UNIVERSIDADE ESTADUAL DE CAMPINAS
Faculdade de Engenharia El´etrica e de Computa¸c˜ao
Nathaly Ver´
onica Orozco Garz´
on
Bit Error Rate and Spectral Efficiency Analysis
of Opportunistic Wireless Systems
An´
alise da Probabilidade de Erro de Bit e da Eficiˆencia
Espectral de Sistemas Oportunistas Sem Fio
Campinas 2018
UNIVERSIDADE ESTADUAL DE CAMPINAS
Faculdade de Engenharia El´etrica e de Computa¸c˜ao
Nathaly Ver´
onica Orozco Garz´
on
Bit Error Rate and Spectral Efficiency Analysis
of Opportunistic Wireless Systems
An´
alise da Probabilidade de Erro de Bit e da Eficiˆencia
Espectral de Sistemas Oportunistas Sem Fio
Thesis presented to the School of Electrical and Computer Engineering of the University of Camp-inas in partial fulfillment of the requirements for the degree of Doctor in Electrical Engineering, in the area of Telecommunications and Telematics.
Tese apresentada `a Faculdade de Engenharia El´etrica e de Computa¸c˜ao da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obten¸c˜ao do t´ıtulo de Doutora em Engenharia El´etrica, na ´area de Telecomunica¸c˜oes e Telem´atica.
Supervisor/Orientador : Prof. Dr. Celso de Almeida Este exemplar corresponde `a vers˜ao final
da tese defendida pela aluna Nathaly Ver´onica Orozco Garz´on, e orientada pelo Prof. Dr. Celso de Almeida
Campinas 2018
Agência(s) de fomento e nº(s) de processo(s): CAPES ORCID: http://orcid.org/0000-0002-5232-7529
Ficha catalográfica
Universidade Estadual de Campinas Biblioteca da Área de Engenharia e Arquitetura
Luciana Pietrosanto Milla - CRB 8/8129
Orozco Garzón, Nathaly Verónica,
Or68b OroBit error rate and spectral efficiency analysis of opportunistic wireless systems / Nathaly Verónica Orozco Garzón. – Campinas, SP : [s.n.], 2018.
OroOrientador: Celso de Almeida.
OroTese (doutorado) – Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação.
Oro1. Sistemas de telefonia celular. 2. Probabilidade de erro (Matemática). 3. Rádio Interferência. 4. Rádio Transmissores e transmissão
-Desvanecimento. I. Almeida, Celso de, 1957-. II. Universidade Estadual de Campinas. Faculdade de Engenharia Elétrica e de Computação. III. Título.
Informações para Biblioteca Digital
Título em outro idioma: Análise da probabilidade de erro de bit e da eficiência espectral de
sistemas oportunistas sem fio
Palavras-chave em inglês:
Cellular phone systems
Error probability (Mathematics) Radio - Interference
Radio - Transmitters and transmission - Fading
Área de concentração: Telecomunicações e Telemática Titulação: Doutora em Engenharia Elétrica
Banca examinadora:
Celso de Almeida [Orientador]
Gonzalo Fernando Olmedo Cifuentes Rodrigo Pereira Ramos
Luiz César Martini Carlos Eduardo Câmara
Data de defesa: 04-04-2018
Programa de Pós-Graduação: Engenharia Elétrica
COMISS ˜AO JULGADORA - TESE DE DOUTORADO
Candidato: Nathaly Ver´onica Orozco Garz´on RA: 142373 Data da Defesa: 04 de abril de 2018
T´ıtulo da Tese: Bit Error Rate and Spectral Efficiency Analysis of Opportunistic Wireless Systems (An´alise da Probabilidade de Erro de Bit e da Eficiˆencia
Espectral de Sistemas Oportunistas Sem Fio)
Prof. Dr. Celso de Almeida (Presidente, FEEC/UNICAMP) Prof. Dr. Gonzalo Fernando Olmedo Cifuentes (DEEE/ESPE) Prof. Dr. Rodrigo Pereira Ramos (UNIVASF)
Prof. Dr. Luiz C´esar Martini (FEEC/UNICAMP) Prof. Dr. Carlos Eduardo Cˆamara (UNIANCHIETA)
A ata de defesa, com as respectivas assinaturas dos membros da Comiss˜ao Julgadora, encontra-se no processo de vida acadˆemica da aluna.
I dedicate this work to my parents, Amparito and Iv´an, to my brothers, Iv´an and Pablo and to my baby An-thonellita. To them, for being my strength, happiness and the reason of my life.
Acknowledgments
I thank God for the blessings along my life, for allowing me to successfully complete one more step in my life.
To my parents, Amparito and Marcelito, who with all their love gave me their good and sweet advices that are the strength I need at all times of my life, I thank them for their unconditional support.
To my brothers, for the joy they give to my life, for their love and motivation. To Florcita and to my baby Anthonellita a little angel who came to fill my house with love. To Prof. Celso de Almeida, for the opportunity and confidence, for the dedicated guidance and support, and the most important for the friendship during the development of this work.
To Prof. Gonzalo Olmedo, Prof. Rodrigo Pereira Ramos, Prof. Luiz C´esar Martini, and to Prof. Jaime Portugheis, members of this dissertation committee, for the comments, suggestions and contributions aimed at improving the present work.
To Henry, companion of this adventure, I thank you for the affection throughout this time, for the motivation and help in this work.
To my friends and colleagues, for the experience and knowledge that we have shared, for the companionship and valuable friendship.
To CAPES and SENESCYT-IFTH, for the finnancial support.
Finally, to all the people who somehow contributed to the accomplishment of this work.
Abstract
Different opportunistic transmission techniques were proposed for wireless communication sys-tems. In this work, we explore the opportunistic technique in which the transmissions are made only when the fading is above a threshold. As result, this technique mitigates almost completely the undesirable effects produced by the fading channel.
Seeking to potentialize the performance of the aforementioned opportunistic technique and aiming to analyze it in different scenarios, in this work different hybrid schemes combining opportunism with other transmission/reception techniques are proposed, modeled and analyzed. In particular, the opportunistic technique is combined with two different diversity schemes. Spatial diversity (or antenna array diversity) with maximal ratio combining (MRC) is firstly considered. Then, by assuming a multiuser scenario, the multiuser diversity technique is also employed with opportunistic transmission.
As wireless communication systems typically employ error correcting codes, in this work opportunistic transmission with error correcting codes are employed. Specifically, convolutional codes and trellis coded modulation (TCM) are chosen in the analysis, once closed-form expres-sions to evaluate the bit error rate (BER) can be obtained.
Later, an opportunistic code division multiple access (CDMA) is proposed. Thus, the per-formance of opportunistic transmission in environments with presence of own-cell interference (or multiple access interference - MAI) and co-cell interference (CCI) are evaluated. Therein, the uplink is analyzed and aspects as the channel reuse factor are considered in the analysis.
Finally, by considering the opportunistic cellular system, the cellular spectral efficiency is evaluated. For this, an procedure to calculate the cell coverage radius for each modulation scheme is employed, by considering that adaptive modulation is used and that a target mean BER must be guaranteed.
In general, BER and the spectral efficiency are performance indicators considered in this work to evaluate the proposed schemes. As result, closed-form expressions are derived and their accuracy are validated by employing Monte Carlos simulations. In the analysis, BPSK, QPSK and M-QAM modulations are considered. Moreover, additive white Gaussian noise (AWGN) and Rayleigh fading are assumed in the channel model.
The results show that the derived expressions are highly accurate to model the performance of the proposed schemes. In addition, it is determined that the hybrid schemes improves the performance in relation to opportunistic systems.
Keywords: Opportunistic transmission; fading channel; bit error rate; spectral efficiency; spa-tial diversity; maximal ratio combining; multiuser diversity; convolutional codes; TCM; CDMA; multiple access interference; co-cell interference.
Resumo
Diferentes t´ecnicas de transmiss˜ao oportunista foram propostas para sistemas de comunica¸c˜oes sem fio. Nesta tese vamos explorar a t´ecnica oportun´ıstica em que as transmiss˜oes s˜ao feitas somente quando o desvanecimento estiver acima de um limiar. Como resultado, esta t´ecnica elimina quase completamente os efeitos indesej´aveis produzidos pelo desvanecimento.
Com o objetivo de se avaliar diferentes cen´arios de opera¸c˜ao, neste trabalho, diferentes es-quemas que combinam oportunismo com outras t´ecnicas de transmiss˜ao/recep¸c˜ao s˜ao propostas, modeladas e analisadas. Em particular, a t´ecnica oportunista pode ser combinada com dois es-quemas de diversidade. Assim, a diversidade espacial (ou diversidade de arranjo de antenas) com combina¸c˜ao de m´axima raz˜ao (MRC) ´e primeiramente considerada. Depois, assumindo um cen´ario multi-usu´ario, a t´ecnica de diversidade multi-usu´ario ´e tamb´em utilizada junto com a transmiss˜ao oportunista.
Como os sistemas de comunica¸c˜oes sem fio empregam tipicamente c´odigos corretores de erros, neste trabalho ´e tamb´em proposto utilizar transmiss˜ao oportunista com estes tipos de c´odigos. Especificamente, c´odigos convolucionais e c´odigos codificados por treli¸ca (TCM) foram escolhidos para esta an´alise, pois estes tipos de c´odigos permitem obter express˜oes fechadas para se avaliar a probabilidade de erro de bit (BER).
A seguir, um sistema celular oportunista de m´ultiplo acesso por divis˜ao de c´odigo (CDMA) ´e proposto. Assim, se pretende avaliar o desempenho da transmiss˜ao oportunista em cen´arios com a presen¸ca de interferˆencia da pr´opria c´elula (ou interferˆencia de m´ultiplo acesso - MAI) e de interferˆencia das co-c´elulas (CCI). Assim, o enlace reverso ´e analisado e aspectos como o fator de reuso de canais s˜ao tamb´em considerados na an´alise.
Finalmente, a eficiˆencia espectral celular ´e avaliada. Para isto, ´e empregado um procedimento para calcular os raios de cobertura para cada esquema de modula¸c˜ao utilizado no sistema celular considerando que uma BER m´edia objetivo deve ser garantida.
Em geral, a BER e a eficiˆencia espectral s˜ao os indicadores de desempenho considerados ao longo deste trabalho, a fim de se avaliar os esquemas propostos. Como resultado, express˜oes fechadas s˜ao derivadas e sua precis˜ao ´e avaliada empregando simula¸c˜oes de Monte Carlo. Nestas an´alises modula¸c˜oes BPSK, QPSK e M-QAM s˜ao consideradas. Ademais, ru´ıdo aditivo Gaus-siano branco (AWGN), perda de percurso e desvanecimento Rayleigh s˜ao assumidos no modelo do canal.
Os resultados mostram que as express˜oes derivadas s˜ao altamente precisas para modelar o de-sempenho dos esquemas propostos. Adicionalmente, foi determinado que os esquemas propostos permitem melhorar o desempenho do sistema oportunista proposto inicialmente.
Palavras-chave: Transmiss˜ao oportunista; canais com desvanecimento; probabilidade de erro de bit; eficiˆencia espectral; diversidade espacial; combina¸c˜ao de m´axima raz˜ao; diversidade multiu-usu´ario; c´odigos convolucionais; c´odigos TCM; CDMA; interferˆencia de acesso m´ultiplo; interferˆencia das co-c´elulas.
List of Figures
2.1 Constellations for different digital modulation schemes. . . 29
a 2-PAM or BPSK modulation . . . 29
b 4-PAM or 4-ASK modulation. . . 29
c 4-QAM or QPSK modulation . . . 29
d 16-QAM modulation . . . 29
e 64-QAM modulation . . . 29
2.2 Gray encoding to 16-QAM modulation. . . 33
2.3 MRC block diagram. . . 44
2.4 Uniform linear antenna array. . . 45
2.5 Mean BER as a function of Eb/N0, employing BPSK, QPSK and M -QAM modulations in an AWGN channel. . . 48
2.6 Mean BER as a function of γb, employing BPSK, QPSK and M -QAM modulations in Rayleigh fading channel. . . 50
2.7 Comparison Between Ordinary and Opportunistic Transmission. Probabi-lity of no Transmission p = 1/2. . . 54
2.8 Convolutional encoder (2,1,2) . . . 58
2.9 Convolutional encoder states diagram (2,1,2). . . 59
2.10 Trellis encoder convolutional (2,1,2). . . 60
2.11 Basic structure of TCM. . . 63
2.12 Modulation Encoded Receiver. . . 64
2.13 Sets partition of the code (2,1,2) and polynomial [5 2] with QPSK modu-lation. . . 65
2.14 Trellis of the code (2,1,2) and polynomial [5 2]. . . 65
2.15 The shortest error event in Trellis of the code (2,1,2). . . 66
3.1 Transmitter . . . 70
3.2 Opportunistic system receiver with antenna array . . . 70
3.3 Mean BER as a function of γc for an opportunistic system employing two antennas and MRC for strategy 1. . . 78
3.4 Mean BER as a function of γc for an opportunistic system employing two antennas and MRC for strategy 2. . . 79
3.5 Mean BER as a function of γc for an opportunistic system employing N antennas and MRC for strategy 1. . . 79
3.6 Mean BER as a function of γc for an opportunistic system employing N
antennas and MRC for strategy 2. . . 80
3.7 Mean BER as a function of Eb/N0 parameterized by different transmission schemes for Nu = 2, q = 1/2 and BPSK modulation. . . 86
3.8 Mean BER as a function of Eb/N0 parameterized by different transmission schemes for Nu = 2, q = 1/2 and 64-QAM modulation. . . 87
3.9 Mean BER as a function of Eb/N0 for the hybrid transmission parameter-ized by Nu employing q = 1/2 and BPSK modulation. . . 88
3.10 Mean BER as a function of Eb/N0 for the hybrid transmission parameter-ized by Nu employing q = 1/2 and 64-QAM modulation. . . 89
3.11 Mean BER as a function of Eb/N0 for the hybrid transmission parameter-ized by Nu employing q = 1/3 and BPSK modulation. . . 89
3.12 Mean BER as a function of Eb/N0 for the hybrid transmission parameter-ized by Nu employing q = 1/3 and 64-QAM modulation. . . 90
4.1 Transmitter and receiver of system. . . 93
a Transmitter. . . 93
b Receiver. . . 93
4.2 Basic structure of TCM. . . 96
4.3 Trellis of TCM code for QPSK modulation. . . 97
4.4 Mean BER as a function of Eb/N0 for different scenarios with BPSK mod-ulation. The encoded scenarios employ code generator [5 7], with encoder rate rc = 1/2, mt= 2, df ree,H = 5 and opportunism with q = 1/2. . . 100
4.5 Mean BER as a function of Eb/N0 for TCM codes with opportunism em-ploying code generator [5 2], encoder rate rc = 1/2, mt = 2, d2f ree,E = 10 and opportunism with q = 1/2 for QPSK modulation. . . 101
4.6 Mean BER as a function of Eb/N0 for TCM codes with opportunism em-ploying code generator [33 14 5 10], encoder rate rc = 1/4, mt = 4, d2 f ree,E = 11.6 and opportunism with q = 1/4 for 16-QAM modulation. . . . 102
4.7 Mean BER as a function of Eb/N0 for different scenarios with spectral efficiency ξ = 1 bits/s/Hz. . . 103
4.8 Mean BER as a function of Eb/N0 in AWGN and fading channels with similar coding gain. . . 104
5.1 Spatial distribution of users. . . 107
5.2 System model . . . 108
5.3 Comparison between CDMA ordinary and CDMA opportunistic transmis-sion by considering that the probability of transmistransmis-sion is q = 1/2. . . 109
5.4 Mean BER as a function of Eb/N0 parameterized by different transmis-sion probabilities in a single user scenario for CDMA ordinary (ORD) and CDMA opportunistic (OPP) systems employing BPSK and QPSK modu-lations, respectively. . . 116
5.5 Mean BER as a function of load factor L, for CDMA ordinary (ORD) and opportunistic (OPP) systems, in presence of own-cell and co-cell interfe-rence, parameterized by the channels reuse factor for a system employing
q = 1/2 with G = 30 and Eb/N0=8 dB. . . 118
5.6 Mean BER as a function of load factor L, for CDMA ordinary (ORD) and opportunistic (OPP) systems, in presence of own-cell and co-cell interfe-rence, parameterized by the channels reuse factor for a system employing q = 1/3 with G = 30, Eb/N0=8 dB. . . 118
5.7 Mean BER as a function of load factor L, for CDMA ordinary (ORD) and opportunistic (OPP) systems, in presence of own-cell and co-cell interfe-rence, parameterized by the channels reuse factor for a system employing q = 1/4 with G = 30, Eb/N0=8 dB. . . 119
5.8 Mean BER as a function of load factor L, for CDMA ordinary (ORD) and opportunistic (OPP) systems, in presence of own-cell and co-cell interfe-rence, parameterized by the channels reuse factor for a system employing q = 1/5 with G = 30, Eb/N0=8 dB. . . 119
5.9 Mean BER as a function of L parameterized by the channel reuse factor for CDMA ordinary (ORD) system using QPSK and opportunistic (OPP) system using q = 1/2 and 16-QAM by considering Eb/N0=8 dB. . . 120
5.10 Mean BER as a function of L parameterized by the channel reuse factor for CDMA ordinary (ORD) system using QPSK and opportunistic (OPP) system using q = 1/4 and 256-QAM by considering Eb/N0=8 dB. . . 121
5.11 Mean BER for as a function of Eb/N0 parameterized by the channel reuse factor for CDMA ordinary (ORD) system using BPSK and opportunistic (OPP) system using q = 1/2 and QPSK by considering Nu = 2 (L = 1/30). 121 5.12 Mean BER for as a function of Eb/N0 parameterized by the channel reuse factor for CDMA ordinary (ORD) system using BPSK and opportunistic (OPP) system using q = 1/2 and QPSK by considering Nu = 4 (L = 1/10). 122 5.13 Mean BER for as a function of Eb/N0 parameterized by the channel reuse factor for CDMA ordinary (ORD) system using BPSK and opportunistic (OPP) system using q = 1/4 and QPSK by considering Nu = 2 (L = 1/30). 123 5.14 Mean BER for as a function of Eb/N0 parameterized by the channel reuse factor for CDMA ordinary (ORD) system using BPSK and opportunistic (OPP) system using q = 1/4 and QPSK by considering Nu = 4 (L = 1/10). 123 6.1 Cellular system model. . . 125
6.2 Internal and external cell radius. . . 127
6.3 Cell coverage radius. . . 128
6.4 Coverage radius as a function of L parameterized by F, by the transmission probability (q) and by the modulation order for G = 10 and Pb,tar = 10−3. . 131
a CDMA ordinary system . . . 131
b CDMA opportunistic, q = 1/2. . . 131
c CDMA opportunistic, q = 1/3. . . 131
6.5 Mean cellular spectral efficiency as a function of L, parameterized by F
and by the transmission probability (q) for G = 10 and Pb,tar = 10−3. . . . 132
a CDMA ordinary system . . . 132
b CDMA opportunistic, q = 1/2. . . 132
c CDMA opportunistic, q = 1/3. . . 132
d CDMA opportunistic, q = 1/4. . . 132
6.6 Coverage radius as a function of L parameterized by F, by Pb,tar and by the modulation order for G = 10 and transmission probability q = 1/3. . . 133
a Pb,tar = 10−2 . . . 133
b Pb,tar = 10−3 . . . 133
c Pb,tar = 10−4 . . . 133
6.7 Mean cellular spectral efficiency as a function of L, parameterized by F for G = 10 and transmission probability q = 1/3. . . 134
a Pb,tar = 10−2 . . . 134
b Pb,tar = 10−3 . . . 134
c Pb,tar = 10−4 . . . 134
6.8 Coverage radius as a function of Nu parameterized by F, by G and by the modulation order for transmission probability q = 1/3 and for Pb,tar = 10−3. 135 a G = 1 . . . 135
b G = 5 . . . 135
c G = 20 . . . 135
6.9 Mean cellular spectral efficiency as a function of Nu , parameterized by F and by G for transmission probability q = 1/3 and for Pb,tar = 10−3. . . 136
a G = 1 . . . 136
b G = 5 . . . 136
List of Tables
2.1 Parameters y, z1, z2 and z3 for the SUI path-loss model. . . 38
2.2 Mean Spectral Efficiency of some Digital Modulation Schemes. . . 46 2.3 Thresholds Values for Different Transmission Probabilities. . . 54 3.1 Opportunistic Transmission Probabilities for Two Antennas, Strategy 1. . . 72 3.2 Opportunistic Transmission Probabilities for Two Antennas, Strategy 2 . . 73 3.3 Strategies and Probability of Occurrence for the Hybrid Transmission . . . 81 3.4 Mean Spectral Efficiency of the Hybrid System for Different Number of
Users and Different Transmission Probabilities. . . 82 4.1 Convolutional Codes Employed for Numerical Results . . . 99 6.1 System Parameters. . . 130
List of Abbreviations
Abbreviation Connotation
AWGN additive white Gaussian noise
ASK amplitude shift keying
BER bit error rate
BS base station
BWEF bit weight enumerating function
CCI co-cell interference
CDMA code division multiple access
DS direct sequence
ECC error correcting codes
FH frequency hopping
i.i.d. independent and identically distributed
IoT internet of things
MAI multiple access interference
MD multiuser diversity
MIMO multiple input multiple output
MRC maximal ratio combining
MSED minimum squared Euclidean distance
NLOS non-line-of-sight
OFDMA orthogonal frequency division multiplexing
OPP opportunistic
PAM pulse amplitude modulation
PDF probability density function
PN pseudo-noise
PSK phase shift keying
QAM quadrature amplitude modulation
QPSK quadrature phase shift keying
RAN radio access network
SER symbol error rate
SIM simulation
SNR signal to noise ratio
SUI Standford University Interim
TCM trellis coded modulation
TTI time transmission interval
UE user equipment
List of Symbols
Symbol Connotation
A amplitude of the signal
sk k-th transmitted symbol
Ts symbol duration
Tb bit duration
g(t) pulse shape that satisfies the Nyquist criterion
M modulation order
θ phase
sp in-phase components of signal
sq in-quadrature components of signal
fc carrier frequency
Eb energy per bit
Es energy per symbol
ξ mean spectral efficiency
Rb bit rate
Rs symbol rate
Rc chip rate
B system bandwidth
BD Doppler spread
Ps symbol error rate
Pb bit error rate
d distance between two symbol
N0 noise power spectral density
σ2 variance of real Gaussian random variables generating the channel gain
P(s|α) conditional symbol error rate f (α) PDF of the random variable α F (α) CDF of the random variable α
f (αc) conditional PDF of the random variable α
F (αc) conditional CDF of the random variable α
γb signal to noise ratio
γc signal to noise ratio per channel
F channel reuse factor
R cell radius
D distance between the center of two co-cells Pr received power at the BS from a UE in its cell
Pt power transmitted by a UE
β path-loss exponent
LIST OF SYMBOLS (cont.)
Symbol Connotation
K propagation factor
Pb,tar target BER
Pt,max maximum transmission power
Nu total number of users in the cell
NI total number of users in the co-cell
ℏu UE antenna height
ℏa BS antenna height
t time variations due to the UE movement
τ denotes multipath delays for a fixed value of t
P total number of multipaths
T delay spread
Bc channel coherence bandwidth
Tc channel coherence time
G spreading factor
λw wavelength
α fading amplitude
αc conditional fading amplitude
HG Haddamard matrix
m transmition threshold
q transmition probability
p non-transmition probability
kc number of message bits
nc number of encoded bits
mt total number of memories employed by the encoder
rc encoder rate
df ree,H Hamming free distance
d2
f ree,E minimum squared Euclidean distance
d2
min minimum square distance
Bd total number of non-zero information bits
C set of all encoded sequences σ2
n variance of the noise components per channel
N number of antennas
G coding gain
R0 inner cell radius
L load factor
h height of the antennas in the tower Te electric tilt
Tm mechanical tilt
(Φv) vertical half power beamwidth
(Φh) horizontal half power beamwidth
x, E[·] expectation, mean
List of Publications
N. Orozco, H. Carvajal and C. de Almeida. “On the Performance of a CDMA
Opportunistic System in Rayleigh Fading Channel with Inter-Cell and Co-Cell In-terference”. International Telecommunications Symposium (ITS), 2014, Sao Paulo, Brazil, Aug. 2014.
N. Orozco, H. Carvajal and C. de Almeida. “Performance Analysis of Opportunistic
Systems Employing Maximal Ratio Combining and Antenna Array”. IEEE 84th
Vehicular Technology Conference (VTC-Fall), 2016, Montreal, Canada, Sept. 2016.
N. Orozco, H. Carvajal and C. de Almeida. “A Hybrid Transmission Scheme
Em-ploying Opportunistic Transmission and Multiuser Diversity”. Wireless and Mobile
Computing, Networking and Communications (WiMob), 2017, Rome, Italy, Oct.
2017.
N. Orozco, H. Carvajal and C. de Almeida. “Performance Analysis of an
Oppor-tunistic System to Counteract the Fading and Interference Effects”. Submitted to
IEEE Latin America Transactions.
N. Orozco, H. Carvajal and C. de Almeida. “Performance Evaluation of Error
Correcting Codes Employing Opportunistic Transmission in Fading Channels”. To be submitted for peer review in a scientific journal.
Contents
1 Introduction 22
1.1 Related Work and Motivation . . . 23
1.2 Contributions and Outline of the Dissertation . . . 25
2 Basic Concepts 27 2.1 Introduction . . . 27
2.2 Digital Modulation Schemes . . . 28
2.2.1 PAM Modulation . . . 28 2.2.2 ASK Modulation . . . 30 2.2.3 BPSK Modulation . . . 31 2.2.4 QPSK Modulation . . . 31 2.2.5 M -QAM Modulation . . . 31 2.2.6 Gray Encoding . . . 33 2.2.7 Adaptive Modulation . . . 33 2.3 Cellular Systems . . . 34 2.3.1 Channel Reuse . . . 34 2.3.2 Interference . . . 35
2.3.3 Perfect Power Control . . . 36
2.3.4 Cellular Spectral Efficiency . . . 36
2.4 Mobile Radio Channel . . . 37
2.4.1 Large-Scale Radio Propagation Loss . . . 37
2.4.1.1 Path Loss . . . 37
2.4.1.2 SUI Model . . . 38
2.4.1.3 Shadowing . . . 38
2.4.2 Small-Scale Fading and Multipath . . . 39
2.4.2.1 Multipath Channel Characterization . . . 39
2.4.2.2 Multipath Channel Parameters . . . 40
2.4.2.3 Types of Small-Scale Fading . . . 40
2.5 Diversity . . . 41
2.5.1 Spatial Diversity . . . 41
2.5.2 Multiuser Diversity . . . 42
2.6 Combination Techniques . . . 43
2.6.1 Maximal Ratio Combining - MRC . . . 43
2.7 Antenna Array . . . 44
2.7.1 Uniform Linear Antenna Array . . . 44
2.8 Performance Indicators . . . 45
2.8.1 Mean Spectral Efficiency . . . 46
2.8.2 Mean Bit Error Rate . . . 46
2.8.2.1 Mean BER in AWGN Channels . . . 47
2.8.2.2 Mean BER in Fading Channels . . . 48
2.9 CDMA System . . . 49
2.9.1 Spreading Factor . . . 50
2.9.2 Spread Spectrum Techniques . . . 51
2.9.3 Cross-Correlation Function . . . 51 2.9.4 Spreading Sequences . . . 51 2.9.4.1 Pseudo-noise sequences (PN) . . . 51 2.9.4.2 Gold sequences . . . 52 2.9.4.3 Kasami sequences . . . 52 2.9.4.4 Walsh sequences . . . 52 2.9.4.5 Random sequences . . . 53 2.10 Opportunistic Transmission . . . 53
2.10.1 Mean Spectral Efficiency . . . 55
2.10.2 Mean Bit Error Rate . . . 55
2.10.2.1 BPSK . . . 55
2.10.2.2 M -QAM . . . 56
2.11 Error-Correcting Codes . . . 56
2.11.1 Convolutional Codes . . . 57
2.11.1.1 Structural Properties . . . 60
2.11.1.2 Decoding Convolutional Codes . . . 61
2.11.1.3 Mean Spectral Efficiency . . . 62
2.11.1.4 Mean Bit Error Rate . . . 62
2.11.2 TCM Codes . . . 63
2.11.2.1 Modulation Encoded Receiver . . . 64
2.11.2.2 Sets Partitioning . . . 64
2.11.2.3 Mean Spectral Efficiency . . . 66
2.11.2.4 Mean Bit Error Rate . . . 66
3 Opportunistic Transmission Employing Diversity Techniques 68 3.1 Introduction . . . 68
3.2 Opportunistic Transmission Employing Antenna Array at the Receiver . . 69
3.2.1 System Description . . . 69
3.2.2 Transmission Strategies . . . 71
3.2.2.1 Strategy 1 . . . 72
3.2.2.2 Strategy 2 . . . 73
3.2.3.1 Strategy 1 . . . 74
3.2.3.2 Strategy 2 . . . 76
3.2.4 Numerical Results . . . 77
3.3 Opportunistic Transmission Employing Multiuser Diversity . . . 80
3.3.1 System Description . . . 80
3.3.2 Mean Spectral Efficiency . . . 81
3.3.3 Mean Bit Error Rate . . . 82
3.3.3.1 Two Users Scenario . . . 83
3.3.3.2 Nu Users Scenario . . . 84
3.4 Numerical Results . . . 85
4 Error Correcting Codes Employing Opportunistic Transmission 91 4.1 Introduction . . . 91
4.2 System Description . . . 92
4.3 Performance Analysis . . . 95
4.3.1 Convolutional Codes with Opportunism - Mean BER and Coding Gain . . . 95
4.3.2 TCM Codes with Opportunism - Mean BER and Coding Gain . . . 96
4.4 Mean Spectral Efficiency . . . 98
4.4.1 Convolutional Codes with Opportunism . . . 98
4.4.2 TCM Codes with Opportunism . . . 99
4.5 Numerical Results . . . 99
5 CDMA Cellular System Employing Opportunistic Transmission 105 5.1 Introduction . . . 105
5.2 System Description . . . 106
5.2.1 Cellular System . . . 106
5.2.2 Spatial Distribution of Users within the Cells . . . 106
5.2.3 Transmitter and Receiver Description . . . 107
5.3 Received Signals Analysis . . . 109
5.4 Mean Bit Error Rate . . . 113
5.4.1 Single User Scenario . . . 113
5.4.2 Cellular Scenario . . . 113
5.5 Numerical Results . . . 115
6 Mean Cellular Spectral Efficiency of CDMA Opportunistic Systems 124 6.1 Introduction . . . 124
6.2 System Description . . . 125
6.2.1 Propagation Model and Interference . . . 125
6.3 Cell Radius Calculation . . . 126
6.3.1 Internal and External Cell Radius . . . 126
6.3.2 Cell Coverage Radius . . . 126
6.4 Mean Cellular Spectral Efficiency . . . 129
7 Conclusions and Future Works 137 7.1 Conclusions . . . 137 7.2 Future Works . . . 140
22
Chapter
1
Introduction
Wireless communications have had significant evolution during the last years due to the high quality offered services. Thus, this type of communications allow operators to offer different services that can range from a simple call, to data services or even newer applications, such as those related to internet of things (IoT) [1]. As a consequence, new challenges have appeared for researchers and network designers to pursue innovative strategies, that enable high data rates and reliable communications with improved quality and coverage.
Wireless systems are deployed in different environments, where multiple kinds of im-pairments can appear: interference, additive white Gaussian noise (AWGN), path-loss and multipath fading. Hence, different transmission-reception mechanisms are employed to counteract and to mitigate the undesirable effects of these impairments. In particular, there are several techniques that take advantage of the random nature of the fading, so that reliability and performance of wireless systems can be improved. Among these tech-niques are the so-called diversity techtech-niques, which exploit that different signal replicas (branches) are affected by independent fadings and therefore, the probability that all these replicas are highly affected or degraded at the same time is low [2]. These techniques can be employed in both transmission and reception stages. Therein, an important concept is the so-called diversity order, which is defined by the number of decorrelated spatial branches available between a transmitter and a receiver. Thus, as the diversity order increases, the system performance is improved. When the number of branches tends to infinity, the system behaves as if fading effects had disappeared [3]. Nevertheless, a high number of branches requires large bandwidth and high implementation costs.
In [4,5], we have proposed a transmission scheme that takes advantage of the random nature of the fading channel, but under a concept different from that used by diversity techniques. Specifically, the idea behind this scheme is that transmission occurs only when the fading amplitude is greater than a certain threshold. As a consequence, we have called this as opportunistic transmission. This type of transmission has the main
1.1. Related Work and Motivation 23 characteristic that the system performance behaves as if the fading had been almost completely eliminated. For this scheme to work, it is required that the fading amplitude is available at the transmitter. As the fading amplitude is estimated in the receiver, this communication is made through feedback links, which is widely used in the literature, in multiple-input-multiple-output (MIMO) systems employing precoding [6–8]. Thus, the cost and implementation complexity of the opportunistic transmission are low. The unique drawback of this scheme is related to time intervals in which the transmission is not made which affects the spectral efficiency. Nevertheless, along this work, it is showed that this loss can be compensated employing high order modulations and, despite this, opportunistic transmission outperforms systems employing diversity techniques.
The remainder of this chapter is organized as follows. In Section 1.1, some related works are summarized. Additionally, in this section the motivations of this dissertation are introduced. Finally, in Section1.2, the outline of this dissertation is presented.
1.1
Related Work and Motivation
In the literature, different approaches employ mechanisms of opportunistic transmis-sion. In [9], some opportunistic transmission strategies are proposed for multiuser systems. The main idea behind this approach is that bursty transmissions reduce the interference levels, because no transmission periods for one user represent no interference for another user. However, the fading aspects are not considered for the scheme proposed in the aforementioned reference. This idea is being recently considered in cognitive ratio net-works (CRN) [10], where the presence of primary and secondary users require transmission schemes allowing communication for the two types of users [11]. Thus, secondary users are opportunist as they transmit only when the primary user does not.
Another approach that is slightly related to our opportunistic scheme is the so-called multiuser diversity (MD) [12]. This technique arises from scenarios with multiple users, which are affected by independent fadings. Thus, the user with the best fading amplitude is the one that transmits. Hence, when the number of mobile users in the network is high, the probability of finding a user with a high fading amplitude increases. As a result, the system diversity order is given by the number of users competing by the channel. On the other hand, if the system has only one channel available, then delays appear for users who are not transmitting. This technique has been analyzed in several scenarios [13–15].
From the aforementioned, opportunistic systems in multiuser scenarios have not yet been fully analyzed. In addition, taking advantage of the similar characteristics that MD has with the proposed opportunistic system, a hybrid system combining these two techniques is an interesting proposal to improve system performance.
There are some techniques used to combine the signal replicas. The optimum com-bination technique is called maximal ratio combining [16], which maximizes the received
1.1. Related Work and Motivation 24 signal-to-noise ratio (SNR). These techniques are widely studied in wireless communi-cations mainly in systems employing antenna arrays in the reception [17–20]. Hence, motivated by the optimum performance of MRC and considering the proposal stated in the previous paragraph, a hybrid system combining opportunistic transmission and MRC is a communications scheme that deserves attention.
It is well known that wireless systems require error correcting codes in order to ensure an acceptable performance [2, 21,22]. Several error correcting codes have been proposed in the literature, among them are the well-known convolutional codes and trellis coded modulation (TCM) [23, 24]. These codes have been widely studied in the literature and they still continue to be subject of analysis [25–27]. In some cases, trellis codes provide closed form expressions for the bit error rate (BER) in fading channels [28–30]. Therefore, the performance of opportunistic transmission with the aforementioned error correcting codes deserves to be studied.
One of the biggest problems in multiuser scenarios is the presence of interference. Techniques as orthogonal frequency division multiple access (OFDMA) are only affected by interference arriving from co-cells, which can be mitigated by employing channel reuse [31]. On the other hand, techniques as code-division-multiple access (CDMA) are affected by own-cell interference (or multiple access interference - MAI) and co-cell interference (CCI). When orthogonality between the sequences is lost, MAI is the main interference that affects the system [32]. In these cases, multiuser detectors are typically employed [33–36]. However, their complexity increases with the number of users. Therefore, the bursty transmission of the opportunistic scheme can be an interesting approach to diminish not only the MAI but also the CCI, at the same time that low detection complexity is guaranteed. For this reason, an opportunistic CDMA system is an interesting proposal.
Different works have studied the spectral efficiency of some opportunistic schemes [37–39]. These studies have been carried out by considering only single cell scenarios. However, in practice, wireless systems operate in cellular scenarios where MAI and CCI affect the system performance. Therefore, a multicell scenario should be considered in this type of studies. A different approach to calculate this cellular spectral efficiency is employed in [40,41], where a target BER (maximum BER) is required by a communication service. Thus, this approach is interesting to evaluate the cellular spectral efficiency of the opportunistic system in cellular environments and with this analysis, parameters that maximize the cellular spectral efficiency are obtained.
Due to the current demand for high transmission rates required by wireless commu-nications and to ensure the quality of services and their applications, it is important to conduct survey improvements for communications systems. For this reason and the as-pects mentioned in previous paragraphs, novel hybrid schemes that combine opportunism with known transmission/reception techniques in different scenarios are proposed.
1.2. Contributions and Outline of the Dissertation 25
1.2
Contributions and Outline of the Dissertation
This work contains four main contributions, which are addressed in separate chap-ters. These contributions are based on the motivations described in the previous section. In general, this dissertation presents the performance analysis of hybrid schemes that combine opportunistic transmission with other techniques in different operation scenar-ios. The performance indicators considered for the analysis are the mean BER and the mean spectral efficiency. Furthermore, additive white Gaussian noise (AWGN), path-loss, Rayleigh fading and interference (MAI and CCI) are considered in the channel model. Moreover, BPSK, QPSK and M -QAM modulations are considered in the mathematical modeling. As a result, exact and approximated closed-form expressions to evaluate the BER of the hybrid transmission schemes are obtained. The accuracy of the obtained expressions is validated employing Monte Carlo simulations.
Chapter 3. This chapter contains the contributions published in [42, 43]. In this
chapter, two hybrid schemes combining opportunistic transmission with diversity techniques are proposed and analyzed. In particular, opportunistic transmission employing antenna array at the receiver and opportunistic transmission combined with multiuser diversity are described. Exact and approximated closed-form expres-sions to evaluate the mean BER of these hybrid transmission schemes are derived. Moreover, the mean spectral efficiency of these schemes is also analyzed. Finally, some numerical results are presented to verify the tightness of the derived equations.
Chapter 4. This chapter contains the contributions reported in [44]. In this
chap-ter, upper-bound closed-form expressions to evaluate the mean BER of a hybrid scheme combining error correcting codes with opportunistic transmission are de-rived. Furthermore, the mean spectral efficiency of this scheme is also analyzed. A comparison between hybrid schemes and ordinary transmissions are also performed. Finally, some simulations and discussions are carried out in order to verify the ac-curacy of the analytical expressions.
Chapter5. This chapter contains the contributions based on the results reported in
[45] and published in [46]. Hence, exact closed-form expressions to evaluate the mean BER of CDMA cellular systems employing opportunistic transmission are derived. In the analysis, a cellular system with presence of MAI and CCI is considered. A comparison between opportunistic CDMA and ordinary CDMA is also performed. Finally, some numerical results are provided to verify the accuracy of the analytical expressions and to provide insight into the system performance.
Chapter 6. This chapter presents the analysis of the mean cellular spectral
1.2. Contributions and Outline of the Dissertation 26 evaluate the mean cellular spectral efficiency are derived. These expressions are a function of the load factor, the channel reuse factor, the transmission probability employed in the opportunism and the target mean BER. The analysis are performed based on an approach that calculates the cell coverage radius by considering differ-ent modulations employed in the cellular system. Moreover, the analysis depends on several system operating parameters. Operation parameters that maximize the cellular spectral efficiency are obtained.
Chapter 7. This chapter summarizes our main conclusions and points out some
27
Chapter
2
Basic Concepts
2.1
Introduction
In this chapter, the basic concepts of wireless digital communication systems are pre-sented. This will help to understand the terms considered in the development of this dissertation. In our daily life it is normal to deal with all kinds of digital information as is the case of cell phones. Therefore, it is important to know how to treat this infor-mation and know its meaning. In terms of transmission, it is necessary to find methods for transmitting this information and later recovery, what must be efficiently used so that the capacity and coverage of a communication network can be maximized. For this reason in this dissertation terms like combination techniques, error-correcting codes and opportunistic transmissions are described.
The channel is the physical medium through which the information travels from one point to another. The characteristics of a channel are of fundamental importance for an effective communication, because of them depends the quality of the signals received in the destination. For this reason in this dissertation the different channel types are analyzed.
The main objective of cellular systems is to offer quality in the communication services into a determined area for the largest number of users. Thus, channel reuse and multiple access techniques are fundamental to achieve this objective. Additionally, new communi-cation services require higher data rates. Consequently, modulation schemes are another important aspect that should be considered in the analysis of a cellular system. In addi-tion, performance indicators of communication systems are analyzed, such as the spectral efficiency of a digital transmission system, due to the importance of the radio-electric spectrum at the present time as a limited resource.
For a better understanding this chapter is organized as follows: in Section 2.2 digital modulation schemes are analyzed. In Section2.3parameters associated to cellular system are detailed. In Section 2.4 the mobile radio channel is presented. Furthermore, we describe diversity in Section2.5. In Section 2.6 the combination technique maximal ratio
2.2. Digital Modulation Schemes 28 combining is described and antenna array is stated in Section2.7. Performance indicators as spectral efficiency and mean BER are described in Section 2.8. In Section 2.9 the CDMA System is detailed and the opportunistic transmission is described in the Section 2.10. Finally, error-correcting codes are analyzed in Section 2.11.
2.2
Digital Modulation Schemes
In digital communications, the modulator is one of the main elements of a transmitter. Thus, when the signal that carries the information is chosen, the limitations of the channel must be considered. Moreover, digital modulation is the process by which digital symbols are transformed into waveforms compatible with the characteristics of the channel. In the receiver the inverse process occurs known as demodulation, in which the information of the modulated signal is extracted.
In the case of base-band modulation, the waveforms generally take the form of the pulse format, but in the case of band-pass modulation the pulse format is modulated by a sinusoid known as a carrier. The choice of a modulation scheme depends on the characteristics of the medium.
The sequence of bits to be transmitted are in base-band. Therefore, to transfer the spectrum a carrier is necessary, through a process known as modulation. There are several methods of spectrum transfer. A digital signal can be modulated by a sinusoidal carrier, mainly changing one of the following parameters: amplitude, phase or frequency. However, to understand the analysis made in the next chapters, we will describe only the modulation schemes that will be used: PAM, ASK, BPSK and M-QAM.
Digital modulation also consists of mapping one or more bits of information into a symbol, which corresponds to a waveform. The waveforms can be represented graphically by a constellation diagram, as shown in Fig. 2.1. The distance between any two symbols of the constellation is called the Euclidean distance, and the distance between the two closest symbols is called the Euclidean minimum distance named d [47].
2.2.1
PAM Modulation
Pulse Amplitude Modulation (PAM) is a base-band modulation technique widely used in digital communications. Its simplicity facilitates the development of the main design bases of the receiver. The base-band PAM consists of modifying the amplitudes of a pulse train according to the transmitted information. PAM is widely used in metallic conduc-tors, such as cables, where the signal spectrum can extend to zero frequency. Therefore, the transmitted PAM signal can be written as
2.2. Digital Modulation Schemes 29
Im
Re d
-A A
(a) 2-PAM or BPSK modulation
Im
Re d
-A
-3A A 3A
(b) 4-PAM or 4-ASK modulation.
Im Re d -A A A -A (c) 4-QAM or QPSK modulation Im Re d -A A A -A -3A 3A -3A 3A (d) 16-QAM modulation Im Re Im d A -3A -A -5A -7A 3A 5A 7A -A A d
(e) 64-QAM modulation
2.2. Digital Modulation Schemes 30 s(t) = ∞ X k=−∞ xkg(t − kTs), (2.1)
where xk = Ask, with A the amplitude of the transmitted signal and sk the k-th
trans-mitted symbol that belongs to a constellation formed by M symbols. Ts is the symbol
duration. t is the time and g(t) is the pulse shape that satisfies the Nyquist criterion. If we include in the PAM signal two sinusoidal carriers with the same frequency (90 degrees of phase difference), the band-pass signal can be q in its general form as
sc(t) = sp(t) cos(2πfct + θ) − sq(t) sin(2πfct + θ), (2.2)
where θ is the initial phase of the carrier. The signs sp(t) and sq(t) are in-phase and
quadra-ture components of PAM signal. The in-phase signal modulates a cosine carrier, whereas the quadrature signal modulates a sine carrier having the property of being orthogonal to each other. In this way, it is possible to transmit two PAM signals simultaneously, without interference, thereby increasing spectral efficiency, in relation to a system that uses only in-phase component, as is the case of binary modulations. The in-phase M -ary modulations, as well as the M -ary modulations that combine amplitude and phase, use in-phase and quadrature components. The Fig. 2.1a and 2.1b present the 2-PAM and 4-PAM modulations, respectively. The Amplitude-Shift Keying (ASK), Phase-Shift Keying (PSK), and Quadrature Amplitude Modulation (QAM) are special cases of a scheme of PAM modulation with carrier and will be analyzed below [48].
2.2.2
ASK Modulation
ASK is a modulation in which the amplitude of a cosine carrier, with constant fre-quency and phase, is varied. The transmitted signal is given by
sc(t) = ∞
X
k=−∞
xkg(t − kTs) cos[2πfc(t − kTs) + θ]. (2.3)
Thus, the in-phase and quadrature components are given by
sp(t) = ∞ X k=−∞ xkg(t − kTs) sq(t) = 0, (2.4)
where xk = 0, A, ..., (M − 1)A. This modulation is known as M-ASK unipolar. If xk =
±A, ±3A, ..., ±(M − 1)A, then it would be M-ASK polar. These types of amplitude modulation have the same power spectral density, but the polar modulation presents
2.2. Digital Modulation Schemes 31 better performance. Fig. 2.1b shows the constellation diagram of a 4-ASK modulation.
2.2.3
BPSK Modulation
The 2-PSK modulation scheme, also known as binary PSK or BPSK is the simplest of the PSK modulation schemes. The BPSK modulation varies the phase of a carrier according to the bit to be transmitted, that is, its amplitude and frequency does not change. Thus, it uses two stages each assigned to a unique combination of binary digits. Thus, two forms of bipolar waves with amplitude A are used, where the carrier phase at 0 degrees occurs when a bit 1 is transmitted and the 180 degree occurs when a 0 bit is transmitted. Fig. 2.1a shows the constellation of the BPSK modulation. Therefore, a modulated signal can be written as [49]
sc(t) = ∞
X
k=−∞
Ag(t − kTs) cos[2πfc(t − kTs) + πbk], (2.5)
where g(t) is the pulse format, A is the amplitude, bk = 1 or bk = 0. For the BPSK
scheme, the bit duration is equal to the symbol duration, that is, Tb = Ts.
2.2.4
QPSK Modulation
Quadrature Phase-Shift Keying (QPSK) is a modulation technique derived from PSK, but in this case, phase and quadrature parameters of the carrier are used to modulate the information signal. Since two parameters are now used, there are more possible types of symbols in this constellation, which allows more bits to be transmitted per symbol. For example, if we want to transmit 2 bits per symbol, instead of 1 bit per symbol as in the BPSK case above, since we will have 4 possible types of symbols, the carrier can assume 4 different phase values, each corresponding to one bit [50]. Fig. 2.1c shows the constellation diagram of the QPSK modulation.
2.2.5
M -QAM Modulation
QAM is a modulation whose symbols simultaneously carry information using the am-plitude and phase of two orthogonal carriers. In this way, QAM modulation requires less energy per symbol than amplitude or phase modulations. An M -QAM signal can be written as sc(t) = ∞ X k=−∞ xp,kg(t−kTs) cos[2πfc(t−kTs)+θ]− ∞ X k=−∞ xq,kg(t−kTs) sin[2πfc(t−kTs)+θ], (2.6)
2.2. Digital Modulation Schemes 32 where xp,kand xq,kare independent PAM signals that assume values ±A, ±3A, ..., ±(
√ M − 1)A. Figures2.1c, 2.1dand 2.1e show the QAM, 16-QAM and 64-QAM modulation con-stellation diagrams, respectively.
The M -QAM modulation scheme can be obtained through the Cartesian product of two√M -PAM modulation schemes, one in-phase and another quadrature. The M -QAM modulation is widely used in communications systems with the aim of accommodating more bits per second in a limited bandwidth and thus allowing a more efficient use of the band, which represents an increase in the spectral efficiency of the system.
The energy per symbol of a pass-band M -QAM signal is equal to Es =
1 2x
2T
s, (2.7)
where x2 is the mean power of the constellation. The relation between the energy per
symbol and the energy per bit is given by Eb =
Es
log2M. (2.8)
In the M -QAM scheme there are M = 2l waveforms, where l ≥ 2 represents the
number of transmitted bits per symbol. Considering that l is an even number, then the M -QAM constellation is a square constellation, since√M is integer. In this case the real part and the imaginary part xp and xq of the symbols are chosen from the real alphabet
√
M -ary ±A, ±3A, ..., ±(√M − 1)A. The k-th element of this alphabet can be written as (−√M + 1 + 2k)A for k ∈ 0, ...,√M − 1. The mean power of the constellation of the base-band M -QAM modulation is given by
x2 = E[|x|2] = E[x2 p] + E[x2q] = 2E[x2p] = 2√1 M √ M −1 X k=0 A2(−√M + 1 + 2k)2. (2.9)
This summation has a closed form, so the mean power of the constellation can be written as
x2 = 2
3A
2(M − 1). (2.10)
Finally, although the construction criterion employed for QAM and PSK is different, it is important to indicate that 4-QAM and QPSK (quadrature PSK) are equivalent schemes. Thus, both present the same performance when their mean power is the same.
2.2. Digital Modulation Schemes 33 Im Re -A A A -A -3A 3A -3A 3A (0010) (0110) (1110) (1010) (0011) (0111) (1111) (1011) (0001) (0101) (1101) (1001) (0000) (0100) (1100) (1000)
Figure 2.2: Gray encoding to 16-QAM modulation.
2.2.6
Gray Encoding
Gray encoding is a binary coding system created by Frank Gray [51]. The coding is unweighted, meaning that from one code to another only one bit varies. This allows for the minimization of the number of wrong bits in each wrong symbol. Gray encoding is now used in sequential systems using the Karnaugh maps, since the beginning of the project to look for simpler and faster transitions is still valid.
Thus, this type of encoding is widely used in digital modulation schemes in which multiple bits are sent in a single symbol. Therefore, it is important to define a bit encoding function in symbols. In addition, the used encoding function changes the bit error rate, so in this work we will use the Gray encoding. Fig. 2.2 shows the Gray encoding of a 16-QAM constellation.
2.2.7
Adaptive Modulation
The main disadvantage when fixed modulation (non adaptive) is employed is the fact that the BER system performance changes as a function of the channel conditions and the interference levels. However, some applications require a target BER (Pb,tar) or a
maximum BER in order to ensure the quality of a communication service, otherwise the service drops, which affects the system spectral efficiency. Therefore, it is necessary to adapt the modulation scheme employed so that the target BER can be guaranteed. Moreover, in practical systems, there is no need for the system to guarantee lower BER than that required by a communication service.
By the above, adaptive modulation is a technique that allows for the assurance of a given target BER. Thus, this technique consists of transmitting a signal with the
high-2.3. Cellular Systems 34 est possible modulation order provided that coverage conditions are adequate. If these conditions deteriorate, then more robust modulations are used. Hence, the transmitter requires information about the channel and interference conditions in order to select the adequate modulation order. Thus, a permanent communication between the transmitter and the receiver is necessary. In practical cellular systems, control information for adap-tive modulation is exchanged at every time transmission interval (TTI) between the UE and the BS.
2.3
Cellular Systems
In cellular networks the service area is divided into smaller circular areas called cells, whose coverage is provided by a base station (BS) inside this area. Cellular systems have been designed in order to diminish radio spectrum congestion problems and to increase capacity.
Each cell has an BS, which communicates simultaneously with all mobile radio sta-tions (UE) located inside a cell and passes the voice and data traffic to a switching and control center. The radio link for signals transmission from the BS to the UE is known as downlink and the radio link for signals transmission from the UE to the BS is called uplink. In performance analysis, the uplink is typically preferred as the maximum power of transmission of the UEs is much lower than that of the BS [31].
2.3.1
Channel Reuse
Only a part of the total number of channels available in the system is assigned to each cell. Thus, the number of simultaneous voice and data transmission channels that can occur in a cellular network is limited by the spectrum of available frequencies. In order to ensure that these channels are not affected by transmissions from other users on other cells operating at the same frequency, channel allocation in the network must be such that there is sufficient separation between the transmitters.
Frequency reuse consists of the allocation in each cell of a subset of the available channels in a cellular system. The group of adjacent cells using the entire set of available channels is called a cluster and the number of cells in each cluster is known as channel reuse factor (F) [31]. The total number of channels is reused only in different clusters, which guarantees that two different cells employing the same channels (co-cells) are separated by a large distance so that interference levels are reasonable for an adequate operation of the cellular system.
Although a cell can be ideally considered as a circular region, this geometric repre-sentation implies some overlapping areas when some circular cells are considered into a plane. Therefore, regular hexagons are conventionally employed to represent cells. As
2.3. Cellular Systems 35 a consequence of this geometry, it is possible to employ only some integer values for F, which can be obtained as [31]
F = a2+ ab + b2, (2.11)
where a and b are non-negative integer numbers. If F = 1, then all the system channels are allocated to each cell. In this case, reuse scheme is called as universal channel reuse. This reuse scheme is widely used in the CDMA access technique.
The reuse distance is defined as the minimum distance between centers of two cells, belonging to different clusters, which use the same subset of channels. This distance is given by
D = R√3F, (2.12)
where R is the outer cell radius.
2.3.2
Interference
Interference is all undesirable signal arriving to a receiver and it can be considered as the main limiter of the cellular system capacity. In the uplink, the interference is produced by other UEs in the same cell and in the co-cells. In the downlink, the interference is produced by the BSs in the co-cells. Generally, the mean interference affecting the uplink is stronger than that affecting the downlink [52].
Frequency reuse implies that in a certain area with cellular service there are several cells that use the same subset of channels. These cells are called co-channel cells, and interference between signals from these cells is called co-channel interference (CCI). A greater reuse distance results in decreased CCI. However, this leads to a higher number of cells per cluster, resulting in reduced spectral efficiency due to the decrease in the number of channels per cell. On the other hand, If the interference is produced by users in the same cell, then it is called multiple access interference (MAI).
Unlike thermal noise, whose effects can be mitigated by increasing the transmission power, MAI and CCI effects are not diminished as the transmission power increases. In fact, a power raise produces an increase of both types of interference. Consequently, other techniques must be employed in order to diminish the interference effects.
An important measure of performance in cellular systems is the SIR, defined as the ratio between the power of the interest signal and the power resulting from the co-channel interfering signals. The SIR is a random variable, affected by phenomena such as the location of BSs within its own cell, the characteristics of receiving antennas and fading, among other factors.
2.3. Cellular Systems 36
2.3.3
Perfect Power Control
The transmitted power represents an important degree of freedom to be considered in the planning of wireless communications systems. In cellular networks, the power levels transmitted by each UE are under constant control by the corresponding BS. In this way, power control can contribute with several functionalities, such as connectivity, power and interference management. In terms of connectivity management, power control allows each UE to transmit only with enough power to maintain a certain quality in the reverse link. Even without interference or energy limitation, the receiver must be able to detect a minimum level of power received so that it can remain connected to the transmitter.
In cellular systems, the power control helps to combat the near-far problem. Thus, CDMA and OFDMA based systems employ highly efficient power controls [53], [54], which solve the problem of a nearby UE overpowering the BS receiver and drowning out the signals of far away UEs. Hence, for our system model, we consider perfect power control, which is performed by altering the transmitted power of each UE in the same cell in order to obtain equal received power for all users at the BS. With this strategy, the output power for each UE can be written as [31]
Pt = K−1Pr0r
β, (2.13)
where Pr0 denotes the constant received power at the BS from each user in the same
cell and r is the distance between the UE and its BS. The factor rβ allows the UEs
transmitted signals to reach the BS with the same power level. Additionally, K and β are the propagation factor and the propagation path-loss exponent, respectively. These factors are analyzed in more detail in Subsection 2.4.1.1. In (2.13), the product K−1rβ
allows the UEs transmitted signals to reach the BS with the same power level, because, as analyzes in the aforementioned subsection, the considered path-loss increases as a power of the distance. In addition, it is important to consider that Pt ≤ Pt,max, where Pt,max is
the maximum transmission power of an user equipment.
2.3.4
Cellular Spectral Efficiency
Spectral efficiency refers to the bit rate that can be transmitted over a given bandwidth in a communications system. In cellular networks, the spectral efficiency per cell can be defined as the ratio of the total bit rate, resulting from the sum of the bit rate of each user in a cell, to the bandwidth of the system, that is
ξ = PNu
ℓ=1Rb,ℓ
2.4. Mobile Radio Channel 37 where Nu is the total number of users in the cell, Rb,ℓ is the ℓ-th user bit rate and B is
the total system bandwidth. The cellular spectral efficiency depends on other parameters such that the interference levels and the techniques employed to mitigate them. The influence of these parameters on the cellular spectral efficiency is analyzed with more detail in Chapter 6.
2.4
Mobile Radio Channel
The important challenge for wireless systems comes from transmitting the signals through the communication channel itself. The requirements in such systems are such that the signals have to propagate under adverse conditions, most of times in non-line-of-sight (NLOS) between transmitter and receiver. Various obstacles of various sizes, terrain ripples, relative movement between transmitter and receiver, fading, interference from other signals, noise and various other factors weaken, cause delay and distort the transmitted signal in a very unpredictable way. The planning of a wireless communication network that works properly under these conditions poses a challenge, especially when services with high data rates are required. The wireless communication channel imposes severe limitations on system performance. Two important phenomena that affect the propagation of a signal in a wireless communication channel are path loss and fading. They are described below [52].
2.4.1
Large-Scale Radio Propagation Loss
Large scale phenomena result from signal attenuation when it travels a certain distance and they are also result of the signal attenuation produced by obstacles between the transmitter and the receiver. As a consequence, there are two large scale phenomena: path-loss and shadowing. They are detailed as follows.
2.4.1.1 Path Loss
Path loss refers to the decay of the received signal power as a function of the distance between transmitter and receiver. Currently there are several models used in cellular networks. These different models consider that path-loss increases as a power of the distance. Hence, the received power can be written as
Pr = KPtr−β, (2.15)
where Pt is the transmitted power and r is the distance between the transmitter and
the receiver. Additionally, K is the propagation factor and β is the propagation path-loss exponent. The calculation of these last parameters depends on the model employed.
2.4. Mobile Radio Channel 38 Popular models used by wireless carriers for coverage modeling include Okumura-Hata, COST231-Hata [55], SUI model [56] and Omnidirectional Path Loss Models [57]. In the present work the SUI model is employed and it is detailed below.
2.4.1.2 SUI Model
In this work the Stanford University Interim (SUI) model is considered because it includes frequencies smaller than 3.5 GHz. Thus, SUI model considers frequency bands allocated for 4G cellular systems and additionally, it considers the 3.5 GHz band which is a candidate for 5G networks deployment [58]. In the SUI model, the distance r, in (2.15), is given in meters and satisfies 100 m ≤ r ≤ 104 m, and, from the expressions given in
[56], it is possible to show that K = 5625 π2 2000 xf−(2+x) c rβ−20 ℏ u 2 0.1y , (2.16) β = z1 − z2ha+ z3 ℏa, (2.17)
where fc is the carrier frequency in MHz satisfying fc ≤ 3500 MHz, ℏa and ℏu denote the
BS antenna height and UE height in meters, respectively, where 10 m ≤ ℏa ≤ 80 m and
1 m ≤ ℏu ≤ 10 m. Moreover, x is equal to 0.6, when fc ≥ 2000 MHz, and is equal to 0,
otherwise. In addition, y is equal to 0 when ℏu < 2 m, otherwise, the values shown in
Table 2.1 must be used. The parameters z1, z2 and z3 are constants used to model the
terrain types and their values are also shown in Table 2.1. In this table, category A is used for hilly terrain with moderate-to-heavy tree densities, category B is employed for intermediate path-loss conditions and category C considers a flat terrain with light tree densities.
Table 2.1: Parameters y, z1, z2 and z3 for the SUI path-loss model.
Category A Category B Category C
y 10.8 10.8 20
z1 4.6 4 3.6
z2 0.0075 0.0065 0.005
z3 12.6 17.1 20
2.4.1.3 Shadowing
Shadowing is the effect that the received signal power fluctuates due to objects ob-structing the propagation path between transmitter and receiver. These fluctuations are experienced on local-mean powers, that is, short-term averages to remove fluctuations due to multipath fading. Thus, the power of the received signal can increase or diminish
2.4. Mobile Radio Channel 39 considerably and, in some cases, there is complete signal loss during time periods, which depends on the obstacle size. Shadowing is modeled by a log-normal distribution [52].
2.4.2
Small-Scale Fading and Multipath
The presence of several obstacles in a wireless channel causes the transmitted signal to propagate to the receiver through multiple paths due to the various reflections, scattering and diffractions undergone. The resultant produces a phenomenon known as fading caused by destructive sum between the versions of the transmitted signal that arrive at the receiver. These versions of the transmitted signal, which constitute the so called multipath propagation, combine on the receiver antenna to give a resulting signal whose amplitude can vary considerably over short distances and in short time intervals.
2.4.2.1 Multipath Channel Characterization
Small-scale variations of a radio signal can be directly related to the channel impulse response. Thus, a radio channel can be modeled as a linear filter with a time variant impulse response. The filter nature is due to the sum of amplitudes and delays of different signal versions arriving at the BS. Furthermore, the time variant nature is produced by the UE movement.
Radio channel impulse response is a function of t and τ , where t represents time variations due to the UE movement and τ denotes multipath delays for a fixed value of t. The equivalent base-band impulse response of a multipath channel can be written as [16]
h(t, τ ) = P X ℓ=1 αℓ(t) exp − iφℓ(t) δt − τℓ(t) , (2.18)
where P is the total number of multipaths, αℓ(t), φℓ(t) and τℓ(t) are the amplitude, phase
and delay of the ℓ-th multipath during the instant of time t. Furthermore, δ(t) denotes the Dirac delta.
In a NLOS scenario, the received signal is composed by different reflected components of the transmitted signal, among which there is no dominant component. Moreover, the channel impulse response can be modeled as a zero-mean complex Gaussian process. Consequently, for a given t, the envelope of this process (α = |h(t, τ)|) can be modeled by a Rayleigh distribution, whose probability density function (PDF) is given by [59]
fα(α) =
α σ2e
−α2
2σ2, α ≥ 0, (2.19)
where σ2 is the variance of the zero-mean real Gaussian random variables that generate
the Rayleigh random variable. Additionally, the resultant phase (φ) of this process is a random variable uniformly distributed over [0, 2π).
