joumana implementação e avaliação do desempenho de
TRANSCRIPT
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
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
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
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
4.3.2.2 Results of MIMO-GFDM system for 4Tx and 4Rx antennas . . . . 64
4.3.2.3 Results of MIMO-GFDM system for 2Tx and 4Rx antennas . . . . 65
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
4.14 SIMO OFDM and GFDM BER performance for QPSK modulation and 2Rx antennas with
α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.15 SIMO OFDM and GFDM BER performance for QPSK modulation and 4Rx antennas with
different roll-off-factor and multipath channel used . . . . . . . . . . . . . . . . . . . . . . 59
4.16 SIMO OFDM and GFDM BER performance for QPSK modulation and 4Rx antennas with
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
modulation with α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . 64
4.22 4 × 4MIMO OFDM and GFDM BER performance by using ZF equalizer for QPSK
modulation with α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . 64
4.23 4 × 4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSK
modulation with α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . 65
4.24 2x4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSK
modulation with α = 0.5 and multipath channel used . . . . . . . . . . . . . . . . . . . . 65
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
shown in figure 2.4.
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
shown in figure 2.11.
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
1Tx-2Rx GFDM MF Receiver
1Tx-2Rx GFDM ZF Receiver
(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 Receiver
1Tx-2Rx GFDM MF-SIC Receiver
1Tx-2Rx GFDM MF-DSSIC Receiver
1Tx-2Rx GFDM ZF 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
1Tx-4Rx GFDM MF Receiver
1Tx-4Rx GFDM ZF Receiver
(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
1Tx-4Rx GFDM MF Receiver
1Tx-4Rx GFDM ZF Receiver
(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 Receiver
1Tx-4Rx GFDM MF-SIC Receiver
1Tx-4Rx GFDM MF-DSSIC Receiver
1Tx-4Rx GFDM ZF 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.
4.3.2.2 Results of MIMO-GFDM system for 4Tx and 4Rx antennas
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
4Tx-4Rx GFDM MF Receiver(MMSE Equalizer)
4Tx-4Rx GFDM MF-SIC Receiver(MMSE Equalizer)
4Tx-4Rx GFDM MF-DSSIC Receiver(MMSE Equalizer)
4Tx-4Rx GFDM ZF Receiver(MMSE Equalizer)
Figure 4.23: 4 × 4MIMO OFDM and GFDM BER performance by using MMSE equalizer for QPSKmodulation with α = 0.5 and multipath channel used
4.3.2.3 Results of MIMO-GFDM system for 2Tx and 4Rx antennas
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
2Tx-4Rx GFDM MF Receiver(MMSE Equalizer)
2Tx-4Rx GFDM MF-SIC Receiver(MMSE Equalizer)
2Tx-4Rx GFDM MF-DSSIC Receiver(MMSE Equalizer)
2Tx-4Rx GFDM ZF Receiver(MMSE Equalizer)
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.
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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.
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