM achieves the best performance. Compared

with LDS-OFDM, GO-MC-CDMA and turbo structured LDS-OFDM, the JSG-OFDM

scenario − 3 can obtain about 1.5 - 1.8 dB gain in the medium to high SNR region.

Apparently, as the system loading increases, the gap to the optimal single user bound

becomes wider.

To reveal the theoretical threshold of the joint sparse graph, we analyse its maximum

achievable throughput by EXIT charts. It was proved in [118] and [119] that the

capacity of an iterative system is equal to the area under the EXIT curve of the inner

code, provided that the bit stream input to the receiver has independently distributed

bits and the MAP algorithm is used for the detection or the decoding. For the joint


0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0(dB)

BE

R

GO−MC−CDMA, separative detection and decoding

LDS−OFDM, separative detection and decoding

Turbo structured LDS−OFDM, turbo iterative detection and decoding

JSG−OFDM scenario−1, joint detection and decoding



JSG−OFDM scenario−3, 10 OFDM symbols in 1 frame, joint detection and decoding

single user bound

Fig. 3.9: Performance of 100% loaded systems

0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0(dB)

BE

R

GO−MC−CDMA, separative detection and decoding

LDS−OFDM, separative detection and decoding

Turbo structured LDS−OFDM, turbo iterative detection and decoding




JSG−OFDM scenario−3, 10 OFDM symbols in 1 frame, joint detection and decoding

single user bound

Fig. 3.10: Performance of 150% loaded systems


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

capa

city

(bi

t/sym

bol)

JSG−OFDM capacity

2.5 dB

1.1 dB

Fig. 3.11: Maximum effective throughput of JSG-OFDM

sparse graph, assuming that the area under the EXIT curve of the CND&PND is

represented byA, then the maximum achievable throughput at a particular Eb/N0 value

is given by A(Eb/N0). In other words, if A is calculated for different Eb/N0 values, the

threshold of the joint sparse graph can be evaluated. Fig. 3.11 quantifies the maximum

effective throughput of the joint sparse graph, where the SNR represent Es/N0, and

the horizontal dotted line represents the throughput of the scheme considered. More

explicitly, 0.5 bit/symbol is the effective throughput of half rate coded and BPSK

modulated system. The circle and the rectangle are respectively located at the SNR

required for 100% and 150% loaded JSG-OFDM scenario − 3 to achieve an identical

throughput at a target BER of 10−5. The SNR values shown next to the circle and the

rectangle indicate the distance to the capacity. As can be seen that the 100% loaded

JSG-OFDM scenario − 3 is capable of operating within 1.1 dB from the capacity

curve. When the system loading is increased to 150%, the gap becomes 2.5 dB. Hence,

as expected, the lower the system loading employed, the closer the joint sparse graph

operates to capacity.


3.5.3 Convergence Behavior

To show the convergence behavior of JSG-OFDM, Fig. 3.12 depicts the performance

at different iterations of 100% loaded JSG-OFDM scenario − 1. As expected, over

AWGN channel at Eb/N0 = 9 dB, the BER stops falling down after 5 iterations, which

is accurately predicted by the joint detection and decoding trajectory presented in

Fig. 3.4. Moreover, over ITU Pedestrian Channel B at Eb/N0 = 13 dB, the receiver

needs 4 iterations to reach the message convergence, which concurs with the trajectory

prediction plotted in Fig. 3.5. Therefore, EXIT chart analysis and convergence behavior

of the joint sparse graph are verified by BER simulations.

1 2 3 4 5 610

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Number of iterations

BE

R

AWGN at Eb/N

0 = 9 dB

ITU Pedestrian Channel B at Eb/N

0= 13 dB

Fig. 3.12: Performance at different iterations for JSG-OFDM

3.5.4 Performance of Different Users

To gain more insight to the joint sparse graph, we present another result showing the

performance of individual users. Fig. 3.13 illustrates the performance of the worst user

and the best user in 100% loaded JSG-OFDM scenario− 3. It shows that some users

have better performance than the others. To be more precise, we can see that at low


SNR region the performance gap is not as obvious as in the high SNR region. This

phenomenon can be explained by the dominating effect of noise at low SNRs.

0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Worst userBest userOverall

Fig. 3.13: Performance of different users in JSG-OFDM

3.5.5 Near-far Effect

The near-far problem is a condition in which a receiver captures a strong signal and

thereby makes it impossible for the receiver to detect a weaker signal. The joint sparse

graph does not give equal multiuser efficiency, and it does not result in the same

performance for all the users as indicated by Fig. 3.13, so it is necessary to investigate

the near-far effect of the JSG-OFDM. Fig. 3.14 shows the performance of near-far

resistance for JSG-OFDM scenario− 3 with different loads. The simulation is carried

out for the case when Eb/N0 = 16 dB for the first user, and Eb/N0 of other users is

different. The BER of the first user is plotted against ∆Eb/N0 which represents the

difference in Eb/N0 between the user of interest and the other users. More explicitly,


when the first user’s SNR Eb/N0 = 16 dB, the other users’ SNR equals to ∆Eb/N0 plus

16 dB. It can be seen that unequal received power has a minor effect on the performance

of user of interest under different loadings. It is due to the iterative processing, or in

other words the near-far problem can be alleviated by the joint sparse graph and the

MPA. We can conclude that JSG-OFDM is robust against unequal received powers.

−3 −2 −1 0 1 2 310

−6

10−5

10−4

10−3

10−2

∆Eb/N

0(dB)

BE

R

100% loaded JSG−OFDM150% loaded JSG−OFDM

Fig. 3.14: Near-far effect of JSG-OFDM

3.5.6 Multipath Diversity

To test the multipath diversity of the joint sparse graph, we simulate the JSG-OFDM

scenario− 3 over different multipath channel models, i.e., ITU Pedestrian Channel A,

and the ITU Pedestrian Channel B. Fig. 3.15 shows the comparison results, and it can

be seen that the performance of ITU Pedestrian Channel A is inferior to that of ITU

Pedestrian Channel B, indicating that the multipath diversity can be exploited to the

JSG-OFDM system.


0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0(dB)

BE

R

JSG−OFDM scenario−3, ITU Pedestrian Channel BJSG−OFDM scenario−3, ITU Pedestrian Channel A

Fig. 3.15: Performance of JSG-OFDM over different multipath channels

3.5.7 Comparison with MMSE Detector

JSG-OFDM is further compared with MC-CDMAwhich is a conventional OMA scheme.

We set the numbers of users and variable nodes to be 12 and 480, respectively, while

keeping the 120 chips and the BPSK modulation, thus the system loading is increased

to 480/(120×2) = 200%. A linear MMSE detector, which is the optimal linear detector

that maximizes SINR, is used in MC-CDMA. Fig. 3.16 shows the comparison result. It

can be seen that, under the overloaded condition, JSG-OFDM outperforms MC-CDMA

significantly. At BER of 3 × 10−3, there is more than 6.5 dB gain by employing JSG-

OFDM. Therefore, the joint sparse graph is a much more effective technique to handle

overloaded transmissions.

3.5.8 Detection Complexity Comparison

As the same LDPC code is applied to all the investigated systems and the decoding

complexity is therefore the same, we focus on the comparisons of detection complexity.

Let X be the constellation alphabet for the transmitted symbol, which is related to the


0 2 4 6 8 10 12 14 16 18 2010

−5

10−4

10−3

10−2

10−1

100

Eb/N

0(dB)

BE

R

MC−CDMAJSG−OFDM

Fig. 3.16: Performance comparison with MMSE detector

modulation order. In GO-MC-CDMA, the detector complexity increases exponential-

ly with the number of symbols in each group, which results in a complexity order of

O(| X |8

). In LDS-OFDM, the detector complexity increases exponentially with the

number of symbols per subcarrier which is dc,lds, thus its complexity order is O(| X |6

).

In turbo structured LDS-OFDM, the detector complexity is several times higher than

that of LDS-OFDM. Apparaently, the complexity of the LDS-OFDM detector is less

than that of GO-MC-CDMA and turbo structured LDS-OFDM. Thus, we compare the

complexity between JSG-OFDM and LDS-OFDM. It is noteworthy that due to the

similar MPA, the detection complexity order of the JSG-OFDM is O(| X |6

)which is

the same as that of LDS-OFDM. However, as the convergence behavior and the inter-

section point of the EXIT chart are different between LDS-OFDM and JSG-OFDM,

the complexity is slightly different, which will be discussed in the sequel.

We express the complexity of detection in terms of equivalent additions. The basic

operations performed by MPA include: i) addition, ii) subtraction, iii) multiplication

by ±1, iv) division by 2, v)comparison and vi) max(x, y). The i) − v) operations

correspond to one equivalent addition, and the vi) operation corresponds to two equiv-

alent additions, since it first uses a compare operation to compare the two input values

3.6. Summary 69

and then stores the result in a register [140]. TABLE 3.4 summarizes the computation-

al requirements for a load of 100%. On one hand, for LDS-OFDM and JSG-OFDM

(including scenario − 1 and scenario − 3), the equivalent addition operations drop

dramatically when Eb/N0 increases, which means channel conditions affect the number

of iterations significantly. This is due to the property of the message passing algorith-

m, more explicitly, as shown in the joint detection and decoding, the iteration can be

terminated promptly if the syndrom equals to zero. Therefore, the number of addi-

tion operations is a function of Eb/N0. On the other hand, the receiver complexity of

JSG-OFDM, including scenario − 1 and scenario − 3, is obviously higher than that

of LDS-OFDM. This is related to the more complicated process on the variable n-

odes in the JSG-OFDM system. However, by careful design of the joint sparse graph,

the detection complexity of JSG-OFDM scenario− 3 is less than that of JSG-OFDM

scenario− 1. This can be attributed to the optimization of degree distribution which

reduces the density of the graph.

TABLE 3.4: Equivalent number of addition operations for detection

System 4 dB 8 dB 12 dB 16 dB 20 dB

LDS-OFDM 249019 179565 112956 85971 63502

JSG-OFDM scenario− 1 396513 286375 180572 136693 101237

JSG-OFDM scenario− 3 391206 282613 175934 132067 96326

3.6 Summary

In this chapter, a JSG-OFDM system has been proposed and analysed. Unlike any

previous single graph, the JSG-OFDM is based on a joint sparse graph which combines

NOMA (LDS-OFDM) and FEC coding (LDPC codes). The system framework of JSG-

OFDM is designed, and the joint detection and decoding, which applies MPA on the

joint sparse graph, is presented. JSG-OFDM is a novel system that jointly performs

detection and decoding on one entire sparse graph (Type-A receiver in Fig. 2.7). In

addition, the iterative structure of JSG-OFDM receiver is illustrated. Its convergence

behavior is analysed by EXIT charts and indicated by the trajectories over different


channels. Furthermore, degree distribution and short cycle of the joint sparse graph

are investigated using EXIT chart. It is shown that these two parameters affect the

performance of the joint detection and decoing significantly. According to the design

guidelines of the joint sparse graph, three scenarios of JSG-OFDM are presented, and

similar well-known multiple access systems are compared. The simulation results show

that the JSG-OFDM scenario−3 (degree distribution of Deg′d and girth of 8) achieves

the best performance. Its performance improvement is mainly due to the offline op-

timization of the joint sparse graph to exploit frequency domain diversity in addition

to avoiding strong interference to corrupt all the subcarriers. In general, by carefully

designing for specific applications, JSG-OFDM can improve the LDS based system’s

performance.

Chapter 4

Joint Sparse Graph for

FBMC-IOTA (JSG-IOTA)

System

As a promising NOMA, LDS has, however, never been applied to FBMC systems. These

motivate us to investigate overloaded FBMC systems by synergistically using techniques

of the joint sparse graph. In this chapter, we use a sparse graph to express the weight

matrix which is used to calculate the intrinsic interference in FBMC systems with IOTA

function based pulse. We further propose a joint sparse graph for the FBMC-IOTA

system, namely JSG-IOTA. The joint sparse graph combines single graphs of LDWM,

LDS and LDPC codes, which represent multi-carrier modulation, NOMA and FEC

coding techniques, respectively. By employing MPA, a joint detection and decoding

algorithm based on the joint sparse graph is presented. The iterative structure of

JSG-IOTA receiver is illustrated, and its EXIT chart is analysed. Furthermore, design

guidelines for the joint sparse graph are derived through the EXIT chart analysis.

Numerical results show the superiority of JSG-IOTA to similar systems such as OFDM,

IOTA, LDS-OFDM, LDS-IOTA and turbo structured LDS-IOTA.

71

72 Chapter 4. Joint Sparse Graph for FBMC-IOTA (JSG-IOTA) System

4.1 JSG-IOTA System Model

Consider an uplink MIMO communications with K users transmitting to the same base

station where each user and the base station are equipped with NT and NR antennas,

respectively. The JSG-IOTA system is schematically shown in Fig. 4.1 and Fig. 4.2.

Let the processing gain be N , and each user has a data vector consisting ofM symbols.

Denote J as the number of parity-check equations in the LDPC code. We assume that

perfect CSI is available at the receiver.

user 1

LDPC

encoder

symbol

mapper

LDS

spreader

Re{} IFFT

Im{} IFFT

filter

banks

filter

banks

G(n)

G(n-N/2)

j(n+2(u-1)+1)

j(n+2(u-1))

LDPC

encoder

symbol

mapper

LDS

spreader

Re{} IFFT

Im{} IFFT

filter

banks

filter

banks

G(n)

G(n-N/2)

j(n+2(u-1)+1)

j(n+2(u-1))

user K

LDPC

encoder

symbol

mapper

LDS

spreader

Re{} IFFT

Im{} IFFT

filter

banks

filter

banks

G(n)

G(n-N/2)

j(n+2(u-1)+1)

j(n+2(u-1))

LDPC

encoder

symbol

mapper

LDS

spreader

Re{} IFFT

Im{} IFFT

filter

banks

filter

banks

G(n)

G(n-N/2)

j(n+2(u-1)+1)

j(n+2(u-1))

Fig. 4.1: JSG-IOTA transmitter model

4.1. JSG-IOTA System Model 73

T

ime

Fre

qu

ency

u-2

u-1

u

u+

1

u+

2

n-2

0

0

0

0

0

n-1

0

0

0.2

486

0

0

n

0

-0.5

756

1

0.5

756

0

n+

1

0

0

-0.2

486

0

0

n+

2

0

0

0

0

0

R

eal

bra

nch

I

mag

inar

y b

ranch

(

b)

LD

WM

of

the

intr

insi

c in

terf

erence

of

JSG

-IO

TA

T

ime

Fre

qu

ency

u-2

u-1

u

u+

1

u+

2

n-2

0

0

0

0

0

n-1

0

0

0.2

486

0

0

n

0

0.5

756

0

-0.5

756

0

n+

1

0

0

-0.2

486

0

0

n+

2

0

0

0

0

0

intr

insi

c-in

terf

eren

ce n

od

es

FF

T

filt

er

ban

ks

FF

T

filt

er

ban

ks

G(-

n)

G(N

/2-n

)

j(n+

2(u

-1))

j-(n

+2(u

-1))

S/P

real

bra

nch

1st

eq

ual

izer

P/S

real

bra

nch

N

th e

qu

aliz

er

S/P

imag

bra

nch

1st

eq

ual

izer

imag

bra

nch

N

th e

qu

aliz

er

S/P

S/P

P/S

Re{

}

Intr

insi

c

inte

rfer

ence

Im{}

Intr

insi

c

inte

rfer

ence

par

ity-c

hec

k n

od

es

var

iab

le n

od

es

chip

no

des

LD

PC

LD

S

xv 1

,1

v 1,2

xv K

,1

v K,2

v 1,M

v K,M

use

r 1

use

r K

p1,J

p1,1

pK

,J

pK

,1

c 1

c 2

c N

JSG

i 1,1

i 1,2

i T,N

LD

WM

FF

T

filt

er

ban

ks

FF

T

filt

er

ban

ks

G(-

n)

G(N

/2-n

)

j(n+

2(u

-1))

j-(n

+2(u

-1))

(a)

Blo

ck d

iagra

m o

f th

e JS

G-I

OT

A r

ecei

ver

Fig.4.2:JSG-IOTA

receiver

model


At the transmitter shown in Fig. 4.1, a modulated data stream is initially generated in a

conventional manner, by multiplying the data symbols with a LDS signature (a random

sequence of chips) and subsequently applying the IOTA modulation to impose the chips

onto respective subcarrier frequencies. The IOTA modulators can be implemented by

separate IFFT blocks followed by a bank of filters for the I and Q components, which

are combined after polyphase filtering. An N/2 rotation of IFFT output is used to

shift the zero frequency subcarrier to middle position. Unlike conventional systems,

the LDS spreader is configured to guarantee that the ratio of dv,lds to N is small

enough (much less than 1), where dv,lds is the number of chips that are spread by one

symbol. Meanwhile, the number of symbols that are superimposed on each chip, dc,lds,

is much less than the total number of symbols. Consequently, each user will experience

interference from only a small number of other users data symbols.

The JSG-IOTA receiver shown in Fig. 4.2 (a) is implemented by filter banks followed

by the FFT block, where the FFT operations are conducted separately for the I and Q

branches. Due to the multiple transmit and receive antennas as well as multiple subcar-

riers, the equalization is performed on per-subcarrier basis, i.e., signals corresponding

to the same subcarrier at different antennas are jointly equalized. More explicitly, the

processing is arranged to perform serial-to-parallel conversion on the subcarrier’s data

received from the real and the imaginary branches of each antenna, and distribute the

subcarrier’s data to corresponding real and imaginary branch equalizers, according to

the subcarrier index. Subsequently, after parallel-to-serial conversion, the real part of

the signal from the I channel is combined with the imaginary part of the signal from the

Q channel, and further passed to the next processing stage. Usually, the residual signal

from the I and the Q channels is regarded as the intrinsic interference and discarded

in the following process. In fact, the intrinsic interference can be determined by mul-

tiplying neighboring signals with a weight matrix which can be determined using the

ambiguity function of the pulse shaping filter [141] [142]. We find that some elements of

the weight matrix are very small and can be safely ignored in order to reduce the com-

putational complexity, consequently a low density weight matrix is formed and shown

in Fig. 4.2 (b). Therefore, the sparse graphical block in Fig. 4.2 (a) can be configured

to include four types of nodes: intrinsic-interference nodes in,u(n ∈ [1, N ], u ∈ [0,Z]),

4.2. Joint Detection and Decoding 75

chip nodes cn(n ∈ [1, N ]), variable nodes vk,m(k ∈ [1,K],m ∈ [1,M ]) and parity-check

nodes pk,j(k ∈ [1,K], j ∈ [1, J ]), representing the intrinsic interference corresponding

to the symbol on the nth subcarrier during the time of index u, the nth chip, the mth

data symbol and the jth parity-check equation of the kth user, respectively. A single

graph, labeled with LDWM in the receiver, represents the low density weight matrix

due to intrinsic interference of IOTA. Another single graph, labeled with LDS in the

receiver, represents the low density signature due to LDS [64]. The other single sparse

graph, as labeled with LDPC in the receiver, represents the low density parity-check

matrix due to LDPC code [124]. These three types of single sparse graphs stem from

the processes of FBMC-IOTA modulation, NOMA and FEC coding, respectively. In

our proposed JSG-IOTA scheme, chip nodes are used to connect intrinsic-interference

nodes and variable nodes through low density edges, meanwhile, variable nodes are

connected to parity-check nodes by low density edges. As such, a joint sparse graph

is modeled and labeled with JSG in the figure, where LDWM, LDS and LDPC codes

are well linked together. In the joint sparse graph, users’ signals that use the same

chip will be superimposed, and the number of symbols that interfere with each other

at one chip is much less than the total number of symbols, thus the system can achieve

good performance in overloaded conditions. The joint sparse graph is arranged to pro-

cess the chips from the received signals to recover the transmitted data. Note that

applying MPA on the joint sparse graph performs not only detection and interference

utilization, but also decoding at the same time. Furthermore, the JSG-IOTA receiver

is different from the turbo structured receiver, as there is no outer-inner turbo style

iteration. Hence, the JSG-IOTA is based on a joint parse graph which combines IOTA

modulation, NOMA and sparse graph coding techniques. In the next section, joint

detection and decoding on such graph will be described.

4.2 Joint Detection and Decoding

According to the JSG-IOTA system model, we present joint detection and decoding on

the joint sparse graph using MPA.

The spreading signature and the parity-check matrix for the kth user are Sk = [sk,1, ..., sk,M ] ∈


CN×M and Hk = [hk,1, ...,hk,J ] ∈ BM×J , respectively. The weight matrix for the

nth chip is Wn = [wn,1, ...,wn,U ] ∈ CK×U . As for the multi-user scenario, let S =

[S1, ...,SK ] ∈ CN×MK , H = [H1, ...,HK ] ∈ BM×JK and W = [W1, ...,WN ] ∈ CK×UN

be the spreading signatures, the parity-check matrices of LDPC codes and the weight

matrices of intrinsic interferences, respectively. We also defineAu = diag(a1,u, ..., aK,u) ∈

CK×K as the transmit amplitude of users during the time of index u, and Ek,u =

diag(ek,1,u, ..., ek,N,u) ∈ CN×N as the corresponding channel gain for the kth user dur-

ing the time of index u, where ak,u and ek,n,u are both scalars. Moreover, ψn =

{(k,m) : snk,m ̸= 0} and εk,m = {n : snk,m ̸= 0} are the set of data symbols (which

may belong to different users) that interfere on chip cn and the set of chips that vk,m

is spread on, respectively; γk = {(n, u) : wkn,u ̸= 0} and ηn,u = {k : wkn,u ̸= 0} are

the set of intrinsic interferences that connect to chip ck and the set of chips that con-

nect to intrinsic-interference node in,u, respectively; ϕk,j = {(k,m) : hmk,j ̸= 0} and

ωk,m = {(k, j) : hmk,j ̸= 0} are the set of data symbols that connect to parity-check node

pk,j and the set of parity-check nodes that connect to vk,m, respectively.

Let Lcn→in,u be the log-likelihood ratio (LLR) delivered from the chip node cn to the

intrinsic-interference node in,u, Lin,u→cn be the LLR delivered from in,u to cn. Similarly,

Lvk,m→cn and Lvk,m→pk,j are the LLRs delivered from the variable node vk,m to the

chip node cn and the parity-check node pk,j , respectively. The LLRs delivered from

cn and pk,j to vk,m are given by Lcn→vk,m and Lpk,j→vk,m , respectively. Lvk,m is the

final estimation of vk,m. In JSG-IOTA, each user’s chip will be transmitted over an

orthogonal subcarrier. Let v′k,m,n,u = snk,mvk,m be the signal at nth chip generated by

the LDS spreader during the time of index u, the received spreading sequence for the

data symbol m of the kth user can be represented by rk,m,n,u = ak,uek,n,uv′k,m,n,u. The

received signal in a multi-carrier system (including CP-based OFDM and FBMC-IOTA)

can be written in a general form as

y(t) =K∑k=1

M∑m=1

N∑n=1

+∞∑u=−∞

rk,m,n,ugn,u(t) + z(t) (4.1)

where z(t) and gn,u(t) are the AWGN with variance σ2A and the synthesis basis which is

obtained by the time-frequency shifted version of the prototype function, respectively.


In the OFDM, the synthesis basis can be expressed as [22]

gn,u(t) =

exp(j2π(n− 1)Ft) uT0 − Tcp ≤ t ≤ uT0 + T

0 otherwise

(4.2)

where F = 1/T is subcarrier frequency spacing, Tcp is the length of CP and T0 = T+Tcp

is OFDM symbol duration.

In JSG-IOTA,

gn,u(t) = exp(j((n− 1) + u)π/2)exp(j2π(n− 1)v0t)g(t− uτ0) (4.3)

where g(t) is the well-localized IOTA pulse filter, and v0τ0 = 1/2. The transmitted

signals have symbol duration τ0 and subcarrier spacing v0. One can either set v0 = F ,

τ0 = T/2 or v0 = F/2, τ0 = T [19]. Here, we adopt the former approach, i.e., the

subcarrier spacing is kept the same as in OFDM, but symbol duration is reduced by

half. The received signal is [23] [143]

y(t) =

K∑k=1

M∑m=1

N∑n=1

+∞∑u=−∞

[rRk,m,n,ugn,2u(t) + rIk,m,n,ugn,2u+1(t)] + z(t)

=K∑k=1

M∑m=1

N∑n=1

+∞∑u=−∞

[rRk,m,n,ug(t− 2uτ0) + jrIk,m,n,ug(t− (2u+ 1)τ0)]

× exp(j((n− 1) + 2u)/2)exp(j2π(n− 1)v0t) + z(t)

(4.4)

The demodulated signal can be expressed as

v̂′R

k,m,n,u = Re

{∫y(t)g∗n,2u(t)dt

}(4.5)

v̂′I

k,m,n,u = Im

{∫y(t)g∗n,2u+1(t)dt

}(4.6)

By sampling y(t) at rate 1/Ts during time interval [uT − τ0, uT + τ0], the received

signal can be written as

y(uT + iTs) =

K∑k=1

M∑m=1

N∑n=1

+∞∑l=−∞

[rRk,m,n,lg(uT + iTs − lT ) + jrIk,m,n,lg(uT + iTs − lT − T/2)]

× exp(jπ((n− 1) + 2l)/2)exp(j2π(n− 1)i/N) + z

(4.7)


where i = −N/2, ..., N/2 − 1. Denoting yi[u] = y[uN + i] = y(uT + iTs), the above

equation can be reformed as

yi[u] =∑q

g(qT + iTs)

{N∑n=1

rRk,m,n,u−qexp[jπ((n− 1) + 2u− 2q)/2]exp[j2π(n− 1)i/N ]

}

+∑q

g(qT + iTs −T

2)

{N∑n=1

jrIk,m,n,u−qexp[jπ((n− 1) + 2u− 2q)/2]exp[j2π(n− 1)i/N ]

}

+ z

=∑q

{gi[q]D

iN (r

Rk,m,n,u−q) + gi−N/2[q]D

iN (jr

Ik,m,n,u−q)

}+ z

= gi[u]⊗DiN (r

Rk,m,n,u) + gi−N/2[u]⊗Di

N (jrIk,m,n,u) + z

(4.8)

where ⊗ denotes the convolution operation, and

DiN (xk,m,n,u) =

N∑n=1

xk,m,n,uexp(jπ((n− 1) + 2u)/2)exp(j2π(n− 1)i/N) (4.9)

gi[u] = g[uN + i] = g(uT + iTs) (4.10)

The phase correction (j((n−1)+2u) for the I channel and j((n−1)+2u+1) for the Q channel)

before the IFFT operation is due to the first exponential term in (4.9). An N/2 rotation

of IFFT output is needed here to shift the zero frequency subcarrier to middle position.

At the receiver, by sampling the received signal at rate 1/Ts, (4.5) can be reformed as

v̂′R

k,m,n,u = Re

TsN/2−1∑i=−N/2

+∞∑l=−∞

y(lT + iTs)g∗n,2u(lT + iTs)

= Re

Tsexp[−jπ((n− 1) + 2u)/2]

N/2−1∑i=−N/2

+∞∑l=∞

yi[l]gi[l − u]exp[−j2π(n− 1)i/N ]

= Re

Tsexp[−jπ((n− 1) + 2u)/2]

N/2−1∑i=−N/2

yi[u]⊗ gi[−u]exp[−j2π(n− 1)i/N ]

= Re

Tsj((n−1)+2u)

N/2−1∑i=−N/2

yi[u]⊗ gi[−u]exp[−j2π(n− 1)(i+N/2)/N ]

(4.11)

where

gi[−u] = g[−uN + i] = g(−NT + iTs) (4.12)


By repeating the above process on the imaginary branch of (4.6),

v̂′I

k,m,n,u = Im

{Tsj

−((n−1)+2u)N∑i=1

yi−1[u]⊗ gi−1−N/2[−u]exp[−j2π(n− 1)(i− 1)/N ]

}(4.13)

Owing to the real-orthogonality condition on g(t), i.e., Re{gn,u(t)g

∗n0,u0(t)

}= δn,n0δu,u0 ,

(4.5) and (4.6) can be written as

v̂′k,m,n,u =

∫y(t)g∗n,u(t)dt

= ak,uek,n,uv′k,m,n,u +

∑(n′,u′ )̸=(n,u)

ak,u′ek,n′,u′v′k,m,n′,u′

∫gn′,u′(t)g

∗n,u(t)dt︸︷︷︸

in,u

+ zn,u

(4.14)

Since the prototype function g(t) is chosen to be well localized both in time and fre-

quency, the intrinsic interference in,u in (4.14) only depends on a restricted set of

time-frequency positions (n′, u′) around the signal of interest. Assuming that the chan-

nel remains relatively constant at those positions, the intrinsic interference in,u can be

approximated as

in,u = ak,uek,n,u∑

(n′,u′) ̸=(n,u)

v′k,m,n′,u′

∫gn′,u′(t)g

∗n,u(t)dt︸︷︷︸

jv′(i)k,m,n,u

= ak,uek,n,ujv′(i)k,m,n,u

(4.15)

Combining (4.14) and (4.15) yields

v̂′k,m,n,u = ak,uek,n,u[v′k,m,n,u + jv′

(i)k,m,n,u] + zn,u (4.16)

In Fig. 4.2 (a), the input to the real and the imaginary branch equalizers at the

JSG-IOTA receiver can be expressed as

yRk,m,n,u = ak,uek,n,u[v′Rk,m,n,u + jv′

(i)k,m,n,u] + zRn,u (4.17)

yIk,m,n,u = ak,uek,n,u[v′(r)k,m,n,u + jv′

Ik,m,n,u] + zIn,u (4.18)

where v′(i)k,m,n,u and v′

(r)k,m,n,u are the intrinsic interference for the real and imaginary

FFT chains, respectively. Given the knowledge of the channel state, the transmitted


signal can be recovered by zero forcing (ZF) equalization, that is

v̂′k,m,n,u = Re{yRk,m,n,u/ak,uek,n,u

}+ jIm

{yIk,m,n,u/ak,uek,n,u

}+ (zRn,u/ak,uek,n,u) + (zIn,u/ak,uek,n,u)

= v′Rk,m,n,u + jv′

Ik,m,n,u + z′n,u

(4.19)

where z′n,u denote the combined noise term. An MMSE equalization can be designed

similarly.

For the joint sparse graph, there are two sets of soft information coming from the in-

trinsic interference: the first one is combined by the Q component of the output of the

real branch equalizer and I component of the output of the imaginary branch equal-

izer, i.e., v′(r)k,m,n,u + jv′

(i)k,m,n,u, while the second one is calculated based on neighboring

time-frequency positions around the signal of interest. If the difference between these

two values is small enough, we reach a decision that its correlated information is highly

reliable, and set Pr(v̂′k,m,n,u = v′k,m,n,u) = 1. Otherwise the soft information needs to

be updated. The weight matrix of the intrinsic interference is represented by a sparse

graph to propagate the information, and each message will be calculated iteratively

from the previous values of the neighbouring nodes. In the joint detection and decod-

ing, intrinsic-interference nodes and variable nodes update at the same time. For the

intrinsic-interference nodes in error,

Lin,u→cn = log

∑cn=1

exp(∑

n′∈ηn,u\n

cn′2 Lcn′→in,u − 1

2σ2A∥ v′(r)k,m,n,u + jv′

(i)k,m,n,u − in,u ∥2)

∑cn=0

exp(∑

n′∈ηn,u\n

cn′2 Lcn′→in,u − 1

2σ2A∥ v′(r)k,m,n,u + jv′

(i)k,m,n,u − in,u ∥2)

(4.20)

In the joint sparse graph, the updating of Lvk,m→cn not only receives chip nodes infor-

mation, but also utilizes the information that comes from parity-check nodes.

Lvk,m→cn =∑

n′∈εk,m\n

Lcn′→vk,m +∑

j∈ωk,m

Lpk,j→vk,m (4.21)

where εk,m \n is the set of chips (excluding cn) that vk,m is spread on. When executing

the MPA for joint detection and decoding, the more types of nodes that are connected

to a variable node, the more reliable information that can be utilized when processing

that variable node.


Similarly, Lvk,m→pk,j also involves message from both sides

Lvk,m→pk,j =∑

j′∈ωk,m\j

Lpk,j′→vk,m +∑

n∈εk,m

Lcn→vk,m (4.22)

where ωk,m \ j is the set of parity-check nodes (excluding pk,j) that connect to the

variable node vk,m.

In terms of chip nodes and parity-check nodes, their extrinsic messages are calculated

at the same time. In the single graph, chip nodes only utilize information from variable

nodes [64]. However, in the joint sparse graph, chip nodes gather information from

both intrinsic-interference nodes and variable nodes,

Lcn→in,u =∑

(n′,u′)∈γn\(n,u)

Lin′,u′→cn +∑

(k,m)∈ψn

Lvk,m→cn (4.23)

For the updating of Lcn→vk,m ,

Lcn→vk,m = f(vk,m|v̂′k,m,n,u, Lin,u→cn , Lvk′,m′→cn , (k′,m′) ∈ ψn \ (k,m)) (4.24)

where ψn \ (k,m) is the set of data symbols (excluding vk,m) that interfere on the chip

cn. To approximate the maximum a posteriori (MAP) probability detector, the right

hand side of (4.24) represents marginalization function and can be written as

f(vk,m|v̂′k,m,n,u, Lin,u→cn , Lvk′,m′→cn , (k′,m′) ∈ ψn \ (k,m))

= log(N∑n=1

p(v̂′k,m,n,u|v)pn(v|vk,m))

= log(

N∑n=1

p(v̂′k,m,n,u|v)∏

(k′,m′)∈ψn\(k,m)

pn(vk′,m′))

(4.25)

where v is the transmitted vector, p(v̂′k,m,n,u|v) and pn(vk′,m′) are given as

p(v̂′k,m,n,u|v) =1√2πσA

exp(− 1

2σ2A∥ v̂′k,m,n,u − rT[n]v[n] ∥2) (4.26)

pn(vk′,m′) = exp(Lvk′,m′→cn) (4.27)

where v[n] and r[n] denote the vector containing the symbols transmitted by every

user that spread its data on the nth chip and their corresponding received signature,


respectively. Substituting (4.26) and (4.27) into (4.25), the formula becomes

Lcn→vk,m =

κn,k,mmaxv[n]

∗(∑(n,u)

Lin,u→cn +∑

(k′,m′)∈ψn\(k,m)

Lvk′,m′→cn − 1

2σ2A∥ v̂′k,m,n,u − rT[n]v[n] ∥2)

(4.28)

where κn,k,m denotes the normalization coefficient and

max∗(a, b) , log(ea + eb) (4.29)

The LLR of the parity-check nodes is updated as

Lpk,j→vk,m = α−1(∑

(k′,m′)∈ϕk,j\(k,m)

α(Lvk′,m′→pk,j )) (4.30)

where ϕk,j \ (k,m) is the set of data symbols (excluding vk,m) that connect to the

parity-check node pk,j , and

α(x) = sign(x)× (− log tan(| x | /2)) (4.31)

where sign(x) represents the sign of x, and the inverse of α(x) is

α−1(x) = (−1)sign(x) × (− log tan| x |2

) (4.32)

In the joint sparse graph, parity-check nodes are available, thus it is possible to termi-

nate the iteration by syndrome computing. A posteriori probability of the transmitted

symbo vk,m is calculated as

Lvk,m =∑

n∈εk,m

Lcn→vk,m +∑

j∈ωk,m

Lpk,j→vk,m (4.33)

The estimated value of the variable node vk,m is obtained by making a hard decision, i.e.,

v̂k,m = argmaxvk,m

Lvk,m . If the result of syndrome computing for each user equals to zero,

or the maximum iteration number is reached, the process is terminated. Otherwise,

the iteration goes on.

In the next section, we carry out theoretical analysis of the joint sparse graph using

the EXIT chart.

4.3. EXIT Chart Analysis of JSG-IOTA 83

4.3 EXIT Chart Analysis of JSG-IOTA

EXIT chart is used to construct good iteratively-decoded FEC codes. In this section,

we shall illustrate how EXIT charts can be utilized to analyse the convergence behavior

of joint detection and decoding in JSG-IOTA.

4.3.1 Iterative Structure of the Joint Sparse Graph

First, we explain the iterative structure of the joint sparse graph. According to the

algorithm presented in Section 4.2, the updating of chip nodes is based on a priori in-

formation coming from connected intrinsic-interference nodes and variable nodes. The

same rule applies to the updating of variable nodes, where a priori information coming

from chip nodes and parity-check nodes is utilized. As for intrinsic-interference nodes

and parity-check nodes, their extrinsic messages are updated only based on one side

of a priori information, i.e., connected chip nodes and variable nodes, respectively.

For convenience, the sets of intrinsic-interference nodes, chip nodes, variable nodes and

parity-check nodes are hereinafter referred to as intrinsic-interference nodes decoder

(IND), chip nodes detector-decoder (CNDD), variable node detector-decoder (VND-

D) and parity-check node decoder (PND), respectively. Fig. 4.3 shows the iterative

structure of the joint sparse graph, where the extrinsic LLR is considered as a priori

information by the other detector or decoder. The edge interleavers connect different

types of nodes, each of which represents a sparse signature or matrix. Note that such

an iterative structure is more complicated than any previous single sparse graph which

only has the middle part labeled as LDS [64] or the right part labeled as LDPC [126]

in this figure. Moreover, the iterative part of LDWM has never been proposed before.

Chip Node

Detector & Decoder 1

ld s

ld s

Parity Check Node

Decoder 1

ld p c

ld p c

To receiver

Variable Node

Detector & Decoder

From IOTA demodulator

-

-

-

-

LDS LDPC

Intrinsic Interference Node

Decoder 1

ldw m

ldw m

-

-

LDWM

Fig. 4.3: Iterative structure of the joint sparse graph


To explain the JSG-IOTA receiver more clearly, we present a tree structure of the joint

sparse graph in Fig. 4.4. As the channel and IOTA demodulated information is fed

into chip node directly, the tree structure is rooted at chip node cn where we name it

level 0 of the tree. According to Fig. 4.2 and Fig. 4.3, each chip node is linked to some

intrinsic-interference nodes and variable nodes via low density edges, we respectively

use long dash lines and bold lines to distinguish these two connections in Fig. 4.4.

Hence, at level 1 of the tree, there are two types of nodes, i.e., intrinsic-interference

nodes (pentagons) and variable nodes (circles), which are connected to cn at level 0 by

different lines. For the intrinsic-interference nodes at level 1, each of them is linked to

other chip nodes (rectangles) at level 2 via long dash lines. For the variable nodes at

level 1, each of them is not only linked to some chip nodes at level 2 via bold lines, but

also connected to some parity-check nodes (triangles) at level 2 via other type of lines,

i.e., short dash lines. Similarly, the chip nodes and the parity-check nodes at level 2 can

generate more intrinsic-interference nodes and variable nodes via corresponding types

of lines, which are drawn at level 3. Note that at level 3, the intrinsic-interference nodes

have only one type of connection to chip nodes at level 2, while the variable nodes have

two types of connection to chip nodes and parity-check nodes at level 2. Obviously,

such a tree structure is novel as it has four types of nodes and three types of edges.

Note that different levels of the tree have specific types of nodes, i.e., the odd level

(level 1 or 3) consists of intrinsic-interference nodes and variable nodes, while the even

level (level 2) consists of chip nodes and parity-check nodes. Chip nodes and variable

nodes are important due to their bridge function on the tree, and messages of different

nodes can be passed to any other types of nodes via the edges.

Additionally, Fig. 4.5 shows a folded view of the joint sparse graph. Based on the joint

detection and decoding presented in Section 4.2 and the tree structure shown in Fig.

4.4, chip nodes and parity-check nodes update their messages at the same time, then

intrinsic interference-nodes and variable nodes calculate their message simultaneously.

Therefore, it is reasonable to place even level nodes, i.e., chip nodes (rectangles) and

parity-check nodes (triangles), on one side, while to draw odd level nodes, i.e., intrinsic-

interference nodes (pentagons) and variable nodes (circles), on the other side. For chip

nodes, they are connected to intrinsic-interference nodes through low density edges


cn

x x

x x x x x x x xlevel 3

level 2

level 1

level 0

Fig. 4.4: Tree structure of the joint sparse graph

p1, J

p1, 1

c1

c2

cN

xv1, 1

v1, 2

xvK, 1

vK, 2

v1, M

vK, M

chip nodes

of user 1

of user K

PK, J

PK, 1

of user 1

variable nodes

of user K

v

parity check nodes

parity check nodes

variable nodes

i1,1

i1,2

iN,T

intrinsic interference nodes

Fig. 4.5: Folded view of the joint sparse graph


(represented by long dash lines), and they are also used to be spread on for variable

nodes through sparse edges (represented by bold lines). Since variable nodes belong

to different users, they are not only linked to chip nodes through low density edges,

but also linked to corresponding groups of parity-check nodes through sparse edges

(represented by independent groups of short dash lines). IOTA modulation, NOMA,

FEC coding and the combination of these single sparse graphs, are clearly depicted in

the figure. This provides a basis for the following analysis.

4.3.2 EXIT Chart Analysis

4.3.2.1 EXIT Curve for IND&VNDD

In this thesis, IA,IND&V NDD refers to the average mutual information between the

bits on the IND&VNDD edges and the a priori LLR, IE,IND&V NDD is the average

mutual information between the bits on the IND&VNDD edges and the extrinsic LLR.

In order to compute an EXIT curve for intrinsic nodes and variable nodes, Lcn→in,u ,

Lcn→vk,m and Lpk,j→vk,m are modelled as Gaussian-like distributions. Then the mutual

information between the variable node’s extrinsic messages and actual values of symbols

on the edges is calculated. A priori LLR can be calculated by

A = µAx+ zn (4.34)

where zn is an independent Gaussian random variable with variance σ2A and mean

zero; x is the original bits on the graph edge; µA = σ2A/2. The mutual information

IA,IND&V NDD = I(X;A) can be calculated by

IA,IND&V NDD =1

2

∑x=−1,1

∫ +∞

−∞pA(β|X = x) log2

2pA(β|X = x)

pA(β|X = −1) + pA(β|X = 1)dβ

(4.35)

Since the conditional probability density function pA(β|X = x) depends on LLR of A,

we can write

IA,IND&V NDD(σA) =1−∫ +∞

−∞

exp(−((β − σ2A/2)2/2σ2A))√

2πσAlog2(1 + e−β)dβ (4.36)


For abbreviation we define

B(σ) , IA,IND&V NDD(σA = σ) (4.37)

with

limσ→0

B(σ) = 0 (4.38)

limσ→∞

B(σ) = 1 (4.39)

where σ ≥ 0. Considering (4.20), (4.21) and (4.22) together with the fact that the sum

of several normally distributed random variables is also normally distributed with the

mean and variance equal to the sum of theirs, the EXIT function of IND&VNDD can

be expressed as

IE,IND&V NDD(IA,IND&V NDD, di,ldwm, dv,lds, dv,ldpc)

= B(√

(di,ldwm + dv,lds + dv,ldpc − 1)(B−1(IA,IND&V NDD))2)(4.40)

where di,ldwm is the degree of intrinsic-interference node in the sparse graph of LDWM,

dv,lds and dv,ldpc are the degrees of variable node in sparse graphs of LDS and LDPC

codes, respectively. Unlike the single sparse graph where only one type of node is

considered [64] [126], both LDWM, LDS and LDPC nodes affect the IND&VNDD

performance.

4.3.2.2 EXIT Curve for CNDD&PND

Let IA,CNDD&PND refers to the average mutual information between the bits on the

CNDD&PND edges and the a priori LLR, IE,CNDD&PND is the average mutual in-

formation between the bits on the CNDD&PND edges and the extrinsic LLR. A chip

node has incoming messages from the connected intrinsic-interference nodes and vari-

able nodes in addition to the FBMC-IOTA demodulator, whereas a parity-check node

only has messages coming from neighbored variable nodes. The output LLR of chip

nodes and parity-check nodes are calculated by (4.23), (4.28) and (4.30). We model

Lin,u→cn , Lvk,m→cn and Lvk,m→pk,j as the output of multipath fading channels, and then

calculate the mutual information of the output with regards to the actual value on the

edges. Considering the complexity of the calculation in chip nodes and parity-check

nodes, their EXIT curves are computed by simulations over multipath fading channels.


4.3.2.3 Analysis

System parameters are listed in TABLE 4.1 for the following EXIT chart analysis. Fig.

4.6 illustrates the EXIT charts over SUI-3 channel at Eb/N0 = 12 dB, and it can be

concluded:

TABLE 4.1: System parameters

Number of users 4

Number of chip nodes 64

Number of variable nodes 128

Number of intrinsic-interference nodes 128

Number of parity-check nodes 64

FFT size 64

Multiuser SIMO 1× 4

System loading 200%

Chips linked to each variable node dv,lds = 2

Variable nodes linked to each chip dc,lds = 4

Chips linked to each intrinsic-interference node di,ldwm = 4

Intrinsic-interference nodes linked to each chip dc,ldwm = 4

Parity-check nodes linked to each variable node dv,ldpc = 3

Variable nodes linked to each parity-check node dp,ldpc = 6

Modulation OQPSK

1) The curve of VND in LDS-IOTA is higher than that of IND&VNDD in JSG-IOTA.

This is because the edge number connecting to VND in LDS-IOTA is different from

that connecting to IND&VNDD in JSG-IOTA. As a result, according to (4.40), these

two curves are different.

2) The curve of CND in LDS-IOTA is higher than that of CNDD&PND in JSG-IOTA

when IA,CNDD&PND ≤ 0.97. This follows from the fact that the CNDD could receive

information from the IOTA demodulator and neighbored variable nodes as well as

intrinsic-interference nodes, but the PND only uses the information from the connected

variable nodes (shown in Fig. 4.3). Hence, the PND pulls down the average extrinsic

information of CNDD&PND at the first few iterations.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CNDD&PND

& IE,IND&VNDD

I E,C

ND

D&

PN

D &

IA

,IN

D&

VN

DD

VND in LDS−IOTACND in LDS−IOTAtrajectory in LDS−IOTAIND&VNDD in JSG−IOTACNDD&PND in JSG−IOTAtrajectory in JSG−IOTA

Fig. 4.6: EXIT chart at Eb/N0 = 12 dB

3) The intersection point of IND&VNDD and CNDD&PND in JSG-IOTA, is higher

than that of VND and CND in LDS-IOTA. This phenomenon implies that the JSG-

IOTA is more capable of eliminating the MUI than LDS-IOTA.

4) The detection and decoding trajectories in LDS-IOTA and JSG-IOTA are plotted in

Fig. 4.6, and are marked by blue solid lines and red dotted lines, respectively. For each

trajectory, we can see that the iterative process starts with IA,CNDD&PND = 0 since

no prior information is available to the CND or CNDD&PND in the beginning. In the

following steps, the output LLR is exchanged between the two corresponding curves.

The trajectories closely follow the transfer curves of the components in LDS-IOTA and

JSG-IOTA, which indicates that the EXIT charts analysis is valid for the joint sparse

graph.

5) For LDS-IOTA, the trajectory shows that at least seven iterations are necessary to

reach the intersection point. Whereas for JSG-IOTA, the trajectory indicates that only

five iterations are needed to reach the intersection point. This is attributed to the more

efficient message passing and the more reliable information utilized by chip nodes and


variable nodes in JSG-IOTA than that in LDS-IOTA. Therefore, the JSG-IOTA can

reach its intersection point faster than the LDS-IOTA.

4.4 EXIT Chart Assisted Joint Sparse Graph Design

In this section, we discuss how to use EXIT charts to optimize the joint sparse graph.

4.4.1 Degree Distribution

let DIND(x), DCNDD(x), DV NDD(x), and DPND(x) denote the degree distribution

polynomials of intrinsic-interference nodes, chip nodes, variable nodes and parity-check

nodes, respectively. They are defined as

DIND(x) =

di,ldwm∑d=1

PIND(d)xd−1 (4.41)

DCNDD(x) =

dc,ldwm+dc,lds∑d=1

PCNDD(d)xd−1 (4.42)

DV NDD(x) =

dv,lds+dv,ldpc∑d=1

PV NDD(d)xd−1 (4.43)

DPND(x) =

dp,ldpc∑d=1

PPND(d)xd−1 (4.44)

where PIND(d), PCNDD(d), PVNDD(d) and PPND(d) are the fractions of all edges con-

nected to corresponding nodes. According to Fig. 4.2 (b), each intrinsic-interference

node is determined by four neighboring time-frequency positions around the signal of

interest, hence we fix di,ldwm = 4. However, other degree distributions can be optimized

by EXIT chart analysis.

The joint sparse graph in TABLE 4.1 is a regular graph without any optimization.

Although its intersection point is higher than that of LDS-IOTA, which is shown in

Fig. 4.6, the average level of CNDD&PND in JSG-IOTA is much lower than that of

CND in LDS-IOTA. Similar to JSG-OFMD, our approach here is based on invoking

EXIT chart analysis for optimizing the shape of the EXIT curve in order to achieve

4.4. EXIT Chart Assisted Joint Sparse Graph Design 91

the (1, 1) convergence point. According to Section 4.3, the information coming from

the IOTA demodulator serves as input source of the joint sparse graph, and it is fed

into chip nodes in each iteration of the joint detection and decoding as well as intrinsic

interference utilization. As mentioned previously, the mutual information determines

the dependence between detected symbols and their exact values, thus the EXIT curve

level has to be considered. If the density of the edges in PND is reduced, the EXIT curve

of CNDD&PND should be lifted up and a higher intersection point can be achieved.

Therefore, several schemes of degree distribution are developed in TABLE 4.2, where

Dega is the case of a regular joint sparse graph presented in TABLE 4.1, other schemes

are developed for irregular joint sparse graphs. We can see that compared to Dega,

Degc and Degd slightly decrease the degree of PND, then the polynomials of VNDD

and CNDD are altered accordingly. On the contrary, Degb increases the density of

edges of PND.

TABLE 4.2: Degree distribution

Scheme DIND(x) DCNDD(x) DVNDD(x) DPND(x)

Dega x3 x7 x4 x5

Degb x3 0.1x6 + 0.8x7 + 0.1x8 0.575x4 + 0.425x5 0.15x5 + 0.85x6

Degc x3 0.075x6 + 0.85x7 + 0.075x8 0.315x3 + 0.685x4 0.63x4 + 0.37x5

Degd x3 0.045x6 + 0.91x7 + 0.045x8 0.375x3 + 0.625x4 0.75x4 + 0.25x5

Fig. 4.7 shows EXIT charts for different degree distribution over SUI-3 channel at

Eb/N0 = 12 dB. In TABLE 4.2, Degc and Degd slightly decrease the weight of the

PND, consequently in Fig. 4.7, the average mutual information between the bits and

the extrinsic values of CNDD&PND are both increased. More importantly, their in-

tersection points become higher, which means better performance can be achieved. By

contrast, Degb increases the density of edges of PND, but its average mutual informa-

tion and intersection point are both dropped. Therefore, a lower density of PND in

general results in a scheme that is more robust to interference on the joint sparse graph.

It is noteworthy that although the PND weight of Degd is less than that of Degc, but

the intersection point of Degd is lower than that of Degc, indicating Degc outperforms


Degd. This is related to the function of PND, i.e., performing parity-check for error cor-

rection. As explained above, it is necessary to design the degree distributions carefully

and strike a balance between the optimization processing of the joint sparse graph and

the original function of the parity-check node. This ensures efficient operations of belief

propagation executed at the receiver of JSG-IOTA. For the joint sparse graph, Degc is

a preferable choice since it has the highest intersection point among these schemes.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CNDD&PND

& IE,IND&VNDD

I E,C

ND

D&

PN

D &

IA

,IN

D&

VN

DD

IND&VNDD of Dega

CNDD&PND of Dega

IND&VNDD of Degb

CNDD&PND of Degb

IND&VNDD of Degc

CNDD&PND of Degc

IND&VNDD of Degd

CNDD&PND of Degd

Fig. 4.7: EXIT chart for different degree distributions

4.4.2 Short Cycle

Fig. 4.8 shows EXIT charts for different girths of the joint sparse graph over SUI-3

channel at Eb/N0 = 12 dB. We choose the optimal Degc to be the degree distribution.

When the girth equals to 8, some degrees need to be modified marginally (labelled by

Deg′c): DIND(x) is x3, DCNDD(x) is 0.07x

6 + 0.86x7 + 0.07x8, DV NDD(x) is 0.31x3 +

0.69x4 and DPND(x) is 0.62x4 +0.38x5. It can be seen from this figure that similar to

JSG-OFDM, the curves of matrices with girth of 4 and 6 are very close to each other,

whereas matrix with girth of 8 outperforms others. Therefore, degree distribution and

short cycle both affect the system performance.

4.4. EXIT Chart Assisted Joint Sparse Graph Design 93

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,CNDD&PND

& IE,IND&VNDD

I E,C

ND

D&

PN

D &

IA

,IN

D&

VN

DD

IND&VNDDCNDD&PND, girth = 4, Deg

c

CNDD&PND, girth = 6, Degc

CNDD&PND, girth = 8, Deg’c

Fig. 4.8: EXIT chart for different schemes

4.4.3 Maximum Achievable Throughput

TABLE 4.3: JSG-IOTA scenarios

Scenario Degree distribution Girth

scenario− 1 Dega 6

scenario− 2 Degb 4

scenario− 3 Deg′c 8

To reveal the theoretical threshold of the joint sparse graph, we analyse its maximum

achievable throughput by EXIT charts. Similar to JSG-OFDM, assuming that the area

under the EXIT curve of the CNDD&PND is represented by A, then the maximum

achievable throughput at a particular Eb/N0 value is given by A(Eb/N0). For com-

parisons, three scenarios of the JSG-IOTA that have different degree distributions and

girths are given in TABLE 4.3, and their maximum throughputs of the joint sparse

graph are quantified in Fig. 4.9, where the SNR represent Es/N0. It can be seen

that, as expected, JSG-IOTA scenario− 3 owns the highest capacity in the scenarios.


Compared to the maximum achievable throughput of scenario−3, there are respective

degradations for that of scenario− 1 and scenario− 2. Thus scenario− 3 is the best

option for JSG-IOTA, which will be further verified by performance simulations.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

SNR (dB)

Cap

acity

(bi

ts/s

ymbo

l)

JSG−IOTAscenario−1JSG−IOTAscenario−2JSG−IOTAscenario−3

Fig. 4.9: Maximum effective throughput of the joint sparse graph

4.5 Performance Evaluation

In this section, JSG-IOTA is evaluated and compared with systems such as OFDM,

IOTA, LDS-OFDM, LDS-IOTA and turbo structured LDS-IOTA, where OFDM and

IOTA represent conventional systems without LDS structure. The performance is eval-

uated using Monte Carlo simulations over SUI-3 channel, and the simulation parameters

are listed in TABLE 4.1. For fair comparisons, a half rate quasi-cyclic LDPC code is

adopted by all the systems [125]. For OFDM-based systems (including OFDM and

LDS-OFDM), we use QPSK modulation. For IOTA-based systems (including IOTA,

LDS-IOTA, turbo structured LDS-IOTA and JSG-IOTA), we use offset quadrature

phase-shift keying (OQPSK) modulation, and the number of filter taps for each sub-

carrier is 5. For LDS-based systems (including LDS-OFDM and LDS-IOTA), the LDS


is optimized by EXIT charts, and iterative detectors are used [68]. For turbo struc-

tured LDS-IOTA, there are eight outer-inner turbo iteration between the detector and

the decoder, and the turbo structure is optimized by EXIT charts [17]. The maximum

iterations are limited to eight for LDS-OFDM, LDS-IOTA and JSG-IOTA.

4.5.1 BER Comparison

Fig. 4.10 shows BER results for systems with a load of 200%. As we can see that, LDS-

OFDM and LDS-IOTA significantly outperform OFDM and IOTA, respectively. This

is due to the LDS structure which can effectively eliminate the MUI and exploit the

frequency diversity under overloaded conditions. Meanwhile, IOTA and LDS-IOTA

respectively yield slight gain over OFDM and LDS-OFDM. Hence, compared with

OFDM systems, IOTA-based systems achieve improved power efficiency (better BER

performance) and spectral efficiency due to the elimination of CP. Among all the IOTA-

based systems, the performance of LDS-IOTA is inferior to that of turbo structured

LDS-IOTA and JSG-IOTA. Moreover, each of the three JSG-IOTA scenarios achieves

superior performance over other systems. With the degree distribution (Deg′c) and the

cycle structure (girth of 8), JSG-IOTA scenario− 3 achieves the best performance. Its

performance improvements at BER of 10−6 are: 0.3 dB over JSG-IOTA scenario− 1,

0.7 dB over JSG-IOTA scenario− 2, 1.3 dB over turbo structured LDS-IOTA, 1.5 dB

over LDS-IOTA, and 1.9 dB over LDS-OFDM, respectively. Furthermore, to investigate

how the IOTA intrinsic interference utilization affects the system performance, we also

simulate the JSG-IOTA scenario − 3 excluding the low density weight matrix of the

intrinsic interference, which is referred to as JSG-IOTA scenario−3 without LDWM in

the figure. It can be seen that, compared with JSG-IOTA scenario− 3, there is a loss

of about 0.5 dB when JSG-IOTA scenario− 3 without LDWM is adopted. Therefore,

the intrinsic interference utilization of the joint sparse graph can profit extra gain to

the system.

In addition, the performance of 300% loaded systems is simulated and shown in Fig.

4.11. Similarly to the 200% loading case, JSG-IOTA scenario−3 still achieves the best

performance. Compared with LDS-OFDM, LDS-IOTA and turbo structured LDS-


6 8 10 12 14 16 18 20

10−6

10−5

10−4

Eb/N

0(dB)

BE

R

OFDMIOTALDS−OFDMLDS−IOTATurbo structured LDS−IOTAJSG−IOTAscenario−1JSG−IOTAscenario−2JSG−IOTAscenario−3JSG−IOTAscenario−3 without LDWM

Fig. 4.10: Performance of different systems with 200% loading

6 8 10 12 14 16 18 2010

−6

10−5

10−4

Eb/N

0(dB)

BE

R

OFDMIOTALDS−OFDMLDS−IOTATurbo structured LDS−IOTAJSG−IOTAscenario−1JSG−IOTAscenario−2JSG−IOTAscenario−3JSG−IOTAscenario−3 without LDWM

Fig. 4.11: Performance of different systems with 300% loading


IOTA, JSG-IOTA scenario− 3 attains approximately 1.3 - 1.9 dB gain in the medium

to high SNR region.

4.5.2 Convergence Behavior

The convergence behavior of 200% loaded LDS-IOTA and JSG-IOTA scenario− 1 at

Eb/N0 = 12 dB is shown in Fig. 4.12, indicating the performance of the two systems

at different iterations. At the first iteration, the performance of LDS-IOTA is almost

identical to that of JSG-IOTA. However, as the iterative process proceeds, BER of JSG-

IOTA drops much faster than that of LDS-IOTA, indicating a better convergence rate

can be achieved by employing the joint sparse graph. After 5 iterations, the performance

of JSG-IOTA becomes saturated, whereas LDS-IOTA needs 7 iterations to reach its

lowest BER. Such results concur with the trajectory prediction of the EXIT chart

plotted in Fig. 4.6. Therefore, the EXIT chart analysis and the convergence behavior

are verified by the BER simulation results.

1 2 3 4 5 6 7 810

−6

10−5

10−4

10−3

10−2

10−1

100

Number of iterations

BE

R

LDS−IOTAJSG−IOTA

Fig. 4.12: Performance on different iterations at Eb/N0 = 12 dB


4.5.3 Performance of Different Users

In Fig. 4.13, we show the performance of the best user and the worst user in LDS-IOTA

and JSG-IOTA scenario− 3 for the system loading of 200%. It indicates that for both

two schemes, some users have poorer performance than the others, and in the low SNR

region the performance degradation is not as obvious as in the high SNR region. This

phenomenon can be explained by observing the signal constellation at each chip and

the dominating effect of noise at SNRs. Therefore, it can be seen that the joint sparse

graph does not give equal multiuser efficiency or in other words it does not result in the

same performance for all the users. But the performance gap between the best user and

the worst user in JSG-IOTA is slightly smaller than that of LDS-IOTA, which means a

fairer and a more uniform user experience can be achieved by utilizing the joint sparse

graph.

6 8 10 12 14 16 18 20

10−6

10−5

10−4

Eb/N

0(dB)

BE

R

Worst user in LDS−IOTABest user in LDS−IOTAOverall in LDS−IOTAWorst user in JSG−IOTABest user in JSG−IOTAOverall in JSG−IOTA

Fig. 4.13: Performance of different users


4.5.4 Dynamic Subcarrier Allocation

In JSG-IOTA system, the generated chips at the output of the LDS spreader are

mapped to the subcarriers of the employed IOTA signal. In the simulations we have

carried out so far, we assume that a static subcarrier allocation is employed, i.e., at

transmitters, individual subcarriers are allocated to users for transmission without the

knowledge of CSI. However, to maximize the sum-rate with fairness consideration for

JSG-IOTA, it is necessary to investigate dynamic subcarrier allocations. In other word-

s, transmitters periodically estimate the uplink channel states of all subcarriers for each

user. Based on the obtained CSI, transmitters assign the subcarriers and power to each

user through a reliable signaling channel. Fig. 4.14 shows the effect of the subcarrier

allocation in 200% loaded JSG-IOTA scenario−3, where the dynamic scheme allocates

subcarriers to the user who has the largest channel gain [69]. As revealed by the figure,

the dynamic subcarrier allocation improves the performance significantly. Compared

to the static subcarrier allocation, there is about 2 - 3 dB gain. It should be noted

that for the dynamic subcarrier allocation, CSI is required at both transmitters and

receivers, while for the static subcarrier allocation, CSI is only required at receivers.

6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

Eb/N

0(dB)

BE

R

Static subcarrier allocationDynamic subcarrier allocation

Fig. 4.14: Performance of different subcarrier allocation schemes


4.6 Summary

In this chapter, a joint sparse graph combing pulse shaping property (LDWM of FBMC-

IOTA), NOMA (LDS) and FEC (LDPC codes) was proposed. Differing from any single

graph, in the JSG-IOTA receiver, multiuser detection, intrinsic interference utilization

and channel decoding are jointly performed on one entire sparse graph. Hence it is a

Type-A receiver shown in Fig. 2.7. EXIT charts are utilized to analyse the JSG-IOTA

receiver in details, consequently the design guidelines and the threshold of the joint

sparse graph were obtained. Simulations show that the JSG-IOTA scenario−3 (degree

distribution of Deg′c and girth of 8) achieves the best performance. Its performance

improvement is mainly due to the intrinsic interference utilization and the capability

of the joint sparse graph.

Chapter 5

Sparse Code Multiple Access

(SCMA)

Although LDS performs well under overloaded conditions, its performance is not ideal

with high-order constellations. Based on the LDS technique, SCMA is proposed by

introducing constellation shaping gain [71]. It is a codebook-based NOMA technique

via code domain multiplexing. In this chapter, present novel codebook design for SCMA

systems. The design criteria of SCMA codebooks are discussed, and its performance

comparison with LDS is evaluated. Considering long codewords’ construction and high-

degree distribution, two approaches are proposed to optimize the SCMA performance,

i.e., copy-and-permute operation on protographs and 3D codebook design.

5.1 Criteria of SCMA Codebook Design

The SCMA system model and the codebook design criteria are presented in this section.

5.1.1 SCMA System Model

In SCMA, according to predefined codebook sets, bit streams are directly mapped to

sparse codewords, and the whole process can be interpreted as a coding procedure from

the binary domain to a multidimensional complex domain as shown in Fig. 5.1.

101

102 Chapter 5. Sparse Code Multiple Access (SCMA)

LDS

Spreader

FEC

Encoder QAM

Mapper

SCMA Encoder

Fig. 5.1: Merging of QAM modulator and LDS spreading in a SCMA encoder

Multidimensional lattice constellation design is a challenging problem which has been

studied in different aspects of communications. The SCMA codebook design is even

more complicated as multiple layers are multiplexed with different codebooks. A SCMA

encoder is defined as v = f(b), where b and v respectively represent the bit sequence

and the SCMA codeword vector. The N dimensional complex codeword v is a sparse

vector with dv,lds ≪ N non-zero entries. Let c denote an dv,lds dimensional complex

constellation point such that: c = g(b). A SCMA encoder can be redefined as f , sg

where s simply maps the dv,lds dimensions of a constellation point to an N dimensional

SCMA codeword. In fact, s is the low density spreading in LDS. The resulting code-

book contains of M codewords each consisting of N complex values from which only

maximum dv,lds are non-zero specified by s. The difference between LDS and SCMA

is that LDS only consider spreading, i.e., f , s, while SCMA considers both spreading

and constellation such that f , sg.

A SCMA encoder contains K separate layers or users each defined by

Γk = fk(Sk, gk(b);M,dv,lds, N), k ∈ [1,K] (5.1)

where S = {S1, ...,SK} and Γ = {Γ1, ...,ΓK} represent the low density signature

and the SCMA codebook set. The constellation function gk generates the constel-

lation set. The matrix Sk maps the constellation point to SCMA codeword to for-

m the codeword set vk. In summary, a SCMA code can be represented by Γ =

f([Sk]Kk=1, [gk]

Kk=1;K,M, dv,lds, N). SCMA codewords are multiplexed overN shared or-

thogonal resources, e.g. OFDM subcarriers. The received signal after the synchronous

layer multiplexing can be expressed as

y =

K∑k=1

EkSkgk(bk) + z (5.2)

5.1. Criteria of SCMA Codebook Design 103

where Ek and z are the corresponding channel gain for the kth user and the AWGN,

respectively.

The SCMA detection is the same to that of the LDS detection [68]. The algorithm

iteratively updates the belief associated to the edges in the factor graph by passing the

extrinsic information of constellation points between resource nodes and layer nodes.

Note that resource nodes and layer nodes in SCMA respectively correspond to chip

nodes and variable nodes in LDS. At each resource node of SCMA, the received signal

is combined with the extrinsic information passed by the resource nodes through the

rest of the edges connected to that resource node. At each layer node, the a priori

information of the transmitted layers (usually assumed to be uniformly distributed)

is combined with the extrinsic information passed by the resource nodes through the

rest of edges connected to that layer node. Finally, after a few iterations, the detector

converges to reliable soft information of the transmitted layers.

5.1.2 Multi-stage Optimization Approach of SCMA Codebooks

The codebook design problem of SCMA can be defined as

Γ = argmaxS,g

f([Sk]Kk=1, [gk]

Kk=1;K,M, dv,lds, N) (5.3)

Reference [74] points out that the solution of this multi-dimensional problem is still

unknown, a multi-stage optimization approach is the suboptimal solution for the issue.

We summarize the multi-stage optimization procedures according to [74] as follows.

5.1.2.1 Low Density Signature

As described before, the mapping matrix is actually the low density signature of the

LDS scheme, and it is used to determine the number of layers interfering at each

resource node which in turn defines the complexity of the MPA detection. The sparser

the codewords structure, the lower complexity is the MPA detection. Optimization of

the mapping matrix is the same as the LDS scheme, which has been discussed and

analyzed in Chapter 3.


5.1.2.2 Constellation Points

Having the mapping matrix S+, the optimization problem of an SCMA is reduced to

g+ = argmaxgf([S+, g;K,M, dv,lds, N) (5.4)

The problem is to define K different dv,lds dimensional constellations each containing

M points. To simplify the optimization problem, the constellation points of the layers

are modeled based on a mother constellation and the layer-specific operators, i.e. gk ,

(∆k)g, k ∈ [1,K], where ∆k denotes a constellation operator. According to the model,

the SCMA code optimization problem turns into

g+, [∆+k ]Kk=1 = arg max

g,[∆k]Kk=1

f([S+, g = [(∆k)g]Kk=1;K,M, dv,lds, N) (5.5)

As a suboptimal approach to the above problem, the mother constellation and the

operators are determined separately.

5.1.2.3 Mother Multi-dimensional Constellation

The target is to design a multi-dimensional lattice constellation. A compact multi-

dimensional constellation can be designed by minimizing the average alphabet energy

for a given minimum Euclidian distance between the constellation points. A unitary

operation (lattice rotation) can be applied directly on the lattice constellation without

sacrificing the Euclidian distance of the constellation. The lattice rotation can be op-

timized to improve the product distance of the constellation and induce dependency

among the lattice dimensions, and reduce the number of projections per lattice di-

mensions to reduce the detection complexity. Also, the dimensional power properties

of the constellation can be changed by lattice rotation, for better convergence of the

MPA receiver by taking advantage of near-far effect of the overlaid codeword. Shaping

gain of multi-dimensional constellations is the major source of the performance gain of

SCMA over LDS. After optimizing the constellation set, the corresponding constella-

tion function is defined to setup the mapping rule between the binary words and the


constellation alphabet points. Following the Gray mapping rule, the binary words of

any two closet constellation points can have a Hamming distance of 1.

1) Design metrics and rotated constellations

Large minimum Euclidean distance of a multi-dimensional constellation ensures a good

performance of the SCMA system with a small number of layers where there are no

collisions between the layers over a resource node. Once the number of layers grows, two

or more layers may collide over a resource node. Under this condition, it is important

to induce dependency among the nonzero elements of codewords to be able to recover

colliding codewords from the other resource nodes. In addition, power imbalance across

the dimensions of codewords introduces near-far effect among colliding layers. It helps

MPA detector to operate more effectively to remove interferences among layers.

Having a constellation with a desirable Euclidian distance profile, a unitary rotation

can be applied to the base constellation in order to control dimensional dependency and

power variation of the constellation while maintaining the Euclidian distance profile.

Similar to the code design for communications over fading channels, a unitary rotation

can be applied to maximize the minimum product distance of the constellation. There-

fore, the design objective encapsulates both the sum distance and the product distance

between the points in the mother constellation.

2) Rotated lattice constellations

In general, the base constellation can be any multi-dimensional constellation with a

maximized minimum Euclidean distance. At low rates, constellation can be designed

by heuristic optimization, but at higher rates a structured construction way is required.

Lattice constellation is a structural approach of the base constellation design. As a

special case of lattice constellations, we can consider the base constellation to be formed

by orthogonal QAMs on different complex planes. It is equivalent to a constellation

from the lattice. Gray labeling is an advantage of this type of lattice constellations.

3) Shuffling multi-dimensional constellations in real and imaginary axes

If a complex constellation is built such that its real part is independent of its imaginary

part, it can help reduce the decoding complexity while maintaining dependency among


the complex dimensions of the resulted multi-dimensional constellation. Using this

technique, the complexity order of MPA reduces from Mdc,lds to Mdc,lds/2 which results

in significant complexity saving especially for large constellation sizes.

A shuffling is to construct a dv,lds dimensional complex mother constellation from Carte-

sian product of two dv,lds dimensional real constellations, where each of them is con-

structed by the same method described in the previous section. One of these two dv,lds

dimensional real constellations corresponds to the real part of the points of the complex

mother constellation and the other one corresponds to the imaginary part.

Fig. 5.2 shows an example of the shuffling to construct a 16-point SCMA mother

constellation with two nonzero positions (dv,lds = 2). The optimum rotation angle

that maximizes the minimum product distance is tan−1((1 +√5)/2) [74]. First, two

QPSK constellations are rotated using the optimum angle. Each point of the rotated

constellations can be queued according to the axis value: X1(11 01 10 00), X2(10 11

00 01), Y1(11 01 10 00), Y2(10 11 00 01). Subsequently, a shuffling is performed to

separate real and imaginary parts. One of these two real constellations corresponds

to the real part of the points of the complex mother constellation and the other one

corresponds to the imaginary part.

To explain the SCMA principle more clearly, we show a 150% loaded SCMA as an

example. There are 6 users and 4 subcarriers, each user is spread on 2 subcarriers,

thus N = 4, K = 6 and dv,lds = 2. We use the 16-point constellation presented in

Fig. 5.2 as the constellation scheme. The LDS matrix is shown in (5.6), where a0 = 1,

a1 = exp(j2π27 ), a2 = exp(j4π27 ) [63]. Note that each row and each column of the LDS

matrix in (5.6) represent a subcarrier and a user, respectively. TABLE 5.1 illustrates

the generated SCMA codewords which is a combination of the LDS matrix in (5.6) and

the constellation in Fig. 5.2.

a0 a1 a2 0 0 0

a1 0 0 a0 a2 0

0 a2 0 a1 0 a0

0 0 a0 0 a1 a2

(5.6)


16 Points Constellation for dv,lds = 2

a

b

Fig. 5.2: 16-point SCMA constellation for dv,lds = 2

TABLE 5.1: SCMA codewords for 16-point

Information bits SCMA codeword

User 1 0000 [(a+ ja)a0, (b+ jb)a1, 0, 0]

User 2 0101 [(−b− jb)a1, 0, (a+ ja)a2, 0]

User 3 0011 [(a− ja)a2, 0, 0, (b− jb)a0]

User 4 0101 [0, (−b− jb)a0, (a+ ja)a1, 0]

User 5 1100 [0, (−a+ ja)a2, 0, (−b+ jb)a1]

User 6 0111 [0, 0, (−b− ja)a0, (a− jb)a2]


4) Rotation to Minimize Number of Projection Points

For the sake of simplicity of the MPA detection, it is more desirable to use mother

constellations that have a smaller number of projections per resource node (or complex

dimension). Let m denote the number of projections per complex dimensions of an

M point constellation. It is obvious that m < M . As m decreases, the complexity

of the corresponding MPA detector is also reduced by mdc,lds . During the process of

mother constellation design, the rotation matrix can be set in a way so as to lead to

the lower number of projected points. It makes the minimum product distance equal

to zero and degrades the performance of the SCMA system. Consequently, there is

a trade-off between the performance requirement and the complexity in this case. As

an example, Fig. 5.3 shows a solution with 9-projections per complex dimension of a

16-point constellation [74].

16 Points Constellation with 9 projection points for dv,lds = 2

a

a

Fig. 5.3: 16-point SCMA constellation with 9-projection-point for dv,lds = 2

Similarly, we show the generated SCMA codewords for 16-points with 9-projection-

point in TABLE 5.2. Such SCMA codebook is a combination of the LDS matrix in

(5.6) and the constellation in Fig. 5.3.


TABLE 5.2: SCMA codewords for 16-point with 9-projection-point

Information bits SCMA codeword

User 1 0000 [(a+ ja)a0, (0 + j0)a1, 0, 0]

User 2 0101 [(0 + j0)a1, 0, (a+ ja)a2, 0]

User 3 0011 [(a− ja)a2, 0, 0, (0 + j0)a0]

User 4 0101 [0, (0 + j0)a0, (a+ ja)a1, 0]

User 5 1100 [0, (−a+ ja)a2, 0, (0 + j0)a1]

User 6 0111 [0, 0, (0− ja)a0, (a+ j0)a2]

5.1.2.4 Constellation Function Operators

By having a solution for the mother constellation, the original SCMA optimization

problem is further reduced to

[∆+k ]Kk=1 = arg max

[∆k]Kk=1

f([S+, g = [(∆k)g+]Kk=1;K,M, dv,lds, N) (5.7)

Here, we limit the operators to those with unitary representation over real domain

which guarantees that the Euclidian distances between different codewords are not al-

tered. Three typical operators are complex conjugate, phase rotation, and dimensional

permutation of the lattice constellation. The codebooks of different SCMA layers are

constructed based on the mother constellation g and a layer-specific operator ∆k for

layer k. The task of the MPA detector is to separate the interfering symbols in an

iterative fashion. As a basic rule, interfering symbols at a resource node are more

easily separated if their power level is more diverse. Intuitively, the strongest sym-

bol is first detected and then it helps the rest to be detected by removing the next

strongest symbols, consecutively. Based on this reasoning, the mother constellation

must have a diverse average power level over the constellation dimensions. This target

can be achieved by appropriate rotation of the lattice constellation as discussed in the

previous section. Assuming the dimensional power level of the mother constellation is

diverse enough, the permutation operators of the SCMA codebooks must be selected

in a way to capture as much power diversity as possible over the interfering layers. The


power variation over the layers can be optimized following the approach described in

the following: the permutation of each codebook set is designed to avoid interfering the

same dimensions of a mother constellation over a resource node.

5.1.3 Performance Comparison with LDS

In the following, the performance of SCMA is evaluated and the performance gain of

SCMA over LDS is quantified by a simple exemplary case. SCMA codewords or LDS

modulated signatures are carried over OFDM subcarriers in SUI-3 channel [144]. The

SCMA and LDS follow the sparse graph with basic parameters: N = 4, K = 6 and

dv,lds = 2. The users number is 6 and the subcarrier number is 4, hence the system

loading is 150%. Four and sixteen point constellations are considered in the simulations.

According to the results shown in Fig. 5.4, for both constellations, SCMA outperforms

LDS in terms of BER, confirming that SCMA provides shaping gains over LDS due to

the multi-dimensional codebooks. In addition, the 16-point SCMA with 9-projection-

point, which is shown in Fig. 5.3, is also evaluated. It can be seen that, although the

9-projection-point scheme reduces the detection complexity, its BER is much higher

than the 16-point SCMA scheme.

6 8 10 12 14 16 18 20 22 24 26 28 3010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

LDS 4−pointSCMA 4−pointLDS 16−pointSCMA 16−pointSCMA 16−point with 9−projection−point

Fig. 5.4: Performance of 150% loaded LDS and SCMA

5.2. Design of SCMA Codebooks Based on Protographs 111

5.2 Design of SCMA Codebooks Based on Protographs

Existing SCMA codebooks, e.g., those presented in [71–75], are strictly designed for

very short codewords, i.e., N = 4 and K = 6, which means a 4-point FFT is adopted

in the OFDM modulation. In practical multi-carrier systems, the subcarrier number is

definitely larger than 4. For example, 128, 256, 512 or even larger FFT is used in prac-

tical OFDM systems. To increase the subcarrier (resource node) number, reference [74]

points out that several short SCMA codewords can be linked together to form a long

codeword. However, simple combination of short SCMA codewords ignores some im-

portant characters of sparse graph and cannot achieve ideal transmission performance.

In this section, we design the SCMA codebooks using protographs.

5.2.1 Extension of SCMA Codewords by Copy Operation

For convenience, we define the existing short SCMA codewords as a template called a

protograph. Note that the protograph was proposed for LDPC codes’ design [145] [146],

but it has never been applied to any NOMA technique. A protograph can be any Tanner

graph, typically one with a relatively small number of nodes. As a simple example, we

consider a protograph shown in Fig. 5.5 (a). This small Tanner graph consists of 2

resource nodes and 3 layer nodes, connected by 5 edges, and can be recognized as a

protograph of a (N = 2, K = 3) SCMA codeword. According to [74], to increase

the subcarrier number, a larger graph can be obtained by a copy operation, which is

illustrated in Fig. 5.5 (b). In this figure, the protograph has been copied P times,

where the P is determined by the FFT size requirement. Here the same-type vertices

of the P copies are in close proximity, but the overall graph consists of P disconnected

subgraphs.

The advantage of the extension method shown in Fig. 5.5 is the simplicity. On the

transmitter side, protographs only need to be copied to form a larger Tanner graph,

without any other operation. On the receiver side, as each copy of the protograph is

exactly the same to each other, a low complexity protograph decoder can be utilized

for all protographs. Nevertheless, there are some drawbacks of this method:


resource nodes

layer nodes

edges

(a) Protograph (b) Copy p times

Fig. 5.5: Extension of SCMA codewords by copy operation

1) Each protograph in Fig. 5.5 (b) is independent subgraph, consequently when iterative

detection is performed, each node cannot receive soft message from other protographs

or far-distant nodes. In graph theory, one of the main advantages of the sparse graph

is that far-distant nodes’ message can be propagated to correct errors.

2) Separate protographs cannot obtain interleaving gain. According to the LDPC

theory, intrinsic interleaver of the sparse graph is an important factor to achieve a

satisfactory performance.

3) The large graph generated by protographs is not optimized. For example, there is a

length-4 cycle in the protograph in Fig. 5.5 (a). These short cycles still exist in Fig.

5.5 (b) as no extra processing is performed. It has been proved in Chapter 3 and 4 that

short cycle will degrade the performance of an iterative detector.

Therefore, although the extension is straightforward, the generated SCMA codeword

may not be optimal.

5.2.2 Construction of SCMA Codebooks by Copy-and-permute Op-

eration

To solve above problems, we propose an improved approach to construct SCMA code-

books based on protographs. In our proposal, the protograph still serves as a blueprint

for constructing large SCMA codewords of arbitrary size, but the large Tanner graph

is optimized. This operation consists of first making several copies of the protograph,

and then permuting the edges among the disconnected protographs. The main steps

are illustrated in Fig. 5.6 and introduced as follows.

5.2. Design of SCMA Codebooks Based on Protographs 113

(b) Copy p times (c) Permute the edges (a) Protograph

resource nodes

layer nodes

edges

Fig. 5.6: Construction of SCMA codebooks by copy-and-permute operation

1) Choose a protograph with a relatively low number of nodes. In Fig. 5.6 (a), we take

the same protograph shown in Fig. 5.5 (a) as an example.

2) Copy the protograph P times. In Fig. 5.6 (b), the protograph has been copied

P times, which is similar to that of Fig. 5.5 (b). After the replication, we obtain a

temporary graph, where each set has a size P times larger than the corresponding sets

in the protograph.

3) Permute the edges of the nodes in the P replicas of the protograph to obtain the

final graph. The permutations are performed in a way to maximize the girth of the

large graph. In Fig. 5.6 (c), the edges of the P copies of the protograph have been per-

muted among the P copies of the corresponding layer nodes and resource nodes. More

explicitly, we set a target girth in advance, and calculate the girth of the joint graph

in a typical run. If the girth is less than the target, we permute the edge connections

of two protographs which have at least P/2 protographs’s distance. The requirement

for the minimum distance is to make sure that the message in the iterative detection

comes from the node as far as possible, which will lead to a better convergence. The

permutation operation continues repeatedly until the target girth is achieved. After

the permutation, the P subgraphs are interconnected and shown in Fig. 5.6 (c), con-

sequently a new (N = 2P , K = 3P ) SCMA codeword is derived.

In general, we can apply the copy-and-permute operation to any protograph to derive

larger graphs of various sizes. When the protograph is replicated P times, each proto-

graph edge becomes a bundle of P edges, connecting P layer nodes to P resource nodes.

The copies of the protograph are interconnected by permuting these layer-to-resource

pairings within each bundle. The derived graph is the graph of a SCMA codeword P

times as large as the SCMA codeword corresponding to the protograph, with the same


overloadings and degree distributions.

As can be seen from Fig. 5.6, the key of our proposal is the permutation operation.

Similar to the optimization of the joint sparse graph, the design criteria of the permu-

taion operation is to increase the girth of the graph. By doing so, separate protographs

become correlated, meaning that the message from far-distant nodes can be exchanged.

In addition, the large sized interleaving is exploited in the graph structure. More im-

portantly, short cycles can be eliminated during the optimization processing.

5.2.3 Performance Evaluation

6 8 10 12 14 16 18 20 22 24 26 28 3010

−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

SCMA 4−point by copy operationSCMA 4−point by copy−and−permute operationSCMA 8−point by copy operationSCMA 8−point by copy−and−permute operation

Fig. 5.7: Performance of 200% loaded SCMA by different construction methods

To compare the above two construction approaches, Fig. 5.7 shows BER results for

SCMA over SUI-3 channel. A (N = 8, K = 16) protograph with 8 resource nodes and

16 layer nodes is employed. We assume that the FFT size is 128, thus 16 protographs

(P = 16) are copied or copied-and-permuted to generate the SCMA codebooks. The

system overloading is 200%. Four and eight point constellations are considered in the

simulation. It can be seen that the copy-and-permute operation outperforms the copy

5.3. Design of 3D SCMA Codebooks 115

operation. For both constellations, there is about 1 dB gain in the medium to high

SNR region. According to the analysis presented in Section 5.2.2, such gain comes from

interleaving and graph optimization by the copy-and-permute operation. Therefore, the

graph design is very important to the construction of SCMA codebooks.

5.3 Design of 3D SCMA Codebooks

State-of-the-art SCMA codebooks are strictly designed for very limited effective spread-

ing factor, i.e., dv,lds = 2, which means a 2D rotation is considered to the lattice con-

stellation [71–75]. To the best of our knowledge, there does not exist a SCMA codebook

with dv,lds larger than 2. In this section, we aim to design 3D SCMA codebooks.

5.3.1 Limitations of 2D SCMA Codebooks

In Chapter 3, it has been proved analytically and numerically that the performance of

LDS is mainly determined by the degree distributions of different nodes. SCMA is built

upon LDS, thus the analysis presented in Chapter 3 is also valid for SCMA. The advan-

tage of SCMA codebooks with dv,lds of 2 is the low complexity, as the computational

complexity of MPA is directly related to the density of a graphical model. The smaller

dv,lds is, the lower complexity can be achieved. In LDPC codes, by optimizing the

degree distribution, i.e., by varying the column weights and row weights of the parity

check matrix, the performance can be improved. Similar to the LDPC decoding, in SC-

MA, the layer nodes with high-degree can obtain more information from their adjacent

resource nodes so that it tends to converged more quickly than the low-degree layer

nodes. These layer nodes offer more extrinsic information in initial iterations which can

be fed back to enhance the detection performance. More explicitly, the more reliable

information, provided by the high-degree nodes, can be used to improve the detection

performance even in poor channel conditions. In terms of LLR propagation, the LLRs

for the high-degree nodes converge quickly to large values, whereas the low-degree n-

odes converge slowly to smaller LLRs. The more reliable LLR information provided by

the high-degree nodes, can be used to provide more reliable LLR for computing soft


symbol average value. The enhanced soft symbols can be used to improve the detection

performance in the following iterations. Hence, dv,lds of 2 represents the weakest link

in the SCMA codebook and its message may converge slowly than that high-degree

nodes.

5.3.2 Construction of SCMA codebooks with dv,lds of 3

Due to the fact that dv,lds of 2 is not the optimum degree distribution, we develop 3D

SCMA codebooks, i.e., dv,lds = 3, to bridge this gap. In this case, more than 2 rotated

constellations are needed to generate the mother constellation.

Fig. 5.8 shows an example of the shuffling to construct a 4-point SCMA constellation

with dv,lds of 2, which is similar to that of Fig. 5.2. To extend the dv,lds to 3, it is

necessary to consider the BPSK in 3D constellations, which is shown in Fig. 5.9. First

of all, two BPSK points in 3D constellations, which are marked by dotted circles, are

respectively rotated using the same angle to different directions. The optimum rotation

angle is tan−1((1+√5)/2) [74]. Each point of the rotated constellation is then marked

by a solid cycle and can be queued according to the axis value: X1(0 1), X2(1 0),

X3(1 0), Y1(0 1), Y2(1 0), Y3(0 1). Subsequently, a shuffling is performed to separate

these axes. This idea is a straightforward extension to that of 2D constellation, where

three complex mother constellations are generated. By doing so, a 4-point SCMA

constellation with dv,lds of 3 is constructed.

5.3.3 Performance Evaluation

The performance of 200% loaded SCMA with 4-point constellation and different dv,lds

is simulated over SUI-3 channel and shown in Fig. 5.10. The FFT size is 128. For

dv,lds of 2, the optimized SCMA codebooks, which is generated by copy-and-permute

operation in section 5.2.2, is employed for the comparison. For dv,lds of 3, three different

constellations corresponding to the three edges of each layer node, are generated by the

approach shown in Fig. 5.9. According to Fig. 5.10, by increasing dv,lds and rigorous

constellation design, the SCMA performance can be further improved. At BER of

10−5, 4 dB gain can be achieved by dv,lds = 3 compared to dv,lds = 2. It should be

5.3. Design of 3D SCMA Codebooks 117

X2

X1

Y2

Y1

Rotated BPSK 1 Rotated BPSK 2

0 0

1 1

Y1

X1

01 11

00 10

Y2

X2

10 00

11 01

4 Points Constellation points for dv,lds = 2

Fig. 5.8: 4-point SCMA constellation for dv,lds of 2

X3

X2

X1

0

1

Rotated BPSK 1

Y3

Y2

Y1

0

1

Rotated BPSK 2

Y1

X1

01 11

00 10

Y2

X2

10 00

11 01

Y3

X3

11 01

10 00

4 Points Constellation points for dv,lds = 3

Fig. 5.9: 4-points SCMA constellation for dv,lds of 3


noted that according to the graph theory and the analysis of degree distribution, the

SCMA performance will not be improved infinitely when dv,lds increases. Also larger

dv,lds means higher computational complexity. Therefore, in practical system design, it

is necessary to strike a balance between the performance requirement and the receiver

complexity.

6 8 10 12 14 16 18 20 22 24 26 28 3010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

SCMA 4−point for dv,lds

= 2

SCMA 4−point for dv,lds

= 3

Fig. 5.10: Performance of 200% loaded SCMA by different dv,lds

5.4 Summary

As an enhanced version of LDS, SCMA combines the techniques of multi-dimensional

constellation shaping and the low density spreading. It has become a promising can-

didate for overloaded transmissions with high-order constellations in 5G networks. In

this chapter, the SCMA system model and codebook design criteria are studied. Based

on this investigation, we optimize the SCMA structure by copy-and-permute operation

on protographs, and design SCMA codebooks with dv,lds of 3. Simulation results show

that the proposed approaches improve the SCMA performance.

Chapter 6

Conclusions and Future Works

This chapter provides a summary of this thesis’ contributions, and discusses how the

proposed algorithms in this thesis contributed to the field of NOMA.The perspective

regarding future works is further discussed.

6.1 Summary of Contributions

In Chapter 3, inspired by the similar structures of LDS-OFDM and LDPC codes, a joint

sparse graph for OFDM systems is proposed. Variable nodes act as bridge functions

to connect chip nodes and parity-check nodes, then the low density signature of LDS-

OFDM and the low density parity-check matrix of LDPC codes are naturally linked to

form a joint sparse graph. Such joint sparse graph is different from any technique of

single graphs, as it combines NOMA (LDS-OFDM) and FEC techniques (LDPC codes).

On the receiver side, a joint receiver performing simultaneous detection and decoding

is designed. The joint detection and decoding is different from turbo-style iterations.

In addition, to examine the behavior of the joint sparse graph, EXIT charts are utilized

to analyze the convergence property of MPA. Based on EXIT charts analysis, design

principles of the joint sparse graph are studied, illustrating that degree distributions

and short cycles determine the system’s performance. Simulations show the superiority

of JSG-OFDM over GO-MC-CDMA, LDS-OFDM and turbo structured LDS-OFDM.

119

120 Chapter 6. Conclusions and Future Works

In Chapter 4, the idea of the joint sparse graph is extended to the FBMC-IOTA wave-

form. Considering that there is intrinsic interference of the real and imaginary branches

of FBMC transmissions, we propose to model such intrinsic interference by a low densi-

ty weight matrix. Then a joint sparse graph containing LDWM, LDS and LDPC codes

is designed. The key insight is that all of these techniques are based on low density

structure, and MPA is the common algorithm for the receiver. Therefore, a joint re-

ceiver for JSG-IOTA to jointy detect and decode becomes possible. Such joint sparse

graph combines multi-carrier modulation (LDWM), multiple access (LDS) and channel

coding (LDPC codes) techniques, and the iterative structure as well as convergence

behavior is analyzed by EXIT charts. Similar to JSG-OFDM, design guidelines for the

JSG-IOTA are provided.

In Chapter 5, SCMA is studied, and its codebook design’s criteria are investigated.

Different from LDS, the processes of bit to symbol mapping and LDS spreading are

merged in the SCMA encoder. As a result, compared with LDS, SCMA with multi-

dimensional constellation codebooks can attain the extra constellation shaping gain. To

construct longer SCMA codewords, a copy-and-permute operation on the protograph

is applied to the SCMA scheme. Moreover, 3D constellation with dv,lds of 3 is proposed

for the SCMA codebook design. We show that SCMA outperforms LDS with high-

order constellations, and the SCMA performance can be further improved by optimized

designs.

In general, NOMA can overcome some problems of OMA based techniques via non-

orthogonal resource allocation, and is an advantageous technique in future wireless

communications. We have developed code domain NOMA techniques for uplink in this

thesis. We start with LDS based NOMA. In order to design a joint receiver to achieve a

better BER performance, LDS is researched and optimized in three directions: i) LDS

+ LDPC codes; ii) LDS + advanced waveforms; and iii) LDS + multi-dimensional

constellation shaping. By careful design of the LDS graph structure, code domain

NOMA can be improved and optimized. Our proposed NOMA schemes can be applied

to MTC systems. Compared with OMA techniques, code domain NOMA increases

the supported user number and spectral efficiency, while the disadvantages include a

relative higher receiver complexity and the uncertainty of randomly constructed sparse

6.2. Future Works 121

graphs. More explicitly, not all of the low density signatures perform well under fully-

loaded and overloaded conditions. Even with identical parameters such as dv,lds and

dc,lds, randomly generated low density signatures by computer searching may behave

significantly different from each other. It is hard for a single factor to determine and

improve the LDS performance, e.g. the degree distribution, to meet the performance

requirements in future wireless communications. Therefore, it is important to construct

good low density signatures based on overall considerations for practical systems.

6.2 Future Works

Recently, the research activities of LDS and SCMA have attracted increasing attention

due to their ability to support overloaded transmissions. With the contributions in

mind, the following three topics for future investigations are highlighted:

1. Although code domain NOMA including LDS and SCMA have been analyzed and

optimized in the thesis, the codebook design and optimization are still open issues.

Different from techniques of sparse graph coding, LDS and SCMA are multiple

access schemes for the multiuser scenario, and the channel condition of different

users is random and dynamic. Thus the research in this area is more challenging

than conventional sparse graphs. To date, there does not exist a systematic

approach for the system design. It is thus of vital importance to establish an

unified framework for the design and optimization of NOMA schemes.

2. Due to the use of MPA for the detection of LDS and SCMA, the receiver com-

plexity is a big challenge in practical applications, especially when the size of the

sparse graph is large or the constellation order is high. It is necessary to continue

the research on receiver design, by finding approaches other than MPA to reduce

the receiver complexity while maintaining satisfactory performance.

3. SCMA blind detection should be further developed to include decoding of user’s

data with no complete knowledge of SCMA codebook sets. This is of particular

interest to the vehiclar communications, where the users’ number is dynamic, and

122 Chapter 6. Conclusions and Future Works

the roadside access point is random. This necessitates the blind detection of LDS

sparse graph or SCMA codebooks, the MPA cannot be performed otherwise.

4. Although current code domain NOMA mainly focuses on uplink transmissions, it

is possible to design downlink LDS/SCMA schemes by designing low complexity

nonlinear precoding techniques, which is an interesting topic for future research.

The output of this thesis and future research contribute to the state-of-the-art on

mobile communications, and can be used by industry to design, optimize and investigate

performance of future communication systems.

Appendix A

Appendix

123

124 Appendix A. Appendix

TABLE A.1: Summary of the joint detection and decoding

INIT If no priors available, set Lvk,m→cn = 0, Lvk,m→pk,j = 0, ∀k, ∀m, ∀n, ∀j

For Iteration = 1 : Maximum iteration number

For n = 1 : N

For ∀k,m ∈ ψn

Update Lcn→vk,m using (3.9)

End

End

For j = 1 : J

For ∀k,m ∈ ϕj

Update Lpk,j→vk,m using (3.11)

End

End

For k = 1 : K

For m = 1 : M

For n ∈ εk,m, j ∈ ωk,m

Update Lvk,m→cn using (3.14)

Update Lvk,m→pk,j using (3.15)

Update Lvk,m using (3.16)

End

Hard Decision according to (3.17)

End

End

If syndrome computing for each user equals to zero, Quit the iterations

End

Bibliography

[1] J. Gozalvez, “Prestandard 5G developments [Mobile Radio],” IEEE Vehicular

Technology Magazine, vol. 9, no. 4, pp. 14–28, December 2014.

[2] G. Jiann-Ching, L. Pei-Kai, C. Yih-Shen, A. Hsu, H. Chien-Hwa, and L. Gabriel,

“On 5G radio access architecture and technology [Industry Perspectives],” IEEE

Wireless Communications, vol. 22, no. 5, pp. 2–5, October 2015.

[3] A. Osseiran, F. Boccardi, V. Braun, K.Kusume, M. Patrick, and M. Michal,

“Scenarios for 5G mobile and wireless communications: the vision of the METIS

project,” IEEE Communications Magazine, vol. 52, no. 5, pp. 26–35, May 2014.

[4] C. W. Hau, F. Zhong, and R. Haines, “Emerging technologies and research chal-

lenges for 5G wireless networks,” IEEE Signal Processing Letters, vol. 21, no. 2,

pp. 106–112, April 2014.

[5] F. Boccardi, R. W. Heath, A. Lozano, T. L. Marzetta, and P. Petar, “Five dis-

ruptive technology directions for 5G,” IEEE Communications Magazine, vol. 52,

no. 2, pp. 74–80, February 2014.

[6] G. Wunder, P. Jung, M. Kasparick, and T. Wild, “5GNOW: non-orthogonal,

asynchronous waveforms for future mobile applications,” IEEE Communications

Magazine, vol. 52, no. 2, pp. 97–105, February 2014.

[7] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and H. Kenichi,

“Non-orthogonal multiple access (NOMA) for cellular future radio access,” in

IEEE Vehicular Technology Conference (VTC Spring), June 2013.

125

126 Bibliography

[8] X. Chen, A. Beijebbour, A. Li, H. Jiang, and H. Kayama, “Consideration on suc-

cessive interference canceller (SIC) receiver at cell-edge users for non-orthogonal

multiple access (NOMA) with SU-MIMO,” in IEEE International Symposium

on Personal, Indoor, and Mobile Radio Communications (PIMRC), September

2015.

[9] A. Benjebbour, A. Li, K. Saito, Y. Saito, Y. Kishiyama, , and T. Nakamura,

“NOMA: from concept to standardization,” in IEEE Conference on Standards

for Communications and Networking (CSCN), October 2015.

[10] K. Higuchi and A. Benjebbour, “Non-orthogonal multiple access (NOMA) with

successive interference cancellation for future radio access,” IEICE Transactions

on Communications, vol. 98, no. 3, pp. 403–414, March 2015.

[11] D. Linglong, W. Bichai, Y. Yifei, H. Shuangfeng, I. Chih-Lin, and W. Zhaocheng,

“Non-orthogonal multiple access for 5G: solutions, challenges, opportunities, and

future research trends,” IEEE Communications Magazine, vol. 53, no. 9, Septem-

ber 2015.

[12] S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5G

systems,” IEEE Signal Processing Letters, vol. 22, no. 10, pp. 1647–1651, March

2015.

[13] S. Qi, H. Shuangfeng, I. Chin-Lin, and P. Zhengang, “Energy efficiency opti-

mization for fading MIMO non-orthogonal multiple access systems,” in IEEE

International Conference on Communications (ICC), June 2015.

[14] X. Xiong, W. Xiang, K. Zheng, H. Shen, and X. Wei, “An open source SDR-based

NOMA system for 5G networks,” IEEE Wireless Communications, vol. 22, no. 6,

pp. 24–32, December 2015.

[15] D. Zhiguo, P. Mugen, and H. V. Poor, “Cooperative non-orthogonal multiple

access in 5G systems,” IEEE Communications Letters, vol. 19, no. 8, pp. 1462–

1465, June 2015.

Bibliography 127

[16] M. Al-Imari, P. Xiao, and M. Imran, “Uplink non-orthogonal multiple access for

5G wireless networks,” in International Symposium on Wireless Communications

Systems, August 2014, pp. 781–785.

[17] R. Razavi, M. Al-Imari, M. A. Imran, R. Hoshyar, and C. Dageng, “On receiver

design for uplink low density signature OFDM (LDS-OFDM),” IEEE Transac-

tions on Communications, vol. 60, no. 11, pp. 3499–3508, November 2012.

[18] Y. Mingjie and H. Hungyun, “Moving towards non-orthogonal multiple access in

next-generation wireless access networks,” in IEEE International Conference on

Communications (ICC), June 2015.

[19] P. Banelli, S. Buzzi, G. Colavolpe, A. Modenini, F. Rusek, and A. Ugolini, “Mod-

ulation formats and waveforms for 5G networks: who will be the heir of OFDM?:

An overview of alternative modulation schemes for improved spectral efficiency,”

IEEE Signal Processing Magazine, vol. 31, no. 6, pp. 80–93, November 2014.

[20] H. Saeedi-Sourck, W. Yan, and J. W. M. Bergmans, “Complexity and perfor-

mance comparison of filter bank multicarrier and OFDM in uplink of multicar-

rier multiple access networks,” IEEE Transactions on Signal Processing, vol. 59,

no. 4, pp. 1907–1912, January 2011.

[21] N. J. Baas and D. P. Taylor, “Pulse shaping for wireless communication over

time- or frequency-selective channels,” IEEE Transactions on Communications,

vol. 52, no. 9, pp. 1477–1479, September 2004.

[22] J. A. Lopez-Salcedo, E. Gutierrez, G. Seco-Granados, and A. L. Swindlehurst,

“Unified framework for the synchronization of flexible multicarrier communication

signals,” IEEE Transactions on Signal Processing, vol. 61, no. 4, pp. 828–842,

January 2013.

[23] B. Farhang-Boroujeny, “OFDM versus filter bank multicarrier,” IEEE Signal

Processing Magazine, vol. 28, no. 3, pp. 92–112, May 2011.

[24] P. Siohan and C. Roche, “Cosine-modulated filterbanks based on extended Gaus-

128 Bibliography

sian functions,” IEEE Transactions on Signal Processing, vol. 48, no. 11, pp.

3052–3061, November 2000.

[25] C. Sae-Young, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design

of low-density parity-check codes within 0.0045 db of the Shannon limit,” IEEE

Communications Letters, vol. 5, no. 2, pp. 58–60, February 2001.

[26] D. Tse and P. Viswanath, “Fundamentals of wireless communication,” Cambridge

University Press, Tech. Rep., 2005.

[27] G. Guifen and P. Guili, “The survey of GSM wireless communication system,”

in International Conference on Computer and Information Application (ICCIA),

December 2010.

[28] L. Daoben, “The perspectives of large area synchronous CDMA technology for

the fourth-generation mobile radio,” IEEE Communications Magazine, vol. 41,

no. 3, pp. 114–118, March 2003.

[29] R. Fantacci, F. Chiti, D. Marabissi, and G. Mennuti, “Perspectives for present

and future CDMA-based communications systems,” IEEE Communications Mag-

azine, vol. 43, no. 2, pp. 95–100, February 2005.

[30] E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and

wideband CDMA cellular networks,” IEEE Communications Magazine, vol. 36,

no. 9, pp. 48–54, September 1998.

[31] H. Chen, H. Chiu, and M. Guizani, “Orthogonal complementary codes for inter-

ference free CDMA technologies,” IEEE Wireless Communications, vol. 13, no. 1,

pp. 68–79, February 2006.

[32] F. Hasegawa, J. Luo, K. Pattipati, P. Willett, and D. Pham, “Speed and accuracy

comparison of techniques for multiuser detection in synchronous CDMA,” IEEE

Transactions on Communications, vol. 52, no. 4, pp. 540–545, April 2004.

[33] G. Bacci and M. Luise, “Performance comparison of energy-efficient power control

for CDMA code acquisition and detection,” in IEEE Global Telecommunications

Conference, December 2010, pp. 781–785.

Bibliography 129

[34] S. Ulukus and R. D. Yates, “Iterative construction of optimum signature sequence

sets in synchronous CDMA systems,” IEEE Transactions on Information Theory,

vol. 47, no. 5, pp. 1989–1998, July 2001.

[35] G. H. Khachatrian and S. S. Martirossian, “A new approach to the design of codes

for synchronous-CDMA systems,” IEEE Transactions on Information Theory,


[36] W. Ying-Wah and C. Shih-Chun, “Coding scheme for noiseless and noisy asyn-

chronous CDMA systems,” IEEE Transactions on Information Theory, vol. 56,

no. 8, pp. 3786–3792, August 2010.

[37] H. H. Nguyen and E. Shwedyk, “A new construction of signature waveforms for

synchronous CDMA systems,” IEEE Transactions on Broadcasting, vol. 51, no. 4,

pp. 520–529, December 2005.

[38] S. Waldron, “Generalized Welch bound equality sequences are tight frames,”

IEEE Transactions on Information Theory, vol. 49, no. 9, pp. 2307–2309, Septem-

ber 2003.

[39] J. H. Cho, “Multiuser constrained water-pouring for continuous-time overloaded

gaussian multiple-access channels,” IEEE Transactions on Information Theory,

vol. 54, no. 4, pp. 1437–1459, April 2008.

[40] A. Kapur, M. K. Varanasi, and C. T. Mullis, “On the limitation of general-

ized Welch-bound equality signals,” IEEE Transactions on Information Theory,

vol. 51, no. 6, pp. 2220–2224, June 2005.

[41] K. Alishahi, S. Dashmiz, P. Pad, and F. Marvasti, “Design of signature sequences

for overloaded CDMA and bounds on the sum capacity with arbitrary symbol

alphabets,” IEEE Transactions on Information Theory, vol. 58, no. 3, pp. 1441–

1469, March 2012.

[42] O. Mashayekhi and F. Marvasti, “Uniquely decodable codes with fast decoder for

overloaded synchronous cdma systems,” IEEE Transactions on Communications,

vol. 60, no. 11, pp. 3145–3149, November 2012.

130 Bibliography

[43] J. Bingham, “Multicarrier modulation for data transmission: An idea whose time

has come,” IEEE Communications Magazine, vol. 28, no. 5, pp. 5–14, May 1990.

[44] 3GPP, “Physical layer aspects for evolved Universal Terrestrial Radio Access

(UTRA),” 3GPP Std. TR 25.814 v.7.0.0, Tech. Rep., 2006.

[45] J. Gozalvez, “Tentative 3GPP timeline for 5G [Mobile Radio],” IEEE Vehicular

Technology Magazine, vol. 10, no. 3, pp. 12–18, September 2015.

[46] J. Tao, X. Weidong, C. Hsiao-Hwa, and N. Qiang, “Multicast broadcast services

support in OFDMA-based WiMAX systems [advances in mobile multimedia],”

IEEE Communications Magazine, vol. 45, no. 8, pp. 78–86, August 2007.

[47] S. Srikanth, P. A. M. Pandian, and X. Fernando, “Orthogonal frequency divi-

sion multiple access in WiMAX and LTE: a comparison,” IEEE Communications

Magazine, vol. 50, no. 9, pp. 153–161, September 2012.

[48] IEEE, “Standard for local and metropolitan area networks. Part 16: Air interface

for broadband wireless access systems,” Tech. Rep., May 2009.

[49] Y. Kishiyama, A. Benjebbour, and T. Nakamura, “Future steps of LTE-A: evo-

lution toward integration of local area and wide area systems,” IEEE Wireless

Communications, vol. 20, no. 1, pp. 12–18, February 2013.

[50] M. O. Pun, M. Morelli, and C. C. J. Kuo, “Iterative detection and frequency syn-

chronization for OFDMA uplink transmissions,” IEEE Transactions on Wireless

Communications, vol. 6, no. 2, pp. 629–639, February 2007.

[51] J. Ketonen, M. Juntti, and J. R. Cavallaro, “Performance-complexity comparison

of receivers for a LTE MIMO-OFDM system,” IEEE Transactions on Signal

Processing, vol. 58, no. 6, pp. 3360–3372, February 2010.

[52] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Communica-

tions Magazine, vol. 35, no. 12, pp. 126–133, December 1997.

[53] M. Juntti, M. Vehkapera, J. Leinonen, and V. Zexian, “MIMO MC-CDMA

communications for future cellular systems,” IEEE Communications Magazine,

vol. 43, no. 2, pp. 118–124, February 2005.

Bibliography 131

[54] K. Fazel and S. Kaiser, “Multi-carrier and spread spectrum systems,” in John

Wiley & Sons - IEEE Press, 2003.

[55] W. Zhuwei, Y. Dacheng, and L. Milstein, “Multi-user resource allocation for a

distributed multi-carrier DS-CDMA network,” IEEE Transactions on Communi-

cations, vol. 60, no. 1, pp. 143–152, January 2012.

[56] C. Chih-Wen and K. Chien-Cheng, “A novel interference-avoidance code reassign-

ment for downlink two-dimensional-spread MC-DS-CDMA systems with power

control,” IEEE Transactions on Vehicular Technology, vol. 59, no. 6, pp. 3104–

3108, July 2010.

[57] F. Vanhaverbeke and M. Moeneclaey, “Sum capacity of equal-power users in

overloaded channels,” IEEE Transactions on Communications, vol. 53, no. 2, pp.

228–233, February 2005.

[58] A. M. Tulino, L. Li, and S. Verd, “Spectral efficiency of multi-carrier CDMA,”

IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 479–505, Feburary

2005.

[59] C. Xiaodong, Z. Shengli, and G. B. Giannakis, “Group-orthogonal multicarri-

er CDMA,” IEEE Transactions on Communications, vol. 52, no. 1, pp. 90–99,

January 2004.

[60] F. Riera-Palou, G. Femenias, and J. Ramis, “On the design of uplink and

downlink group-orthogonal multicarrier wireless systems,” IEEE Transactions

on Communications, vol. 56, no. 10, pp. 1656–1655, October 2008.

[61] M. Mithun and K. Preetam, “Overloaded WH-spread CI MC-CDMA with iter-

ative interference cancellation,” IEEE Communications Letters, vol. 15, no. 12,

pp. 1391–1393, December 2011.

[62] A. Montanari and D. Tse, “Analysis of belief propagation for non-linear problems:

The example of CDMA, or: How to prove tanaka’s formula,” in IEEE Information

Theory Workshop, March 2006.

132 Bibliography

[63] J. van de Beek and B. M. Popovic, “Multiple access with low-density signatures,”

in IEEE Global Telecommunications Conference (GLOBECOM), November 2009.

[64] R. Hoshyar, F. Wathan, and R. Tafazolli, “Novel low-density signature for syn-

chronous CDMA systems over AWGN channel,” IEEE Transactions on Signal

Processing, vol. 56, no. 4, pp. 1616–1626, April 2008.

[65] F. Wathan, R. Hoshyar, and R. Tafazolli, “Iterated SISO MUD for synchronous

un-coded CDMA systems over AWGN channel: performance evaluation in over-

loaded condition,” in International Symposium on Communications and Infor-

mation Technologies, October 2007, pp. 397–402.

[66] ——, “Dynamic grouped chip-level iterated multiuser detection based on Gaus-

sian forcing technique,” IEEE Communications Letters, vol. 12, no. 3, pp. 167–

169, March 2008.

[67] J. Choi, “Low density spreading for multicarrier systems,” in IEEE Eighth Inter-

national Symposium on Spread Spectrum Techniques and Applications, September

2004, pp. 575–578.

[68] R. Hoshyar, R. Razavi, and M. Al-Imari, “LDS-OFDM an efficient multiple access

technique,” in IEEE 71st Vehicular Technology Conference, May 2010.

[69] M. Al-Imari, M. A. Imran, R. Tafazolli, and C. Dageng, “Subcarrier and power

allocation for LDS-OFDM system,” in IEEE Vehicular Technology Conference

(VTC Spring), May 2011.

[70] Z. Zhaoyang, C. Shaolei, and W. Kedi, “Non-coded rateless multiple access,”

in International Conference on Wireless Communications & Signal Processing

(WCSP), October 2012.

[71] H. Nikopour and H. Baligh, “Sparse code multiple access,” in IEEE International

Symposium on Personal Indoor and Mobile Radio Communications (PIMRC),

September 2013.

[72] H. Nikopour, E. Yi, A. Bayesteh, K. Au, H. Mark, B. Hadi, and M. Jianglei,

Bibliography 133

“SCMA for downlink multiple access of 5G wireless networks,” in IEEE Global

Communications Conference (GLOBECOM), December 2014.

[73] U. Vilaipornsawai, Z. Liqing, H. Nikopour, E. Yi, and A. Bayesteh, “Uplink

contention based SCMA for 5G radio access,” in IEEE Global Communications

Conference (GLOBECOM) Workshops, December 2014.

[74] M. Taherzadeh, H. Nikopour, A. Bayesteh, and H. Baligh, “SCMA codebook

design,” in IEEE Vehicular Technology Conference (VTC Fall), September 2014.

[75] A. Bayesteh, E. Yi, H. Nikopour, and H. Baligh, “Blind detection of SCMA

for uplink grant-free multiple-access,” in International Symposium on Wireless

Communications Systems (ISWCS), August 2014.

[76] Z. Shutian, X. Baicen, X. Kexin, C. Zhiyong, and X. Bin, “Design and analysis of

irregular sparse code multiple access,” in International Conference on Wireless

Communications & Signal Processing (WCSP), October 2015.

[77] Z. Yuan, G. Yu, and W. Li, “Multi-user shared accessfor 5G,” Telecommunication

Network Technology, vol. 5, no. 5, pp. 28–30, May 2015.

[78] Z. Jie, L. Bing, S. Xin, R. Liping, and X. Rongrong, “Pattern division multiple

access (PDMA) for cellular future radio access,” in International Conference on

Wireless Communications & Signal Processing (WCSP), October 2015.

[79] S. Verdu, “Multiuser detection,” in Cambridge University Press, 1998.

[80] Z. Junshan and T. Konstantopoulos, “Multiple-access interference processes are

self-similar in multimedia CDMA cellular networks,” IEEE Transactions on In-

formation Theory, vol. 51, no. 3, pp. 1024–1038, March 2005.

[81] G. D. Forney, “Maximum-likelihood sequence estimation of digital sequences in

the presence of intersymbol interference,” IEEE Transactions on Information

Theory, vol. 18, no. 3, pp. 363–378, May 1972.

[82] W. V. Etten, “Maximum likelihood receiver for multiple channel transmission

systems,” IEEE Transactions on Communications, vol. 24, no. 2, pp. 276–283,

February 1976.

134 Bibliography

[83] S. Verdu, “Minimum probability of error for asynchronous gaussian multiple ac-

cess channels,” IEEE Transactions on Information Theory, vol. 32, no. 1, pp.

85–96, January 1986.

[84] D. N. C. Tse and S. V. Hanly, “Linear multiuser receivers: effective interfer-

ence, effective bandwidth and user capacity,” IEEE Transactions on Information

Theory, vol. 45, no. 2, pp. 641–657, August 1999.

[85] C. Sacchi, M. Donelli, L. D’Orazio, R. Fedrizzi, and F. G. B. D. Natale, “Ge-

netic algorithm-based MMSE receiver for MC-CDMA systems transmitting over

time-varying mobile channels,” Electronics Letters, vol. 43, no. 3, pp. 172–173,

February 2007.

[86] Z. Keli, L. G. Yong, and S. Qinghua, “Complexity reduction for MC-CDMA

with MMSEC,” IEEE Transactions on Vehicular Technology, vol. 57, no. 3, pp.

1989–1993, May 2008.

[87] Y. Chi-Hsiao, “MMSE multiuser receiver for uniformly quantized synchronous

CDMA signals in AWGN channels,” IEEE Communications Letters, vol. 11, no. 9,

pp. 705–707, September 2007.

[88] M. K. Varanasi, C. T. Mullis, and A. Kapur, “On the limitation of linear MMSE

detection,” IEEE Transactions on Information Theory, vol. 52, no. 9, pp. 4282–

4286, September 2006.

[89] A. L. Sacramento and W. Hamouda, “Multiuser decorrelator detectors in MIMO

CDMA systems over Nakagami fading channels,” IEEE Transactions on Wireless

Communications, vol. 8, no. 4, pp. 1944–1952, May 2009.

[90] R. Ming, M. C. Reed, and S. Zhenning, “Successive multiuser detection and

interference cancelation for contention based OFDMA ranging channel,” IEEE

Transactions on Wireless Communications, vol. 9, no. 2, pp. 481–487, February

2010.

[91] W. Tsan-Ming and T. Tsung-Hua, “Successive interference cancelers for multi-

media multicode DS-CDMA systems over frequency-selective fading channels,”

Bibliography 135

IEEE Transactions on Information Theory, vol. 55, no. 5, pp. 2260–2282, May

2009.

[92] J. G. Andrews and T. H. Y. Meng, “Performance of multi-carrier CDMA with

successive interference cancellation in a multipath fading channel,” IEEE Trans-

actions on Communications, vol. 52, no. 5, pp. 811–822, May 2004.

[93] P. Patel and J. Holtzman, “Analysis of a simple successive interference cancella-

tion scheme in a DS/CDMA system,” IEEE Journal on Selected Areas in Com-

munications, vol. 12, no. 5, pp. 796–807, June 1994.

[94] B. A. Al-fuhaidi, H. E. A. Hassan, M. M. Salah, and S. S. Alagooz, “Parallel

interference cancellation with different linear equalisation and rake receiver for

the downlink MC-CDMA systems,” IET Communications, vol. 6, no. 15, pp.

2351–2360, March 2012.

[95] N. S. Correal, R. M. Buehrer, and B. D. Woerner, “A DSP-based DS-CDMA mul-

tiuser receiver employing partial parallel interference cancellation,” IEEE Journal

on Selected Areas in Communications, vol. 17, no. 4, pp. 613–630, April 1999.

[96] F. S. Al-Kamali, M. I. Dessouky, and B. M. Sallam, “Regularized multi-stage

parallel interference cancellation for downlink CDMA systems,” IET Communi-

cations, vol. 3, no. 2, pp. 239–248, February 2009.

[97] G. Xue, J. Weng, T. Le-Ngoc, and S. Tahar, “Adaptive multistage parallel inter-

ference cancellation for CDMA,” IEEE Journal on Selected Areas in Communi-

cations, vol. 17, no. 10, pp. 1815–1827, October 1999.

[98] Y. Bar-Shalom and X. R. Li, “Estimation and tracking: principles, techniques

and software,” Artech House, Tech. Rep., 1993.

[99] J. Luo, K. R. Pattipati, P. K. Willett, and F. Hasegawa, “Near-optimal multius-

er detection in synchronous CDMA using probabilistic data association,” IEEE

Communications Letters, vol. 5, no. 9, pp. 361–363, September 2001.

[100] D. Pham, K. R. Pattipati, P. K. Willett, and J. Luo, “A generalized probabilistic

136 Bibliography

data association detector for multiple antenna systems,” IEEE Communications

Letters, vol. 8, no. 4, pp. 205–207, April 2004.

[101] F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, “Factor graphs and the sum

product algorithm,” IEEE Transactions on Information Theory, vol. 47, no. 2,

pp. 498–519, February 2001.

[102] N. Ruozzi and S. Tatikonda, “Message-passing algorithms: re-parameterizations

and splitting,” IEEE Transactions on Information Theory, vol. 59, no. 9, pp.

5860–5881, September 2013.

[103] S. Arora, C. Daskalakis, and D. Steurer, “Message-passing algorithms and im-

proved LP decoding,” IEEE Transactions on Information Theory, vol. 58, no. 12,

pp. 7260–7271, July 2012.

[104] H. Aymeersch, F. Penna, and V. Savic, “Uniformly reweighted belief propaga-

tion for estimation and detection in wireless networks,” IEEE Transactions on

Wireless Communications, vol. 11, no. 4, pp. 1587–1595, April 2012.

[105] L. Hoang-Yang, “Iterative multiuser detectors for spatial-frequency-time-domain

spread multi-carrier DS-CDMA systems,” IEEE Transactions on Vehicular Tech-

nology, vol. 60, no. 4, pp. 1640–1650, May 2006.

[106] L. Ying, V. Chandrasekaran, and A. Anandkumar, “Feedback message passing

for inference in Gaussian graphical models,” IEEE Transactions on Signal Pro-

cessing, vol. 60, no. 8, pp. 4135–4150, May 2012.

[107] L. Tiejun and L. Feichi, “Graph-based low complexity detection algorithms in

multiple-input-multiple-out systems: an edge selection approach,” IET Commu-

nications, vol. 7, no. 12, pp. 1202–1210, August 2013.

[108] D. Reinhard, “Graph theory,” in Springer-Verlag Heidelberg, 2005.

[109] J. Bruck and H. Ching-Tien, “Fault-tolerant cube graphs and coding theory,”

IEEE Transactions on Information Theory, vol. 42, no. 6, pp. 2217–2221, Novem-

ber 1996.

Bibliography 137

[110] D. Burshtein and G. Miller, “Expander graph arguments for message-passing

algorithms,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 782–

790, February 2001.

[111] M. Hamdi, V. Krishnamurthy, and G. Yin, “Tracking a Markov-modulated sta-

tionary degree distribution of a dynamic random graph,” IEEE Transactions on

Information Theory, vol. 60, no. 10, pp. 6609–6625, September 2014.

[112] R. Mori, T. Tanaka, and K. Kasai, “Effects of single-cycle structure on iterative

decoding of low-density parity-check codes,” IEEE Transactions on Information

Theory, vol. 59, no. 1, pp. 238–253, January 2013.

[113] M. E. O’Sullivan, “Algebraic construction of sparse matrices with large girth,”

IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 718–727, February

2006.

[114] H. Jun and K. M. Chugg, “Optimization of scaling soft information in iterative de-

coding via density evolution methods,” IEEE Transactions on Communications,

vol. 53, no. 6, pp. 957–961, June 2005.

[115] W. Chih-Chun, S. R. Kulkarni, and H. V. Poor, “Density evolution for asymmet-

ric memoryless channels,” IEEE Transactions on Information Theory, vol. 51,

no. 12, pp. 4216–4236, December 2005.

[116] C. Sae-Young, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product

decoding of low-density parity-check codes using a Gaussian approximation,”

IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 657–670, February

2001.

[117] S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated

codes,” IEEE Transactions on Communications, vol. 49, no. 10, pp. 1727–1737,

October 2001.

[118] L. Hanzo, T. Liew, B. Yeap, R. Tee, and S. Ng, “Turbo coding, turbo equalisa-

tion and space-time coding: EXIT-chart-aided near-capacity designs for wireless

channels,” in John Wiley & Sons, second edition - IEEE Press, 2011.

138 Bibliography

[119] M. El-Hajjar and L. Hanzo, “EXIT charts for system design and analysis,” IEEE

Communications Surveys & Tutorials, vol. 16, no. 1, pp. 127–153, February 2014.

[120] D. J. C. Mackay, “Information theory, inference, and learning algorithms,” Cam-

bridge University Press, Tech. Rep., 2003.

[121] E. Sharon, A. Ashikhmin, and S. Litsyn, “Analysis of low-density parity-check

codes based on EXIT functions,” IEEE Transactions on Communications, vol. 54,

no. 8, pp. 1407–1414, August 2006.

[122] M. Ardakani, T. H. Chan, and F. R. Kschischang, “EXIT-chart properties of the

highest-rate LDPC code with desired convergence behavior,” IEEE Communica-

tions Letters, vol. 9, no. 1, pp. 52–54, January 2005.

[123] T. M. Cover and J. A. Thomas, “Elements of information theory,” in John Wiley

& Sons - IEEE Press, 2006.

[124] R. G. Gallager, “Low-density parity-check codes,” IRE Transactions on Infor-

mation Theory, vol. 8, no. 1, pp. 21–28, January 1962.

[125] C. Jinghu, R. M. Tanner, Z. Juntan, and M. P. C. Fossorier, “Construction of

irregular LDPC codes by quasi-cyclic extension,” IEEE Transactions on Infor-

mation Theory, vol. 53, no. 4, pp. 1479–1483, April 2007.

[126] B. L. Gal, C. Jego, and C. Leroux, “A flexible NISC-based LDPC decoder,” IEEE

Signal Processing Magazine, vol. 62, no. 10, pp. 2469–2479, March 2014.

[127] M. Baldi, F. Bambozzi, and F. Chiaraluce, “On a family of circulant matrices for

quasi-cyclic low density generator matrix codes,” IEEE Transactions on Infor-

mation Theory, vol. 57, no. 9, pp. 6052–6067, September 2011.

[128] A. Barbieri and G. Colavolpe, “On the information rate and repeat-accumulate

code design for phase noise channels,” IEEE Transactions on Communications,


[129] J. Abouei, J. D. Brown, and K. N. Plataniotis, “On the energy efficiency of

LT codes in proactive wireless sensor networks,” IEEE Transactions on Signal

Processing, vol. 59, no. 3, pp. 1116–1127, November 2010.

Bibliography 139

[130] N. Bonello, Y. Yuli, S. Aissa, and L. Hanzo, “Myths and realities of rateless

coding,” IEEE Communication Magazine, vol. 49, no. 8, pp. 143–151, August

2011.

[131] A. Shokrollahi, “Raptor codes,” IEEE Transactions on Information Theory,

vol. 52, no. 6, pp. 2551–2567, June 2006.

[132] T. L. Narasimhan and A. Chockalingam, “EXIT chart based design of irregular

LDPC codes for large-MIMO systems,” IEEE Communications Letters, vol. 17,

no. 1, pp. 115–118, November 2012.

[133] T. L. Narasimhan, A. Chockalingam, and B. S. Rajan, “Factor graph based joint

detection/decoding for LDPC coded large-MIMO systems,” in IEEE Vehicular

Technology Conference (VTC Spring), May 2012, pp. 1–5.

[134] R. Koetter, A. C. Singer, and M. Tuchler, “Turbo equalization,” IEEE Signal

Processing Magazine, vol. 21, no. 1, pp. 67–80, January 2004.

[135] A. Mirzaee and C. D’Amours, “Turbo receiver for DS-SS systems employing

parity bit selected spreading codes,” IEEE Communication Letters, vol. 16, no. 4,

pp. 426–428, February 2012.

[136] J. Boutros and G. Caire, “Iterative multiuser joint decoding: unified framework

and asymptotic analysis,” IEEE Transactions on Information Theory, vol. 48,

no. 7, pp. 1772–1793, January 2002.

[137] O. Sanchez, C. Jego, and M. Jezequel, “Analysis of the convergence process by

EXIT Charts for parallel implementations of turbo decoders,” IEEE Communi-

cation Letters, vol. 17, no. 7, pp. 1427–1430, July 2013.

[138] K. Li and X. Wang, “EXIT chart analysis of turbo multiuser detection,” IEEE

Transactions on Wireless Communications, vol. 4, no. 1, pp. 300–311, January

2005.

[139] E. Institute, “Selection procedures for the choice of radio transmission technolo-

gies of the UMTS,” Tech. Rep., 1998.

140 Bibliography

[140] I. A. Chatzigeorgiou, R. D. Rodrigues, J. Wassell, and R. A. Carrasco, “Com-

parison of convolutional and turbo coding for broadband FWA systems,” IEEE

Transactions on Broadcasting, vol. 53, no. 2, pp. 494–503, June 2007.

[141] U. Jayasinghe, N. Rajatheva, and M. Latva-Aho, “Application of a leakage based

precoding scheme to mitigate intrinsic interference in FBMC,” in IEEE Interna-

tional Conference on Communications (ICC), June 2013, pp. 5268–5272.

[142] M. G. S. Sriyananda and N. Rajatheva, “Analysis of self interference in a basic F-

BMC system,” in IEEE Vehicular Technology Conference (VTC Fall), September

2013, pp. 1–5.

[143] J. Du, P. Xiao, and J. Wu, “Design of isotropic orthogonal transform algorithm-

based multicarrier systems with blind channel estimation,” IET Communications,

vol. 6, no. 16, pp. 2695–2704, November 2012.

[144] V. Erceg, K. Hari, and S. Smith, “Channel models for fixed wireless applications,”

IEEE 802.16.3c-01/29r4, Tech. Rep., 2003.

[145] Y. Fang, B. Guoan, G. Yongliang, and F. C. M. Lau, “A survey on protograph

LDPC codes and their applications,” IEEE Communications Surveys & Tutorials,

vol. 17, no. 4, pp. 198–2016, May 2015.

[146] M. Karimi and A. H. Banihashemi, “On the girth of quasi-cyclic protograph

LDPC codes,” IEEE Transactions on Information Theory, vol. 59, no. 7, pp.

4542–4552, March 2013.

Non-Orthogonal Multiple Access Schemes for Future Cellular...

Documents

Transcript of Non-Orthogonal Multiple Access Schemes for Future Cellular...