joumana implementação e avaliação do desempenho de

Universidade de AveiroDepartamento de Eletrónica,Telecomunicações e Informática

2020

Joumana

Kassam

Implementação e avaliação do desempenho de

sistemas MIMO GFDM

Implementation and performance evaluation of

MIMO GFDM systems

“Success is not final, failure is not fatal: it is the courage to con-

tinue that counts”

— Winston Churchill


2020

Joumana

Kassam


sistemas MIMO GFDM


MIMO GFDM systems


2020

Joumana

Kassam


sistemas MIMO GFDM


MIMO GFDM systems

Dissertação apresentada à Universidade de Aveiro para cumprimento dos

requisitos necessários à obtenção do grau de Mestre em Engenharia Elec-

trónica e Telecomunicações, realizada sob a orientação científica do Doutor

Professor Adão Silva, Professor Auxiliar da Universidade de Aveiro do Depar-

tamento de Eletrónica, Telecomunicações e Informática da Universidade de

Aveiro, e do Doutor Daniel Castanheira, investigador auxiliar no Instituto de

Telecomunicações pólo de Aveiro.

This work is supported by the European Regional Development Fund (FEDER), through the Competitiveness

and Internationalization Operational Program (COMPETE 2020) of the Portugal 2020 framework, Regional OP

Centro (CENTRO 2020), Regional OP Lisboa (LISBOA 14-20) and by FCT/MEC through national funds, under

Project MASSIVE5G (AAC no 02/SAICT/2017).

Global Platform for Syrian Students Scholarship.

o júri / the jury

presidente / president Professor Doutor António Luís Jesus Teixeira

Professor Associado C/ Agregação, Universidade de Aveiro

vogais / examiners committee Professor Doutor Rui Miguel Henriques Dias Morgado Dinis

Professor Associado Com Agregação, Universidade Nova de Lisboa

Professor Doutor Adão Paulo Soares da Silva

Professor Auxiliar, Universidade de Aveiro

agradecimentos /

acknowledgements

First of all, I would like to thank my supervisor Professor Adão Silva and my

co-supervisor Doctor Daniel Castanheira for their continuous support, help,

exceptional supervision, mentoring, and review of my thesis document with

their expert opinions.

I would like to thank the Global Platform for Syrian Students represented

by former President Jorge Sampaio and his Diplomatic Adviser Dr. Helena

Barroco. I am really grateful to the Portuguese for the enormous opportunity

that was given to me for achieving my goal by proceeding the higher studies.

My heartiest gratitude goes to my husband and all my family for their

love, trust, affection, patience, and support throughout this study period. I am

also grateful to all my friends and my colleagues in IT for providing assistance

and a friendly working environment.

Last but not least, thank you very much to the University of Aveiro, the

Department of Electronics, Telecommunications, and Informatics and the

Instituto de Telecomunicações for providing the necessary conditions of work

and learning.

Palavras Chave 5G, Além 5G, Esquemas de modelação, GFDM, MIMO, Técnicas de cancela-

mento de interferência.

Resumo A tecnologia OFDM é utilizada nos sistemas de telecomunicações 4G e será

também nos sistemas 5G. Apesar das suas características e resultados,

é possível melhorar a sua performance em termos de eficiência espectral.

GFDM é um novo conceito de modulação digital de multiportadora não

ortogonal. Esta tem como objetivos alcançar uma maior eficiência espectral,

um melhor controlo de emissões OOB(emissões fora da banda), devido à sua

flexibilidade para escolher um filtro de modelação de pulso, e ainda reduzir

o PAPR comparativamente ao OFDM. A eficiência espectral em redes sem

fios pode ainda ser melhorada através do uso da tecnologia MIMO, tendo

sido adotada em vários sistemas comerciais. Assim sendo, a combinação

da tecnologia MIMO com a modulação GFDM permite melhorar considera-

velmente o desempenho dos sistemas, já que melhora a eficiência espectral

e combate de forma eficaz o desvanecimento através da combinação dos

sinais independentes, provenientes das múltiplas antenas. Além disso,

esta combinação consegue proporcionar um ganho de multiplexagem que

melhora a performance da rede.

Esta dissertação foca-se na implementação e avaliação da modulação

GFDM, para os diferentes tipos de estruturas de antenas SISO, SIMO e

MIMO. Em primeiro lugar, implementou-se o sistema SISO-GFDM, conside-

rando a adição de ruido branco Gaussiano e desvanecimento de Rayleigh

do canal. Vários equalizadores no domínio da frequência foram implemen-

tados para mitigar o desvanecimento e remover a ICI (interferência entre

portadoras) residual, tais como os equalizadores MF e ZF. Posteriormente,

o sistema SISO para um único utilizador for estendido para um sistema

SIMO e MIMO multiutilizador, onde um conjunto de utilizadores equipados

com apenas uma antena transmitem, usando os mesmos recursos rádio,

para uma estação base equipada com múltiplas antenas. Estes sistemas

enfrentam interferências entre portadores e entre utilizadores que têm que

ser mitigadas. Assim, foram projetados e implementados dois equalizadores

sub ótimos, ZF e MMSE, para remover essas interferências. O sistema

implementado GFDM é comparado como o OFDM em termos de taxa de erro

(BER) e da densidade espectral de potência. Os resultados mostram que

as técnicas propostas são bastante eficientes a remover as interferências

levando a uma melhoria significativa do desempenho do sistema.

Keywords 5G, Beyond 5G, Modulation schemes, GFDM, MIMO, Interference Cancella-

tion techniques.

Abstract The Orthogonal Frequency Division Multiplexing (OFDM) technology has

been used in 4G and 5G mobile telecommunications systems. Despite its

features and advanced results, it has some challenges to enhance spectral

efficiency. Generalized Frequency Division Multiplexing (GFDM) is a new dig-

ital non-orthogonal multicarrier modulation concept. It aims to achieve higher

spectral efficiency, better control of Out-Of-Band (OOB) emissions due to its

flexibility to choose the pulse shaping filter, and obtain a reduction in Peak

to Average Power Ratio (PAPR) compared to the OFDM. MIMO can further

improve the spectral efficiency of the wireless network and has adopted in

several standards. Therefore, the combination of MIMO transmission with

GFDM technique is almost able to present optimum results due to its ability to

have diversity gain by combining independent signals from multiple antennas

in order to mitigate the fading phenomenon. Besides, it can also achieve

multiplexing gain that improves the throughput of the networks.

This study addresses the implementation and evaluation of a GFDM

system for different antenna structures such as SISO, SIMO, and MIMO. First,

SISO-GFDM system is implemented, considering Additive White Gaussian

Noise (AWGN) channel and Rayleigh fading channel. Several frequency

domain equalizers are used to mitigate the fading and remove the residual

Inter-Carrier Interference (ICI) such as Matched Filter (MF) and Zero Forcing

(ZF) equalizers. Then, the system was extended to SIMO and Multi-User

MIMO (MU-MIMO), where a set of single-antenna users transmit to the

base station, equipped with a multi-antenna array, using the same radio

resources. In MU-MIMO system besides the ICI, it also suffers from multi-user

interference. Therefore, in this case, two sub-optimal receiver equalizers have

been implemented to deal with both ICI and multi-user interferences such as

(ZF and MMSE equalizer). The GFDM system is compared with the OFDM in

terms of bit error rate (BER) and power spectral density. The results show that

the Interference Cancellation (IC) techniques (Serial Interference Cancellation

(SIC) and Double Sided Serial Interference Cancellation (DSSIC)) are quite

efficient to mitigate both the multi-user interference and the adjacent ICI,

improving the overall system performance.

Acronyms

0G Generation 0

16-QAM 16 Quadrature Amplitude Modulation

1G First Generation

2G Second Generation

3G Third Generation

3GPP Third Generation Partnership Project

3GPP2 Third Generation Partnership Project 2

4G Fourth Generation

5G Fifth Generation

6G Sixth Generation

AMPS Analog Mobile Phone System

AWGN Additive White Gaussian Noise

BER Bit Error Rate

CDMA Code Division Multiple Access

CDMA EV-DO CDMA EVolution-Data Only

CP Cyclic Prefix

CSI Channel Sate Information

D2D Device-to-Device

DAS Distributed Antenna System

dB Decibels

D-BLAST Diagonal Bell Labs Space-Time Architecture

DFDMA Distributed Frequency Division Multiple Access

DFE Decision-Feedback Equalization

DFT Discrete Fourier Transform

DoF Degrees-of-Freedom

DSSIC Double Sided Serial Interference Cancellation

DTV Digital Television

EDGE Enhanced Data GSM Evolution

EGC Equal Gain Combining

FBMC Filter Bank Multi Carrier

FDD Frequency Division Duplex

FDMA Frequency Division Multiple Access

FFT Fast Fourier Transform

GFDM Generalized Frequency Division Multiplexing

GPRS General Packet Radio Services

i

GSM Global System for Mobile communication

HD High Definition

HSPA High Speed Packet Access

HSDPA High Speed Downlink Packet Access

HSUPA High Speed Uplink Packet Access

IC Interference Cancellation

ICI Inter Carrier Interference

IDFT Inverse Discrete Fourier Transform

IEEE Institute of Electrical and Electronics Engineers

IFFT Inverse Fast Fourier Transform

IMT International Mobile Telecommunications

IMTS Improved Mobile Telephone System

IoT Internet of Things

IP Internet Protocol

ISI Inter Symbol Interference

ITU International Telecommunication Union

LAN Local Area Network

LFDMA Localized Frequency Division Multiple Access

LOS Line-of-Sight

LSTC Layered Space-Time Code

LTE Long Term Evolution

M2M Machine-to-Machine

MF Matched Filter

MIMO Multiple Input Multiple Output

MISO Multiple Input Single Output

mMIMO Massive Multiple Input Multiple Output

MMS Multimedia Message Service

MMSE Minimum Mean Square Error

mmW millimeter Wave

MRC Maximal Ratio Combining

MTS Mobile Telephone System

MU-MIMO Multiple-User MIMO

NFV Network Function Virtualization

NLOS Non Line-of-Sight

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

OOB Out-Of-Band

OQAM Offset Quadrature Amplitude Modulation

PAPR Peak to Average Power Ratio

PDF Probability Density Function

PDP Power Delay Profile

PL Path Loss

PSD Power Spectral Density

PSTN Public Switched Telephone Network

PTT Push To Talk

QoS Quality of Service

ii

QPSK Quadrature Phase Shift Keying

RAT Radio Access Technology

RF Radio Frequency

RRC Root Raised Cosine

SC Selection Combining

SC-FDMA Single Carrier FDMA

SDN Software Defined Networks

SIC Serial Interference Cancellation

SIMO Single Input Multiple Output

SISO Single Input Single Output

SMS Short Message Services

SNR Signal-to-Noise power Ratio

STBC or SFBC Space-Time/Frequency Block Coding

STTC Space-Time Trellis Code

SU-MIMO Single-User MIMO

SVD Singular Value Decomposition

TDD Time Division Duplex

TDMA Time Division Multiple Access

UFMC Universal Filtered Multi Carrier

UMTS Universal Mobile Telecommunication System

V-BLAST Vertical Bell Labs Space-Time Architecture

WAN Wide Area Network

WAP Wireless Application Protocol

WCDMA Wide band Code Division Multiple Access

WiMAX Worldwide Interoperability for Microwave Access

WLAN Wireless Local Area Network

WRAN Wireless Regional Area Networks

WWW World Wide Web

ZF Zero Forcing

iii

Contents

Acronyms i

Contents v

List of Figures vii

List of Tables ix

1 Introduction 1

1.1 History and evolution of mobile telecommunications . . . . . . . . . . . . . . . . . . . 1

1.2 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Structure of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Basic Concepts 11

2.1 Wireless Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Radio-Propagation Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.2 Propagation characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.3 Channel characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.3.1 Doppler Spread and Coherence Time . . . . . . . . . . . . . . . . . 15

2.1.3.2 Delay Spread and Coherence Bandwidth . . . . . . . . . . . . . . . 17

2.1.3.3 Fading distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Modulation Schemes suitable in 4G and 5G Technologies . . . . . . . . . . . . . . . . 20

2.2.1 Orthogonal Frequency Division Multiplexing (OFDM) . . . . . . . . . . . . . 20

2.2.2 Single Carrier-Frequency Division Multiple Access (SC-FDMA) . . . . . . . . 24

2.3 Modulation Schemes suitable for beyond 5G Technology . . . . . . . . . . . . . . . . 26

2.3.1 Filter Bank Multi Carrier (FBMC) . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3.2 Universal Filtered Multi Carrier (UFMC) . . . . . . . . . . . . . . . . . . . . 27

2.3.3 Generalized Frequency Division Multiplexing (GFDM) . . . . . . . . . . . . . 28

3 Multiple Antennas Technologies 31

3.1 Introduction to MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

v

3.1.1 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.1.1 Time and Frequency Diversity . . . . . . . . . . . . . . . . . . . . . 33

3.1.1.2 Space Antennas Diversity . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.2 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.2.1 Linear sub-optimal receiver architectures . . . . . . . . . . . . . . . 41

4 Implementation of a GFDM System 45

4.1 SISO-GFDM System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Low Complexity SISO-GFDM Transmitter Model . . . . . . . . . . . . . . . . 45

4.1.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.3 Low Complexity SISO-GFDM Receiver Model . . . . . . . . . . . . . . . . . . 47

4.1.4 SISO Interference Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.1.5 Results of SISO-GFDM system . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.1.5.1 Results of linear equalization schemes MF and ZF . . . . . . . . . . 53

4.1.5.2 Results of Interference Cancellation (IC) schemes . . . . . . . . . . 55

4.2 SIMO-GFDM System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2.1 SIMO-GFDM System with 2Rx antennas . . . . . . . . . . . . . . . . . . . . 57

4.2.2 Results of SIMO-GFDM system . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2.2.1 Results of SIMO-GFDM system for 2Rx antennas . . . . . . . . . . 58

4.2.2.2 Results of SIMO-GFDM system for 4Rx antennas . . . . . . . . . . 59

4.3 MIMO-GFDM System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3.1 MIMO-GFDM System with 2Tx and 2Rx antennas . . . . . . . . . . . . . . . 61

4.3.2 Results of MIMO-GFDM system . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3.2.1 Results of MIMO-GFDM system for 2Tx and 2Rx antennas . . . . 63



4.4 Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Conclusion and Future Work 67

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

References 69

vi

List of Figures

1.1 Cellular mobile communications evolution [5] . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 GSM network architecture [10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Comparison between 1G, 2G, and 3G [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Comparison between the principle of OFDMA and CDMA [15] . . . . . . . . . . . . . . . 6

1.5 Comparison between 4G and 5G mobile telecommunications networks [16] . . . . . . . . 7

1.6 5G use cases [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1 Radio wave propagation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Components of channel response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Channel modeling [26] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Fast Fading and Slow Fading [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Rayleigh distribution PDF [35] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Rician distribution PDF [36] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.7 The orthogonality concept in OFDM Signal [40] . . . . . . . . . . . . . . . . . . . . . . . 20

2.8 Block diagram of an OFDM system [41] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.9 The duration of OFDM [41] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.10 The duration of OFDM after inserting the Cyclic Prefix [41] . . . . . . . . . . . . . . . . 23

2.11 The difference between OFDM and OFDMA [43] . . . . . . . . . . . . . . . . . . . . . . . 24

2.12 Block diagram of an SC-FDMA system [41] . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.13 Subcarrier mapping methods for multiple users [41] . . . . . . . . . . . . . . . . . . . . . 26

2.14 Block diagram of an FBMC system [20] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.15 Block diagram of an UFMC system [20] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.16 GFDM Transmitter System Model [48] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.17 GFDM Receiver System Model [48] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.18 The self-interference in the k-th subcarrier from adjacent subcarriers [48] . . . . . . . . . 30

3.1 Single and Multiple antennas configurations [50] . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Time diversity illustration [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Performance of repetition coding [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4 Space antennas diversity [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5 Receive diversity scheme [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6 MIMO System [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7 Schematic of linear receiver architectures [53] . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 Low complexity SISO-GFDM transmitter system model [55] . . . . . . . . . . . . . . . . 46

vii

4.2 Low complexity SISO-GFDM receiver system model [56] . . . . . . . . . . . . . . . . . . 47

4.3 Block diagram of a SISO-GFDM receiver with the equalization process . . . . . . . . . . 49

4.4 SISO-GFDM receiver with Interference Cancellation block [48] . . . . . . . . . . . . . . . 49

4.5 Interference Cancellation Unit [48] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.6 Basic SIC flowchart [48] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.7 Double Sided SIC flowchart [48] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.8 SISO-GFDM BER performance for QPSK modulation with different roll-off-factor and

AWGN channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.9 SISO-GFDM BER performance for QPSK modulation with different roll-off-factor and

multipath channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.10 SISO OFDM and GFDM Basic SIC and DSSIC BER performance for QPSK modulation

with α = 0.5 and AWGN channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.11 SISO OFDM and GFDM Basic SIC and DSSIC BER performance for QPSK modulation

with α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.12 Low complexity SIMO-GFDM receiver system model for 2Rx antennas . . . . . . . . . . 57

4.13 SIMO OFDM and GFDM BER performance for QPSK modulation and 2Rx antennas with

different roll-off-factor and multipath channel used . . . . . . . . . . . . . . . . . . . . . . 58


α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59


different roll-off-factor and multipath channel used . . . . . . . . . . . . . . . . . . . . . . 59


α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.17 Low complexity 2 × 2MIMO-GFDM transmitter system model . . . . . . . . . . . . . . . 61

4.18 2 × 2MIMO channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.19 Low complexity 2 × 2MIMO-GFDM receiver system model . . . . . . . . . . . . . . . . . 62

4.20 2 × 2MIMO OFDM and GFDM BER performance by using ZF equalizer for QPSK

modulation with α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . 63

4.21 2 × 2MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSK


4.22 4 × 4MIMO OFDM and GFDM BER performance by using ZF equalizer for QPSK


4.23 4 × 4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSK


4.24 2x4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSK


4.25 PSD comparison between OFDM and GFDM with α = 0.5 of RRC pulse shaping filter . 66

viii

List of Tables

2.1 Parameters of a well designed OFDM System [41] . . . . . . . . . . . . . . . . . . . . . . 23

4.1 OFDM and GFDM Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2 Power Delay Profile used in simulation [25] . . . . . . . . . . . . . . . . . . . . . . . . . . 54

ix

CHAPTER 1Introduction

The overview of history and birth of radio communications generations is the main topic,

before explaining the motivations and objectives of this dissertation, in terms of the features

of every generation, started with First Generation (1G) to end with Fifth Generation (5G) of

the wireless system. Then, it is presented the structure of this document.

1.1 History and evolution of mobile telecommunications

The birth of radio communication was between the 19th and 20th centuries. Many

experiments and theories were studied and proven before talking about radio communication,

starting with Faraday that predicted the existence of electromagnetic fields to James Clerk

Maxwell in 1864, who was focused on his theoretical and mathematical researches to clarify

that the electromagnetic waves could be propagated through free space [1]. Besides many

scientists worked on this subject by testing a series of experiments to prove Maxwell’s theory.

In 1886–88, Heinrich Rudolf Hertz confirmed the existence of Maxwell’s electromagnetic waves

by using the frequency in the radio spectrum [1].

There are many interested people who are wondering about the first radio communication

and the first mobile phone in the history of science. The Italian inventor Guglielmo Marconi in

1895 was the first scientist in using the radio waves for successfully transmitting and receiving

radio signals. Therefore, transmitting weather information was the first voice transmissions

over a distance of about one mile in 1900, and in 1901 he achieved transmitting the first

voice communication crossed the Atlantic. Then, many scientists and engineers started

working to develop and improve the ways of communications by using Radio Frequency (RF)

waves [1] [2]. While in the 1970s at Motorola, the engineer Martin Cooper was worked to

invent the first mobile phone that was considered the first generation of mobile communi-

cation, where it was a handheld device, was able to make of two-way connection wirelessly.

This led to an evolution of many technologies and standards in wireless systems in the future [2].

1

The development of cellular wireless communications systems was not limited to a specific

stage, it had gone through several evolution stages from simple technologies to more developed

ones that are using in our life and nowadays has experienced a remarkable change. This returns

to the huge demand for more advanced connections to serve more users at the same time [3].

In the last few decades, it can be noted the advancement of mobile wireless communication

through the Generations (G) that refers to a change in the nature of the system and each

one has some standards in terms of the technology used, data rates, frequency, speed and so

on. It was started with the First Generation 1G, Second Generation (2G), ..., ending with an

upcoming generation 5G and the innovation of generations is still going on [4]. The evolution

of mobile generations will be described to identify the advanced wireless technologies that

were used and explaining how improvements have been made from the 1G to the next ones as

shown in figure 1.1.

Figure 1.1: Cellular mobile communications evolution [5]

Wireless system is began with pre-cellular mobile telephony technology that indicated

to Generation 0 (0G) [6]. It is used by public services such as police radiotelephones. 0G

involves different technologies as Push To Talk (PTT), Mobile Telephone System (MTS),

and Improved Mobile Telephone System (IMTS) [6]. Pre-cell phone mobile technology was

developed in the 1970s to arrive the first generation of mobile network [7].

1G

The first generation of mobile network started deploying in Japan in 1979 to arrive US,

Finland, UK and Europe in the beginning of 1980s, where the first mobile phones were

introduced in 1982 and continued until the early of 1990. It was based on Analog Mobile

Phone System (AMPS) technique that depends on analog radio signals only for voice services.

The voice call can be modulated by Frequency Division Multiple Access (FDMA) with

bandwidth of 10 MHz, channel capacity of 30 KHz and frequency band of 800 and 900 MHz

with velocities up to 2.4kbps [4]. Due to the technology limitations, this system has many

disadvantages. It has low and limited capacity, poor voice quality, unreliable handoff, poor

battery life, large phone size, less security, limited number of users, very low level of spectrum

efficiency, and there is no possibility for roaming between similar systems [4] [6] [8].

2

2G

The 1G is analog telecommunication standard uses circuit switching, continued until has

been replaced by 2G in late 1980s and finished in late 1990s that uses circuit switching as

well as packet switching and based on digital signals for voice transmission besides the Short

Message Services (SMS), and Multimedia Message Service (MMS) at low speed from 14.4 to

64kbps data rate [9] with bandwidth of 20-200KHz [8]. Unlike the 1G systems, 2G systems

provide the Internet service and thus the core network used is Public Switched Telephone

Network (PSTN) [3]. 2G phones used a new digital technology for wireless transmission

known as Global System for Mobile communication (GSM) technology as shown in figure

1.2, it uses digital modulation to improve the voice quality that based on Time Division

Multiple Access (TDMA) and Code Division Multiple Access (CDMA) standards, in addition

to use the CODEC for compressing and multiplexing digital voice data [8]. 2G systems used

combination of TDMA and FDMA which means each frequency slot is divided into time slots,

i.e., multiple users are able to connect the network with a specific frequency slot [3] [10]. This

led to better quality and capacity, enhance the spectral effieciency, security, and the number

of users. Besides the roaming, encrypted voice transmission and SMS services [4] [9].

Figure 1.2: GSM network architecture [10]

Although the lower data rate of 2G systems and the limited number of users and hard-

ware capability, the demand of using its services experienced exponential growth in mobile

telecommunication systems and this led to develop the cellular wireless technology to 2.5G

system for acheiving higher data rate between 64-115kbps [8] and based on General Packet

Radio Services (GPRS) that was introduced and successfully deployed. Beside Enhanced

Data GSM Evolution (EDGE) that is considered 2.75G and an extended version of GSM, is

able to support up to 473.6kbps [11]. 2.5G and 2.75G networks support services like Wireless

Application Protocol (WAP), mobile games and Internet communication services such as

send/receive emails, web browsing, camera phones [8] [10].

3

3G

From 2G to Third Generation (3G) technology, which means increasing the data rate trans-

mission to reach 2Mbps [3] [12]. This technology was launched in the year 2000, supported

for multimedia cell phone (smartphone) [8]. 3G is based on International Telecommunication

Union (ITU) standards under the International Mobile Telecommunications (IMT) program

(IMT-2000) [6] [12]. In 2G systems, to download a 3 minutes MP3 song, this will take time

about 6-9 minutes [4], while in 3G system it needs just around 11 seconds for downloading [8].

This led to increasing the bandwidth and transfer rate for accommodating the applications

that depend on web and audio and video files. Besides offer users with a wider range of

advanced services and this requires improving the spectral efficiency and achieving a greater

network capacity [6] [12]. Figure 1.3 shows the comparison between the previous generations

with 3G.

Figure 1.3: Comparison between 1G, 2G, and 3G [12]

Herein, the core network used is a combination of Circuit switching and Packet switching

where several access technologies had an important role in this wireless generation such as

CDMA and Wide band Code Division Multiple Access (WCDMA). In CDMA, for each user,

there is a unique code for using the channel at the same time, which means each user is able

to use completely the available bandwidth and thus a large number of users have the ability

to use the channel simultaneously [3]. It provides a 1.25MHz channel width with a data rate

up to 144kbps [8]. In WCDMA or Universal Mobile Telecommunication System (UMTS),

more amount of users can use the channel in comparison with CDMA, it has 5MHz channel

width with data rate up to 2Mbps [8]. Therefore, the main features of 3G are: achieving

higher data rate and higher quality 3D games, provides faster communication and mobile

applications, enhanced security, supporting location tracking, maps and TV streaming, and

enhanced audio and video streaming. But all of these require higher bandwidth and large and

expensive 3G cell phones [4] [6] [11].

For standarization of 3G technologies, Third Generation Partnership Project (3GPP) and

Third Generation Partnership Project 2 (3GPP2) were created to work for that purpose

and both of them are based on CDMA although the carrier bandwidth and data rates were

different. Besides defining technologies for achieving higher data rates above 1Mbps [13] by

using the time division among the data flows on the downlink within the cell. 3GPP system is

4

also called High Speed Packet Access (HSPA) while 3GPP2 ia called CDMA EVolution-Data

Only (CDMA EV-DO).

Enhancing the data rate is always required and thus was existing in 3G systems by applying

two improvement technologies which are: High Speed Downlink Packet Access (HSDPA) and

High Speed Uplink Packet Access (HSUPA). HSDPA is considered 3.5G, based on WCDMA

with data transmission speed up to 8-10Mbps with a bandwidth of 5MHz [6] [12]. While

HSUPA refers to 3.75G, it has higher data rate, is an improving uplink speed of UMTS

/ WCDMA system to be initially up to 1.4Mbps and then it reached to 5.8Mbps in the

later releases [6] [12]. These two mobile telecommunications technologies are related and

complimentary to each other and allow the possibility to the concept of Multiple Input

Multiple Output (MIMO) system to be introduced and thus the data rate can reach to more

than 42Mbps [3].

4G

Moving to the Fourth Generation (4G) systems means achieving higher data rate speed

of 100Mbps for mobile user [8] [6] and up to 1Gbps for fixed stations [6] and thus higher

quality audio/video streaming. To make this system efficient, it is necessary to design of new

terminals. 4G is considered as a successor to 2G and 3G standards and the extension of 3G

technology with more advanced multimedia services offers and more bandwidth. Noting that

the core network used is based on Internet Protocol (IP) and the frequency band is between

2000 to 8000MHz with frequency spectrum used between 5-20MHz [3].

In this generation of cellular telecommunication systems, Long Term Evolution (LTE)

is considered a 4G standard, it is designed by the ITU in the late 1990s [14] and based on

GSM / EDGE and UMTS / HSPA technologies [3]. It is able to achieve around 100Mbps

for downlink speed and 50Mbps for uplink speed [3]. 3G technologies are developed by

ITU to IMT-2000 which was focused on publishing a set of requirements for 3G cellular

communication systems and this led to launch another process which is IMT-Advanced by

publishing a set of requirements for a 4G mobile communication system in 2008 [14]. The

requirement of ITU for the second process IMT-Advanced exceeded the capabilities of LTE

because it needed at least 600Mbps for downlink and 270Mbps for uplink with a bandwidth

40MHz [14]. Therefore, 3GPP was found that LTE-Advanced is able to improve and enhance

the capabilities of LTE by achieving a maximum data rate of 1000Mbps for the downlink and

500Mbps for the uplink and according to this standards, LTE-Advanced was designed to be

compatible with LTE [14].

In the other hand, the multiple access techniques are able to allow the base station to

communicate with different mobiles simultinuously and thus 4G systems use multi carrier

schemes such as Orthogonal Frequency Division Multiple Access (OFDMA) technique due to

the data traffic is different from voice and it needs high peak rates just for short durations

5

[13]. Besides, in case of using multiple antennas, Orthogonal Frequency Division Multiplexing

(OFDM) as shown in figure 1.4 is better than CDMA due to the orthogonality where the

high data rate modulated stream is placed into many modulated narrowband closed-spaced

subcarriers and thus improving the throughput by using a new dimension of spatial diversity

[3] [15]. OFDMA technique is used as a downlink multiple access technique while Single

Carrier FDMA (SC-FDMA) is used as an uplink multiple access technique (more details

about OFDM and SC-FDMA are described in chapter 2).

Figure 1.4: Comparison between the principle of OFDMA and CDMA [15]

Therefore, 4G has many features complementary to 3G such as achieving higher data

rate up to 1Gbps and higher quality video streaming, high security and mobility, expanded

multimedia services to include digital television in High Definition (HD) technique and

reduced latency for mission critical applications. However, 4G requires complicated expensive

hardware and infrastructure because it needs high end mobile devices compatible with 4G

technology and also uses more battery [4] [7].

5G

As highlighted before, it can be noted that 4G is one of the most used and dominant cellular

communications technologies in the world by delivering the required speeds. Although all

features of previous generations, there are still some challenges such as high energy consumption

and the spectrum efficiency that can not be accommodated by 4G mobile telecommunication

systems. Therefore, 5G in the near future is considered the next wireless system that will be

deployed in 2020 [9]. The comparison between 4G and 5G is depicted in figure 1.5, where

with 5G technology, it can be possible to handle best and advanced technologies [9] with

much reliability, ultra-fast Internet and multimedia services, better levels of connectivity and

coverage, and without the limitations and obstacles of the previous generations [6].

6

Figure 1.5: Comparison between 4G and 5G mobile telecommunications networks [16]

5G seeks to extend the frequency bands used for mobile telecommunications systems,

besides using advanced modulation techniques to be able to achieve its features by applying

small cell deployment, and utilizing wider frequency spectrum. This requires frequency

bandwidth for cellular phones ranging between several hundred MHz to several GHz [7], to

achieve data rate speed up to 10Gbps [17]. Therefore, 5G networks will be operated in the

millimeter waves (fall between 30 and 300GHz band of the spectrum) which means a high

spectrum frequency band between 28GHz and 60GHz [5].

Furthermore, designing the 5G cellular architecture has the main role in this kind of

mobile generation. It is worked for separating the outdoor and indoor scenarios to avoid

the obstacles and penetrations through buildings walls. Distributed Antenna System (DAS)

and massive MIMO technology are working to achieve that [7]. This will lead to use smart

beam antenna systems. In addition, 5G technology will be a single unified IP standard of

different wireless networks and a combination of wireless technologies broadband such as Local

Area Network (LAN), Wide Area Network (WAN), Institute of Electrical and Electronics

Engineers (IEEE)802.11, and highly supportable to wireless World Wide Web (WWW)

technology [4]. It also uses beamforming technology to improve the spectrum efficiency by

applying massive element antenna technologies [18].

Figure 1.6 summarizes the use cases of 5G and it can summarize its features as: it has

higher security and reliability with low latency in milliseconds [19], i.e. low latency with a

round-trip delay of 1ms [20] (this is because of the new distributed network of base station)

[17], achieving ultra-fast mobile Internet (up to 10Gbps in indoor and outdoor environments

and 100Mbps in urban and suburban environments) [17], providing high speed and capacity

[19] (up to 25 Mbps connectivity speed [4]), low power consumption, clarity in audio/video by

HD Clarity technique, high resolution for cell phone user besides achieving a high broadcasting

data (in Gbps) in terms of supporting almost 65000 connections [4]. In addition, 5G will be

used by smart appliances remotely besides the closed-circuit cameras that provide security

and high quality. 5G is not limited in a specific stage, but it can reach to so-called Internet

of Things (IoT) which means connecting the applications, appliances, sensors, objects, and

7

devices with the Internet and this requires transmitting, collecting, analyzing and processing

data in an efficient network [5]. Moreover, health care can be included in the features of 5G

in terms of the smart medical devices that have the ability to make remote surgery [5].

Figure 1.6: 5G use cases [19]

Last but not least, the capabilities of 5G wireless technology are still introducing more

features and seek to achieve higher data rates, low latency, ultra-high reliability, higher

capacity, and massive device connectivity. Therefore, it is necessary to work with combination

of many advanced technologies such as Software Defined Networks (SDN), Network Function

Virtualization (NFV), Interference Cancellation (IC), Device-to-Device (D2D), Machine-

to-Machine (M2M), multiple Radio Access Technology (RAT), besides advanced multiple

antenna techniques MIMO and massive MIMO [17].

Currently, the researchers are still working towards the next generations of wireless com-

munications beyond 5G or Sixth Generation (6G), which means using higher frequencies than

the ones used in 5G to achieve more data rates speed [21]. Therefore, these new generations

should be able to solve the problems that were faced the previous generations especially in

the areas that 5G is not able to achieve high enough data throughput or low enough latency [21].

1.2 Motivation and Objectives

The specifications of the future wireless networks 5G for 2020 were almost defined,

where OFDM was already adopted. However, because it has some drawbacks such as

high Peak to Average Power Ratio (PAPR) and high Out-Of-Band (OOB) emissions, it is

of paramount importance to propose and evaluate new different modulation schemes for

future systems (beyond 5G or 6G). In recent years, some different schemes such as Filter

8

Bank Multi Carrier (FBMC), Universal Filtered Multi Carrier (UFMC), and Generalized

Frequency Division Multiplexing (GFDM) have been proposed. Herein, GFDM modulation

technique is considered the generalization of OFDM and the most flexible nonorthogonal

multicarrier transmission scheme in comparison with the other multicarrier modulations

techniques. The main purpose of GFDM is dividing the available spectrum into multiple

spectral segments for each user and thus each segment has a different bandwidth [22]. It can

be considered that GFDM is able to combine the flexibility and simplicity of OFDM with

advanced mechanisms to avoid interference [23]. In addition to this, MIMO technology also

has the main role in 5G wireless network due to its ability to achieve a higher data rate, better

spectral efficiency, diversity, and multiplexing gain. Therefore, the combination of GFDM

technique with MIMO can be considered as near-optimum detection schemes [24]. Moreover,

GFDM uses one Cyclic Prefix (CP) between GFDM frames unlike OFDM that requires a

CP between two time slots. Noting that both schemes employ the CP to avoid the Inter

Symbol Interference (ISI), but in GFDM the interference between time slots can be avoided by

choosing an appropriate pulse shaping filter [25] and this leads to better spectral efficiency [23].

GFDM reduces PAPR and has low OOB radiation in comparison with OFDM (that has

this problem because of the rectangular pulse shaping filter used in the transmitter [24]) and

this gives GFDM more capability for spectrum fragmentation [22] [23] [25]. On the other

hand, the main drawback of GFDM is the Inter Carrier Interference (ICI) since one band

suffers interference from the two adjacent bands and thus more complex receivers should be

employed as compared with OFDM. The receiver design should deal with both ICI and the

channel fading [25].

The objectives and contributions of this work include,

1. Implementation and evaluation of a single-user SISO-GFDM system, recently proposed

in the literature.

2. Extension of this system to Single Input Multiple Output (SIMO) system, then to

multi-user scenarios and terminals equipped with multiple antennas, i.e., a Multi-User

MIMO-GFDM system. Most of the works in the literature only consider simple single-

user Single Input Single Output (SISO) scenarios and therefore is quite important to

access GFDM systems in more realistic multi-user MIMO scenarios.

3. For both systems, two different receivers are used: Matched Filter (MF) and Zero Forcing

(ZF) receivers. Besides applying the IC techniques that are playing an important role

in improving the performance of GFDM system. These techniques: Serial Interference

Cancellation (SIC) and Double Sided Serial Interference Cancellation (DSSIC) were

applied to GFDM-MF receiver.

4. In addition, since GFDM suffers from ICI, it is needed to employ different linear

equalization techniques for each scenario such as ZF and Minimum Mean Square

Error (MMSE).

9

The implemented GFDM systems are evaluated under realistic multipath Raleigh fading

channels. Where the performance is compared with the conventional OFDM systems and

presented in terms of Bit Error Rate (BER). Furthermore, one of the most important

advantages of the GFDM is the reduction of the OOB radiation and thus the Power Spectral

Density (PSD) of the GFDM is computed and also compared with the one obtained with the

OFDM system.

1.3 Structure of the dissertation

This document is divided into more four chapters are organized as follows:

Chapter 2 presents an overview of the radio communications’ basic concepts in terms

of radio propagation mechanisms and channel characterization. It also presents the OFDM

modulation adopted by LTE and also by 5G systems. Then, it is presented the most relevant

modulation schemes that can be used in the future systems.

Chapter 3 introduces the multiple antennas technologies, starting with an introduction

to MIMO systems, highlighting the diversity and its types. Then, it presents the concept of

multiplexing and finally the linear receiver architectures that used in MIMO systems.

Chapter 4 presents the implementation of GFDM system model in different cases: SISO,

SIMO with 2 or 4 antennas, and MIMO system for 2 and 4 transmit-receive antennas. Then,

comparing the BER performance of all systems with OFDM and also implementation the

PSD of both schemes.

Chapter 5 presents the main conclusions and possible future work.

10

CHAPTER 2Basic Concepts

Talking about the digital era means getting all the information we need by access the

Internet. The sophisticated technologies have the main role in changing our daily life

because it is working for many mind-blowing discoveries and better facilities in order to

achieve easier electronic communication everywhere. For this reason, it must be necessary

to keep going in achieving higher capacity, higher data rate, and better Quality of Service (QoS).

Transferring the information between two or many points over the air requires appropriate

signal formatting and terminals equipped with multiple antennas to efficiently deal with the

adversity of the propagation channel. This chapter covers some of the most basic concepts

related to the wireless system in terms of the wireless channel models and the modulation

schemes that are necessary for future communication systems.

2.1 Wireless Channel Models

The channel in wireless communication has an essential role in exchanging information

between communication devices, which is considered as a medium between the transmitter

and the receiver to transfer an information signal. The transmitted signal must be modified

to take into account the physical processes that occur in the channel. Transferring the signal

from the transmit antenna to the receive antenna has an effect on the characteristics of

that signal, which depends on several factors, such as the environment (in case of existing

buildings or any other objects that cause reflection, refraction and diffraction of the signal),

the shadowing, the path of the signal, and the noise. Modeling the real-world environment

is almost impossible task. Therefore, there are many channel models that approximate the

effetcs of specific real-world environments.

Considering that the transmitted signal is x(t), the impulse response of the channel

11

between the transmitter and the receiver is h(t) and the received signal is y(t) as

y(t) = x(t) ⊛ h(t) + n(t), (2.1)

the received signal consists of two parts, the first part is obtained by applying the convolution

on the transmitted signal and the channel response, while the second one corresponds to

the noise component n(t) [26]. In the frequency domain, the convolution is converted to

multiplication operation as

Y (f) = X(f)H(f) + N(f). (2.2)

There are two main parameters that are used to determine the performance of digital

transmission: the transmission bit rate and the bit error rate [27]. Herein, it is very important

to mention Shannon’s formula that determines the channel capacity C of a band-limited

information transmission channel with Additive White Gaussian Noise (AWGN) measured by

bits per second (bps) [27], as

C = W log2

(

1 +S

N

)

, (2.3)

this formula gives an expression to determine the maximum achievable bit rate that is possible

to be transmitted without errors over an ideal channel of bandwidth W measured in Hz

and of a given Signal-to-Noise power Ratio (SNR)(

SN

)

in a non-logarithmic scale by using

channel coding, where S is the average signal power and N is the average noise power, both

measured in Watt [27]. Noting that S = EbR and N = N0W where Eb, R, and N0 represent

the bit energy in Joules (J), bit rate in bps, and the noise power spectral density in Watts/Hz

respectively. Thus, Shannon’s formula can be expressed [27] as

C = W log2

(

1 +S

N

)

= W log2

[

1 +

(

Eb

N0

)(

R

W

)]

. (2.4)

If R < C, the bit error rate can be made negligible and the efficiency of the channel capacity

C may increase in case of increasing the ratio RC [27].

The received SNR is the power ratio between the received signal power Pr and the noise power

Pn, and can be mathematically expressed as

SNR =Pr

N0B. (2.5)

Each of these powers can be determined by several factors, where the received power is

determined by the transmitted power, Path Loss (PL), shadowing and multipath fading while

the noise power is determined by the bandwidth of the transmitted signal and the spectral

properties [28]. In addition, the received SNR can be given in terms of the signal energy per

bit Eb or per symbol Es as

SNR =Pr

N0B=

Es

N0BTs=

Eb

N0BTb, (2.6)

where Ts is the symbol time and Tb is the bit time. Noting that for binary signaling SNR = Eb

N0

and for multilevel signaling SNR = Es

N0[28].

12

2.1.1 Radio-Propagation Mechanisms

The propagation of the signal from the transmitter to the receiver has many paths as

illustrated in figure 2.1, if the signal reaches the destination through a single path without

facing any kind of propagation mechanisms, this means that the signal is propagated in a

Line-of-Sight (LOS) path. But, in case of propagating in one or more indirect paths, this

called Non Line-of-Sight (NLOS) propagation [27].

Figure 2.1: Radio wave propagation mechanisms

The main NLOS propagation mechanisms are [27] [29]:

• Absorption occurs when a radio wave passes through an object such as trees, where a

part of the strength of this signal is absorbed as a heat. The resulting signal strength in

the other side will be weak in this case.

• Reflection occurs when a radio wave hits an object has a wavelength much larger than

the wavelength of the signal such as a wall. Thus, the signal will be reflected off the

surface.

• Refraction occurs when a radio wave hits an object has a different density from the

one which related to the signal such as a cloud. In this case the direction of the signal

will be shifted from the original direction. Noting that the reflection is accompanied by

the refraction, that means the strength of reflected or refracted waves depends on the

type of object.

• Diffraction occurs when a radio wave impinges on a sharp surface such as mountains,

irregular edges and tops of buildings. The signal will be diffracted (broken up) and

bended around the sharp corners of the object to create few diffracted signals from the

original one.

• Scattering occurs when a radio wave impinges on an object that has irregular dimensions

smaller than the wavelength of the signal such as street signs and lamp posts. The

signal will ricochet off the rough surface area of an object and create several signals

from the original one. This leads to propagating the signal in a wide area and losing

energy. In the end, the resulting signal will arrive at the receiver from almost the same

location with slight differences in delay.

13

2.1.2 Propagation characteristics

In a realistic urban environment, the transmitted signal faces several obstacles because

of the buildings, trees, and many other objects which affect the path of the signal that

spread randomly as mentioned before in section 2.1.1. These phenomena originate three

types of distinct variations on the received signal: Path Loss, Shadowing effect and multipath

propagation as shown in 2.2.

Figure 2.2: Components of channel response

The left-hand side of figure 2.3 represents the logarithmic ratio of received-to-transmitted

power in Decibels (dB) against the logarithmic distance [26], while the right-hand side of this

figure shows the three components of the channel response: propagation PL, shadowing, and

multipath fading.

Figure 2.3: Channel modeling [26]

The previous mechanisms lead to classify two main distinct scales of fading: Large Scale

Fading and Small Scale Fading as,

14

Large-Scale Fading describes the average signal-power attenuation or Path Loss at the

receiver after propagating over a large area and over a very long distance (hundreds of

wavelengths). It also represents the fluctuations of the signal strength over distances from tens

to hundreds of meters, where the power fluctuates around a mean value. The interference may

cause a significant dropping (variation) in the strength of the signal caused by the obstacles

during the paths. It could be estimated the path loss as a function of distance by two main

factors: mean-path loss and log-normally distributed variation about the mean [26] [27] [30] [31].

If there is a strong attenuation, the signal will be blocked, and the received signal

power variation due to shadowing can happen over distances (10-100 m in outdoor en-

vironments and less in indoor environments) [28] that are proportional to the length of

the obstructing objects. As a consequence of shadowing, the received signals which have

the same distance from the transmitter, may have different received power and also a

lognormal distribution. For that random attenuation, there is a need for a statistical model

to characterize this attenuation, the most common one is log-normal shadowing model [28] [31].

Small-Scale Fading is also called multipath fading, it describes the very small changes

of the amplitude and phase of the electromagnetic waves during propagating over a short

distance (few of wavelength) and a short period of time (seconds) [27]. As mentioned, the

signal is exposed to some obstacles during its path, which leads to several reflected signals,

reaching the receiver at different time instants and with different intensities and phases. This

phenomenon is usually called multipath propagation [26] [29]. Since each reflected signal

has a different phase and amplitude, sometimes they are in phase and other times in an

opposite phase, the overall received may have significant instantaneous power variations. So,

the received signal power may be increased or decreased [26].

2.1.3 Channel characterization

The main parameters that characterize the multipath channel can be described as,

2.1.3.1 Doppler Spread and Coherence Time

According to [27], Doppler spread and coherence time are both parameters that describe

the time-varying nature of channel causes frequency dispersion to determine if the channel

is facing fast fading or slow fading in terms of the transmitted signal bandwidth Bs and

the symbol duration Ts. Noting that the Doppler spread Bd is inversely proportional to the

coherence time Tc.

Doppler Spread Bd is a range of frequencies that the received Doppler spectrum is nonzero

and is considered as a measure of spectral broadening caused by motion which means by the

time rate of change of the mobile channel [27]. There are no effects of the Doppler spread and

considered negligible at the receiver in case of the Doppler spread Bd is much lower than the

bandwidth of the transmitted signal Bs [32]. Therefore, Doppler spread is only important for

15

a low data rate such as a slow-fading channel.

Coherence Time Tc is a statistical measure of the time duration over which the channel

impulse response remains invariant. If the coherence time Tc of the transmitted signal is

much lower than the symbol period Ts, the channel will change during the transmissions of

the signal and this affects the signal and causes distortion [32]. Therefore, if there are two

signals transmission with a symbol period greater than the coherence time, these two signals

will be affected by the channel differently [27].

Small-scale fading based on Doppler spread causes the transmitted signal to go through

fast fading in case of high Doppler spread or slow fading in case of low Doppler spread, as


Figure 2.4: Fast Fading and Slow Fading [33]

Fast Fading: it occurs when the symbol period of the transmitted signal Ts is greater than

the coherence time of the channel Tc [27] [31] as

Ts > Tc. (2.7)

This means that the impulse response of the channel changes rapidly during the symbol

duration and this type of fading is expected to occur when the coherence time is about less

than hundreds of symbol periods [27], noting that fast-fading phenomenon happens to a very

low data rate [27] where the rate of change of the transmitted signal is smaller than the

rate of change of the channel characteristics [32]. Therefore, the channel varies faster than

transmitted base-band signal variations and it called a fast-fading channel.

Slow Fading: it occurs when the coherence time of the symbol period Ts is less than the

coherence time of the channel Tc [27] [31] as

Ts < Tc. (2.8)

This means that the impulse response of the channel changes at a rate much slower than

the impulse response of the transmitted signal [32] and this type of fading is expected to

16

occur when the coherence time is almost in thousands of symbol periods [27]. Therefore,

the channel variations slower than transmitted base-band signal variations and it called a

slow-fading channel.

2.1.3.2 Delay Spread and Coherence Bandwidth

According to [27], Delay Spread and Coherence Bandwidth are both parameters that

describe the time dispersion nature of the channel in a local area to determine if the channel

is facing flat fading or frequency-selective fading in terms of the transmitted signal bandwidth

Bs and the symbol duration Ts. Noting that the coherence bandwidth Bc is inversely

proportional to the root-mean-square delay spread στ .

Delay Spread στ is the difference between the arrival time of the earliest component and

the arrival time of the latest component. Therefore, it is a random variable and also is

considered in wireless communications as a measure of the multipath profile of the channel [27].

Coherence Bandwidth Bc is a statistical measure of the range of frequencies over which

the channel impulse response is considered flat, which means there is a possibility for all

spectral components to pass through the channel with a linear phase and equal gain [27].

Therefore, if there are two signals transmission with a frequency separation greater than

the coherence bandwidth, these two signals will be affected by the channel quite differently [32].

Small-scale Fading based on multipath time delay spread is divided into two types of

fading. If there is a small delay spread, this will lead to Flat Fading, while if there is a large

delay spread, this will lead to Frequency Selective Fading as,

Flat Fading: it occurs when all frequency components of the transmitted signal fall within

the coherence bandwidth fade simultaneously [27] and the amplitude of the received signal

changes with time [32]. Herein, the gain of the signal is constant and the phase is linear due

to the coherent bandwidth Bc is greater than the bandwidth of the transmitted signal Bs [27]

[31] as

Bs < Bc. (2.9)

Frequency Selective Fading: it occurs when some frequency components in the transmitted

signal fade, while other frequency components not fade [27]. Besides, the coherent bandwidth

Bc is smaller than the bandwidth of the transmitted signal Bs [27] [31] as

Bs > Bc. (2.10)

The channel is considered as a frequency-selective channel when there is a large spread in

multipath delays and this causing ISI. Therefore, it is necessary to clarify two points [27]:

• If there is no mobility in a frequency-selective channel: the channel will be time-invariant

and the Doppler shift is zero. Thus, there is a big need for the equalization process to

minimize the effect of ISI.

17

• If there is mobility in a frequency-selective channel: the channel will be time-varying

and the Doppler shift is nonzero.

While the channel is considered as a frequency-selective fading channel when the channels are

dependent on frequency and also time-varying. As a result, these types of channels require a

complex equalization because it is characterized by time-varying ISI [27] [32].

2.1.3.3 Fading distribution

In multipath propagation, there is a time-varying signal different from path to path where

each path has diferent Doppler shift, time delay, and path attenuation [27]. Therefore, there

are multipath propagation channels, each one has own characteristics. The best example for

time-varying linear channel is called Rayleigh fading, which is used to simulate the small

fluctuations when there is no direct ray component. If there are a large number of paths, the

envelope of the received signal is statistically described in a case of NLOS component by a

Rayleigh distribution and in case of LOS component is called Rician distribution [27] [34].

Rayleigh Distribution: it is considered as the worst fading type because all components of

the received signal envelope distribution for channels are NLOS. As depicted in figure 2.5,

when the component of the channel h(t) are independent, the Rayleigh Probability Density

Function (PDF) of the amplitude r = |h| = α [34] is

f(r) =r

σ2e− r

2

2σ2 , (2.11)

where E{r2} = 2σ2 and r ≥ 0.

Figure 2.5: Rayleigh distribution PDF [35]

Therefore, it is the most commonly used signal model in wireless communications where

the power is exponentially distributed and the phase is independently distributed from the

amplitude [34].

18

Rician Distribution: in this type of distribution, the components of the received signal

envelope distribution for channels are LOS. This leads to a complex Gaussian channel with

non-zero mean. The Ricean PDF of the amplitude r = |h| is depicted in figure 2.6, and can

be expressed mathematically [34] as

f(r) =r

σ2e− r

2+v2

2σ2 I0

(

rv

σ2

)

, (2.12)

where r ≥ 0 and I0 is the modified Bessel function of order zero and 2σ2 = E{α2}.

Figure 2.6: Rician distribution PDF [36]

Noting that h = αejφ + vejθ where α follows the Rayleigh distribution (the amplitude)

and v2 is the power of the LOS signal component where v > 0 is a constant value. The angle

θ and φ are assumed to be mutually independent and uniformly distributed on [−π, π] [34].

The Rayleigh fading channel is equal to Rician fading channel if the Rice factor K → ∞where there is NLOS component and it can be expressed [34] as

K =v2

2σ2, (2.13)

considering that it is a relation between the power of the LOS components (Rician component)

and the power of the NLOS components (Rayleigh component).

The channel models are usually modeled by Power Delay Profile (PDP) and also called

the multipath intensity profile, which is supplied as a table of values for different scenarios

that can be used to simulate the channel. PDP represents the average power associated with

a given multipath delay, where for each individual reflected path, there is a different time

delay depending on the length of these signals [28].

19

2.2 Modulation Schemes suitable in 4G and 5G Technologies

The secured data communication and higher data rates transmission for the next-

generations wireless communications are considered the main factors of increasing the demands

on the QoS. The digital communications techniques become more developed and reliable,

where it has the ability to operate at higher spectral efficiency. For this reason, the communi-

cation systems are incorporating the multi-carrier transmission techniques to achieve their

purpose of getting a higher data rate transmission. Therefore, Orthogonal Frequency Division

Multiplexing (OFDM) was adopted in the 4G systems and will be also used in the 5G systems

due to its ability to achieve high data rates. The main drawback of OFDM is the high PAPR

and thus the Single-Carrier FDMA (SC-FDMA) is a modified form of Orthogonal Frequency

Division Multiple Access (OFDMA), was developed for the LTE uplink. It has a similar

throughput performance but with lower PAPR [37]. These techniques will be described in

detail as follows:

2.2.1 Orthogonal Frequency Division Multiplexing (OFDM)

OFDM is a digital multi-carrier modulation technique that employs multiple carriers

within the assigned bandwidth [38]. The basic principle of OFDM is to transmit, in parallel,

a large number of a lower rate data stream over a number of different orthogonal subcarriers

instead of transmitting high-rate data stream with a single subcarrier [39], which means

splitting a big data stream into a high number of narrow band subcarriers. Noting that each

one of these subcarriers is made orthogonal to one another [40], in order to be spaced very

close together with no overhead as shown in figure 2.7. OFDM is able to be modulated with a

specific type of digital modulation schemes such as Quadrature Phase Shift Keying (QPSK),

16 Quadrature Amplitude Modulation (16-QAM) and so on. In addition, the symbol duration

is much larger than the source symbol duration on each subcarrier [27] and this reduces the

impact of ISI. However, for eliminating the effect of ISI completely, the CP or guard interval

was almost the solution to achieve that by introducing it between each OFDM symbol. Thus,

the mechanism of this CP is summarized that the OFDM symbol will be extended cyclically

to avoid the ICI between the adjacent subcarriers [39] [40].

Figure 2.7: The orthogonality concept in OFDM Signal [40]

20

The main goal of applying OFDM modulation is the orthogonality between the carriers

because this helps in increasing the overall spectral efficiency of the system where there is no

ICI between closely spaced carriers. First, it is necessary to choose the spectrum required

that depends on the input bits data and the type of digital modulation where the data will be

transmitted over independent carriers, each one has a required phase and amplitude. Thus,

to ensure the orthogonality between the chosen carrier frequencies, the Inverse Fast Fourier

Transform (IFFT) and Fast Fourier Transform (FFT) operations are considered the key to

achieving that [27] [38] [41]. Herein, the basic model of OFDM transceiver is illustrated in

figure 2.8.

Figure 2.8: Block diagram of an OFDM system [41]

At the transmitter, the input bits stream will be modulated first by using one of the digital

modulation types and converted to parallel bits by serial-to-parallel conversion block. The

parallel resulting flow was defined in the frequency domain, so IFFT is used to transform

the data into the time domain. Then, to eliminate the ISI and ICI at the receiver caused by

the multipath delay spread in the channel, it is necessary to add the CP to the beginning of

the symbol which is a copy of the last part of the symbol [20]. The length of CP should be

greater than the delay spread of the channel where in this case the length of symbols will be

extended [42].

At the receiver, the same steps of the block diagram of the transmitter will be applied but

in a reverse way. Starting to converting the analog signal to a digital one then removing the

CP which was inserted between each of the symbols. The series of symbols will be divided

into several symbols that should back to the frequency domain by FFT. In the end, the

symbols will be converted to serial ones to be ready for the demodulation process for receiving

the binary information sent by the transmitter [20] [42].

21

According to[41], considering that Nc is the number of subcarriers modulated with a

bandwidth B, the spacing between the subcarrier is given by

∆f =B

Nc, (2.14)

while the symbol duration of OFDM signal for kth subcarrier where k = 0, ..., Nc − 1 is

Tk =1

∆f. (2.15)

Moving to the receiver before looking at the implementation of the transmitter, the received

signal r(t) can be expressed as

r(t) = Re

{

Nc−1∑

k=0

dkrect(t/T )ej2πtfkej2πtfc

}

, (2.16)

where dk is the complex data symbols for kth subcarrier, T is the duration of time slot, fk is

the symbol frequency of the kth subcarrier and fk is the carrier frequency refers to fk = kT .

Moreover, the received signal after removing the RF carrier which means after the baseband

processing is given by

s(t) = r(t)e−j2πfct =Nc−1∑

k=0

dkej2πkt/T . (2.17)

In case of sampling the received signal at a rate of Nc

T , the set of Nc samples sn can be

expressed as

sn = s(nT/Nc) =Nc−1∑

k=0

dkej2πkn/Nc , (2.18)

where n = 0, 1, ..., Nc − 1, and this leads to expressing the relation between the sequance of

received signal sn at a rate of Nc

T and the sequance of complex data dk as

{sn} = IFFT{dk} ⇒ {dk} = FFT{sn}, (2.19)

this means that the implementation of the OFDM modulation can be carried out replacing

the bank of modulators by an IFFT operation [41].

As mentioned before, the signal will be transmitted over a multipath channel, so it will

not be confined to the duration of the OFDM time slot but will spread over TOF DM + τmax

where τmax is the maximum time delay, this leads to overlapping of OFDM symbols as shown

in figure 2.9.

Figure 2.9: The duration of OFDM [41]

22

Therefore, inserting of CP is really needed to a fully remove the ISI when the time of CP

or guard interval is greater than the maximum time delay as TG > τmax and also causes a loss

in spectral efficiency because it reduces the transmission rate [41]. In the result, the duration

of OFDM signal can be presented in figure 2.10 and written as

T ‘OF DM = TOF DM + TG. (2.20)

Figure 2.10: The duration of OFDM after inserting the Cyclic Prefix [41]

For designing a convenient OFDM system, there are few parameters as shown in table 2.1

that should be taken into consideration.

TCP > τmax ISI free

∆f >> 2fD,max ICI free

TOF DM << Tc Time invariance

Table 2.1: Parameters of a well designed OFDM System [41]

There are several advantages for OFDM modulation and it can be summarized as follows [20]

[41] [42]:

• OFDM is highly reliable and more resistant because of dividing the subcarrier into

several narrowband subcarriers.

• OFDM is more efficient to implement the modulation and demodulation processes by

using IFFT and FFT operations.

• OFDM eliminates ISI and ICI by inserting of a CP which means increasing the symbol

duration.

• OFDM shows that spectral efficiency increases as increasing the number of users.

• OFDM has a very low symbol rate to make sure that all subcarriers are completely

orthogonal.

• OFDM has good performance in terms of flexibility and robustness in a frequency

selective channel.

• OFDM requires a simple equalization technique in the frequency domain resulting from

the low complexity of the base-band receiver, and in this case, the output signal has low

distortion.

• OFDM is able to be compatible with multiple antennas technologies.

23

Eventhough these advantages, OFDM system has some drawbacks as [27] [42]:

• OFDM has more OOB emissions, this because of using the rectangular pulse shaping

filter in the transmitter.

• OFDM has high PAPR, this because of the large peak signal that formed by the random

sum of the phase subcarriers that occurs when the signals in the K sub-channels add

constructively in phase. This means the amplifiers require a large power back-off.

Therefore, to reduce this problem, it can be by phase adjustments or by peak clipping

that may cause some distortion in the signal.

Moreover, OFDM modulation can be extended to OFDMA for the implementation of a

multi-user communication system, where it allows to transmit low data rate from several

users at the same time, i.e., OFDM system is allocating all of the available subcarriers while

OFDMA is distributing just a subset or group of subcarriers to each user for being able to

multiple transmission simultaneously, where each group is named a subchannel [41] [43], as


Figure 2.11: The difference between OFDM and OFDMA [43]

In addition, in OFDM technique, the issue of orthogonality of the subcarriers is considered

almost easy, while in OFDMA, different users transmit at the same time, each one has

own subcarrier frequencies, this causes a frequency offset that leads to creating a multiple

access interference. OFDMA signals have also a high PAPR because in the time domain, the

multicarrier signal consists of the sum of many narrowband signals, which can be added up

constructively or destructively and this reduces the efficiency and increases the cost of the RF

power amplifier to avoid the distortion [37] [44].

2.2.2 Single Carrier-Frequency Division Multiple Access (SC-FDMA)

SC-FDMA is a single carrier multiple access techniques, has similar performance and the

same structure of OFDM. The main advantages of SC-FDMA over OFDMA is the lower

PAPR of the transmitting signal. According to [41], SC-FDMA combines the low PAPR of

single-carrier systems with robust resistance to multipath channels, lower complexity at the

24

transmitter, lower sensitivity to carrier frequency offset, and flexible subcarrier frequency

allocation offered by OFDMA. Figure 2.12 shows the model of SC-FDMA transceiver.

Figure 2.12: Block diagram of an SC-FDMA system [41]

At the transmitter, after applying the modulation process on the input bits stream

and converted it to parallel flows and before applying the IFFT operation, the data

symbol first will be transformed into the frequency domain by N -point FFT and then

each N -FFT outputs will map to one of the M orthogonal subcarriers to transform the

subcarrier amplitudes to a complex time-domain signal [44]. Where, M = QN , taking

into consideration M > N and Q is an integer value (the bandwidth expansion factor of

the symbol) that is considered the number of simultaneous users that is supported by the

system. In this way, each subcarrier after the IFFT process contains a part of each symbol.

Noting that the next steps of SC-FDMA are exactly the same as the OFDM transmitter model.

At the receiver, the received signal will be transformed into the frequency domain through

M -point FFT and de-mapped the subcarriers. Hence, the resulting signals will be processed

by some equalization techniques that will be described in chapter 4 in detail. Finally, the

original signal will be obtained by applying the IFFT process on the equalized symbols to be

in the time domain [44].

Moreover, SC-FDMA subcarriers can be mapped for multiple users in the frequency

domain into two methods [41] [45], as depicted in figure 2.13:

1. Distributed subcarriers mapping (Distributed Frequency Division Multiple

Access (DFDMA)): that means the user is assigned a set of non-contiguous subcarriers

that occupied the whole spectral.

2. Localized subcarriers mapping (Localized Frequency Division Multiple Ac-

cess (LFDMA)): that means allocating a set of adjacent subcarriers to each user.

25

Figure 2.13: Subcarrier mapping methods for multiple users [41]

At this time, in case of adopting the second method of subcarriers mapping which is

LFDMA, the SC-FDMA technique will be outperformed the OFDMA by exploiting its PAPR

benefits [45].

Besides the SC-FDMA has a good PAPR performance gain, there are also some other

advantages such as [45]:

• SC-FDMA has lower sensitivity to carrier frequency errors.

• SC-FDMA has a high spectral efficiency if the number of users is large (more than 12)

and the bandwidth allocation is also high (more over 100 MHz).

As well as that, SC-FDMA has some drawbacks that can be mentioned as follows [41] [45]:

• SC-FDMA has an ISI problem that can be mitigated by using the techniques of in-

terference cancellation or frequency domain equalization that causes a complex signal

processing. Noting that the main function of the equalizer is to restore the orthogonality

and that can be fully done by Zero Forcing equalizer, but it causes noise enhancement.

• SC-FDMA has almost a less flexible resource allocation and spectral efficiency compared

to OFDMA.

2.3 Modulation Schemes suitable for beyond 5G Technology

As discussed before, the demands of increasing the capacity, low latency, and the higher

data rate for better QoS are still in a continuous increase. Therefore, for the future wireless

communications, beyond 5G or 6G, many multicarrier technologies are considered as an

alternator of the OFDM technique [20] [42], and will be highlighted below.

26

2.3.1 Filter Bank Multi Carrier (FBMC)

FBMC is one of the waveform candidates for beyond 5G cellular networks and was

developed from OFDM modulation. The main principle of FBMC is passing every symbol

through a bank of filters (pulse shaping filter) to mitigate the OOB emissions, taking into

consideration the length of filter which has to be equal to four times of the symbol length and

this leads in case of transmitting a large number of symbols to good spectral efficiency [42].

Figure 2.14: Block diagram of an FBMC system [20]

The mechanism of FBMC can be shown in figure 2.14, it seeks to achieve full capacity by

imploying Offset Quadrature Amplitude Modulation (OQAM) after mapping the input bit

stream. Besides, there is a delay in the imaginary part of the complex data symbol by the

half duration of the symbol, because the real and the imaginary parts essentially were not

transmitted simultaneously. Then, a serial to parallel conversion is done before filtering the

symbols in frequency domain and finally, the serialized resulting flow will be obtained in time

domain after using IFFT operation. It can be noted that the transmitter and receiver use

IFFT/FFT operations and frequency spreading. FBMC is considered flexible and robustness

against distortion in addition to FBMC/OQAM have the ability to achieve full capacity by

imposing the orthogonality only in the real domain [20] [46].

2.3.2 Universal Filtered Multi Carrier (UFMC)

UFMC has the characteristics to be as a middle solution to combine the advantages of

OFDM and FBMC. The main principle of UFMC as shown in figure 2.15, is dividing the full

band into a set of sub-bands, and also dividing the signal (input bits stream) into a set of

substreams with a lower data rate to be ready for the filtering process over a filter of length L

much shorter than in FBMC technique, and then the response of all filtered sub-bands are

summed. Noting that, zeros will be inserted for the unallocated carriers where there is an

N-IFFT block for each sub-band. Besides, the possibility to apply a different filter in each

sub-band, where each one has a fixed number of subcarriers [20] [47]. In order to recover the

bit stream, there is a 2N-FFT block at the receiver side which is decimated by a factor 2, in

addition to the equalization process per subcarrier to equalize the sub-band filtering and the

joint effect of the channel [20].

27

Figure 2.15: Block diagram of an UFMC system [20]

Moreover, the need for inserting the CP is not necessary and it is optional in case of

improving the ISI protection [42]. UFMC is suitable for short burst transmission because it

has a short filter length, has high spectral efficiency, band-limited transmission, lower OOB

emissions than OFDM and thus has high robustness against the ICI between the adjacent

subcarriers [20] [46] [47].

2.3.3 Generalized Frequency Division Multiplexing (GFDM)

GFDM is also one of the waveform candidates for beyond 5G cellular networks. It is a

generalized form of OFDM but here the carriers are not orthogonal to each other, and thus it

is considered as the most flexible digital multicarrier scheme. The main principle of GFDM

is dividing the input bits stream into several subcarriers and several subsymbols. For each

subcarrier, the impulse response of the pulse shaping filter will apply circularly. Therefore,

the subcarrier filtering reduces the OOB emissions and the PAPR, but the ICI will increase

and cause a degraded in the performance of the GFDM system [42] [46] [48]. GFDM is the

main objective of this dissertation in order to overcome the high PAPR of OFDM system and

this scheme will be discussed specifically in chapter 4 to illustrate the methods that improve

the performance of GFDM system.

The input bit streams d[ℓ] , ℓ = 0, ..., KM − 1 will be modulated and divided into sequence

of complex valued data symbols dk[m], each sequence (as a vector) is spread on k = 0, ..., K − 1

subcarriers and m = 0, ..., M − 1 time slots, which means that for each GFDM frame, each of

the K subcarriers transmits M data symbols [48] as

D =

d0

d1

...

dK−1

=

d0[0] . . . d0[M − 1]...

...

dK−1[0] . . . dK−1[M − 1]

, (2.21)

the previous frame structure (2.21) shows that the kth row and mth column represent the

transmitted symbols in the kth subcarrier and mth time slot respectively.

28

In the transmitter model, as shown in figure 2.16, the complex-valued data symbols dk[m]

are up-sampled by zero-padding MN − 1 zeros, resulting in

dNk [n] =

M−1∑

m=0

dk[m]δ[n − mN ], (2.22)

where δ[.] is the Dirac function and N is the number of samples (up-sampling factor).

Figure 2.16: GFDM Transmitter System Model [48]

Therefore, the pulse shaping filter g[n] with the length of filter L ≤ M is applied on the

transmitted samples dNk [n] by using a circular convolution ⊛, where n = 0, ..., NM − 1 is the

sample index and N ≥ K to avoid the aliasing, which means that in case of increasing the

length of g[n] this will allow the sampling rate to be increased [25]. Thus, the resulting signal

is shifted by a subcarrier center frequency wkn = ej 2π

Nkn where 1

N is the subcarrier spacing.

According to [25]: "In GFDM the frequency spacing between two adjacent subcarriers is not

dependent of the number of subcarriers K, as in OFDM, but it depends on the number of

samples N". The resulting subcarrier transmit signal xk[n] can be formulated [48] as

xk[n] = (dNk ⊛ g)[n].wkn, (2.23)

and expressed in a block structure as

X =

x0

x1

...

xK−1

=

x0[0] . . . x0[MN − 1]...

...

xK−1[0] . . . xK−1[MN − 1]

. (2.24)

In the result, the transmitted signal x[n] of GFDM is obtained by summing up all sub-carrier

signals as given

x[n] =K−1∑

k=0

xk[n]. (2.25)

Initially, the transmitter and the receiver will be operated in ideal concurrency, which means

without regard to any channel and noise. Consequently, the received signal is equal to the

transmitted signal y[n] = x[n].

29

In the receiver model, as depicted in figure 2.17:

Figure 2.17: GFDM Receiver System Model [48]

The received data symbols dk[m] of Matched Filter approach for GFDM system [48] is obtained

first by applying a digital down conversion w−kn = e−j 2π

Nkn on the received signal y[n] as

yk[n] = y[n].w−kn. (2.26)

Then, convolving the signal with the receiver filter by using the circular convolution operator

⊛ as

dNk [n] = (yk ⊛ g)[n]. (2.27)

After that, applying the down sampling technique according to

dk[m] = dNk [n = mN ]. (2.28)

Finally, the received symbols dk[m] are de-mapped to produce a sequence of bits d[n].

In GFDM, the self interference occurs due to the cyclic pulse shaping filters that lead to

losing the orthogonality between the subcarriers and thus it is needed to employ complex

equalizers to remove the interference. In the case of using Root Raised Cosine (RRC) filters

in the transmitter and the receiver sides, only the adjacent subcarriers interfere causing ICI

[48] as shown in figure 2.18,

Figure 2.18: The self-interference in the k-th subcarrier from adjacent subcarriers [48]

This figure shows the interference of data between the adjacent subcarriers in the frequency

domain and more detail will be given in chapter 4.

30

CHAPTER 3Multiple Antennas Technologies

The demands for technological development of wireless communication are still increasing and

thus the research work has progressed to create novel networking protocols with new coding

techniques and higher data rate transmission, besides the interference and the noise mitigation

techniques. This can be achieved by developing antenna techniques through the use of multiple

antenna technologies that can be used efficiently in different strategies to enhance mobile

wireless communication systems. This chapter introduces the multiple antennas systems and

the main goals of these systems in terms of diversity and multiplexing gain. Besides, it also

describes some of the linear equalizers that are used to mitigate the problems of interference.

3.1 Introduction to MIMO

Wireless communications systems are always in a need to be improved in order to achieve

high data rate communication services. Although the radio spectrum is limited, designing

efficient signaling techniques that have a higher capacity is the key to obtain that, and can

improve the performance of the system. This can be done by designing a system with one

or more input signals and one or more output signals, i.e., one or multiple antennas in the

transmitter and one or multiple antennas in the receiver such as Single Input Single Output

(SISO), Single Input Multiple Output (SIMO), Multiple Input Single Output (MISO), and

Multiple Input Multiple Output (MIMO) [27] [49] as shown in figure 3.1:

31

Figure 3.1: Single and Multiple antennas configurations [50]

1. SISO refers to the wireless communications system with one transmitting antenna

and one receiving antenna. It is simple but is affected by problems caused by multi-

paths. SISO systems are used in Wi-Fi, radio, TV broadcast and Bluetooth technologies.

2. SIMO refers to the wireless communications system with one transmitting antenna and

multiple receiving antennas. The received signals from all antennas are combined to

minimize the errors and thus maximizing the SNR. SIMO systems are used in Digital

Television (DTV), Wireless Local Area Networks (WLANs), and mobile communications.

3. MISO refers to the wireless communications system with multiple transmitting antennas

and one receiving antenna. In this case, the signal is preprocessed before transmission

to improve the reliability of the communication link. The preprocessing depends on

the knowledge of the channel before transmission. MISO systems are used in DTV,

WLANs, and mobile communications.

4. MIMO refers to the wireless communications system with multiple transmitting an-

tennas and multiple receiving antennas. The capacity of this configuration is much

higher than the capacity of the other three ones and MIMO systems are used in al-

most all advanced wireless communication systems (WLAN, Worldwide Interoperability

for Microwave Access (WiMAX), ...) and, in 3G, 4G, and 5G. As a result, MIMO

configurations are considered the best in achieving higher spectral efficiency.

It can be noted that the main goal of multiple antennas system (SIMO, MISO, and

MIMO schemes) is achieving diversity and antenna gains, multiplexing gain, and multiple

access users spatial separation. The difference between diversity and multiplexing technique

is that in diversity, the reliability of the system may obtain by using two or more indepen-

dent copies of the transmitted data symbol. Therefore, the diversity technique improves

32

the SNR and the reliability of the system, while spatial multiplexing techniques allow to

increasing the transmission data rate of the system without additional bandwidth and power

[50] [51]. The following subsection describes in detail the aim of the multiple antennas systems.

3.1.1 Diversity

The diversity is mainly used in radio communications and it is obtained by transmitting

and receiving multiple replicas of the same signal through different independent paths, in

order to protect the signal from any kind of fading and enhance the reliability of the signals

[51]. Diversity techniques can be effective, where each transmission is affected independently

of the others. Diversity has many important roles in wireless communications in terms

of reducing the variability of the carrier-to-interference ratio that leads to improving the

frequency-reuse factor, system capacity and thus the performance of the system [27]. As

discussed before, about fading and the scales of fading, macro-diversity and micro-diversity

(also called antenna diversity) techniques are the solution to combat the Large Scale Fading

and Small Scale Fading respectively [27].

• Macro-diversity or Macroscopic diversity techniques in Large Scale Fading can be

obtained either by using the transmitters on the same frequency that receive the signal

and then retransmitting an amplified version of it. This leads to existing an additional

delay, or by using the simulcasting method i.e., transmitting the signal from different

sites at the same time and this requires more synchronization.

• Micro-diversity or Microscopic diversity techniques in Small Scale Fading can be

obtained by using two antennas, the first antenna receives a null while the second one

receives the strong signal. In this case, there is no possibility to occur deep fading and

thus selecting the optimized signal.

Diversity can be achieved in time, frequency, and space provided the terminals are equipped

with multiple antennas.

3.1.1.1 Time and Frequency Diversity

In single antenna systems, diversity can be achieved in time and/or frequency [52].

Time diversity occurs when transmitting the same signal several times at different time

slots, where the duration of these intervals is greater than the coherence time of the channel

that depends on the Doppler spread of the signal. This almost causes an independent fading

to the transmitted copies of the message signal [27] [28]. Figure 3.2 illustrates the relation of

time diversity with interleaving and coding over symbols at different coherence time periods.

Noting that the code gives the redundancy while the interleaving ensures that the bits related

to the codeword are completely separated in order to undergo different types of fading [53].

33

Figure 3.2: Time diversity illustration [53]

Therefore, in the case of occurring a deep fading to the path, just 1 bit of each codeword

will be affected [53]. The repetition coding is considered the simplest code in time diversity and

thus the number of independent paths L (also called diversity order) increases the performance

of the system towards the AWGN channel as shown in figure 3.3.

Figure 3.3: Performance of repetition coding [53]

With repetition coding, the data rate decreases by the diversity order L and this is the

main drawback of time diversity [53]. In addition, time diversity is not effective in the case

that the transmitter or receiver is not moving, where this makes the coherence time quite

longer [27].

34

Frequency diversity occurs when transmitting the same signal several times at different

carrier frequencies. The separation among the carrier frequencies must be greater than the

coherence bandwidth that depends on the multipath Delay spread of the channel. Taking

into consideration that repeating of the same signal at different carriers leads to a lowering in

spectral efficiency. For this reason, the main drawback of frequency diversity is the needed of

more bandwidth [27] [28] [53].

3.1.1.2 Space Antennas Diversity

In the case where the terminals are equipped with multiple antennas, the diversity can be

achieved in space. Contrarily to time or frequency diversity, space diversity can be achieved

without increasing the bandwidth and power, which makes it quite interesting for practical

wireless communication systems. Space-diversity is already used in the LTE standard [52].

Antenna diversity can be divided into transmit diversity and receive diversity as shown in

figure 3.4:

Figure 3.4: Space antennas diversity [53]

1. Receive diversity:

The received signals on each antenna branch are combined to improve the SNR and

thus decrease the BER [28]. Moreover, the receive diversity is able to provide [53]:

• Diversity gain: associated with the channels that are independent.

• Antenna gain: associated with the noise terms that are independent on each

antenna branch.

Figure 3.5 illustrates the scheme of receive diversity with one transmit antenna and

multiple receive antennas Mr.

35

Figure 3.5: Receive diversity scheme [53]

From this figure, it can be mentioned that the received signal model is given by

y1

...

yMr

=

h1

...

hMr

s +

n1

...

nMr

, (3.1)

where, y is the received signal, H is the channel, s is the transmitted signal, and n is

the noise. Besides, g is the equalizer to obtain the estimated symbols s as

s =[

g1, · · · , gMr

]

y1

...

yMr

+[

g1, · · · , gMr

]

n1

...

nMr

. (3.2)

There are several methods of combining diversity signals, each one has its own way

in combining the fading signals and varies in the performance and complexity, such as

Maximal Ratio Combining, Equal Gain Combining, and Selection Combining [53]. To

apply these linear techniques, the fading signals are supposed to be uncorrelated in the

diversity branches and thus the signals from the different branches or fading paths can

be uncorrelated [27].

Maximal Ratio Combining (MRC) is a simple technique, also known as a MF.

The output signal is a linear sum up of all branches or independent fading paths with

co-phasing and optimal weighting. Because of the fading, there is a fluctuation in the

level of the diversity signals and this leads to a continuous changes in the weights of

signals [27] [53]. The weight of each diversity signal is proportional to the SNR of the

diversity signal, and thus the optimal MRC equalizer weights or coefficients is

gm = h∗m, m = 1, ..., Mr. (3.3)

Therefore, the soft estimated data symbol is

s =Mr∑

m=1

|hm|2s +Mr∑

m=1

h∗mnm, (3.4)

36

and the output SNR of MRC equalizer is

SNRΣ =

Mr∑

m=1|hm|2

σ2. (3.5)

The antenna gain for MRC increases linearly with the number of antennas Mr.

Equal Gain Combining (EGC) is a simpler version of MRC technique, the output

signal is a linear sum up of all branches or independent fading paths with equal weighting

after co-phasing. Noting that this equalizer does not require the knowledge of channel

amplitude [27] [53]. The optimal EGC equalizer weights or coefficients is

gm =h∗

m

|hm| , m = 1, ..., Mr. (3.6)

Therefore, the soft estimated data symbol is

s =Mr∑

m=1

|hm|s +Mr∑

m=1

h∗m

|hm|nm, (3.7)

and the output SNR of EGC equalizer is

SNRΣ =

(

Mr∑

m=1|hm|

)2

σ2. (3.8)

The antenna gain for EGC is lower than MRC, but it also increases linearly with the

number of antennas Mr.

Selection Combining (SC) is a very simple technique, it works on a different principle,

unlike MRC and EGC, i.e., selecting the independent received signals that have a high

SNR among the received signals and discarding the others. The performance of this

equalizer is improved when the number of receiver antennas Mr is increased [27] [53].

SC depends on selecting the channel that has the largest amplitude as

|h|max = max [|h|1, ..., |h|Mr], (3.9)

and the output SNR of SC equalizer is

SNRΣ =|h|2max

σ2. (3.10)

The antenna gain for SC increases with the number of antennas Mr, but not linearly [53].

2. Transmit diversity:

In this case, the transmitter is equipped with multiple antennas. It can be noted

that the transmit diversity in cellular systems requires more space, power, and

processing capability at the transmitter side [28]. To design transmit diversity, it

37

should take into account if the complex channel gain is known at the transmitter or

not. Therefore, transmit diversity can be achieved by using two different techniques:

closed-loop techniques (where the channel gain is known and thus, the system of

transmit diversity is similar to the system of receive diversity) and open-loop techniques

(where the channel gain is unknown and thus, the system of transmit diversity re-

quires a combination of time and space diversity by using new techniques) [53], as follows:

Open-loop techniques: in this case, the most used techniques are the so-called

space-time/frequency coding, where the data symbols are encoded in time-space or in

frequency-space before transmission. In past years, several types of codes were proposed,

such as Space-Time/Frequency Block Coding (STBC or SFBC), Space-Time Trellis

Code (STTC), and Layered Space-Time Code (LSTC) as follows [53]:

a) Space-Time/Frequency Block Coding (STBC/SFBC): uses simple decod-

ing techniques to achieve maximum diversity order but it is not able to provide

coding gain. It works with two schemes called:

• Alamouti scheme: is the simplest coding scheme, can be applied for 2 trans-

mit antennas and M receive antennas. This is because only exist orthogonal

codes for 2 antennas assuming complex constellations, i.e., the code used on

antenna 1 is orthogonal to the one used on antenna 2. It achieves a diversity

order of 2 × M , which means the maximum possible for a system with two

transmitting antennas and achieves an antenna gain of M . This scheme has a

full diversity, does not require a bandwidth expansion since the code rate is

one, and it is adopted in the LTE standard [28] [53].

• Tarokh code scheme: is slightly more complex than Alamouti schemes and

designed for a system with more than two transmit antennas. This scheme

also has a full diversity order but requires a bandwidth expansion since the

code rate is lower than 1, contrarily to the Alamouti code [53].

b) Space-Time Trellis Code (STTC): is able to achieve diversity gain as well as

coding gain. It is taking into consideration the joint design of channel coding,

modulation, transmit and receive diversity schemes. For that reason, it also

achieves coding gain. However, the price to be paid is the increasing complexity

and therefore is difficult to implement in practical systems.

c) Layered Space-Time Code (LSTC): is designed to transmit independent data

symbols on each antenna to achieve more multiplexing gain instead of diversity gain.

Closed-loop techniques: in this case, the Channel Sate Information (CSI) is assumed

to know at the transmitter side and the signals are precoded before the transmission.

38

This leads to enabling beamforming or precoding techniques that work to decrease the

complexity of the receiver system and get a higher SNR [53]. There are two different

methods for CSI acquisition [28] [53]:

a) Time Division Duplex (TDD): means that for the same carrier frequency, it

can assign orthogonal timeslots for each user to transmit and receive, thus there

is channel reciprocity between the downlink and the uplink. The main advantage

of this technique is that it is possible to use the channel measurements in one

direction to estimate the channel in the other direction.

b) Frequency Division Duplex (FDD): means there are different frequencies

for downlink and uplink communications. Therefore, for CSI knowledge, the

channel will be feedbacked from the receiver to the transmitter. Noting that each

direction has its frequencies, but if these frequencies are separated by more than

the coherence bandwidth which related to the channel multipath, this will lead to

obtaining an independent fading.

3.1.2 Multiplexing

As seen before, SIMO and MISO systems provide both diversity gain and antenna gain

but not capacity gain. However, in some cases the operaters are interested to provide capacity

gains instead of diversity. MIMO systems can achieve spatial multiplexing gains. The

multiplexing gain that is obtained from the MIMO systems has the main role in increasing

the uplink or downlink capacity region that was extensively studied and related to adding

multiple antennas in the transmitter and receiver [28]. Multiplexing gain can be exploited by

spatially multiplexing several data symbols that provide an increase in the capacity of the

channel at the same bandwidth without any additional power [53]. Spatial multiplexing can

be used in two scenarios as:

Single-User MIMO (SU-MIMO): is a system with multiple transmitting antennas and

multiple receiving antennas, it works to specify the bandwidth of a wireless access point to a

single device. In SU-MIMO multiple data streams are transmitted or received between two

wireless devices at the same time by using multiple antennas. This leads to achieve high

speed data rate. However, herein it can be noted that the multiplexing gain is limited by the

number of transmitting and receiving antennas [54].

Multiple-User MIMO (MU-MIMO): is a system with multiple transmitting antennas

and multiple receiving antennas, it works to specify the bandwidth of a wireless access point

to multiple devices simultaneously. In MU-MIMO multiple data streams are transmitted

to multiple devices at the same time and the same frequency resources by using multiple

antennas. This leads to improve the overall system capacity [53] [54].

39

Let’s focus on a Single User MIMO systems presented in figure 3.6, with a number of

transmitting antennas Mt and a number of receiving antennas Mr. In this case, the received

signal can be written as

y = Hx + n, (3.11)

Figure 3.6: MIMO System [53]

where x = [x1, x2, ..., xMt]T is the overall transmitted signal, y = [y1, y2, ..., yMr

]T is the

received signal on the Mr antennas and n = [n1, n2, ..., nMr]T is the noise [53]. The overall

channel matrix H of size Mt × Mr (i = 1, ..., Mr and j = 1, ..., Mt) can be represented as

H =

h11 h12 h1Mt... hij

...

hMr1 · · · hMr Mt

. (3.12)

Such as for the diversity case, there are two types of multiplexing schemes depending if

the channel is known or not at the transmitter side.

CSI knowledge is available at the transmitter side: in this case, the channel can

be converted into a set of parallel channels by using Singular Value Decomposition (SVD)

technique to decompose the channel matrix H. This leads to no interference among

data symbols during the transmitting process. Although the capacity scales linearly with

rank(H) 6 min(Mt, Mr), it can be possible to maximize the capacity by applying Water

filling technique that depends on the water level, where the channels that are above the water

level are discarded since they are considered bad channels, whereas the available power can

be distributed by the good channels and this will provide gain for a lower SNR [53].

CSI knowledge is not available at the transmitter side: in this case, there is a need

for using more sophisticated receiver architectures to separate the transmitted data streams

over the transmitting antennas Mt. There are two types of advanced architectures [24] [53]:

40

• Vertical Bell Labs Space-Time Architecture (V-BLAST): the decoding is done

over a transmitted block at the bit level. This architecture is optimal but is too complex,

the complexity is increasing exceptionally with the length of the block of data streams.

• Diagonal Bell Labs Space-Time Architecture (D-BLAST): the decoding is

done over a transmitted block at the symbol level. It is a sub-optimal technique but

the complexity is much lower compared with V-BLAST and thus it is more suited for

practical applications.

3.1.2.1 Linear sub-optimal receiver architectures

The equalization process is considered the solution to alleviate the interferences that exist

in any wireless communications system. In a general way, the equalization can be classified

into two main categories [28]:

• Linear techniques: are simple to implement but their use is not effective in most

wireless applications, because it suffers from noise enhancement. Moreover, they are not

able to remove the residual ICI in the multicarrier systems. However, these techniques

usually present a good complexity-performance trade-off.

• Nonlinear techniques: are able to remove the residual interferences between the

carriers but it has a higher complexity than linear techniques. In addition, Decision-

Feedback Equalization (DFE) is the most common nonlinear technique with simple

implementation and capability to cancel noise enhancement.

In this dissertation, the focusing will be on the linear equalizer techniques. Figure 3.7

describes the schematic of linear receiver architectures.

Figure 3.7: Schematic of linear receiver architectures [53]

41

The data symbols si is transmitted by the transmitting antennas Mt to reach each receiving

antennas Mr and added up. The received vector y can be written [53] as

yMr×1 =Mt∑

i=1

hi(Mr×1)si + nMr×1, (3.13)

where hi is the channel between a given transmitting antennas and the receiving antennas,

and n is the AWGN noise added at the receiver. Focusing on the kth data symbol, equation

(3.13) can rewrite as

yk = hksk +∑

i6=k

hisi + nk. (3.14)

In this case, it should be noted that the kth data symbol faces interference from the other

data symbols. Therefore, the interference can be mitigated by using equalizers such as (ZF)

or MMSE [53].

Zero Forcing (ZF) Equalizer: the goal of ZF equalization is to design a linear equalizer

vector gk of size 1 × Mr for each data symbol to cancel the ISI [53]. This equalizer works to

force the ISI equal to zero. This may lead to noise enhancement that decreases the overall

performance of the system. It is not widely used even though it is simple to design [27] [28].

The estimated data symbol s can be presented after applying the equalizer vector gk on the

equation of received signal (3.14) as

sk = gkyk = gkhksk +∑

i6=k

gkhisi + gknk, (3.15)

where gkhksk is the desired signal,∑

i6=kgkhisi is the interference, and gknk is the noise [53].

Taking into account that gk must be orthogonal to the channels of other symbols to cancel

the interference as

gkhi = 0, i 6= k. (3.16)

The vector of all estimated data symbols s can be written as

sk = Gy = GHs + Gn, (3.17)

where the matrix H contains the channels of all data symbols with a size of Mt × Mr as

H = [ h1 · · · hMt], the vector s = [ s1 · · · sMt

]T contains all of the transmitted data

symbols.

Herein, the matrix of GZF has the solution to remove the interferences in case of Mr > Mt

by applying the pseudoinverse of the matrix H as given

GZF = (HHH)−1HH , (3.18)

replacing this matrix in the previous expression of estimated symbol (3.17) as

sk = (HHH)−1HHHs + Gn = IMts + Gn. (3.19)

42

Therefore, the ZF equalizer is able to remove the ISI, while the main drawback of this

equalizer is the noise enhancement at low SNR region [27] [53].

Minimum Mean Square Error (MMSE) Equalizer: this equalizer minimizes the ex-

pected value of the squared difference between the desired data symbol s and the estimated

data symbol s [53] [27] as

ε = E[

‖s − s‖2]

= E[

‖s − Gy‖2]

. (3.20)

The matrix of GMMSE can be given as

GMMSE = (HHH + σ2IMt)−1HH . (3.21)

For a high SNR (SNR → ∞), the variance decreases toward 0 (σ2 → 0) and thus the MMSE

equalizer tends to the ZF equalizer [53].

MMSE provides a better balance between ISI mitigation and noise enhancement. Moreover,

it is more robust than ZF equalizer in case of existing a large ISI and noise [53] [27].

43

CHAPTER 4Implementation of a GFDM System

This chapter describes the system model and main equalization techniques for GFDM SISO,

SIMO, and MIMO systems and compares the BER performance in two types of channels:

AWGN and multipath channel. MF, ZF, and MF with the IC equalization techniques are

implemented and its performance evaluated. Furthermore, the GFDM performance is compared

against OFDM. This chapter starts with the SISO-GFDM system description and results,

then follows the SIMO-GFDM, and MIMO-GFDM description and results.

4.1 SISO-GFDM System Model

According to [55] and [56], it is better to replace the previous GFDM model (figure 2.16

and figure 2.17) described in section 2.3.3 by low complexity transmitter and receiver models

based on a sparse representation of the pulse shaping filter in the frequency domain, which is

convenient for the hardware implementation. Furthermore, this implementation as a structure

is closer to the one used in OFDM systems. First, the modulation process is applied to the

binary data. Then, the resulting signal is converted from time to frequency domain, follows

the GFDM processing in frequency domain and finally, the signal is converted back to time

domain. The resulting data bits are obtained through the demodulation process.

4.1.1 Low Complexity SISO-GFDM Transmitter Model

The modification on the previous GFDM model (figure 2.16) is shown in the block diagram

of low complexity GFDM transmitter processing in figure 4.1 which is modeled in base-band.

45

Figure 4.1: Low complexity SISO-GFDM transmitter system model [55]

The first block in this figure illustrates the converting process from time to frequency

domain. The data dk[m] can be represented by matrix D defined in (2.21), where dk refers to

the kth column of the data matrix D. By applying Discrete Fourier Transform (DFT) matrix

given by

WM =1√M

{wk,n}M×M , wk,n = e−j2π(k−1)(n−1)

N (4.1)

to each dk, the result is WM dk which represents the data at subcarrier k in the frequency

domain [55]. The transformed vector {WM dk}M×1 is passed through the second block

“frequency domain processing” that contains three stages. These stages correspond to the 3

blocks in figure 4.1, corresponding the first to the upscaling, the second to the filtering, and

the third to the upconversion operations. Each operation may be represented by a matrix

and thus the signal at the output of each block is equal to the signal at the input multiplied

by the corresponding matrix. Therefore, the resulting frequency samples will be multiplied

by the repetition matrix R(L) = {IM , IM , ..., IM }T to duplicate the samples L times, where

IM is an identity matrix. Then, the matrix of pulse shaping filter Γ = diag(WLM g) that

contains the frequency samples of the filter is applied on each subcarrier. At last, the kth

subcarrier signal is circular up-converted by multiplication with a permutation matrix P(k)

to upconvert the signal from base-band to band-pass, where P(1) = {ILM , 0LM , 0LM , ...}T ,

P(2) = {0LM , ILM , 0LM , ...}T , . . . with 0LM a matrix that contains zero elements [55].

Finally, in the last block, all subcarriers signal are superimposed and the signal will be

transformed to the time domain x by applying Inverse Discrete Fourier Transform (IDFT)

matrix WHNM , as formulated in equation (4.2) [55]

x = WHNM

∑

k

P(k)ΓR(L)WM dk. (4.2)

At this point, it is important to notice that this signal and the signal x[n], defined in (2.25),

are identical.

In addition, the GFDM processing at the transmitter may be represented by a single

matrix. This representation facilitates the application of standard receiver methods such as

MF, ZF, and MMSE. Using the matrix representation (4.2) may be rewritten [56] as follows

x = Ad, (4.3)

46

where A = WHNM [A0, A1, . . . , AK−1] is the complex-valued modulation matrix that contains

all transmitted signals as Ak = P(k)ΓR(L)WM , k = 0, . . . , K−1 and d = [dT0 , dT

1 , . . . , dTK−1]T

is the data vector.

4.1.2 Channel Model

The transmitted signal propagates through the wireless channel, which introduces distor-

tions that depend on the specific characteristics of the channel. In this study, the focusing

will be on two types of channel: AWGN and multipath channel [56].

The received signal y of size KM is equal to the transmitted signal x of size KM plus the

channel noise n as mentioned before:

y = Hx + n. (4.4)

Here, y is the unequalized received vector and n ∼ N (0, σ2) is a vector of AWGN samples

that has zero mean and variance σ2, where the Eb/N0 depends on the noise variance σ2.

AWGN Channel: in AWGN channels, the channel H is equal to the identity matrix H = I.

Therefore, y = x + n.

Multipath Channel: in multipath channels, H is not equal to the identity matrix I, it is a

convolution matrix in the case of CP is used both in GFDM and OFDM (circular channel

matrix), constructed from the channel response h and based on PDP.

4.1.3 Low Complexity SISO-GFDM Receiver Model

The low complexity GFDM Matched Filter (MF) receiver is presented in figure 4.2. The

operations are the same as the one performed at the transmitter (figure 4.1) but in reverse

order and transposed conjugate [56]. Therefore, the estimate of subcarrier k data symbols is

dk = WHM (R(L))T Γ

(L)Rx(P(k))T WNM y. (4.5)

Figure 4.2: Low complexity SISO-GFDM receiver system model [56]

As depicted in figure 4.2, first the received signal y is converted to the frequency

domain. Then, the transpose of the permutation matrix P(k) will be applied to make

47

circular down-conversion on the kth subcarrier to zero frequency. Follows the conjugated

transmitter filter which is considered as a receiver filter Γ(L)Rx =

(

Γ(L)Tx

)∗with only LM filter

coefficients. Thus, the down-sampling process by a factor L, represented by (R(L))T is

needed to get M samples that match with the transmitted data in terms of the number of

symbols on the kth subcarrier. Finally, it is necessary to transform the resulting signal to

the time domain by applying IDFT matrix WHM to obtain the estimate of data bits dk{M×1}

[56].

The previous description details the MF receiver operations. The same operations may

be represented using a single matrix as in (4.3). Indeed using the matrix representation, it

is possible to implement three standards linear GFDM receivers (MF, ZF, and MMSE) by

using the matrix A [25]. This study focuses on MF and ZF receivers which may be described

using the GFDM matrix representation as follows:

1. Matched Filter Receiver (MFR)

For the MF receiver approach, the recovered data vector dMF is obtained as

dMF = AHy, (4.6)

where AH is the Hermitian (Conjugate and Transpose) of matrix A, and y is the

received signal.

2. Zero Forcing Receiver (ZFR)

The recovered vector dZF of ZF receiver is based on the inverse of matrix A as

dZF = A−1y. (4.7)

Considering that the matrix A is square. But the dimension of matrix A is KM × NM ,

N > K, this means that this matrix is not square in case of N > K, so it will be possible

to use the pseudoinverse matrix A+ instead of inverse matrix as

A+ = AH(AAH)−1, (4.8)

taking note that A+A is equal to the identity matrix INM .

Despite that, the channel frequency response of a multipath channel has an impact on the

received signal, to compensate that, it is necessary for the receiving signal to be equalized

either in the time domain or frequency domain by using a ZF equalizer [25].

In the frequency domain:

yeq =

{

FFT(y)

FFT(H)

}

. (4.9)

In the time domain:

yeq = IFFT

{

FFT(y)

FFT(H)

}

. (4.10)

48

The equalized sequence in the frequency domain is applied to the previous linear GFDM

detectors (MF and ZF) after converted it to the time domain by using IFFT operation as

shown in figure 4.3:

Figure 4.3: Block diagram of a SISO-GFDM receiver with the equalization process

In this case, the recovered data vector of MF is

dMF = AHyeq, (4.11)

and the recovered data vector of ZF is

dZF = A−1yeq, (4.12)

where yeq is the equalized signal vector.

4.1.4 SISO Interference Cancellation

Figure 4.4 shows the IC unit, where the received data symbols dk[m] will be applied into

the IC block and the cancellation signal z(i)[n] will be subtracted from the received signal

y[n] to get the interference canceled received signal y(i)[n] [48] as

y(i)[n] = y[n] − z(i)[n]. (4.13)

Figure 4.4: SISO-GFDM receiver with Interference Cancellation block [48]

The block of IC unit is shown in figure 4.5. It is needed to cancel the ICI due to the

adjacent subcarriers where i is the sub-iteration index. The main function of the cancellation

49

scheduler is to pass the received symbols d(i)k [m]{K×M} into the cancellation grid for detecting

the interference to get d(i),ek [m]{K×M}, then passed to GFDM TX block to get the IC signal

z(i)[n].

Figure 4.5: Interference Cancellation Unit [48]

The Basic and Double Sided Serial Interference Cancellation techniques are going to be

explained in detail:

Basic Serial Interference Cancellation:

First in this technique, the data matrix d(i),ek [m]{K×M} in the IC unit only in the k − 1th

row has non zero elements, and the interference from succeeding subcarriers will be canceled

because of K sub-iterations [48]. For each sub-iteration like i = k, the ICI due to the k − 1

subcarrier will be canceled from the k subcarrier and then the subcarrier k will be detected.

For example: first, for k = 1, the ICI due to the Kth subcarrier (last subcarrier) is canceled

from the 1st subcarrier and the subcarrier k = 1 is detected. Then, for k = 2, the ICI due to

the 1st subcarrier is canceled from the 2nd subcarrier and the subcarrier k = 2 is detected.

For k = 3, the ICI due to the 2nd subcarrier is canceled from the 3rd subcarrier and the

subcarrier k = 3 is detected and so on [48].

The received symbols vector d(i)k [m]{1×KM} that was shown in the block diagram of

SISO-GFDM receiver with Interference Cancellation (figure 4.4) will be first modulated and

reshaped to be as a matrix with K subcarriers and M timeslots as d(i)k [m]{K×M}. Therefore,

the resulting interference cancellation signal z(i)[n] is obtained as depicted in figure 4.6, by

applying the same previous steps to be up-sampled, filtered and upconverted [48] as

z(i)[n] = (d(i),ek−1 ⊛ g)[n].w(k−1)n. (4.14)

50

Figure 4.6: Basic SIC flowchart [48]

Then, the interference canceled received signal y(i)[n] is equal to subtracting the IC signal

z(i)[n] from the received signal y[n] as shown in the previous equation (4.13).

In the receiver part, the received data symbols d(i+1)k [m] for the kth subcarrier is obtained

due to the interference canceled received signal which is digitally down converted, filtered and

down-sampled as the following expressions [48]

y(i)k [n] = y(i)[n].w−kn (4.15)

d(i+1),Nk [n] = (y

(i)k ⊛ g)[n] (4.16)

d(i+1)k [n] = d

(i+1),Nk [n = mN ]. (4.17)

These steps will be repeated for all subcarriers and in this case, the ICI on the kth subcarrier

will be removed.

Double Sided Serial Interference Cancellation:

In DSSIC, the data matrix in figure 4.5 in both (k − 1)th and (k + 1)th rows has non zero

elements, and the interference from the 2-sides (adjacent subcarriers) will be removed at the

same time. For each sub-iteration like i = k, the ICI due to the k − 1 and k + 1 subcarrier will

be canceled from the k subcarrier and then the subcarrier k will be detected. For example:

first, for k = 1, the ICI due to the Kth subcarrier (last subcarrier) and the 2nd one are

canceled from the 1st subcarrier and the subcarrier k = 1 is detected. Then, for k = 2, the

ICI due to the 1st and 3rd subcarrier are canceled from the 2nd subcarrier and the subcarrier

k = 2 is detected. For k = 3, the ICI due to the 2nd and 4rth subcarrier are canceled from the

3rd subcarrier and the subcarrier k = 3 is detected and so on [48]. In this case, the data for

subcarrier k − 1 is d(i)k−1[m] and for subcarrier k + 1 is d

(i)k+1[m]. These two signals are detected

by passing through the cancellation scheduler to get d(i),ek−1[m] and d

(i),ek+1[m]. As depicted in

figure 4.7, those data will be sent to GFDM Tx block as SIC technique to get the interference

cancellation signal z(i)[n], which could be expressed mathematically [48] as

z(i)[n] = (d(i),ek−1 ⊛ g).w(k−1)n + (d

(i),ek+1 ⊛ g).w(k+1)n. (4.18)

51

Figure 4.7: Double Sided SIC flowchart [48]

Then, as previous steps, this signal will be subtracted from the received signal y[n] to get

the interference canceled received signal y(i)[n] as (4.13). Subsequently, in the receiver side,

the same previous steps will be applied to get the same expressions as (4.15), (4.16), (4.17) [48].

In addition, in the case of multipath channel, the interference cancellation signal z(i)[n]

will be subtracted from the equalized received sequence yeq, according to [25].

4.1.5 Results of SISO-GFDM system

This section focuses on evaluating the performance of GFDM technique in terms of the

average BER, being the latter presented as a function of the Eb/N0, where Eb is the average

bit energy and N0 is the noise power spectral density. Moreover, comparing the performance

of GFDM with OFDM in case of simulating a multipath channel.

Parameters Variables OFDM GFDM

Modulation sheme µ QPSK QPSKSamples per symbol N 64 64

Subcarriers K 64 64Block size M 15 15

Duration of time-slot - 256µs 256µsSubcarrier bandwidth - 3.906KHz 3.906KHz

Filter type - - RRCRoll-off factor α - 0.1, 0.3, 0.5Receiver type - MF and ZF MF and ZF

Channel h AWGN, Multipath Channel AWGN, Multipath Channel

Table 4.1: OFDM and GFDM Simulation Parameters

52

The parameters are shown in table 4.1, taking into consideration that OFDM and GFDM

systems are implemented with QPSK modulation for number of subcarriers K = 64 and

block size M = 15. The number of samples per symbol is equal to the number of subcarriers

N = K = 64. In addition to applying RRC pulse shaping filter with different roll-off-factors

α = 0.1, 0.3, and 0.5. OFDM and GFDM systems will be simulated in different types of

channels.

4.1.5.1 Results of linear equalization schemes MF and ZF

The performance results will be discussed in detail for two types of channels: AWGN

and multipath channel, where MF and ZF receiver approaches will be considered for the

reception of the GFDM signal with roll-off-factor equal to 0.1 and 0.3 to regard the difference,

and taking into account that the ZF equalizer will be used to compensate for the channel effects.

For AWGN channel, figure 4.8 compares the BER performance of a GFDM system with

MF receiver and a GFDM system with ZF receiver for different values of roll-off-factor. Then,

comparing the results with theoretical AWGN curve. The observation that can be made is

that the left-hand side of figure 4.8 displays the error performance when α = 0.1. It can be

noticed that the performance of all curves at low SNR region is similar but the difference is

clearly increasing for GFDM-MF receiver to be worse than GFDM-ZF receiver at high SNR,

about 2dB for BER of 10−5, while GFDM-ZF receiver has exactly the same performance of

AWGN curve and this ensures that the GFDM ZF receiver has a better performance than

MF receiver because of the self-interference that can be eliminated by using ZF.

0 2 4 6 8 10 12 14 16 18 20

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

Theoretical AWGN

GFDM MF Receiver

GFDM ZF Receiver

(a) α = 0.1

0 2 4 6 8 10 12 14 16 18 20

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

Theoretical AWGN

GFDM MF Receiver

GFDM ZF Receiver

(b) α = 0.3

Figure 4.8: SISO-GFDM BER performance for QPSK modulation with different roll-off-factor andAWGN channel used

The right-hand side of figure 4.8 illustrates the performance of the same curves but with

α = 0.3. From this figure, it can be observed that the BER performance of GFDM system

will be worse when the roll-off factor of RRC pulse shaping filter increases. The performance

53

of GFDM with MF and ZF receiver at low SNR is comparable. But as SNR increases, i.e., in

the case of reaching a higher SNR region, GFDM-MF curve will be worse than GFDM-ZF

receiver and the latter presents that there is about 1dB difference in comparison with AWGN

curve for BER of 10−5.

Besides AWGN channel, the results for a multipath wireless channel are also presented in

the following. The multipath channel considered is a fading channel, typically representative

of Wireless Regional Area Networks (WRAN) scenarios for IEEE 802.22 [25]. Table 4.2 lists

the channel PDP that has been considered to evaluate the BER performance of GFDM for

this type of channel.

Channel A Coherence bandwidth = 7.23KHz

Delay (µs) 0 3 8 11 13 21

Path Gain (dB) 0 -7 -15 -22 -24 -19

Table 4.2: Power Delay Profile used in simulation [25]

From table 4.1 and table 4.2 follows that channel A is a flat fading channel, since the

Coherence Bandwidth Bc is higher than the subcarrier spacing Bs.

The GFDM BER performance results of MF and ZF receiver techniques can be presented

in figure 4.9 after simulating Channel A and taking into consideration the previous parameters

with a different roll-of-factor. The left-hand side of figure 4.9 shows the BER performance

of GFDM system with MF receiver and GFDM system with ZF receiver over a multipath

channel and under a ZF equalizer with roll-off-factor α = 0.1, then comparing the results with

the performance of OFDM. It can be observed that the performance of these two receivers

is the same and a bit worse than OFDM. But, it can be noted that the curves of these two

receivers can match the BER performance of OFDM at high SNR.

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

OFDM

GFDM MF Receiver

GFDM ZF Receiver

(a) α = 0.1

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

OFDM

GFDM MF Receiver

GFDM ZF Receiver

(b) α = 0.3

Figure 4.9: SISO-GFDM BER performance for QPSK modulation with different roll-off-factor andmultipath channel used

54

However, implementing the previous systems with roll-off-factor α = 0.3 can be presented

in the right-hand side of figure 4.9, where the BER performance of GFDM system with MF

receiver and GFDM system with ZF receiver is almost the same and a bit worse than OFDM.

But, at high SNR, the performance of ZF receiver for GFDM system is better than MF

receiver by about 1.5dB for BER of 10−4.

The results of these two approaches confirm that the ZF receiver is suitable to remove the

self-interference which is introduced because of the non-orthogonality between the subcarriers.

The MF receiver is used to maximize SNR per subcarriers, and on the contrary it is not

able to remove the interference between the adjacent subcarriers. Therefore, the BER will

be increased because of this high ICI. In this case, the basic SIC and DSSIC algorithms are

suitable solutions to minimize these interferences [48] as follows.

4.1.5.2 Results of Interference Cancellation (IC) schemes

The BER performance results of the two cancellation techniques will take place in figure

4.10 and 4.11 with roll-off-factor equal to 0.5 for AWGN and multipath channel respectively.

The first figure ensures that the BER performance of GFDM is improved by implementing

the cancellation techniques, where GFDM-MF receiver with SIC technique is unable to cancel

out all the ICI and still about 2.5dB worse compared to GFDM-ZF curve for BER of 10−4.

GFDM-MF receiver with DSSIC technique mitigates the ICI from the adjacent subcarriers

as is evident in the improved BER performance to be better than GFDM-ZF receiver at low

SNR region, and also to approximately match the performance of theoretical AWGN. In

contrast, at high SNR for BER of 10−5, GFDM-ZF receiver refers to the relative improvement

in BER performance that is about 1.8dB better compared to GFDM-MF that works with

DSSIC technique and 2dB worse compared to theoretical AWGN BER curve.

0 2 4 6 8 10 12 14 16 18 20

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

Theoretical AWGN

GFDM MF Receiver

GFDM MF-SIC Receiver

GFDM MF-DSSIC Receiver

GFDM ZF Receiver

Figure 4.10: SISO OFDM and GFDM Basic SIC and DSSIC BER performance for QPSK modulationwith α = 0.5 and AWGN channel used

55

Figure 4.11 shows that OFDM system outperforms the GFDM system and GFDM-MF

shows a poor performance as compared with GFDM-ZF because it is highly affected by ICI.

Therefore, GFDM-MF with DSSIC technique has the best performance in the whole SNR

region compared to the other GFDM curves and almost matches the BER performance of

OFDM at high SNR.

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

OFDM

GFDM MF Receiver

GFDM MF-SIC Receiver

GFDM MF-DSSIC Receiver

GFDM ZF Receiver

Figure 4.11: SISO OFDM and GFDM Basic SIC and DSSIC BER performance for QPSK modulationwith α = 0.5 and multipath channel used

It must be concluded that the performance of GFDM-MF improved in the case of applying

the cancellation techniques especially with DSSIC for both types of the channel (AWGN and

multipath channel). But the BER performance of OFDM system is clearly better than all

of the GFDM methods. Although the GFDM systems induce more self-interference than

that of OFDM, the advantages of GFDM make this weakness acceptable. Besides that, the

performance of GFDM systems is also affected by the choice of pulse shaping filter in terms of

the value of the roll-off-factor of RRC filter, noting that increasing this value causes a worse

BER performance for GFDM system and this was definitely clear in the previous results. For

α = 0.1 and 0.3, it should be noted that the results for cancellation techniques were very

similar and thus decided to not include them in the figures.

56

4.2 SIMO-GFDM System Model

From SISO to SIMO system, this means there is a single transmitting antenna at the

transmitter side and more than one receiving antenna at the receiver side. This section

presents the extension of the previous SISO schemes for SIMO where the receiver is equipped

with 2 or 4 antennas.

4.2.1 SIMO-GFDM System with 2Rx antennas

SISO-GFDM transmitter system model which was depicted in figure 4.1 refers to the block

diagram of the SIMO-GFDM transmitter system model too. But here the transmitted signal x

for a given subcarrier will be transmitted through two wireless channels (H =[

HT1 HT

2

]T)

to obtain two receiving signals (y =[

yT1 yT

2

]T) as

y1 = H1x + n1 (4.19)

y2 = H2x + n2. (4.20)

Therefore, in the receiving side as depicted in figure 4.12, each received signal is used to

estimate the channel impulse response and will convert from time to frequency domain to be

ready for the equalization process that will be applied by using ZF technique to get yeq as

yeq = (HH1 H1 + HH

2 H2)−1(HH1 y1 + HH

2 y2). (4.21)

It can be noted that the second part of the formula mentions to the MRC equalizer, but

since the normalization process (the first part of the formula) is necessary, we can consider

that the used equalizer is ZF.

Figure 4.12: Low complexity SIMO-GFDM receiver system model for 2Rx antennas

This equalized signal is converted again to the time domain before processing it in a MF

or ZF detector. The next steps are exactly as well as in the SISO system.

Both SIMO system with 2 and 4 antennas was developed and the obtained results

are presented next, but since the extension to a generic number of receive antennas is

straightforward, only the case with 2 antennas was described.

57

4.2.2 Results of SIMO-GFDM system

The BER performance of the SIMO-GFDM system with 2Rx and 4Rx antennas will be

described in the following subsections,

4.2.2.1 Results of SIMO-GFDM system for 2Rx antennas

The performance of the SIMO-GFDM system for 2Rx antennas can be described in figure

4.13 by applying the same parameters that were shown in the table 4.1 and with the same

multipath channel that is based on the table of PDP 4.2. This figure clarifies the enhancement

of the system performance in terms of reducing the SNR to achieve the same level of BER, i.e.

the slope will be increased due to the diversity gain. For α = 0.1, it can be noted that MF

and ZF receiver for GFDM system have better performance than OFDM and this is because

of the receive diversity which SIMO systems are able to achieve.

0 5 10 15 20

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

1Tx-2Rx OFDM

1Tx-2Rx GFDM MF Receiver

1Tx-2Rx GFDM ZF Receiver

(a) α = 0.1

0 5 10 15 20

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

1Tx-2Rx OFDM



(b) α = 0.3

Figure 4.13: SIMO OFDM and GFDM BER performance for QPSK modulation and 2Rx antennaswith different roll-off-factor and multipath channel used

In case of increasing the value of roll-off-factor, for example for α = 0.3, as can be seen in

the right-hand side of figure 4.13, GFDM MF receiver has a worse performance than ZF, i.e.,

it is not able to cancel the interference among symbols even though the BER value is better

than SISO systems due to multiple antennas at the receiving end.

To solve the problem of symbols interference, this can be done by using the same cancella-

tion techniques likewise SISO systems. Therefore, figure 4.14 shows the impact of applying

these techniques on the performance of the SIMO system. For α = 0.5, it can be noted that

GFDM with MF receiver and DSSIC technique has the ability to remove all ISI and has the

best curve compared to the other curves.

58

0 5 10 15 20

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

1Tx-2Rx OFDM


1Tx-2Rx GFDM MF-SIC Receiver

1Tx-2Rx GFDM MF-DSSIC Receiver


Figure 4.14: SIMO OFDM and GFDM BER performance for QPSK modulation and 2Rx antennaswith α = 0.5 and multipath channel used

In addition, for α = 0.1 and 0.3, there are no implementation results for SIC and DSSIC

techniques since the results will appear overlapped on each other.

4.2.2.2 Results of SIMO-GFDM system for 4Rx antennas

Increasing the number of receiving antennas leads to a lower in BER and better performance

of the overall system. This can be shown in figure 4.15 that clarifies the enhancement of the

system BER performance and the slope keeps on increasing due to the number of receiving

antenna is increased. From these curves that implemented with roll-off-factor equal to 0.1, it

can be noted that 1x4 GFDM-ZF system provides a gain of 11.5dB at BER of 10−6 which

is 1dB better improvement than GFDM-MF and OFDM. Taking into account that at high

SNR region, the BER performance of GFDM-MF matches the performance of OFDM.

0 2 4 6 8 10 12 14 16

Eb/No, dB

10-6

10-5

10-4

10-3

10-2

BE

R

1Tx-4Rx OFDM



(a) α = 0.1

0 2 4 6 8 10 12 14 16

Eb/No, dB

10-5

10-4

10-3

10-2

BE

R

1Tx-4Rx OFDM



(b) α = 0.3

Figure 4.15: SIMO OFDM and GFDM BER performance for QPSK modulation and 4Rx antennaswith different roll-off-factor and multipath channel used

59

Increasing the value of the roll-off-factor in SIMO systems has the same impact as SISO

systems in terms of poor BER GFDM system performance. Therefore, for α = 0.3 in figure

4.15, it can be noted that the BER performance of GFDM-MF has worse performance in

comparison with SIMO-OFDM. In contrast, the BER keeps on decreasing for the GFDM-ZF

system at high SNR and achieves a better performance than SIMO-OFDM.

Figure 4.16 illustrates the bad BER performance at a low SNR region on the whole

GFDM system methods for α = 0.5 and thus it has necessary to avoid that by implementing

the cancellation techniques that have the main role in mitigating the interferences between

symbols. The result of DSSIC technique for SIMO-GFDM system with MF receiver is clearly

shown at low SNR and approximately matched the performance of OFDM, but for BER of

10−5, the error performance of GFDM-ZF becomes much better and matches the performance

of SIMO-OFDM at 10−6.

0 2 4 6 8 10 12 14 16

Eb/No, dB

10-6

10-5

10-4

10-3

10-2

BE

R

1Tx-4Rx OFDM


1Tx-4Rx GFDM MF-SIC Receiver

1Tx-4Rx GFDM MF-DSSIC Receiver


Figure 4.16: SIMO OFDM and GFDM BER performance for QPSK modulation and 4Rx antennaswith α = 0.5 and multipath channel used

From the previous results of SIMO-OFDM and SIMO-GFDM systems, it can be found

that increasing the number of receiving antennas achieves better performance and thus the

BER will be decreased. SIMO systems with 2 antennas can achieve a diversity order of 2

while with 4 antennas the diversity order is equal to 4. This means that the slope of the BER

curve is equal to 2 or 4 for a SIMO with 2 or 4 antennas respectively.

60

4.3 MIMO-GFDM System Model

From SIMO to MIMO system, this means there is more than one transmitting antenna

at the transmitter side and more than one receiving antenna at the receiver side. This

section describes the implemented MIMO-GFDM system for 2 and 4 transmit-receive antennas.

4.3.1 MIMO-GFDM System with 2Tx and 2Rx antennas

For 2 × 2MIMO-GFDM system, the transmitter model is presented in figure 4.17, where

there are two transmitted data vectors x1 and x2 given by

x1 = Ad1 (4.22)

x2 = Ad2. (4.23)

Figure 4.17: Low complexity 2 × 2MIMO-GFDM transmitter system model

Each one of these signals are transmitted through two multipath channels to arrive at the

receiver side as shown in figure 4.18.

Figure 4.18: 2 × 2MIMO channels

61

Thus, the received vectors y1 and y2 of the kth subcarriers and mth timeslots can be

mathematically written as

y1 = H11x1 + H21x2 + n1 (4.24)

y2 = H12x1 + H22x2 + n2. (4.25)

Noting that at the MIMO-GFDM receiver side as shown in figure 4.19, the FFT operation

must be performed for the received signal vectors of each receiving antenna before applying

any type of linear sub-optimal equalizers such as ZF and MMSE to get

yeq= Gy = GHx + Gn, (4.26)

where x = [x1T , xT

2 ]T and H = [H11,H12;H21,H22], each one of these channel is a matrix

with a size of KM × KM . In this case the resulted estimated vectors yeq of size 2KM for

these two equalizers are obtained after replacing the matrix G of ZF or MMSE equalizer by

the highligted matrices (3.18) and (3.21).

Figure 4.19: Low complexity 2 × 2MIMO-GFDM receiver system model

Each resulting vector of the previous estimated data refers to y1eq and y2eq that are

ready to be processed by IFFT operators and to obtain the recovered data vectors of MF as

d1MF = AHy1eq (4.27)

d2MF = AHy2eq, (4.28)

or the recovered data vectors of ZF as

d1ZF = A−1y1eq (4.29)

d2ZF = A−1y2eq (4.30)

Both a MIMO system with (2 × 2 and 4 × 4) antennas was developed and the obtained

results are presented next, but since the extension to a generic number of transmit and receive

antennas is straightforward, only the case with 2 × 2 antennas was described.

62

4.3.2 Results of MIMO-GFDM system

The BER performance of the MIMO-GFDM system with two scenarios (2 × 2, 4 × 4) will

be described in the following subsections as,

4.3.2.1 Results of MIMO-GFDM system for 2Tx and 2Rx antennas

The results of implementing the two approaches (ZF and MMSE) will be shown in the

next two figures, taking into consideration that the channel is a multipath channel and the

value of the roll-of-factor is equal to 0.5.

Figure 4.20 shows the BER performance of MIMO-OFDM and MIMO-GFDM systems

with two transmit antennas and two receive antennas by applying a ZF sub-optimal equalizer

approach. It is observed that the error performance of the MIMO-OFDM and MIMO-GFDM

with MF-DSSIC receiver will be approximately the same in the high SNR region, while

MIMO-GFDM with ZF receiver remains worse than MIMO-OFDM system to have the same

BER performance of MIMO-GFDM with MF-SIC receiver at the high SNR.

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

100

BE

R

2Tx-2Rx OFDM

2Tx-2Rx GFDM MF Receiver(ZF Equalizer)

2Tx-2Rx GFDM MF-SIC Receiver(ZF Equalizer)

2Tx-2Rx GFDM MF-DSSIC Receiver(ZF Equalizer)

2Tx-2Rx GFDM ZF Receiver(ZF Equalizer)

Figure 4.20: 2 × 2MIMO OFDM and GFDM BER performance by using ZF equalizer for QPSKmodulation with α = 0.5 and multipath channel used

The results of implementing a MMSE sub-optimal equalizer approach are going to be

described in figure 4.21. It clarifies that the error performance of MF MIMO-GFDM with IC

techniques and ZF MIMO-GFDM are better than MIMO-OFDM system at the high SNR

region, especially for MF-DSSIC receiver technique that has around 10dB of improvement

compared with MIMO-GFDM MF-SIC receiver for BER of 10−5.

63

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

100

BE

R

2Tx-2Rx OFDM

2Tx-2Rx GFDM MF Receiver(MMSE Equalizer)

2Tx-2Rx GFDM MF-SIC Receiver(MMSE Equalizer)

2Tx-2Rx GFDM MF-DSSIC Receiver(MMSE Equalizer)

2Tx-2Rx GFDM ZF Receiver(MMSE Equalizer)

Figure 4.21: 2 × 2MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSKmodulation with α = 0.5 and multipath channel used

From these two figures, the consclusion is that the MMSE equalizer has a better BER

performance than ZF equalizer. Besides, it is able to cancel the ISI. Moreover, the BER

performance of MF receiver for MIMO-GFDM in both equalizers is the same and is considered

the worst curve among the other curves.


4 × 4MIMO-GFDM BER performance is shown in figure 4.22 and 4.23. It can be observed

from these two figures that increasing the number of transmitting and receiving antennas

to be 4 × 4 has the same BER performance of 2 × 2 OFDM and GFDM systems since all

Degrees-of-Freedom (DoF) are used for data transmission, for both cases.

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

100

BE

R

4Tx-4Rx OFDM

4Tx-4Rx GFDM MF Receiver(ZF Equalizer)

4Tx-4Rx GFDM MF-SIC Receiver(ZF Equalizer)

4Tx-4Rx GFDM MF-DSSIC Receiver(ZF Equalizer)

4Tx-4Rx GFDM ZF Receiver(ZF Equalizer)

Figure 4.22: 4 × 4MIMO OFDM and GFDM BER performance by using ZF equalizer for QPSKmodulation with α = 0.5 and multipath channel used

64

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

100

BE

R

4Tx-4Rx OFDM





Figure 4.23: 4 × 4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSKmodulation with α = 0.5 and multipath channel used


To recognize the effect of the diversity gain of MIMO systems, the performance of a

2 × 4MIMO-GFDM system was evaluated. Noting that for this case 2-antennas at the receiver

would be sufficient to multiplex 2-data streams, and therefore the two extra antennas may be

used to achieve a diversity gain. Figure 4.24 shows the BER performance of 2×4MIMO-GFDM

system compared to 2 × 4MIMO-OFDM system when using MMSE equalizer.

0 5 10 15 20 25 30 35 40

Eb/No, dB

10-5

10-4

10-3

10-2

10-1

BE

R

2Tx-4Rx OFDM





Figure 4.24: 2x4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSKmodulation with α = 0.5 and multipath channel used

65

4.4 Power Spectral Density

PSD is the average power distribution as a function of frequency and it provides the

frequency response of the random or periodic signal. PSD of the signal depends on circular

shift operation and pulse shaping filtering at the transmitter side. The OOB radiation is an

important issue in the cellular communication system and this can be predicted through PSD

expressions that are produced at the transmitter [27] [55] [46].

The PSD of OFDM and GFDM signals are shown in figure 4.25 regarding the positive

part since the other part is identical, for 64 subcarriers and 15 subsymbols by using QPSK

modulation with RRC pulse shaping filter and roll-off-factor is equal to 0.5.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized frequency

-40

-35

-30

-25

-20

-15

-10

-5

0

5

Pow

er

Spectr

al D

ensity

OFDM

GFDM

Figure 4.25: PSD comparison between OFDM and GFDM with α = 0.5 of RRC pulse shaping filter

From this figure, it can be seen that GFDM gives benefits over OOB emissions. In GFDM

system, each subcarrier is shaped with a filter individually and its flexibility provides an

advantage over OOB distortion. Unlike OFDM system that has high OOB emissions because

of its using the rectangular pulse shaping filter. It can be noted that the PSD of GFDM is

lower than OFDM, i.e., GFDM signal is able to transmit the same information with lower

power due to the spectrum fragmentation process in contrast with OFDM that consumes a

large transmission power.

66

CHAPTER 5Conclusion and Future Work

Mobile telecommunications systems of the next generation seek to exceed the 5G capabilities

for achieving higher data rates. As mentioned, GFDM is one of the physical layer waveforms

that have the ability to address the requirements of beyond 5G cellular system. This chapter

briefly summarizes the main conclusion of this work and presents some points to regard in the

future.

5.1 Conclusions

In the last couple of years, cell phones play the main role in changing our world. As seen

about mobile communications history and its evolution, 5G technologies are expected to move

us to a new era with faster communications by the 2020s. Many requirements must be taken

into account to achieve the purpose of 5G, besides improving and creating new techniques to

be acceptable with this large variety of new requirements. Many recent wireless standards are

used the multi-carrier OFDM system because of its advantages in dividing the high data rate

into several low data rate streams. However, the work needs to be expanded to include new

multi-carrier modulation schemes, such as GFDM, which considered the generalization of

OFDM and the most flexible digital modulation.

In this dissertation, the low complexity design for GFDM transceiver was introduced

in detail and compared to other GFDM system models. This design based on a sparse

representation of the pulse shaping filter in the frequency domain based on the FFT/IFFT

algorithm. Moreover, the BER performance of different antennas architectures are related

to many considerable parameters for AWGN and multipath fading channel. First, the

work focused on SISO-GFDM system that depends on MF and ZF receivers and how

self-interference techniques (SIC and DSSIC) can mitigate the ICI that is considered the main

drawback of GFDM. It was shown that the SIC technique is able to reduce the interference

but DSSIC has the ability to eliminate it in both types of channels.

67

SIMO systems provide diversity and antenna gain. Herein, SIMO-GFDM system has

shown the results for 2 and 4 antennas architectures over a multipath fading channel, then

using the ZF equalizer since the signal must be equalized to compensate for the influence of

the channel frequency response in the received signal. As a result, increasing the number

of antennas means improving the performance of the overall system and achieving a lower BER.

MIMO systems provide a multiplexing gain that has the main role in increasing the system

capacity. Herein, the results of BER performance of 2 × 2MIMO-GFDM and 4 × 4MIMO-

GFDM systems for a multipath channel were implemented under two linear equalizer

techniques (ZF and MMSE). It could be observed that MMSE is able to provide better error

performance than ZF due to its ability to achieve a better balance between ISI mitigation

and noise enhancement. But, 2 × 4MIMO-GFDM system was implemented to show the diver-

sity gain and ensure that the diversity order increases the performance toward AWGN channel.

All the results were compared with OFDM system and it can be noted that the OOB

emissions of GFDM are lower than OFDM, which allowing it for higher flexibility for spectrum

fragmentation, besides its ability to achieve higher spectral efficiency.

5.2 Future Work

As seen before about the main purpose of GFDM in overcoming the high PAPR of OFDM

systems besides the flexibility, which will provide significant features in the future mobile

communications. There are some suggestions for future work before finalizing this study, such

as

• In this dissertation, the focusing was on GFDM digital modulation technique. It

would be highly relevant to implement the two other modulation schemes that are also

considered promising candidates for future generations, such as FBMC, and UFMC,

then comparing the systems’ performance results.

• It can be possible to implement the schemes with higher-order constellations (e.g.

16/64/256-QAM) already considered in 5G and comparing with the results of QPSK

used.

• Using Massive Multiple Input Multiple Output (mMIMO) instead of conventional MIMO

due to the great importance of millimeter Wave (mmW) with mMIMO in the future

wireless communication, where the deployment of a large number of antennas is also

considered the key enabling technology for achieving higher data rates and the ability to

access more bandwidth. It could be possible by using some analog/digital beamforming

techniques due to its potential to overcome the limitations caused by the conventional

MIMO systems.

68

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