HYBRID OVERLAY/UNDERLAY COGNITIVE RADIO NETWORKS …

HYBRID OVERLAY/UNDERLAY

COGNITIVE RADIO NETWORKS

WITH MC-CDMA

A thesis submitted to the University of Manchester

for the degree of Doctor of Philosophy

in the Faculty of Engineering and Physical Sciences

June 2014

By

Fahimeh Jasbi

School of Electrical and Electronic Engineering

Microwave and Communication Systems Research Group

Contents

List of Tables 6

List of Figures 7

Abstract 10

Declaration 12

Copyright Statement 13

Acknowledgements 14

List of Abbreviations 15

List of Variables 18

List of Mathematical Notations 20

1 Introduction 22

1.1 Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.2 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.5 List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Theoretical Background 29

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Large-Scale Path Loss and Shadowing . . . . . . . . . . . . . . . . 30

2.3 Small-Scale Fading and Multipath . . . . . . . . . . . . . . . . . . 31

2.4 Multipath Channel Model . . . . . . . . . . . . . . . . . . . . . . 31

2

2.5 Fading Channel Characteristics and Types . . . . . . . . . . . . . 33

2.5.1 RMS Delay Spread and Mean Excess Delay . . . . . . . . 33

2.5.2 Coherence Bandwidth . . . . . . . . . . . . . . . . . . . . 33

2.5.3 Doppler Spread . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5.4 Coherence Time . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5.5 Small-Scale Fading Types . . . . . . . . . . . . . . . . . . 34

2.6 Multi-Carrier Transmission . . . . . . . . . . . . . . . . . . . . . . 35

2.6.1 OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.6.2 Multi-Carrier CDMA . . . . . . . . . . . . . . . . . . . . . 39

2.7 Diversity Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.8 Equalization Techniques . . . . . . . . . . . . . . . . . . . . . . . 46

2.8.1 Zero Forcing Equalizer . . . . . . . . . . . . . . . . . . . . 48

2.8.2 Minimum Mean-Square Error Equalizer . . . . . . . . . . . 48

2.8.3 Chip and Symbol Level Equalization for MC-CDMA System 49

2.9 Basics of Convex Optimization . . . . . . . . . . . . . . . . . . . . 49

2.10 Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 Cognitive Radio 55

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2 Dynamic Spectrum Access . . . . . . . . . . . . . . . . . . . . . . 56

3.2.1 Horizontal Spectrum Sharing . . . . . . . . . . . . . . . . 57

3.2.2 Vertical Spectrum Sharing . . . . . . . . . . . . . . . . . . 58

3.3 CR Definition and Main Functions . . . . . . . . . . . . . . . . . 59

3.4 Underlay Transmission and the Interference Threshold . . . . . . 60

3.5 Non-Contiguous (NC) Transmission . . . . . . . . . . . . . . . . . 63

3.5.1 Overlay Multi-User NC-MC-CDMA . . . . . . . . . . . . . 64

3.5.2 Underlay NC-MC-CDMA . . . . . . . . . . . . . . . . . . 65

3.6 Overlay/Underlay/Hybrid Capacity Comparison . . . . . . . . . . 68

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 Full-Load Hybrid System 72

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Hybrid Systems in the Literature . . . . . . . . . . . . . . . . . . 73

4.3 Full-Load Hybrid System Model . . . . . . . . . . . . . . . . . . . 73

4.4 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3

4.4.1 ZF Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.4.2 Chip-Level MMSE-Based Receiver . . . . . . . . . . . . . 78

4.4.3 Symbol-Level MMSE Based-Receiver . . . . . . . . . . . . 81

4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5 Overload Hybrid System 89

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2 Code Selection and Adaptation in CRNs . . . . . . . . . . . . . . 90

5.3 System Model and Transmitter Structure . . . . . . . . . . . . . . 92

5.4 Code Allocation Algorithm . . . . . . . . . . . . . . . . . . . . . . 96

5.5 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97


5.6.1 Medium PU Interference Level . . . . . . . . . . . . . . . . 101

5.6.2 High PU Interference Level . . . . . . . . . . . . . . . . . 102

5.6.3 Underlay Multi-User Results . . . . . . . . . . . . . . . . . 107

5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6 Hybrid Overlay/Underlay Sum Rate Optimization 110

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.2 Sum Rate Comparison for Different Hybrid Schemes . . . . . . . . 112

6.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.4 AWGN Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.4.1 Full-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.4.2 Mixed OFDM/MC-CDMA . . . . . . . . . . . . . . . . . . 117

6.4.3 Proposed Full-MC-CDMA . . . . . . . . . . . . . . . . . . 118

6.4.4 Proposed Overload MC-CDMA . . . . . . . . . . . . . . . 120

6.5 Rayleigh Fading Channels . . . . . . . . . . . . . . . . . . . . . . 122

6.5.1 Full-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.5.2 Proposed Overload MC-CDMA . . . . . . . . . . . . . . . 126


6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

7 Conclusions and Future Work 134

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4

Appendix A Underlay Full-Load BER Performance with ZF 149

5

List of Tables

2.1 Small Scale Fading Types . . . . . . . . . . . . . . . . . . . . . . 35

2.2 Main system and channel parameters of a W-ATM system [43] . . 44

4.1 ITU Pedestrian B channel PDP . . . . . . . . . . . . . . . . . . . 83

6

List of Figures

2.1 Tap Delay Line model . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 OFDM signal spectrum [33] . . . . . . . . . . . . . . . . . . . . . 36

2.3 OFDM with FFT/IFFT implementation [27] . . . . . . . . . . . . 37

2.4 Block Diagram of a Multi-User MC-CDMA Transmitter . . . . . . 40

2.5 Block Diagram of a Multi-User MC-DS-CDMA Transmitter . . . 41

2.6 Block Diagram of a Multi-User MC-MT-CDMA Transmitter . . . 42

2.7 W-ATM Channel Impulse Response [43] . . . . . . . . . . . . . . 45

2.8 Synchronous MC-CDMA for downlink over W-ATM channel with

MRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1 Dynamic Spectrum Access classifications [56] . . . . . . . . . . . . 56

3.2 Horizontal and vertical spectrum sharing regulatory concept [57] . 57

3.3 Underlay spectrum opportunity and the interference threshold con-

cept [63] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4 Frequency spectra of NC-OFDM subcarriers [56] . . . . . . . . . . 63

3.5 Overlay Multi-User NC-MC-CDMA in AWGN . . . . . . . . . . . 65

3.6 Overlay NC-MC-CDMA in fading channel with different spreading

and MMSE-FDE . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.7 Theoretical vs simulation underlay performance with different spread-

ing in AWGN (SU to PU relative power −30 dB) . . . . . . . . . 68

3.8 Theoretical vs simulation underlay performance with different PU

occupancy levels in AWGN (SU to PU relative power −20 dB) . . 69

3.9 Capacity comparison of overlay, underlay and hybrid scenarios . . 71

4.1 Cognitive Radio System . . . . . . . . . . . . . . . . . . . . . . . 74

4.2 Hybrid MC-CDMA system model . . . . . . . . . . . . . . . . . . 74

4.3 Underlay performance of the proposed full-load hybrid system with

ZF and CL MMSE equalizers for different PU occupancy levels . . 84

7

4.4 Simulation and Numerical underlay BER performance comparison

for ZF. Dashed and solid lines represent simulation and numerical

results respectively . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.5 Chip and symbol level MMSE comparison. Dashed and solid lines

represent CL and SL MMSE performance respectively. . . . . . . 86

4.6 Number of overlay users vs underlay BER performance for fixed

SNR=15 dB with ZF, CL and SL MMSE. PU is assumed to be

occupying 128 subcarriers (25% of the whole bandwidth) . . . . . 87

4.7 NC-MC-CDMA vs proposed hybrid MC-CDMA underlay perfor-

mance with ZF and MMSE . . . . . . . . . . . . . . . . . . . . . 88

5.1 Hybrid overload MC-CDMA system model . . . . . . . . . . . . . 92

5.2 Proposed Transmitter Structure . . . . . . . . . . . . . . . . . . . 93

5.3 Overload Receiver Block Diagram . . . . . . . . . . . . . . . . . . 98

5.4 Proposed full-load and Overload underlay performance comparison

with relative underlay to PU received interference level of −20dB;

Solid lines show the overload and dashed lines show the full-load

results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.5 Underlay performance of the proposed overload hybrid system with

different PU occupancy levels. Total number of subcarriers are 512 103

5.6 Underlay sensitivity of the proposed overload system to PU inter-

ference power level, Mpu = 256 . . . . . . . . . . . . . . . . . . . . 104

5.7 Overlay performance with and without underlay transmission for

the worst case scenario when overlay and underlay power levels are

equal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.8 Underlay NC MC-CDMA sensitivity to PU interference power level

for 256 subcarriers. Dashed lines show the CL and solid lines the

symbol-level while the dotted lines show the proposed system’s

results with Mpu = 256 . . . . . . . . . . . . . . . . . . . . . . . . 106

5.9 Underlay performance for increasing number of underlay users

while overlay is full-loaded with Mpu = 64 . . . . . . . . . . . . . 107

5.10 Overlay Interference to underlay with Mpu = 64. Solid lines show

the underlay performance with overlay and the dashed lines with-

out overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

8

6.2 Sum rate comparison of the four hybrid systems in AWGN for

Npu = 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.3 Sum rate vs. PU interference power level in AWGN for Npu = 4,

and fixed interference threshold level and total transmission power

limit of 1 mW and 280 mW. . . . . . . . . . . . . . . . . . . . . . 128

6.4 Sum rate vs. interference threshold in AWGN for Npu = 4, and

fixed PU interference and total transmission power of 0.5 and 280

mW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.5 Sum rate comparison of the four hybrid systems in AWGN for

different PU occupancy levels . . . . . . . . . . . . . . . . . . . . 130

6.6 Sum rate comparison of the two hybrid systems in Fading channel

for Npu = 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.7 Sum rate comparison of the two hybrid systems in Fading channel

for Npu = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

9

Abstract

There has been a growing demand for wireless communication services in the past

few years. Recent reports reveal that the demand will not only increase in the

number of subscribers but also in more diverse applications such as Machine-to-

Machine (M2M) communications and the Internet of Things. With such demand

for capacity increase, there is a necessity to shift from today’s Static Frequency

Allocation (SFA) to Dynamic Spectrum Access (DSA). The change will make

efficient use of spectrum by utilizing the unused parts in different times, frequen-

cies and spaces. With this regard, cognitive radio (CR) is a powerful potential

candidate for the spectrum scarcity problem.

This work addresses the two main current discussions in Cognitive Radio

Networks (CRN), spectral efficiency and interference mitigation problem. There

are two main spectrum sharing techniques in CRN, overlay and underlay, which

have been thoroughly investigated in the literature. Unlike the relative works

which separate the use of overlay and underlay, this works considers the joint

overlay and underlay as a hybrid system to enhance the spectral efficiency and Bit

Error Rate (BER) performance in CRNs. MC-CDMA is proposed for underlay

transmission for two main advantages. Firstly, for low power spectral density due

to spreading. Secondly, for its capability to mitigate high interference.

Two hybrid MC-CDMA schemes are proposed in this work. The first scheme

spreads the underlay signal through the whole bandwidth to mitigate PU inter-

ference and benefit from the frequency diversity. To maximize data rate, overlay

10

utilizes the available bands while keeping orthogonality with underlay using Or-

thogonal Variable Spreading Factor (OVSF) codes.

To further increase capacity, an overload MC-CDMA system is proposed. In

this scheme, overlay utilizes the full signal dimension, while underlay overloads

the system. Two layered spreading is applied to differentiate overlay and under-

lay users. In order to detect the underlay signal, the overlay signal is detected

first and is cancelled from the received signal. The underlay data is then detected

from this modified signal. The framework is then extended to a multi-user un-

derlay scenario. A code allocation algorithm is proposed in order to achieve low

cross-correlation between the overlay and underlay users. The results show that

the proposed overload system maintains good performance even in high PU in-

terference level. Furthermore, the proposed hybrid capacities are optimized and

compared with the two available hybrid systems in the literature. The proposed

overload system showed to increase capacity significantly, both in AWGN and

fading environment, in compared with the existing methods.

11

Declaration

No portion of the work referred to in this thesis has been

submitted in support of an application for another degree

or qualification of this or any other university or other

institution of learning.

12

Copyright Statement

i The author of this thesis (including any appendices and/or schedules to this

thesis) owns any copyright in it (the Copyright) and he has given The Uni-

versity of Manchester the right to use such Copyright for any administrative,

promotional, educational and/or teaching purposes.

ii Copies of this thesis, either in full or in extracts, may be made only in accor-

dance with the regulations of the John Rylands University Library of Manch-

ester. Details of these regulations may be obtained from the Librarian. This

page must form part of any such copies made.

iii The ownership of any patents, designs, trade marks and any and all other in-

tellectual property rights except for the Copyright (the “Intellectual Property

Rights”) and any reproductions of copyright works, for example graphs and

tables (“Reproductions”), which may be described in this thesis, may not be

owned by the author and may be owned by third parties. Such Intellectual

Property Rights and Reproductions cannot and must not be made available

for use without the prior written permission of the owner(s) of the relevant

Intellectual Property Rights and/or Reproductions.

iv Further information on the conditions under which disclosure, publication

and exploitation of this thesis, the Copyright and any Intellectual Property

Rights and/or Reproductions described in it may take place is available from

the Head of School of Electrical and Electronic Engineering.

13

Acknowledgements

First and foremost, I would like to express my sincere gratitude to my supervi-

sor, Dr. Daniel Ka Chun So, for his continuous support and invaluable guidance

throughout the 4 years of my PhD. Indeed, this work owes much to Dr. So’s

helpful supervision and patient assistance. It is for his continuous guidance, mo-

tivation and encouragement throughout that I could see a successful culmination

of my PhD research project.

I would like to express my gratitude to my advisor Dr Emad A. Alsusa for

providing his valuable advice and words of encouragement at key times during

this study.

I am also greatly thankful to Dr. Khairi A. Hamdi for his instructive advice

and meticulous evaluation of this work. It has been truly a great privilege to

learn and benefit from Dr. Hamdi’s informative comments and valuable insights.

A very special thanks goes to Dr Robin Sloan for his assistance and help along

the way.

My sincere thanks to Dr Denis Denisov, Dr Saralees Nadarajah and Dr Jie

Tang for their time and advice when most needed.

I would also like to thank Prof. Tony Brown, head of the school of Electrical

and Electronic Engineering of the University of Manchester.

I wish to express thanks to my peers, colleagues and good friends Dr. Warit

Prawatmuang, Dr. Abubakr U. Makarfi and Dr. Wahyu Pramudito for always

helping me patiently with trivial doubts and being supportive.

My thanks goes to all my postgraduate colleagues, especially, Tarla, Azwan

and Khaled for their fruitful discussions which helped in mutual learning.

I would also like to thank my dearest friends Priya, Sareh, Mina, Mousumi,

Aisha and Ayda for being a family away from home.

Last but not the least; I am forever indebted to my parents for their patience,

support and love. They have been my pillars of strength throughout my life.

14

List of Abbreviations

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BPSK Binary Phase Shift Keying

CAGR Compound Annual Growth Rate

CDMA Code Division Multiple Access

CI Carrier Interferometry

CIR Channel Impulse Response

CL Chip-Level

CP Cyclic Prefix

CRN Cognitive Radio Network

CR Cognitive Radio

CSI Channel State Information

CU Cognitive User

DFT Discrete Fourier Transform

DSA Dynamic Spectrum Access

DS-CDMA Direct Sequence Code Division Multiple Access

DSS Dynamic Spectrum Sharing

EGC Equal Gain Combining

FCC Federal Communication Commission

FEC Forward Error Correction

FFT Fast Fourier Transform

FIR Finite Impulse Response

IDFT Inverse Discrete Fourier Transform

ISI Inter Symbol Interference

15

ISM Industrial, Scientific, and Medical

IT Interference Threshold

ITU International Telecommunications Union

IUI Inter-User-Interference

KKT Karush Kuhn Tucker

LOS Line of Sight

LTE Long Term Evolution

MC-CDMA Multi-Carrier Code Division Multiple Access

MC-DS-CDMA Multi-Carrier Direct Sequence Code Division Multiple Access

MT-CDMA Multi-Tone Code Division Multiple Access

MCM Multi-Carrier Modulation

MGF Moment Generating Function

MIMO Multiple-input multiple-output

MMSE Minimum Mean Square Error

MRC Maximal Ratio Combining

M2M Machine to Machine

NC Non-Contiguous

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

OVSF Orthogonal Variable Spreading Factor

PAPR Peak-to-Average Power Ratio

PDF Probability Density Function

PDP Power Delay Profile

PO-CI Pseudo-Orthogonal Carrier Interferometry

PSD Power Spectral Density

PU Primary User

QOS Quality of Service

RF Radio Frequency

RMS Root Mean Square

SC Selection combining

SDR Software Defined Radio

16

SER Symbol Error Rate

SFA Static Frequency Allocation

SL Symbol-Level

SNR Signal to Noise Ratio

SINR Signal to Interference plus Noise Ratio

STBC Space-Time Block Code

SY Secondary User

TDL Tap Delay Line

W-ATM Wireless Asynchronous Transfer Mode

WCDMA Wideband Code Division Multiple Access

W-H Walsh-Hadamard codes

WSS-US Wide Sense Stationary Uncorrelated Scattering

ZF Zero Forcing

17

List of Variables

a[i] i-th subcarrier availability

α[j] j-th subband availability

B Total available bandwidth

bk k-th overlay user’s data vector

b¯k

¯k-th underlay user’s data vector

Ch Hybrid spreading code matrix

dk k-th overlay user’s multiplexed data vector

d¯k

¯k-th underlay user’s multiplexed data vector

dh Hybrid data vector

dpu Primary user’s data vector

G Overlay spreading factor

gss[j] Secondary transmitter to secondary receiver’s channel power

on the j-th sub-band

gsp[j] Secondary transmitter to primary receiver’s channel power


gps[j] Primary transmitter to secondary receiver’s channel power


Hss Secondary transmitter to secondary receiver channel matrix

Hsp Secondary transmitter to primary receiver channel mtrix

Î Residual interference from overlay

Ith Interference threshold of the primary system

K Number of secondary users

K Number of overlay secondary users

K¯

Number of underlay secondary users

18

L Number of resolvable paths

M Total number of subcarriers

Mpu Number of occupied subcarriers by all primary users

Msu Number of available subcarriers for overlay cognitive users

N0 Two sided AWGN power spectral density

NB Total number of sub-bands

Nov Total number of overlay sub-bands

Npu Total number of occupied sub-bands by primary user

Ns Number of subcarriers in a sub-bands

n Complex Gaussian noise component

P Number of consecutive overlay symbols sent simultaneously

Pun Underlay signal power

PT Maximum secondary user’s power budget

pco Overlay power per subcarrier

pcu Underlay power per subcarrier

ppu Average primary user received power per subcarrier

pj Allocated power to the j-th subband

pso Overlay symbol power

Ptot Total cognitive radio power budget

r Received signal vector

rc Reconstructed received signal vector

S Overlay scrambling matrix

S¯

Underlay scrambling matrix

spu Primary user data vector containing availability vector a

Ts Symbol duration

τi i-th excess delay

w Equalizer’s coefficient

19

List of Mathematical Notations

(·)H Matrix Hermitian

(·)∗ Complex conjugate

E (·) Expectation operator of a random variable

Erfc(.) Complementary error function

diag (·) A vector that contains all diagonal elements of a matrix

log2 (·) Base-2 logarithm

|·| Amplitude of a scalar

‖·‖ Norm of a vector

IM M ×M Identity matrix

≈ Approximately equal to

⊗ Kronecker product

∗ Convolution

Q(.) Complementary Gaussian distribution function

C Field of complex numbers

R++ Set of positive real numbers

∇2f(x) Hessian matrix of function f

� Generalized inequality, i.e. component-wise inequality be-

tween symmetric matrices

� Strict form generalized inequality

20

K1(.) The first order modified Bessel function of the second kind

< a,b > The inner product of the two matrices a and b

blc Largest integer not higher than l

21

Chapter 1

Introduction

There has been a huge increase in the demand for wireless communication services

over the past few years. Reports reveal that by 2018, more than half of the

IP-traffic will originate from non-PC devices [1]. From 1980, when the first

generation of mobile network was introduced till today’s 4th Generation (4G)

network, wireless communication has made major changes to our society and our

lives. The world has changed from an unconnected to a fully connected world.

Telecom is also modernizing other technologies such as transport, health and

education. According to the reports, traffic is going to increase exponentially

not only in the number of phone subscribers but also in a more diverse range of

applications. For example, Machine-to-Machine (M2M) communications traffic

will grow at a Compound Annual Growth Rate (CAGR) of 84 percent. The

same trend is predicted for other modules such as TVs, tablets and smart-phones

[1, 2, 3]. With the increasing demand on high rate transmissions and the growing

diverse applications of wireless communications, Static Frequency Allocation

(SFA) can not meet such requirements. Furthermore, reports show that the

spectrum is being utilized inefficiently. In other words, different parts of the

spectrum is not being used in different times and geographical locations [4].

Therefore, the paradigm is being shifted from SFA towards Dynamic Spectrum

Access (DSA). There are several regulatory status for DSA, among which

22

CHAPTER 1. INTRODUCTION 23

Cognitive Radio (CR) seems to be a promising solution to satisfy the demand for

capacity increase.

1.1 Cognitive Radio

Cognitive Radio (CR), first proposed by Mitola [5], is an intelligent wireless

communication system that is aware of the environment. As opposed to the

conventional communication systems that were designed with specific parameters,

CR can learn and adapt its internal states by changing its parameters.

In CR, which is a vertical spectrum sharing technique1, Primary Users (PUs)

have the priority to access the spectrum whenever they require. On the other

hand, cognitive users, also called Secondary Users (SUs), are the users with lower

priority and have to use the spectrum in an opportunistic manner as long as they

do not cause harmful interference to PUs. Therefore, the secondary users need

to have cognitive radio capabilities.

The main functions for cognitive radio can be summarized as spectrum

sensing, spectrum management, spectrum sharing and spectrum mobility. First

and foremost, cognitive radio equipments should sense the spectrum to determine

which portions of the spectrum are vacant -known as spectrum sensing. Selecting

the best available channel that meets the requirements of the user is spectrum

management. Coordinating access to other users with a fair scheduling is another

function as spectrum sharing. Lastly, during the transition to a better channel

or due to the presence of the primary user, the Quality Of Service (QOS) should

be maintained which is known as spectrum mobility [6, 7]. The platform for

such a reconfigurable radio is Software Defined Radio (SDR) [8, 9]. SDRs are

flexible radios that their parameters, such as frequency and modulation type, are

controlled by software.

In general, there are two spectrum sharing techniques, overlay and underlay.

1Different regulatory status for DSA will be discussed further in Section 3.2.


Opportunistic spectrum access whenever and wherever the spectrum is not being

used by the primary user via spectrum holes or so called white spaces is referred

to as overlay spectrum sharing. However, the spectrum can also be exploited

using underlay approach which means the secondary users can transmit with the

same bandwidth as the primary users as long as their transmission power do not

exceed the interference threshold limit at the primary receiver [10].

1.2 Motivations

The overlay and underlay CR approaches have been investigated widely in the

literature [11, 12, 13, 14]. In particular, different multiplexing or multiple access

schemes have been proposed for the physical layer of CR systems. Orthogonal

Frequency Division Multiplexing (OFDM) is a strong candidate for overlay

due to its flexibility to fill in the spectrum holes non-contiguously, known as

NC-OFDM [15]. However, a major drawback is the large side lobes that

results in high out-of-band emission which can leak into an active PU band and

hence significantly degrade PU’s performance [16]. Considering this interference,

coexisting primary and secondary users in adjacent bands of an OFDM-based

overlay system is investigated [17]. The framework is then extended to the

case where different interference constraints are set by different PUs in [18].

The non-contiguous transmission approach is applicable to other multicarrier

techniques, such as Multi-Carrier Code Division Multiple Access (MC-CDMA).

Authors in [19] proposed an NC-MC-CDMA scheme that adaptively changes its

transmission parameters according to the available spectrum holes instead of the

sub-band deactivation method.

There has been a shift from the conventional transmitter-centric model by

Federal Communication Commission (FCC) Spectrum Policy Task Force [20] in

2002. The new model introduces interference threshold at the receiver side where

interference takes place rather than interference being controlled at a certain


distance from the transmitter [21]. This is to ensure that the CR system will

not harm the licensee’s performance. Therefore, underlay transmission is more

challenging as utilizing the same spectra as PU may suffer from high interference

and hence considerably degrade its performance. Thus, a major issue in underlay

spectrum utilization is interference mitigation.

In recent years underlay transmission has been widely investigated in the

literature. Yet, spread-spectrum-based techniques are preferable for underlay CR

systems (see e.g. [22]). There are two fundamental advantages of spread spectrum

systems to be utilized in underlay CR. The first advantage stems from the low

power density due to spreading, and the second is the capability to mitigate

high interference levels [20]. While existing literatures agree on utilizing spread

spectrum schemes for underlay due to their interference suppression capabilities

[6, 20, 22], there is a missing link on how to achieve such interference suppression

when all the bandwidth is either occupied by PU or the overlay SU. This is known

as the hybrid CR system where both overlay and underlay are jointly exploited.

Previous works show that the hybrid systems outperform overlay or underlay

on their own in terms of two important performance measures: total achievable

transmission rate [23] and Bit Error Rate (BER) performance [24]. An

OFDMA-based joint overlay and underlay spectrum access mechanism is

proposed in [23]. A hybrid overlay/underlay transmission scheme was proposed

for CR systems in Additive White Gaussian Noise (AWGN) channels in [25].

Overlay carries the modulated data utilizing NC-OFDM, while underlay carries

parity bits using NC-MC-CDMA technique. The performance is also examined for

fading channels in [24], assuming the PU received interfering signal at secondary

receiver to be passing through AWGN channel. In this work, we seek to enhance

the spectral efficiency and interference suppression capabilities of CR system by

jointly utilizing white and grey parts of the spectrum.


1.3 Contributions

The main contributions of this work are highlighted in this section. Two hybrid

schemes are proposed for Cognitive Radio Networks (CRNs). The schemes

address two main issues in CRN: spectral efficiency and interference suppression.

The first scheme is a full-load MC-CDMA system which utilizes the whole

bandwidth, with consideration of the interference threshold of the PU, for

underlay transmission while overlay transmits through the available bands.

The orthogonality between overlay and underlay is maintained with the use of

Orthogonal Variable Spreading Factor (OVSF) codes. Treating the PU bands

as narrow-band interference, the underlay can benefit from the interference

mitigation capability of MC-CDMA while overlay transmits with high power

to achieve higher data rate. At the receiver side, overlay and underlay data

are separately detected. A chip-level and symbol-level MMSE-based modified

equalizers are proposed for underlay detection.

The second scheme is an overload MC-CDMA system. Overlay is used to fully

occupy the white spaces while underlay is overloading the system, utilizing the

whole bandwidth for higher data rate and diversity exploitation. Two layered

spreading is performed namely channelization and scrambling to separate overlay

and underlay users. The number of underlay users overloading the system

depends upon the PU interference threshold. An algorithm is proposed for

the code allocation to maintain the overlay/underlay orthogonality as much

as possible. At the receiver side, the overlay signal is detected first, and is

cancelled from the received signal. The underlay data is then detected from

this modified signal. The proposed overload system has showed to maintain good

performance even in high PU interference levels. Furthermore, the proposed

schemes’ capacities are optimized and compared with the available hybrid systems

in the literature. The overload MC-CDMA significantly improves capacity, both

in AWGN and fading channels.


1.4 Thesis Organization

The remainder of the thesis is organized as follows. Chapter 2 provides an

essential background on wireless communications and related material for the rest

of this thesis. It includes fading channels characteristics and types, Multi-carrier

transmission, frequency domain equalization, and basics of optimization.

Chapter 3 discusses the regulatory history of underlay transmission, the

necessity to change the spectrum allocation policy from fixed to dynamic, and

the evolution of CR. CR regulatory status classifications and the interference

threshold policy are also studied. Next, non-contiguous transmission techniques

and their related performances are simulated and discussed for overlay and

underlay CR system. Finally, overlay, underlay, and hybrid capacities are

compared according to Shannon’s capacity formula.

Existing literature that contributes to hybrid CR systems is reviewed in

chapter 4. A novel full-load hybrid MC-CDMA system is presented and the

chip-level and symbol-level MMSE equalizers are proposed for underlay signal

detection. The BER performance of the underlay system is then evaluated by

simulations and compared with ZF results.

To further improve the spectral efficiency, an overload MC-CDMA scheme

is proposed in Chapter 5. The white spaces are fully utilized by overlay while

underlay is overloading the system, utilizing the whole bandwidth for higher

data rate and diversity exploitation. The framework is then extended to a

multi-user underlay system in which the number of underlay users depends

upon the interference threshold of the PU. The proposed schemes’ capacities

are compared with the available hybrid schemes in the literature for AWGN and

fading channels in Chapter 6.

Finally, chapter 7 concludes the thesis and discusses possible future work.


1.5 List of Publications

1. Fahimeh Jasbi, Daniel K C So, and Emad Alsusa, ”Hybrid

Overlay/Underlay MC-CDMA for Cognitive Radio Networks with MMSE

Channel Equalization,” in Proc. IEEE Global Communications Conference

(GLOBECOM), Atlanta, GA, USA, Dec 2013.

2. Fahimeh Jasbi and Daniel K C So, ”Hybrid Overload MC-CDMA for

Cognitive Radio Networks,” in Proc. IEEE Communications Conference

(ICC), Sydney, Australia, Jun 2014.

3. Fahimeh Jasbi and Daniel K C So, ”Hybrid Overlay/Underlay MC-CDMA

for Cognitive Radio Networks,” in EEE PGR Conference, The University

of Manchester, UK, 2012.

4. Fahimeh Jasbi and Daniel K C So, ”Hybrid MC-CDMA for Cognitive Radio

Networks,” IEEE Trans. Veh. Technol. (submitted).

5. Fahimeh Jasbi and Daniel K C So, ”Comparison of Hybrid Spectrum

Sharing Techniques for Cognitive Radio Networks in frequency selective

fading channels,” IEEE Communication Letters (under preparation).

Chapter 2

Theoretical Background

2.1 Introduction

This chapter covers the theoretical background to overview the concepts and

analytical techniques which will be employed later in this thesis. With this regard,

some basic concepts of wireless communications are reviewed in Sections 2.2 and

2.3. Fading channel characteristics and model are presented in section 2.4 and

2.5. Next, multicarrier transmission techniques, namely Orthogonal Frequency

Division Multiplexing (OFDM) and Multi-Carrier Code Division Multiple Access

(MC-CDMA), are studied in section 2.6. Diversity and equalization techniques

are utilized to combat multipath fading channels. In particular, diversity reduces

the depth and duration of the fades while equalization compensates for Inter

Symbol Interference (ISI) in multipath channels. Therefore, a brief overview of

diversity techniques are reviewed in section 2.7, followed by the two well-known

frequency domain equalization techniques, Zero Forcing (ZF) and Minimum Mean

Square Error (MMSE), in section 2.8. Finally, basics of convex optimization is

reviewed in section 2.9 as a promising tool in solving resource allocation problems

in wireless communication channels.

29

CHAPTER 2. THEORETICAL BACKGROUND 30

2.2 Large-Scale Path Loss and Shadowing

Large-scale propagation models are based on three basic propagation mechanisms

in mobile communication systems: reflection, diffraction, and scattering [26].

Reflection occurs when radio waves hit objects which are large compared to the

propagating wavelength i.e. the Earth’s surface, buildings, and walls. When there

is a curved or sharp-edged obstacle in between the transmitter and receiver, and

even without a line of sight, the radio signal can still propagate by bending around

the obstacle; this is known as diffraction. Diffraction can be explained by Huygens

principle, which states that each wave point in front acts as a secondary point

source. These secondary points propagate through the shadowed region. Lastly,

scattering occurs when the radio wave hits objects which are small compared to

the propagating wavelength and it thus spreads out. However in practice it is

observed that the path loss is significantly different from what is predicted by

models with the basic propagation mechanisms mentioned. Furthermore, it is

random in different locations but with the same T-R separation so that the effect

can be modeled as log-normal (normal in dB) distribution. The effect is called

shadowing. So the path loss can be expressed as

PL(d)[dB] = PL(d0) + 10n log(d

d0

) +Xσ (2.1)

where d0 denotes a reference distance, PL(d0) the mean path loss at d0 and n the

path loss exponent. It should be mentioned that path loss is frequency specific

and different path loss exponents correspond to different types of environments.

Xσ is the shadowing effect with zero mean and standard deviation σ (also in dB).

Hence, the path loss at distance d is considered to be a random variable with PL

mean and standard deviation σ.


2.3 Small-Scale Fading and Multipath

Unlike the large-scale propagation model which estimates the mean received signal

power at large T-R separation, small-scale fading describes the rapid fluctuation

of the signal amplitude over a short time or distance [26]. It happens due

to the fact that the transmitter and receiver antenna height is lower than the

surrounding obstacles and there is no line of sight (LOS) between the transmitter

and receiver so that the travelling signal reflects and scatters. Thus multiple

replicas of the signal arrive at the receiver with slightly time differences. Even

if there is LOS, fading still exists due to reflection from the ground and other

obstacles. The received signal consists of a number of plane waves, each having

random amplitude and phase and thus resulting in constructive or destructive

interference at the receiver. So, one of the effects of small-scale fading is rapid

changes in signal strength. Doppler shift is another small-scale effect which occurs

due to the relative motion between the transmitter and the receiver. It can be

positive or negative depending on the travelling direction of the moving object.

Comparing small-scale fading to large-scale path loss, path loss occurs over

long distances (100-1000m) whereas shadowing occurs over distances proportional

to the length of the obstructing object [27]. However, small-scale effect occurs

with even shorter distances, a few wavelengths of the traveling signal, due to the

constructive and destructive interferences.

2.4 Multipath Channel Model

As mentioned in section 2.3, multipath fading is due to the constructive and

destructive combination of randomly delayed, reflected, scattered and diffracted

signal components [28]. Therefore, the impulse response of a time varying

multipath channel depends on t and τ [26]. The variable t represents the

variations due to motion, whereas τ represents the channel multipath excess

delays. Multipath delay is divided into equal segments called excess delay bins,


Figure 2.1: Tap Delay Line model

each having time delay width equal to ∆τ = τi−1 − τi where τ0 is equal to 0

and is the first path arrived at the receiver. L is the number of resolvable paths

due to the fact that multipath components are equally spaced and any number of

path arrived at the i-th bin is considered as one resolvable component. Therefore,

baseband impulse response of a multipath channel can be represented as:

h(t, τ) =L−1∑i=0

ai(t, τ)exp[j(2πfcτi(t)) + φi(t, τ)]δ(τ − τi(t)) (2.2)

where ai(t, τ), τi(t) and (2πfcτi(t)+φi(t, τ)) are the real amplitudes, excess delays

and phase shifts respectively.

Assuming Wide Sense Stationary Uncorrelated Scattering (WSSUS)1 [29],

channel can be represented by Tap Delay Line (TDL) model as in Fig. 2.1 It

is also assumed that the excess delay bins are equal to the symbol period.

1A Wide-Sense Stationary channel assumes that the autocorrelation function depends ontime differences only. For the case of a flat Rayleigh fading channel, the mean power andthe Doppler spectrum do not change with time, while the instantaneous amplitude can change.Uncorrelated Scattering insures that all taps are faded independently so that the autocorrelationfunction can be shown as: E[h∗(τ1, t)h(τ2, t+ ∆t)] = Rh(τ1; ∆t)δ(τ2 − τ1)[29] and [30]


2.5 Fading Channel Characteristics and Types

Assuming the low-pass complex channel impulse response hi(t, τ) is WSS, the

autocorrelation function can be written as [30]:

Rh(τ2, τ1; ∆t) = E[h∗(τ1; t)h(τ2; t+ ∆t)] (2.3)

where E(.) denotes the expectation function. By letting ∆t = 0 the power delay

profile, also called the multipath intensity profile or delay power spectrum of the

channel, can be obtained from the complex impulse response h(t; τ) as

p(τ) =

∞∫−∞

|h(t; τ)|2dt = Rh(0; τ) (2.4)

which gives the average received power against the excess delays2 [27], [29].

2.5.1 RMS Delay Spread and Mean Excess Delay

The Root Mean Square (RMS) delay spread and mean excess delay are two

parameters obtained from power delay profile that characterize the multipath

fading channels. The mean excess delay, τ , is the first moment and the RMS

delay spread, στ , is the square root of the second central moment of the power

delay profile [26].

2.5.2 Coherence Bandwidth

Coherence bandwidth, Bc, is a parameter related to the RMS delay spread and

is the range of frequencies that the channel can be considered flat i.e. all

spectral components will be passed with approximately equal gain and linear

phase through the channel. In other words, it defines the frequency difference

that is required so that the correlation coefficient is smaller than a given

2Relative delay compared to the first arriving path


threshold. For frequency correlation above 0.9 the coherence bandwidth will be

approximately Bc ≈ 150στ

[26]. Note that the exact relationship between coherence

bandwidth and the RMS delay spread does not exist and the relationship for

different frequency correlations are derived using spectral analysis techniques and

simulations [26],[29].

2.5.3 Doppler Spread

Doppler spread, BD, is a measure of spectral broadening due to the time variations

and is defined as the range of frequencies over which the received signal Doppler

spectrum is non-zero.

2.5.4 Coherence Time

The coherence time, Tc, is the time duration that the channel impulse response

remains fairly constant. In other words, it is the time duration over which

two received signal’s amplitudes are highly correlated. The coherence time for

correlation above 0.5 is defined as Tc ≈ 916πfd−max

, where fd−max is the maximum

Doppler shift and is given by fd−max = ν/λ [26].

2.5.5 Small-Scale Fading Types

Fading channels are of different types according to the signal and channel

characteristics such as bandwidth, period of the transmitted signal, and RMS

delay spread, and Doppler spread for the channel. The delay spread of the

channel being greater than the symbol period, or alternatively the bandwidth

of the signal being greater than the coherence bandwidth of the channel, leads to

frequency selectivity. Consequently, different versions of the transmitted signal

with different phase shifts and gains will be received which leads to ISI in the

receiver. On the other hand, when Doppler spread is greater than the signal

bandwidth, or alternatively coherence time being less than symbol period, signal


Fading Type CharacteristicFlat - Slow Bc > Bs ; Tc > TsFlat - Fast Bc > Bs ; Tc < TsFrequency Selective - Slow Bc < Bs ; Tc > TsFrequency Selective - Fast Bc < Bs ; Tc < Ts

Table 2.1: Small Scale Fading Types

will experience time selective channel, which means that the channel impulse

response changes within the symbol duration. Note that the two propagation

mechanisms, fast/slow and frequency flat/selective, are not mutually exclusive

which is shown in the table 2.1.

2.6 Multi-Carrier Transmission

Multicarrier systems, due to their high rate transmission and flexibility, have

received widespread interest for wireless applications [31]. The basic principle of

multi carrier transmission is the conversion of a high-rate serial data stream to

multiple parallel low-rate substreams. After a serial to parallel conversion each

substream is modulated onto a single sub-carrier. Decreasing the symbol rate

decreases the effects of delay spread and hence makes it less sensitive to ISI.

As mentioned earlier, one benefit with multi-carrier systems is their flexibility.

That is, a large contiguous block of spectrum is not required for high data

rate transmission. So data can be transmitted non-contiguously which makes

multi-carrier transmission an appropriate candidate for Cognitive Radio networks

(CRN). This report mainly focuses on the two multi-carrier techniques, OFDM

and MC-CDMA, for physical layer of cognitive radio systems.

2.6.1 OFDM

Using OFDM for wireless communication was first suggested by Cimini in 1985

[32], but it was in the early 1990s that advances in hardware for digital signal

processing made OFDM applicable for wireless systems [31]. OFDM splits the


Figure 2.2: OFDM signal spectrum [33]

information into M parallel streams, which are then transmitted by modulating

M distinct carriers. Symbol duration on each sub-carrier thus becomes larger by

a factor of M . Therefore, OFDM turns the frequency selective fading channel

into M flat channels. An OFDM signal spectrum is shown in Fig. 2.2. It is

observed that although there are spectral overlaps among sub-carriers, they do

not interfere with each other if the sub-carrier spacing is equal to the reciprocal

value of the OFDM symbol duration (i.e. 1/Ts). This way, each subcarrier will

be in spectral null of other carriers.

Fig. 2.3 shows the transmitter and receiver structure of an OFDM system.

The data is first passed through a modulator which gives M complex data

symbol stream, X[0], X[1], ..., X[M − 1] and is then serial to parallel converted.

The output will be M symbols each to be sent on a single subcarrier. These

symbols are discrete frequency components of the OFDM modulator. The time

domain signal will be obtained by performing IDFT on these M symbols. The

mathematical expression of the signal is

x[m] =1√M

M−1∑i=0

X[i]ej2πmi/M , 0 ≤ m ≤M − 1. (2.5)

The multiplication is identical to taking the IDFT of the signal. The size M


(a) OFDM Transmitter

(b) OFDM Receiver

Figure 2.3: OFDM with FFT/IFFT implementation [27]


square matrix of IDFT coefficients is given by matrix

M =

1 1 1 ... 1

1 ej2πM ej

2.2πM ... ej

(M−1)2πM

... ... ... ... ...

1 ej(M−1)2π

M ej2(M−1)2π

M ... ej(M−1)22π

M

.

IDFT, takes the frequency domain data to the time domain, by using the

computationally efficient FFT algorithm. Cyclic prefix (CP) is then added to

the OFDM signal for the purpose of a proper equalization at the receiver. For

each input sequence of length N , the last µ samples are appended at the beginning

of the sequence. Let Tm be the channel delay spread and Ts the sampling time. µ

samples (µ = Tm/Ts) should be appended to the beginning of the sequence. This

makes the linear convolution with channel impulse response to become a circular

convolution.

At the receiver side CP is first removed as they are affected by ISI. Serial to

parallel conversion is then applied followed by FFT which takes the time domain

signal back to the frequency domain. The DFT matrix can be shown as

M =

1 1 1 ... 1

1 e−j2πM e−j

2.2πM ... e−j

(M−1)2πM

... ... ... ... ...

1 e−j(M−1)2π

M e−j2(M−1)2π

M ... e−j(M−1)22π

M

.

Note that for an OFDM system, it is necessary that the bandwidth for each

subcarrier be smaller than the coherence bandwidth of the channel to ensure

that each subcarrier is going under flat fading. Another requirement is that the

symbol duration be less than the coherence time of the channel to avoid fast

fading.

OFDM without channel coding can not achieve frequency diversity [33].

Therefore, it is commonly accompanied with channel coding and interleaving,


referred to as coded OFDM.

2.6.2 Multi-Carrier CDMA

MC-CDMA is a combination of OFDM and DS-CDMA techniques presented in

[34]. There are three multicarrier schemes, namely MC-CDMA, MC-DS-CDMA,

and Multi-Tone ode Division Multiple Access (MT-CDMA) discussed in [35]. The

three schemes can be categorized into two main groups. In the first group the

spreading is applied in the frequency dimension i.e. each symbol spreads over

all subcarriers and each chip is mapped into a single sub-carrier; whereas in the

second group, symbols are first passed through serial to parallel converter and

each substream is then modulated to a single sub-carrier, meaning that spreading

is in time dimension.

MC-CDMA

In this technique, spreading sequences are applied in frequency dimension and

each chip is being mapped to an individual OFDM subcarrier. El-barbary and

Alneyadi in [36] have compared the DS-CDMA and MC-CDMA performance

with Minimum Mean Square Error (MMSE) and Maximal Ratio Combining

(MRC) detection schemes. It is shown that MMSE detection is more robust than

MRC. The MC-CDMA performance is further compared with that of DS-CDMA

system which shows that for the practical case of Rayleigh fading, MC-CDMA

outperforms DS-CDMA. The effect of delay and Doppler spreads is examined in

[37] and has been compared with OFDM system.

The block diagram of a multi-user MC-CDMA transmitter is shown in Fig.

2.4. In the figure, b(k) is data symbol of the k-th user utilizing the user’s unique

spreading code of length G. The total number of active users is shown by K

and the total available subcarriers is shown by M . With P being the number of

consecutive symbols to be sent by each user M = P × G i.e. the the spreading

factor is not necessarily equal to the user’s spreading factor. One advantage of


Figure 2.4: Block Diagram of a Multi-User MC-CDMA Transmitter

the scheme is that MC-CDMA can utilize the spectrum efficiently and can benefit

from frequency diversity by spreading the data on several narrow-band low-power

subcarriers [38].

MC DS-CDMA

In this scheme, data is first serial to parallel converted and spread in time

domain. Thus, the number of sub-streams is equal to the number of sub-carriers

available. The multiple time-spread streams are then modulated on separate

subcarriers. The block diagram of a multi-user MC-CDMA transmitter is shown

in Fig. 2.5. In contrast to MC-CDMA, in this scheme signal is demodulated

on each sub-carrier separately. Without using Forward Error Correction (FEC)

codes, MC DS-CDMA can not utilize frequency diversity as each subcarrier

is transmitting different substream. Besides, long codes can not be utilized

due to subcarrier separation limitaion. However, [38] and [39] have proposed

MC DS-CDMA that have larger subcarrier separation and transmits the same

data on multiple subcarriers. Therefore, the proposed systems have narrowband

interference suppression capability and better robustness to multipath fading.

Interference suppression capability of the proposed system in [39] is further

analysed in [40].

It is clear that all CDMA-based schemes are common in the sense that they all


Figure 2.5: Block Diagram of a Multi-User MC-DS-CDMA Transmitter


Figure 2.6: Block Diagram of a Multi-User MC-MT-CDMA Transmitter

have bandwidth more than the coherence bandwidth of channel. However, there

is a difference between the MC-CDMA technique and other wideband techniques,

DS-CDMA or MC DS-CDMA, in achieving frequency diversity [41]. The latter

systems can achieve frequency diversity by utilizing Rake receiver whereas the

inherent frequency diversity of MC-CDMA stems from the transmission of a

symbol on different subcarriers.

MT-CDMA

Multi-Tone CDMA, proposed by [42], is very similar to MC DS-CDMA3, but here

the time domain spreading is applied after the IFFT stage. The block diagram of

a multi-user MC-CDMA transmitter is shown in Fig. 2.6. The symbols are first

serial to parallel converted and modulated on separate subcarriers. Frequency

separation between subcarriers is selected such that the spectrum of each

3Some references, e.g. [31], refer to the scheme as a special case of MC DS-CDMA


subcarrier satisfies the orthogonality condition before spreading is performed.

However, the subcarrier orthogonality can not be maintained after spreading. In

this scheme, each subchannel is broadband and therefore more complex receivers

are required. The scheme uses longer codes than in MC DS-CDMA and so

can accommodate more number of users [31, 35, 43]. The capacity of the three

schemes are derived and compared in term of spectral efficiency in [44].

The three Multi-Carrier CDMA schemes were reviewed in this section. In

conclusion, the MC-CDMA scheme seems to be a promising technique to be

utilized in CRNs. Due to its inherent frequency diversity and subcarrier

orthogonality, MC-CDMA will be good candidate to combat PU interference

in CRNs. Its performance in CRNs will be discussed in Chapters (4-6).

2.7 Diversity Techniques

Diversity techniques are used to mitigate the effect of multipath fading channels

by receiving replicas of the independently faded signals. The most well-known

diversity techniques are time, frequency, and space diversity [45]. Time diversity

is achieved by transmitting the signal at different times, where the time difference

is more than the channel coherence time. Time diversity can also be achieved

by applying coding and interleaving [27]. Frequency diversity is achieved by

receiving the signal at different frequencies separated by more than the coherence

bandwidth of the channel so that the signal experiences independent channel

gains. Finally, by utilizing multiple transmit/receive antennas spaced sufficiently

far apart, space diversity will be achieved. It is worth mentioning that MC-CDMA

systems are capable of utilizing frequency diversity due to the fact that they have

bandwidth more than the coherent bandwidth of the channel. Frequency diversity

can be achieved by utilizing Rake receiver in case of MC DS-CDMA whereas

the inherent frequency diversity of MC-CDMA stems from the transmission of a

symbol on different subcarriers which was elaborated in Section 2.6.2.


Parameters Shortened W-ATMCarrier frequency 60 GHzSampling rate 225 MHzBpsk data rate 155 MbpsMax speed of mobile 50 Km/hMax delay 11 samplesRMS delay spread 15.3 nsCoherence bandwidth 65.4 MHzNo. of subcarriers 512No. of guard symbols 64

Table 2.2: Main system and channel parameters of a W-ATM system [43]

Upon receiving the signal, diversity combining schemes are needed to combine

the replicas of the received signal. The three main combining schemes are

Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio

Combining (MRC), among which MRC maximizes the received SNR [26, 27]. In

general, SC selects the observation with highest SNR. EGC, co-phases all the

received signals and adds them together. EGC can be better than SC when

SNRs of all branches are similar. On the other hand, when one branch has a

much larger SNR than the others, SC can have better result. However, MRC

multiplies each branch by the complex conjugate of the channel such that The

output SNR is equal to the sum of the individual SNRs. A detailed discussion

on diversity combining techniques is not covered here as it falls out of the scope

of this research.

In Table 2.2 and Fig. 2.7 the main parameters of Shortened W-ATM4

channel model and the impulse response are shown. The BER performance

of a synchronous MC-CDMA for downlink over W-ATM channel is shown in

Fig. 2.8 with MRC. For this specific channel, since we have three receiving

paths, the maximum diversity order achieved can be no more than 3. It is

observed that for spreading factor (SF=1), which is equal to not spreading,

4Wireless Asynchronous Transfer Mode channel is used here to compare the frequencyselective fading results with the results in the reference [43]. However, the ITU Pedestrian-B channels is used for the rest of this thesis.


0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time Delay ns

Mag

nitid

e

Figure 2.7: W-ATM Channel Impulse Response [43]

0 5 10 15 20 25 30 35 40 45 5010

−6

10−5

10−4

10−3

10−2

10−1

100

SNR

BE

R

SF=1SF=2SF=4SF=8Theoretical

L=2, Theory

L=1, Rayleigh

L=3, Theory

L=4, Theory

Figure 2.8: Synchronous MC-CDMA for downlink over W-ATM channel withMRC


the performance is identical to single-carrier in Rayleigh fading channel. As

the spreading factor increases, the diversity order increases and thus the BER

performance also improves. However, the system performance will not improve

when the spreading factor is more than 4. The theoretical single-user performance

of MRC with L-independent paths and BER is also shown in the figure using [30]:

Pb =

[1

2(1− µ)

]L L−1∑k=0

(L− 1 + k

k

)[1

2(1 + µ)

]k(2.6)

where L is the diversity order and µ is defined as

µ =

√γb

L+ γb. (2.7)

In the above definition, γb is the average energy per bit divided by the noise power

spectral density, N0. Note that channel energy is equal to bit energy over the

number of channels i.e. γc = γb/L. It is worth mentioning that the simulation

result for the case that all the channel taps have the same energy will be exactly

the same as in the theoretical result, which is due to the fact that the assumption

in deriving the above formula was channels with identical powers.

2.8 Equalization Techniques

Equalization is a signal processing technique used at the receiver to compensate

for ISI problem due to frequency selective fading channels [27]. Specifically, in

a CDMA-based system where signals are received with different amplitudes and

phase shifts at the receiver, orthogonality between codes are not maintained.

Thus, to reduce Multi Access Interference (MAI) caused by frequency selective

channel, the received signal should be equalized after FFT and deinterleavd at

the receiver. Frequency Domain Equalization (FDE) specially ZF and MMSE,

will be studied in this section due to the related work in the next chapters.

FDE is a convenient, low-complexity technique which is performed on a block


of data at a time [41]. It includes taking the M -point FFT of the received signal

followed by a type of channel inversion.

In time domain, the transmitted signal is convolved with the Channel Impulse

Response (CIR). Therefore, the received signal will be

y = h ∗ x+ n (2.8)

where ∗ denotes the convolution operation. h and x are the time domain CIR

and transmitted signal respectively, and n is the Gaussian noise. Upon receiving

the signal, CP removal and taking the FFT of y we obtain

y = Hx + n (2.9)

where y, H, x and n are the frequency domain of y, h, x, and n respectively. The

dimensions of y, x and n are M × 1, and H is M ×M diagonal matrix. The i-th

frequency-bin in (2.9) is

y[i] = H[i, i]x[i] + n[i] (2.10)

where H[i, i] is the i-th diagonal element of the channel matrix. Note that CP

insertion, explained in Section 2.6.1, makes the linear convolution with Channel

Impulse Response (CIR) circular. Therefore, the channel matrix H will be

diagonal after the CP insertion. y[i] will be equalized by a filter coefficient

w[i] which depends upon the linear equalization criterion. The signal after

equalization can be expressed as

x′[i] = w[i]y[i]. (2.11)

Taking the IFFT of the equalized signal, the original signal is then detected.


2.8.1 Zero Forcing Equalizer

This technique forces the ISI term to zero at sampling instants by applying the

inverse of the CIR. The equalizers coefficient for the case of OFDM will be

w[i] =1

H[i, i]. (2.12)

Note that H is the frequency domain of the channel. Although this technique

cancels all the interference, it suffers from noise enhancement properties. This

happens at the frequencies with high channel attenuation and the reason is that

noise has been neglected in the equalization process [26, 27].

2.8.2 Minimum Mean-Square Error Equalizer

Minimum Mean-Square Error (MMSE) Equalizer minimizes the mean squared

error between the transmitted symbol and the detected symbol at the output of

the equalizer [27]. MMSE criterion is

w[i] = arg minw[i]

E[|x[i]− x[i]|2]. (2.13)

Substituting x[i] from (2.11) into the above objective function

J = E[|x[i]−w[i]y[i]|2]

= E[|x[i]−w[i](H[i, i]x[i] + n[i])|2]. (2.14)

Solving the above equation for minimum value of w[i], taking the derivative with

respect to w[i] and set it to zero, we will have

w[i] = H∗[i, i](H[i, i]H∗[i, i] +N0/Ex)−1 (2.15)

where E[nn∗] = N0 and E[xx∗] = Ex. Taking into account the noise power,

MMSE provides a balance between interference mitigation and noise enhancement


[27]. This is why MMSE has a better performance in low SNR levels, whereas in

high SNR levels ZF and MMSE will have similar performance.

2.8.3 Chip and Symbol Level Equalization for MC-

CDMA System

The idea of considering other users’ codes for detection of the desired user in a

CDMA-based system is proposed by S. Verdu [46]. Similar concept can be applied

to an MC-CDMA system. For an MC-CDMA system, MMSE criterion mentioned

in Section 2.8.2, can be applied on each subcarrier or each symbol. The former is

performed before despreading and independently on each subcarrier. This method

which does not need other users’ signatures is called chip-level equalization.

The latter considers equalization and despreading jointly. Clearly, symbol-level

equalization will have better performance than chip-level while chip-level is easier

to implement. Chip and symbol-level equalization for MC-CDMA systems is

presented in [34, 47, 48, 49, 50, 51, 52]. Authors in [52] have proposed a linear

equalization for a downlink Multi-code MC-CDMA outperforming the chip-level

equalization with similar complexity as symbol-level while it does not require the

other users signatures.

2.9 Basics of Convex Optimization

In this section, some basics of convex optimization is presented for its applications

in wireless communications and especially in this thesis for capacity maximization

in CR systems.

Optimization problems are classified based on the form of their objective and

constraint functions [53]. A convex problem is a problem in which the objective

and constraint functions are convex and satisfies the inequality

fi(αx+ βy) ≤ αfi(x) + βfi(y) (2.16)


for all x and y ∈ Rn and all α and β ∈ R with α + β = 1, α ≥ 0, β ≥ 0. For

twice differentiable f with convex domain, f is convex if and only if:

∇2f(x) � 0 for all x ∈ dom f (2.17)

Note that Hessian: ∇2f(x)ij = ∂2f(x)∂xi∂xj

i, j = 1, ..., n. Clearly, if f is convex

then −f is concave.

Some frequently used convex functions are: Negative entropy (xlog(x) on

R++), all norms ‖x‖p =

(n∑i=1

|xi|p)1/p

for p ≥ 1 (where p = 2 represents Euclidean

norm) and logo-sum-exp (logn∑k=1

exp xk).

In general, there are methods to prove if a function is convex:

1. Using the definition in Eq. (2.16)

2. For twice differentiable functions show that ∇2f(x) � 0

3. Show that f is derived from simple convex functions by operations

that preserve convexity. Some operations that preserve convexity are:

Non negative weighted sum, composition with affine function, point wise

maximum and supermum, composition and minimization. More elaboration

on these operations is omitted here for brevity.

Standard form optimization problem with objective function, inequality and

equality constraint functions is in the form P1:

Minimize f0(x) (2.18)

subject to fi(x) ≤ 0, i = 1, ...,m (2.19)

hi(x) = 0, i = 1, ...,m. (2.20)

In the standard form problem, the right-hand side of the inequality and equality

constraints are adapted to zero. For the problem, p∗ is the optimal value and is


equal to:

p∗ = inf {f0(x)|fi(x) ≤ 0, i = 1, ...,m, hi(x) = 0, i = 1, ..., p}. (2.21)

For a standard optimization problem P1, which is not assumed to be convex,

Lagrangian is defined as:

L(x, λ, ν) = f0(x) +m∑i=1

λifi(x) +

p∑i=1

νihi(x) (2.22)

in which λi and νi are Lagrange multipliers associated to inequality and equality

constraints respectively.

Accordingly, the Lagrange dual function is the minimum value of the

Lagrangian over x:

g(λ, ν) = inf L(x, λ, ν) = inf

(f0(x) +

m∑i=1

λifi(x) +

p∑i=1

νihi(x)

). (2.23)

Note that the dual function is concave even if the original problem is not convex.

This is due to the fact that the dual function is the pointwise infimum of an affine

function of λ and ν.

The dual function gives a lower bound on the optimal value p∗ for the problem

in P1, i.e. for any positive vectors λ and ν:

g(λ, ν) ≤ p∗. (2.24)

Thus, the lower bound depends on the parameters λ and ν. The best lower

bound that can be obtained from the Lagrangian dual function is attained from

the Lagrange dual problem:

Maximize g(λ, ν) (2.25)

subject to λ � 0. (2.26)


The original problem in P1 is called the primal problem. Dual problem is a convex

optimization problem whether or not the primal problem is convex.

The optimal value of the Lagrange dual problem, d∗, is the best lower bound

on p∗ that can be obtained from the Lagrange dual function. Note that any dual

feasible point is a lower bound on p∗. Therefore, the best one is also a lower

bound. The weak duality inequality defined as:

d∗ ≤ p∗ (2.27)

holds even if the original problem is not convex.

The difference d∗−p∗ is called the optimal duality gap of the original problem

which gives the gap between the optimal value of the problem and the greatest

lower bound on it that can be obtained from the Lagrange dual function. If

d∗ = p∗, the optimal duality gap is zero and strong duality holds, i.e. the best

bound obtained from the Lagrange dual function is tight and therefore, primal

optimal and dual optimal are equal. If Slater’s constraint holds for a convex

problem, it guarantees strong duality.

For affine inequality constrained convex problems the Slater’s condition

reduces to feasibility. Moreover, for a convex problem the Slater’s constraint

guarantees strong duality.

For a convex problem, KKT(Karush Kuhn Tucker) conditions are sufficient

for the points x, λ, ν to be primal and dual optimal with zero duality gap. The


KKT conditions are:

fi(x) ≤ 0, i = 1, ...,m (2.28)

hi(x) = 0, i = 1, ..., p (2.29)

λi ≥ 0 i = 1, ...,m (2.30)

λifi(x) = 0, i = 1, ...,m (2.31)

∇f0(x) +m∑i=1

λi∇fi(x) +

p∑i=1

νi∇hi(x) = 0 (2.32)

where 2.28 and 2.29 state the primal feasibility, and 2.30 states the dual feasibility.

The condition in 2.31 is complementary slakness and finally, stationarity, states

that the gradient of Lagrangian with respect to x vanishes.

To solve a convex optimization problem, there are different algorithms to solve

different classes of convex optimization problems that set a form of hierarchy. The

hierarchy includes unconstrained, equality constrained and inequality constrained

optimization problems. The hierarchy means the problem is being solved by

a set of easier problems. Quadratic optimization problems form the base of

the hierarchy that can be solved by a set of linear equations. Next level is

Newtons method that reduces equality constrained problems to a sequence of

quadratic problems. The topmost level in the hierarchy is interior-point method

which solves an inequality constrained problem by solving a sequence of equality

constrained or unconstrained problems.

2.10 Key Assumptions

To make the general overview of the assumptions and the system model, the

general assumptions of this work are explained in this section. However, more

detailed explanation is also presented in the system model section in each chapter

and also for the specific equations when required.


Throughout this work, the spectrum sensing is assumed to be perfect and

known at the CR transmitter. In other words, the available and unavailable

parts of the spectrum are detected by the spectrum sensing unit and sent to the

CR transmitter. Besides, the average PU interference level on each secondary

sub-band is assumed to be known at the CR receiver.

Another assumption considered is that the interference leakage from the

adjacent PU bands to the overlay bands, and from overlay bands to PU bands is

neglected, as it is small in practice [54, 55]. Furthermore, Cyclic prefix length is

chosen such that it is longer than the maximum delay spread of the channel.

2.11 Summary

In this chapter, relevant background theories of wireless communications are

presented. Large-scale propagation including path loss and shadowing are first

discussed. Next, small-scale propagation including flat and frequency-selective

fading, fast and slow fading is summarized. Multi-carrier transmission techniques,

namely OFDM and MC-CDMA, and the respective transmitter and receiver

structures are presented. The three types of MC-CDMA transmission are briefly

explained and the transmitter structure of a multi-user MC-CDMA is shown

which will be required in the following chapters. Diversity techniques and

frequency domain equalization is briefly discussed. Finally, basics of convex

optimization are presented.

Chapter 3

Cognitive Radio

3.1 Introduction

In recent years there has been an increasing demand for wireless high data

rate services. With the limitations of today’s spectrum utilization and Static

Frequency Allocation (SFA) schemes the high demand for such services cannot

be achieved. There has been a report published by Federal communication

commission (FCC) in 2002 [20], in order to improve the spectrum management

in the United States as a valuable resource, which states that the problem in

electromagnetic radio spectrum usage is more with spectrum access rather than

physical scarcity of the spectrum. According to the report some parts of the

spectrum is largely occupied, some is only partially occupied and the rest is

heavily occupied which means that the spectrum utilization ranges from 15 to 85

percentage only. The inefficient usage of the spectrum makes us think in terms

of utilizing the spectrum dynamically. With this regard, in Section 3.2 Dynamic

Spectrum Access (DSA) regulatory status will be studied. Cognitive Radio (CR),

an example of vertical spectrum sharing technique, and its main functionalities is

reviewed in Section 3.3. Underlay transmission and interference threshold concept

is discussed in Section 3.4. Non-Contiguous (NC) transmission for overlay and

underlay are presented in Section 3.5. Next, the hybrid transmission concept

55

CHAPTER 3. COGNITIVE RADIO 56

Figure 3.1: Dynamic Spectrum Access classifications [56]

is explained in Section 3.6 and the hybrid system capacity is compared with

overlay or underlay transmission on their own. Lastly, a summary of the chapter

is presented in Section 3.7.

3.2 Dynamic Spectrum Access

As mentioned in the previous section 3.1, DSA , as opposed to SFA, aims to

efficiently utilize the spectrum by means of adaptive spectrum management.

In terms of regulatory status DSA focuses on two main approaches, dynamic

licensing and Dynamic Spectrum Sharing (DSS) [56]. The DSA classification

along regulatory is shown in Fig. 3.1. Dynamic licensing gives the exclusive

use to the original owner of the band. It is similar to the DSF but much more

flexible. The spectrum can be sold by the licensed user or adapted dynamically

with regards to the variations of the wireless communication scene. The former is

called spectrum property rights while the latter is dynamic spectrum allocation.


Figure 3.2: Horizontal and vertical spectrum sharing regulatory concept [57]

Whilst dynamic licensing is still limited due to the exclusive rights of the

licensees, dynamic sharing is based on the coexistence of the networks. DSS is

expected to be more spectrally efficient and also more adaptive to dynamics in

wireless communication systems. The spectrum sharing licenses the spectrum

to networks simultaneously while spectrum sharing techniques are adapted to

prevent conflicts. The spectrum sharing, or coexistence, can be applied in two

scenarios, horizontal or vertical, which is shown in Fig. 3.2.

3.2.1 Horizontal Spectrum Sharing

In horizontal spectrum sharing, networks have similar regulatory priorities. That

is why the model is sometimes referred to as open sharing model or spectrum

commons [56]. Medium access protocols are an example for such sharing schemes.

Another example for horizontal spectrum sharing is when dissimilar CRNs, run

by different oparators, use the spectrum. These operators have similar rights to

access the spectrum. Coexistence of the devices in unlicensed spectrum is another

example for horizontal spectrum sharing.


3.2.2 Vertical Spectrum Sharing

In vertical spectrum sharing, a Primary User (PU) exists which is the only licensee

of the spectrum while Secondary User (SU) can opportunistically access the

spectrum provided that it does not affect the PU’s performance. In cognitive

radio networks, proposed by [8], the spectrum sharing approach is considered

to be vertical as it assumes the existence of PU and SUs. In cognitive radio

terminology, primary users are users that have the priority to use a specific

part of the spectrum. On the other hand, secondary or cognitive users are

the users with lower priority and have to use the spectrum in an opportunistic

manner in the way that does not interfere with the primary users. Therefore,

the secondary users need to have cognitive radio capabilities such as sensing

the spectrum to check whether it is being used by the primary user or find the

spectrum holes to exploit the unused part of the spectrum [58]. Opportunistic

spectrum access whenever and wherever the spectrum is not being used by the

primary user via spectrum holes or so called white spaces is referred to as overlay

spectrum sharing [10]. Overlay spectrum sharing requires new protocols and

algorithms for spectrum sharing. However, the spectrum can also be exploited

using underlay approach which means the secondary users can transmit with

the same bandwidth as the primary users as long as their transmission power

do not exceed the interference threshold limit at the primary receiver. Underlay

approach brings about another transmission dimension, namely power dimension,

in addition to the other conventional dimensions frequency, time and space [58].

These parts of the spectra are called grey spaces which are partially occupied

by low-power interferers. Due to their low transmission power, wideband signals

enable underlay spectrum sharing. Power dimension is also called code dimension

due to the fact that the implementation of underlay is via spread spectrum signals

that use random code for generating high frequency signals [6, 21, 56, 57, 58, 59].

More elaboration on overlay and underlay approaches will be considered in Section

3.4.


3.3 CR Definition and Main Functions

There have been many definitions for the cognitive radio in the literature.

Between all, there is an agreement for its basic functionalities [59] which includes

awareness of the environment and ability to adapt and reconfigure. In fact,

cognitive radio is an intelligent wireless communication technique that is aware

of the environment which can learn and adapt its internal states by changing the

parameters which makes it reliable and efficient for today’s wireless applications.

The platform for such reconfigurable radio, as opposed to the conventional

communication systems that were designed with specific parameters, is Software

Defined Radio (SDR) [21] and [60].

Software defined radios [8] are flexible radios which are able to reconfigure

and adapt the air interface with their communication protocols. Such versatile

systems which allow multiple systems to run on a single reconfigurable hardware

can adapt its properties such as modulation type, bandwidth usage and carrier

frequency to the air interfaced network. The modern SDRs can also implement

other necessary operations such as cryptography, forward error correcting and

source coding by means of software [56], [60] and [61].

The main functions for cognitive radio can be summarized as spectrum

sensing, spectrum management, spectrum sharing and spectrum mobility. First

and foremost, cognitive radio equipments should sense the spectrum to determine

which portions of the spectrum are vacant -known as spectrum sensing. Selecting

the best available channel that meets the requirements of the communication

user is spectrum management. Salami et al. [59] have compared centralized

and distributed approaches for spectrum management. Coordinating access to

other users with a fair scheduling is another function as spectrum sharing. Lastly,

during the transition to a better channel or due to the presence of the primary user

the Quality Of Service (QOS) should be maintained which is known as spectrum

mobility [6] and [7]. Due to the crucial role of the spectrum sensing in CRNs, we

will briefly discuss the spectrum sensing concept and challenges.


Spectrum Sensing

Spectrum sensing is considered to be the first step and the most important

component for cognitive radio to get to know about the geographical location

of primary users and the spectrum holes. Conventional sensing methods consider

only three dimensions for sensing which are frequency, time and space. However,

there are other dimensions for the opportunistic use of cognitive radio equipments

such as power [59] and angle dimension. All these new dimensions bring

about new opportunistic access. Radio equipments can use this hyperspace

for transmission and share the environment. On the other hand they make

spectrum sensing more complicated and bring about new challenges for spectrum

sensing [58]. Detecting primary users using spread spectrum signals, is one of the

challenges for cognitive radio spectrum sensing since the power is distributed in

wide range of frequencies. Hidden primary user is another challenging topic in

spectrum sensing. Hidden primary user occurs when secondary user cannot detect

primary user due to severe fading or shadowing and as a result causes interference

when sending in primary user’s frequency range. Cooperative spectrum sensing

is proposed to manage hidden primary user problem [7, 58, 62]. Sensing duration

and frequency are two challenging parameters which should be defined in cognitive

radio spectrum sensing. Sensing duration is the sensing period of time and there

is a trade off between sensing time and accuracy. Sensing frequency is how

frequently the spectrum is being sensed which depends on the frequency band

in use and its interference tolerance level.

3.4 Underlay Transmission and the Interference

Threshold

Underlay is signal with low power spectral density and strict interference concerns.

There has been a long regulatory history for underlay transmission since 1938

when FCC allowed the use of certain low-power remote controls for radio receivers


Figure 3.3: Underlay spectrum opportunity and the interference thresholdconcept [63]

[4]. It was for limited applications and only several narrow-bands. Figure 3.3

shows the spectrum opportunity for underlay transmission. From 1985 underlay

was still limited to Industrial, Scientific, and Medical (ISM) bands till in 1989 the

general rewrite of the unlicensed bands permitted underlay transmission to most

bands, but the ”restricted bands”, up to certain level. In 1998 with the progress

in Ultra-Wide Band (UWB) technology underlay was examined but it had been

the area of dispute over time concerning the noise floor increase and seriously

affecting the licensee’s [10]. Following the spectrum access issues, a Spectrum

Policy Task Force was established in June 2002 to decide on the spectrum policy

changes. The report showed that the problem is with the limitations due to

the static frequency allocation than the physical scarcity of the spectrum. The

report released that some parts of the spectrum were heavily used while some

were used only in specific geographical areas or certain times [4]. Therefore, it

was a necessity to shift from static to Dynamic Spectrum Allocation (DSA) in

order to efficiently utilize the spectrum as a valuable resource. With this regard,

Cognitive Radio (CR) by Mitola [5] seemed to be a promising solution to add

flexibility to spectrum utilization with respecting the licensee’s, Primary User’s

(PUs), concerns.


There has been a shift from the conventional transmitter-centric model by

FCC Spectrum Policy Task Force [20] in 2002. The new model introduces

interference threshold at the receiver side where interference takes place rather

than interference being controlled at a certain distance from the transmitter

[21]. This is to ensure that the CR system will not harm the licensees

performance. With the new model, the cognitive radio receiver estimates the

interference threshold and detects the spectrum holes. The receiver also estimates

the channel-state information and predicts the channel capacity. Then, the

information is forwarded to the transmitter through feedback channel. This

real time interaction between transmitter and receiver helps the transmitter to

actively perform the transmit-power control and dynamic spectrum management.

Adaptive beamforming could also be performed by both the transmitter and

receiver to avoid interference, [21], [63].

As mentioned earlier in section 3.2.2, there are two main spectrum access

mechanisms in CR networks: overlay and underlay. Overlay utilizes the spectrum

holes and vacates the spectrum on PU re-occupancy while underlay can utilize the

spectrum at any time with considering the interference limit of the PU. This is to

ensure that the CR system will not harm the licensee’s performance. Therefore

in CR systems, underlay transmission is more challenging as utilizing the same

spectra as PU may cause high interference to the CR user and hence considerably

degrade its performance. Thus, a major issue in underlay spectrum utilization is

interference mitigation.

There are two fundamental advantages of spread spectrum systems to be

utilized in underlay CR. The first advantage, stems from low power density in

a certain band due to spreading. Secondly, spread-spectrum systems have the

capability to mitigate high interference levels [20]. While the most prominent

reports and references agree on utilizing spread-spectrum-based schemes for

underlay for their interference suppression capabilities [6, 20], there is a missing

link on how to achieve such interference suppression when all the bandwidth is


Figure 3.4: Frequency spectra of NC-OFDM subcarriers [56]

either occupied by PU or the overlay SU. The main purpose of this work is to

address this issue.

3.5 Non-Contiguous (NC) Transmission

Multi-Carrier Modulation (MCM)-based transmission techniques are suitable for

CR systems due to their flexibility. They can exploit non-contiguous parts

of the spectrum for high data rate transmission [25]. Since in CRN the

available subcarriers vary with time depending on the PU activity, non contiguous

transmission capability is vital for CR systems to make efficient use of the

available spectrum opportunities [27, 56]. The hardware implementation of

NC-OFDM is proposed in [64]. Other multi-carrier techniques and a combination

of multiple-access techniques, known as hybrid techniques, are also available in

the literature. Different schemes suit special scenarios 1 [27].

Subcarrier deactivation or nulling2, is one method to avoid interfering with

the subcarriers being utilized by PU. Subcarrier deactivation is shown in Fig. 3.4.

Authors in [65] have claimed that BER performance of an MC-CDMA system

degrades with increasing number of deactivated subcarriers due to the loss of

1The term ”hybrid techniques” used here is different from the concept of the hybridoverlay/underlay systems proposed for CR systems. However, in the proposed systems thehybrid multi-carrier techniques have been utilized.

2No data is being transmitted through the deactivated subcarriers


orthogonality between the spreading codes while this is not the case for an OFDM

system. However, by subcarrier mapping instead of subcarrier deactivation the

issue can be resolved. By subcarrier mapping, the orthogonality between users

in NC-MC-CDMA systems is maintained while NC-MC-CDMA benefits from

achieving diversity when OFDM has not such capability. The only issue with

NC-MC-CDMA is that the length of the spreading code and hence the number

of users is limited depending the type of code being used. However, the issue

can be resolved by utilizing Carrier Interferometry (CI) codes [66]. Another

way to address the issue is utilizing the whole available spectrum for underlay

transmission while maintaining orthogonality with overlay users. The scheme is

more elaborated in Chapters 4 and 5.

3.5.1 Overlay Multi-User NC-MC-CDMA

NC-MC-CDMA can be utilized for overlay CRN, i.e. transmitting

non-contiguously in the available parts of the spectrum updated from the

spectrum sensing unit. One benefit with utilizing MC-CDMA instead of OFDM

is achieving frequency diversity in fading channels. In this section, BER

performance of multi-user NC-MC-CDMA is shown for both AWGN and fading

channels.

Fig. 3.5 compares theoretical and simulation BER performance of a multi-user

NC-MC-CDMA system in AWGN. Perfect synchronization between primary and

secondary user is assumed. The total number of subcarriers is considered to

be 512. Each primary user occupies 32 consecutive subcarriers. It is further

assumed that there are two Primary Users (Kpu = 2) utilizing the spectrum

(i.e. Mpu = 64). There are 4 cognitive users in the system, utilizing WH

codes of length 4. BPSK modulation is considered. As there are 2 PUs in the

system, CUs will be utilizing the remaining spectrum through the 3 available

holes. Since perfect synchronization is assumed and also there is no fading,

MAI does not occur between users and the performance of the system will not


0 2 4 6 8 1010

−6

10−5

10−4

10−3

10−2

10−1

Eb/No

BE

R

Theory

Simulation

Figure 3.5: Overlay Multi-User NC-MC-CDMA in AWGN

degraded. Therefore, the performance of an NC-MC-CDMA in AWGN will be

similar to that of MC-CDMA. Note that the theoretical BER is achieved through

Pb = Q(√

2EbN0

)[30].

Fig. (3.6) shows the BER performance of overlay NC-MC-CDMA in fading

channels. The fading channel is simulated as in [24]. The secondary user’s

performance is analysed as SU’s data spreads, while the primary user’s bandwidth

remains constant. It is observed that underlay performance improves as SU’s data

spectrally spreads from 32 to 128.

3.5.2 Underlay NC-MC-CDMA

In this section, BER performance of a synchronized underlay NC-MC-CDMA

is examined in AWGN channels. AWGN is considered for several reasons.

Firstly, the assumptions and results from this section will lay the foundation

for the rest of this work in the following chapters. Therefore, to examine

the validity of the assumptions, AWGN channel is firstly considered and the


0 1 2 3 4 5 6 7 810

−4

10−3

10−2

10−1

Eb/No

BE

R

M=32

M=64

M=128

Figure 3.6: Overlay NC-MC-CDMA in fading channel with different spreadingand MMSE-FDE

theoretical and simulation results are compared. Moreover, we know that

Gaussian approximation is valid for pure Gaussian noise [30]. However, since

underlay is transmitting within the PU band, the system will encounter PU

interference as well as noise. Yet, the Gaussian approximation is valid since

PU signal and noise are independent. This will be shown in the following.

For the simulation part, the BPSK modulation is considered with

Walsh-Hadamard codes for the underlay MC-CDMA. Assuming underlay to be

utilizing NC-MC-CDMA, the bit error rate performance of the system for the

k-th underlay secondary user’s SINR can be written as [25]

SINR =MEbk∑Kpu

kpu=1 MkpuEbkpu +M N0

2

(3.1)

where Mkpu is the number of subcarriers occupied by the kpu-th primary user and

Ebkpu is the bit energy of the kpu-th primary user. Ebk showing the k-th secondary


user’s bit energy, the underlay BER performance will be

P (e) = Q

(√MEbk∑Kpu

kpu=1MkpuEbkpu +M N0

2

). (3.2)

Note that Gaussian approximation 3 is considered for the PU interference level

on each secondary sub-band. Assuming all the primary users to have the same

bit energy, the BER reduces to:

P (e) = Q

(√2Ebk

2MpuEbpM

+N0

)(3.3)

where Mpu =∑Kpu

kpu=1Mkpu , is the total number of subcarriers occupied by all

primary users.

Utilizing underlay waveform, there will be mutual interference between

the primary and secondary user. To analyse the underlay cognitive radio

performance, two scenarios have been considered. In both scenarios, the primary

user is utilizing OFDM-BPSK modulation and as interference to the cognitive

user. The secondary user transmits with much lower power relative to the primary

user. In the first scenario, the primary user is using 32 contiguous sub-carriers,

i.e. Mpu = 32. The underlay waveform is modelled as MC-CDMA with BPSK

modulation. The secondary user’s performance is analysed as SU’s data spreads,

while the primary user’s bandwidth remains constant. As shown in Fig. 3.7,

underlay performance improves as it spectrally spreads from 32 to 1024. Relative

secondary to primary user is considered to be -30 dB.

In the second scenario, underlay performance is analysed with the change in

the portion of the bandwidth occupied by the primary users. The spread length

for the underlay is fixed to 512 subcarriers while the PU occupancy is increasing

from 32 to 256. The relative underlay to PU power is −20 dB, assuming all

PUs to be transmitting with equal power levels. The solid lines in Fig. 3.8

3The approximation is valid for pure Gaussian noise . However, since the PU signal andthermal noise are independent, the assumption will be still valid for (3.2).


0 1 2 3 4 5 6 7 810

−4

10−3

10−2

10−1

100

Eb/No

BE

R

Simulation

Theory

Baseline

M=32

M=256

M=1024

M=512

Figure 3.7: Theoretical vs simulation underlay performance with differentspreading in AWGN (SU to PU relative power −30 dB)

show the theoretical from Eq. (3.3), and the cross presents the simulation results

for different PU occupancy levels. It is clear that as the number of primary

users increases, performance degrades due to interference increment from the PU

system.

3.6 Overlay/Underlay/Hybrid Capacity

Comparison

The two main spectrum access mechanisms in CRNs, overlay and underlay, were

discussed in Section 3.4. Hybrid systems aim to merge overlay and underlay

systems as a whole, to increase CR spectral efficiency. In the recent years, Overlay

and underlay have been widely investigated in the literature; [14, 17, 18, 19, 67]

for overlay and [11, 13, 68, 69, 70] for underlay, to name a few. However, only a

few have considered the hybrid case of overlay/underlay as an integrated system


0 1 2 3 4 5 6 7 810

−4

10−3

10−2

10−1

Eb/No

BE

R

Simulation

Theory

Baseline

Mpu= 256, 128, 64, 32

Figure 3.8: Theoretical vs simulation underlay performance with different PUoccupancy levels in AWGN (SU to PU relative power −20 dB)

to fully utilize the available spectrum [23, 24, 25].

In this section, the maximum achievable capacity of hybrid systems is

compared with overlay or underlay being solely utilized, using Shannon’s well

known capacity formula [27, 71]:

C = Blog2(1 + SNR) (3.4)

where SNR is the signal to noise ratio and C is the capacity in bits per sec

(bits/sec). AWGN environment is considered first. It has been assumed that

there are a total number of 4096 sub-carriers each having bandwidth of 10KHz.

The whole spectrum is divided to NB sub-bands each having 64 sub-carriers.

Each subband which is not being used by PU, will be utilized by overlay cognitive

system. Underlay CR is assumed to be transmitting through occupied parts of

the spectrum non-contiguously, with respect to the PU interference threshold.

Overlay and underlay are both using MC-CDMA.


Fig. 3.9 compares the overlay, underlay and hybrid MC-CDMA capacities

versus underlay SNR. The hybrid system considered is a mixed OFDM and

MC-CDMA system proposed in [25] where overlay and underlay utilize OFDM

and MC-CDMA respectively. The PU occupancy is 50% of the total bandwidth.

Overlay signal power is assumed to be equal to the primary users’ signal power. In

Fig. 3.9a and 3.9b overlay to underlay signal power is 20dB and 15dB respectively.

The relative overlay to underlay power is maintained for different SNRs. It is

observed that the hybrid system improves the capacity. The result shown in Fig.

3.9 for an MC-CDMA system confirms the results from [23] for an OFDM system.

3.7 Summary

In this chapter the main concepts of cognitive radio systems and SDR, which is the

platform for cognitive radio, were discussed. Dynamic spectrum access techniques

were mentioned and the two main spectrum sharing techniques in CRNs, overlay

and underlay, were discussed. Then we focused on underlay transmission

challenges for CR systems and possible transmission techniques. Non-Contiguous

Multi-Carrier transmission techniques, especially NC-MC-CDMA, were discussed

to be used for overlay and underlay CRNs. Finally overlay, underlay and hybrid

capacities were compared using simulations. In the next chapters, we will propose

two hybrid transmission techniques using the NC-MC discussed in this chapter.


−10 −5 0 5 10 15 200

50

100

150

200

250

300

Underlay SNR in dB

Sys

tem

Cap

acity

(bi

ts/s

)

OverlayHybridUnderlay

(a) Relative overlay to underlay power is 20 dB

−10 −5 0 5 10 15 200

50

100

150

200

250

300

Underlay SNR in dB

Sys

tem

Cap

acity

(bi

ts/s

)

OverlayHybridUnderlay

(b) Relative overlay to underlay power is 15 dB

Figure 3.9: Capacity comparison of overlay, underlay and hybrid scenarios

Chapter 4

Full-Load Hybrid System

4.1 Introduction

In this chapter, a novel Full-load MC-CDMA system is proposed. Unlike the

existing approaches which consider the overlay and underlay separately, in this

work the CR system is considered as a whole. Underlay signal occupies the entire

bandwidth while overlay is utilizing the white parts of the spectrum. Orthogonal

Variable Spreading Factor (OVSF) codes are used to maintain the orthogonality

between overlay and underlay. By maintaining the orthogonality, the underlay

signal can minimize interference from the Primary Users (PUs) while overlay is

transmitting through spectrum holes to maximize data rate.

This chapter starts with a brief summary of the available hybrid systems

for cognitive radio in section 4.2. The system model and the assumptions for

the proposed full-load hybrid MC-CDMA system is explained in section 4.3.

Section 4.4.1 analyses the underlay CR user’s performance with Zero-Forcing

(ZF) equalizer. The instantaneous signal to interference plus noise ratio is also

derived for the case of ZF. The proposed Chip-Level (CL) and Symbol-Level (SL)

Minimum Mean Square Error (MMSE) equalizers are presented in sections 4.4.2

and 4.4.3 respectively and the corresponding SINR for the SL-MMSE is derived.

Finally, the simulations results are discussed in section 4.5.

72

CHAPTER 4. FULL-LOAD HYBRID SYSTEM 73

4.2 Hybrid Systems in the Literature

While overlay and underlay transmissions are excessively investigated in the

literature (e.g. [11, 12, 13, 14, 72]), there are few works on hybrid systems

[23, 24, 25]. Hybrid systems aim to merge overlay and underlay systems

as a whole, to fully utilize the available resources. An OFDMA-based joint

overlay and underlay spectrum access mechanism is proposed in [23] and the

subcarrier-and-power allocation problem maximizing CR user’s rate is studied.

A hybrid overlay/underlay transmission scheme was proposed for CR systems

in AWGN channels in [25]. While authors in [23] consider a spectrum mask of

OFDMA for the hybrid system, authors in [25] propose different transmission

schemes for overlay and underlay. Overlay carries OFDM modulated data

utilizing NC-OFDM, while underlay carries parity bits using NC-MC-CDMA

technique. The performance is also examined for fading channels in [24], assuming

the PU received interfering signal at secondary receiver to be passing thorough

AWGN channel. A disadvantage with the system is that by separating data and

parity bits, mostly linear block codes can be applied to the system. Thus, some

better error correction codes, such as Low Density Parity Check (LDPC) codes,

can not be used as they do not essensially separate data and parity bits. Hence,

the system can not gain much benefit from channel coding. On the other hand,

as underlay is utilizing the occupied parts of the spectrum, it will be sensitive

to the PU interference. In this chapter we proposed a new MC-CDMA hybrid

system to combat these issues.

4.3 Full-Load Hybrid System Model

Fig. 4.1 shows coexisting primary and secondary systems. Primary

OFDMA-based system has total bandwidth B which is divided into M

subcarriers. K cognitive users attempt to access the spectrum opportunistically

via the Cognitive Radio Network (CRN). The secondary transmitter to secondary


receiver’s channel is assumed to be known at the receiver side but not at the CR

transmitter.

Figure 4.1: Cognitive Radio System

It is assumed that the spectrum sensing is performed and the available bands

and the interference threshold for the occupied bands are known to the CRN.

The number of subcarriers occupied by the PU system is represented by Mpu

and the number of subcarriers to be used by the overlay CRN is shown by Msu.

The proposed hybrid MC-CDMA system model is shown in Fig. 4.2. Underlay

is utilizing the whole spectrum while overlay is transmitting non-contiguously

through the spectrum holes detected by the spectrum sensing unit. Subcarrier

availability for the CRN is shown by an M -element availability vector a, in which

ai ∈ {0, 1} with 1 indicating the i-th component to be available, and 0 not

available for the overlay.

Figure 4.2: Hybrid MC-CDMA system model


In this model, the number of cognitive users is equal to the overlay spreading

factor (i.e. K = G). The number of overlay users is K = G − 1 while one user

is transmitting through the entire bandwidth with respecting the interference

threshold of the PU. Spreading factor of G is used for overlay users to spread

the data symbols while the underlay user spreads across the entire spectrum with

code length M to better suppress PU interference and better exploit diversity

gain. P consecutive symbols are spread with the spreading factor G and are

sent in parallel by each overlay user, i.e. Msu = GP . The spread data of each

overlay user is obtained by multiplying the user’s symbols by its specific signature

sequence as

y[k] = b[k]⊗ c[k] (4.1)

where ⊗ denotes the Kronecker product and b[k] of size P × 1 is the k-th user’s

symbol vector. Code vector c[k], of size G×1, is the k-th user’s specific spreading

code in which the elements are normalized such that each code has unit energy.

The column vector y[k] is defined as

y[k] = [b1c1, . . . , b1cG, . . . , bP c1, . . . , bP cG, ]T ∈ CMsu×1. (4.2)

d ∈ CM×1 is the equivalent overlay signal y after respective subcarrier mapping

(according to the availability vector a) and summation over all G overlay users.

The underlay user’s data symbol is represented by b¯

and its M × 1 spreading

code is cK . The spread signal of the underlay user is

d¯

= b¯cK . (4.3)

The transmitted hybrid signal, dh ∈ CM×1, can be shown by

dh =√pcod +

√pcud¯

(4.4)

which is an M × 1 vector consisting of the summation of overlay and underlay


signals.√pco and

√pcu are the overlay and underlay signal energy per subcarrier

respectively. Note that underlay signal power (Pun) should be chosen considering

the PU’s interference threshold (Ith) . Let

Hss = diag[hss[1],hss[2], ...,hss[M ]] (4.5)

be the diagonal M ×M frequency domain complex channel from the secondary

transmitter to the secondary receiver, where hss[i] is the channel gain on the i-th

subcarrier. Note that hss is a vector of M elements bearing channel coefficients

on each subcarrier. Likewise,

Hps = diag[(1− a1)hps[1], (1− a2)hps[2], ..., (1− aM)hps[M ]] (4.6)

is the M ×M frequency domain complex channel from the primary transmitter

to the secondary receiver. Here, the unoccupied subcarriers will be set to zero by

the term (1−ai). Thus, the secondary user’s received signal on the i-th subcarrier

is reperesented as

r[i] = hss[i]dh[i] + hps[i]spu[i] + n[i] (4.7)

where

spu = [(1− a1)dpu[1], (1− a2)dpu[2], ..., (1− aM)dpu[M ]]T (4.8)

is an M by 1 data matrix of the PU. The SU’s received signal in vector form can

be expressed as

r = Hssdh + Hpsspu + n. (4.9)


4.4 Receiver

The receiver for the proposed Full-load model detects independently the overlay

and underlay users’ signals. In other words, overlay performance does not affect

underlay. Therefore, this model is preferable for the cases when the primary user’s

activity is high. Let us define Ch ∈ CM×K as the hybrid spreading code matrix

where the first to the k-th rows belong to the overlay users and the last row is

related to the underlay user which is of length M . Overlay spreading sequence is

assumed to be periodic with period G, i.e. ci+G,k = ci,k. Next, the respective PU

subcarriers of overlay users in Ch are set to zero.

Upon receiving the signal and removing cyclic prefix, Fast Fourier Transform

(FFT) is applied. Passing through an equalizer, the signal on the i-th subcarrier

can be shown be as

y[i] = w[i]r[i] = w[i]hss[i]dh[i] + w[i]hps[i]spu[i] + w[i]n[i] (4.10)

where w is the equalizer weight vector of size 1 by M , and w[i] is the equalizer’s

i-th coefficient. The underlay signal is then despread by multiplying with the

corresponding underlay spreading code and integrating over the symbol period T

which can be shown in time domain as

M∑i=1

1

T

T∫0

w[i]Ch[i,K]e−j2πfitr(t)dt. (4.11)

4.4.1 ZF Receiver

By multiplying the reciprocal of the channel, and despreading using the

orthogonal spreading codes, ZF equalizer forces the Multi-Access Interference

(MAI) component to zero. Therefore, the underlay decision variable consists of


the desired signal, PU interference and noise which can be shown as

zZFun = b¯

+M∑i=1

(1− ai)wZF [i]hps[i]Ch[i,K]spu[i]+M∑i=1

wZF [i]Ch[i,K]n[i] (4.12)

where Ch[i,K] is the underlay user’s i-th chip and wZF [i] is the reciprocal

of the SU transmitter to SU receiver’s channel on the i-th subcarrier, i.e.

wZF [i] = 1/hss[i]. Assuming the interference part to be Gaussian, the underlay

instantaneous SINR for ZF (γZFun ) can be written as

γZFun =Mpsu

N0

∑Mi=1 |wZF [i]|2 + ppu

∑Mpu

i=1 |wZF [i]hps[i]|2(4.13)

where ppu is the average PU symbol energy on each subcarrier. The total number

of subcarriers, M , appears in the numerator of the equation (4.13). This is due to

the fact that in the proposed system, underlay is utilzing the whole bandwidth.

The average underlay probability of error can be calculated using underlay signal

to interference plus noise ratio given in (4.13) by

BER =

∫ ∞0

Q(γ)fγ(γ)dγ (4.14)

where fγ(γ) is the joint pdf of γ which includes M +Mpu random variables. For

simplicity of notation, γZFun is shown by γ in (4.14). The underlay Full-Load BER

performance with ZF equalization is explored in Appendix A. However, the the

theoretical analysis did not lead to a closed form solution to the problem. Yet,

the numerical results will be shown in Section 4.5.

4.4.2 Chip-Level MMSE-Based Receiver

Chip-level equalization minimizes the mean square error between the transmitted

signal and the estimated signal of each subcarrier. The despreading process is

performed on each user’s signal afterwards. Therefore, equalization is performed

independently from despreading. It is a low-complexity single user detection


method. The MMSE criterion for an individual subcarrier is

arg minwCL[i]

E(wCL[i]r[i]− d¯

[i]|2)(wCL[i]r[i]− d¯

[i]|2)∗. (4.15)

Substituting (4.7) and (4.4) into the objective function (4.15) and differentiating

with respect to w∗CL we will have

E [(wCL[i]r[i]− d¯

[i])r∗[i]]

=E[(wCL[i]hss[i]dh + wCL[i]hps[i]spu[i] + wCL[i]n[i]− d¯

).

(d∗hhss[i]∗ + spu[i]

∗hps[i]∗ + n[i]∗)]. (4.16)

It is worth mentioning that since the expectation is not with respect to wCL,

taking the derivetive under the expectation sign will be correct. Setting the

derivative to zero to zero (i.e. dJdWCL

= 0), we will have

E[w[i]hss[i]d[i]d[i]∗hss[i]∗ + w[i]hss[i]d[i]d[i]∗hss[i]

∗ + w[i]hps[i]spu[i]spu[i]∗hps[i]

∗

+ wnn∗ − d[i]d[i]∗hss[i]∗] = 0. (4.17)

Rearranging the formula for w it can be easily shown that the MMSE-FDE on

the i-th underlay subcarrier can be written as

wCL[i] =h∗ss[i]

hss[i]h∗ss[i] +

N0

pcu+pcopcu

aihss[i]h∗ss[i] +

ppupcu

(1− ai)hps[i]h∗ps[i](4.18)

where pco and pcu are the overlay and underlay power per subcarrier respectively.

As mentioned earlier, it is assumed that there is no overlap for overlay and primary

user’s band, while the underlay is orthogonal to the overlay. As a result, the

conventional MMSE-FDE can be used for overlay signal detection which can be

found in the literature, (e.g. [27]). Hence, the overlay signal detection is not

analysed here.

After recombining the signal over all subcarriers across the whole bandwidth


B, the underlay signals’ decision variable with Chip-Level MMSE (CL-MMSE)

is

zCL−MMSEun =b

¯

M∑i=1

wCL[i]hss[i] +K−1∑k=1

β(k,K)b[d iGe, k]

+M∑i=1

{wCL[i]hps[i]Ch[i,K]spu[i] + wCL[i]Ch[i,K]n[i]} (4.19)

where β(k,K) =∑M

i=1 wCL[i]hss[i]Ch[i, k]Ch[i,K] and dle denotes smallest integer

not less than l. The first component contains the desired underlay signal. The

second term is the MAI from overlay users due to the residual interference from

MMSE equalization. The third term is the interference from PU, and the last

part is the noise component. In [73], the instantaneous MMSE filter output

is approximated by Gaussian distribution. On the other hand, it is shown

in 3.5.2 that the addition of the AWGN noise and the PU interference can

be approximated by Gaussian distribution. Therefore, the underlay noise plus

interference power can be approximated by Gaussian distribution as1 σ2Itot

=

σ2Ipu

+ σ2I

+ σ2In

. The variance of the AWGN corresponds to

σ2In =

N0

M

M∑i=1

|wCL[i]|2 (4.20)

The variance of the PU interference will be

σ2Ipu =

ppuM

M∑i=1

|wpu[i]hps[i]|2 (4.21)

where PU to SU channel coefficients are weighted by wpu

wpu[i] =(1− ai)h

∗ss[i]

N0

pcu+ hss[i]h

∗ss[i] +

ppupcu

hps[i]h∗ps[i]

. (4.22)

1Note that the variances are all conditional variances to channel coefficients (Hss and Hps)which is not shown here for notational simplicity


Note that the summation’s upper limit in (4.21) is M . However, the unoccupied

subcarriers are set to zero by the term (1−ai) in (4.22). The overlay interference

to the underlay variance is

σ2I = var[

K−1∑k=1

b[b iGc, k]

M∑i=1

wCL[i]hss[i]Ch[i, k]Ch[i,K]]

=P (K − 1)pso√

M.Gσ2wsuhss (4.23)

where pco is the overlay symbol power and

σ2wCLhss

= E[w2CLh2

ss]− E2[wCLhss] (4.24)

is the variance of the SU to SU channel coefficients

wsu[i] =aih

∗ss[i]

N0

pcu+ (1 +

pcopcu

)hss[i]h∗ss[i]

. (4.25)

In (4.25), the term ai will set the occupied subcarriers to zero.

4.4.3 Symbol-Level MMSE Based-Receiver

Symbol-level equalization considers equalization and despreading jointly and

hence minimizes the mean square error between the transmitted and estimated

symbol at the expense of higher complexity. The MMSE criterion for underlay

symbol is

minw

E[(z − b¯)(z − b

¯)H ] = min

wE[(wSLr− b

¯)(wSLr− b

¯)H ]. (4.26)


Substituting the received vector, r, from (4.9) into MMSE criterion above, bearing

in mind (4.3) and (4.4), and differentiating with respect to w∗SL we will have

E[(wSLr− b

¯)rH]

(4.27)

=E[(wSL(Hssdh + Hpsspu + n)− b)

(dHh HH

ss + sHpuHHps + nH

)](4.28)

=E[wHssdhd

Hh HH

ss + wHpsspusHpuH

Hps + wnnH − bdHh HH

ss

]= 0 (4.29)

Rearranging the formula, the optimal vector can be shown as2

wSL = PuncHhK

HHss.(HssChRdhC

Hh HH

ss + HpsRppHHps + Rnn)−1 (4.30)

where Rdh = E[dhdHh ] is a K×K diagonal matrix of the users’ symbol energy (i.e.

the last element is the underlay user’s symbol energy and the rest are overlay’s),

Rpp = E[spusHpu] and Rnn = E[nnH ] = N0IM . chK is the K-th code of the hybrid

code matrix Ch of size M by 1. The underlay signals’ decision variable with

SL-MMSE is

zSL−MMSEun = wSLr = wSLHsss + wSLHpsspu + wSLn (4.31)

which includes the desired signal and residual interference from overlay users, PU

interference, and noise respectively. SL considers the non-diagonal elements in the

equalization process while the chip-level ignores. This is why the MAI vanishes

with symbol-level detection and equalization. Assuming the MAI component to

be zero for symbol-level equalization, the underlay SINR can be written as

γSLun =pcuwSLHssH

Hssw

HSL

wSLHpsspusHpuHHpsw

HSL +N0wSLwH

SL

. (4.32)

Therefore with the proposed method, overlay will not have interference on

underlay and hence the PU interference will be suppressed by a factor of MMpu

.

2The optimal solotion can also be achieved through Wiener solution [48]


Relative delay (ns) 0 200 800 1200 2300 3700Average Power (dB) 0 -0.9 -4.9 -8.0 -7.8 -23.9

Table 4.1: ITU Pedestrian B channel PDP

4.5 Simulation Results

In this section, simulation results are presented. Simulations are performed using

Matlab. Chip duration and total available bandwidth are assumed to be 100 ns

and 10 MHz respectively. The channels between PU to SU and SU to SU are

modelled as ITU-Pedestrian B [74], for which the PDP is shown in Table 4.1.

It is assumed that there are 16 blocks of 32 subcarriers available, a total of 512

subcarriers. Each PU is using OFDMA and occupies 32 consecutive subcarriers.

The unused blocks can be utilized by overlay SU in blocks of 32 subcarriers while

undelay utilizes the entire spectrum with condisering PU’s interference limit. The

SU underlay power is assumed to be -20dB relative ot PU signal power, while it

is maintained below the PU interference threshold. Overlay is also transmitting

at the same power level as the PU. Overlay is transmitting non-contiguously in

unused spectrum while underlay is exploiting the whole spectrum.

In Fig. 4.3, the underlay BER performance of the proposed hybrid system

with ZF and CL MMSE equalizer for full-loaded system is shown. The baseline

error performance with no PU interference, denoted by ”No PU” in the figure,

for ZF and MMSE are plotted. There are in total 512 subcarriers available.

The SU underlay BER performance is shown for 2, 4, 8, 10, 12 and 14 primary

users, which conforms to 64, 128, 256, 320, 384, and 448 subcarriers of the total

bandwidth being occupied by PU system respectively. In each case, the rest of

the available bandwidth is utilized by overlay CR system. Clearly, the underlay

BER performance decreases with increasing number of subcarriers occupied by

the PU. Though there is an error floor for each case due to the PU interference,

the proposed CL MMSE exploiting 13% (64 of the total 512 subcarriers) of the

total bandwidth for overlay, still exhibits less error floor than ZF baseline. This


0 5 10 15 20 25

10−5

10−4

10−3

10−2

10−1

100

Underlay Eb/No

BE

R

Mpu=448Mpu=384Mpu=320Mpu=256Mpu=128Mpu=64No PU

ZF

Chip−level MMSE

Figure 4.3: Underlay performance of the proposed full-load hybrid system withZF and CL MMSE equalizers for different PU occupancy levels

shows that the proposed method can well exploit diversity gain and suppress the

PU interference with low complexity.

The ZF numerical results are also achieved thorough (4.13). Fig. 4.4 compares

the numerical and simulation results for different PU occupancy levels. Numerical

results are shown by solid, and simulation results are represented by dashed lines.

It is observed that the simulation results are matching the numerical results from

(4.13).

SL MMSE results are presented in Fig. 4.5 for different PU occupancy

levels. The SL results are compared with CL result shown by dashed lines.

It is observed that the symbol-level equalization results in a significant BER

performance improvement for all PU occupancy levels from 64 to 448 subcarriers.

For instance, symbol-level MMSE equalization at Mpu = 320 exploits diversity

gain such that it leads the CL performance for Mpu = 256 PU occupancy level.

Simulation results show that overlay users suffer no degradation from the underlay


0 5 10 15 20 25 3010

−4

10−3

10−2

10−1

100

Eb/No

BE

R

Mpu=480Mpu=352Mpu=256Mpu=128Mpu=32no PU interf.

Figure 4.4: Simulation and Numerical underlay BER performance comparison forZF. Dashed and solid lines represent simulation and numerical results respectively

users as they are orthogonal, which is not shown here for breviry.

Fig. 4.6 illustrates the number of overlay users against the BER performance

for underlay signal. The SNR is fixed at 15dB, and 128 subcarriers are occupied by

PU. The ZF results show that there is no performance degradation with increasing

number of overlay users. This shows that the orthogonality between overlay and

underlay signal is maintained with the proposed method. However, this is not

the case for CL MMSE as there is a slight degradation with increasing number

of overlay users. This is because in ZF, the channel gain is equalized to one

and so, the orthogonality of the spreading codes is maintained. As there is no

MAI, the performance is identical with different number of overlay users. On the

other hand, as MMSE results in residual interference, the code orthogonality is

lost and hence a small amount of MAI is present. Nevertheless, the performance

degradation is small. However, symbol-level MMSE results show that with taking

into account the equalization and despreading process jointly, the orthogonality


5 10 15 20 25

10−4

10−3

10−2

10−1

Underlay Eb/No

BE

R

Mpu=448Mpu=320Mpu=256Mpu=128Mpu=64No PU

Figure 4.5: Chip and symbol level MMSE comparison. Dashed and solid linesrepresent CL and SL MMSE performance respectively.

can be maintained.

Finally, the underlay NC-MC-CDMA [24], is compared with the proposed

system’s underlay performance. The two system’s performances are compared

for different occupancy levels and with ZF and MMSE equalizers in Fig. 4.7.

In each case, NC-MC-CDMA results are shown with dashed, and the proposed

system’s results are shown with solid lines. For all occupancy levels, and both

ZF and MMSE, the proposed system’s performance is showing better BER result

than the underlay NC-CM-CDMA. It is observed that the proposed system’s

performance for the worst case (i.e. Mpu = 480) is still better than the best case

for NC-MC-CDMA (i.e. Mpu = 512). Note that Mpu = 512 is the case when PU

is occupying all the bandwidth and the SU can transmit through the entire band

with considering interference threshold of PU.


5 10 15 20 25 30

10−5

10−4

10−3

10−2

10−1

100

Number of Users

BE

R

ZF

Chip−level MMSE

Symbol−level MMSE

Figure 4.6: Number of overlay users vs underlay BER performance for fixedSNR=15 dB with ZF, CL and SL MMSE. PU is assumed to be occupying 128subcarriers (25% of the whole bandwidth)

4.6 Summary

In this chapter, a full-load hybrid overlay/underlay model was proposed for

cognitive radio networks. In this model, underlay transmits through the entire

spectrum considering the PU interference threshold. The proposed integrated

MC-CDMA scheme maintains the orthogonality between overlay and underlay

using OVSF codes. Utilizing the whole spectrum for underlay transmission,

benefits underlay in higher diversity gain to compensate for the performance

degradation due to PU interference. Thus, it allows a better utilization of the

spectrum than when using only overlay transmission, and at the same time

preserves the orthogonality between the overlay and underlay.


0 5 10 15 20 25 30

10−5

10−4

10−3

10−2

10−1

100

Eb/No

BE

R

NC, Mpu=128NC, Mpu=256NC, Mpu=512Mpu= 480Mpu=256Mpu=128

Figure 4.7: NC-MC-CDMA vs proposed hybrid MC-CDMA underlayperformance with ZF and MMSE

Chapter 5

Overload Hybrid System

5.1 Introduction

In this chapter an overload Hybrid MC-CDMA system is proposed to further

improve the spectrum utilization. In this scheme, overlay utilizes the full signal

dimension, transmitting through the spectrum holes. In addition, underlay users

overload the system while keeping the orthogonality to overlay users as much

as possible. The proposed system applies two-layered spreading, channelization

and scrambling. Channelization is used for user separation and scrambling for

overlay/underlay separation. At the receiver, an interference cancellation-based

receiver is proposed and the performance is examined by simulation.

This chapter starts with a brief overview of the CDMA-based systems’ code

selection and adaptation for CR systems. System model and the transmitter

structure is introduced in Section 5.3 followed by the scrambling code allocation

algorithm in Section 5.4. The receiver structure for the proposed overload system

is explained in Section 5.5. The overload system’s simulation results are presented

in Section 5.6 for medium and high interference levels. The underlay transmission

is then extended to the multi user results.

89

CHAPTER 5. OVERLOAD HYBRID SYSTEM 90

5.2 Code Selection and Adaptation in CRNs

In this section, we will first briefly review the desirable properties of the codes for

CDMA-based systems. Next, some pros and cons of the well-known codes will

be reviewed. Finally, the available adapted codes for MC-CDMA CRNs will be

introduced.

The main desirable characteristics of the codes are:

1. Autocorrelation which is a measure of similarity of a code with the time

shifted versions of the code. Noise-like autocorrelation will lead to zero ISI

in frequency selective fading channels.

2. Orthogonality across users which leads to zero MAI in synchronous

transmission.

3. Crosscorrelation is a measure of similarity between two codes. Zero cross

correlation is desirable for asynchronous transmission for less MAI.

Depending on the applications and preferences, choice of spreading codes

varies based on the above criteria, in addition to some other factor such as

Peak-to-Average Power Ratio (PAPR), code length and number of users to be

accommodated. There has been a huge amount of research on spreading codes

for CDMA-based systems (see e.g. [75, 76, 77, 78, 79, 80]). Here, we will discuss

a brief review on some of the prominent codes and their pros and cons.

OVSF Codes and Walsh-Hadamard codes are examples of orthogonal codes.

Orthogonal codes, in spite of the excellent orthogonality between users, have poor

autocorrelation and crosscorrelation. Orthogonal codes are specially preferred for

synchronous downlink scenarios.

Maximal-Length sequences (m-sequences), Gold codes and Kasami sequences

are examples of non-orthogonal codes. However, they have better correlation and

crosscorrelation properties than orthogonal codes. These codes are preferable for

asynchronous transmission.


There are some research available in the literature on adapting the codes

for dynamic spectrum access (DSA) and CRNs. Chao Zhang has proposed an

algorithm in [81] to adapt Carrier Interferometry (CI) codes for non-contiguous

transmission in CRNs. CI codes were first introduced in by Nassar et al. in [82]

which have the benefit of low PAPR. Another key advantage with the codes is that

they can be generated for any integer code length. Exploiting NC-MC-CDMA in

overlay CRN is very promising due to the flexibility of the system and ability

to adapt to the available bands. However, there is a disadvantage with the

scheme. That is the leaked power, due to the spectral sidelobes, to the adjacent

band utilized by the primary system. Authors in [83] have resolved the issue for

overlay OFDM in CRNs. Also the problem is addressed and resolved for overlay

MC-CDMA in [54, 55].

Overloaded CDMA-bases systems have been widely investigated in the

literature which mainly have repetitive structure and causing delay to the system,

e.g.[84, 85]. Pseudo orthogonal CI proposed in [66] is one of the candidates

for overloaded MC-CDMA CRNs. Taylor et. al. [86] have compared Carrier

Interferometry (CI) and Pseudo-Orthogonal Carrier Interferometry (PO-CI) for

BPSK and also higher modulation techniques. It is shown that although CI

codes show excellent performance for BPSK-CI codes, the performance degrades

dramatically with higher order modulation PO-CI case.

In this work, CI codes are not utilized in the proposed overloaded system

since their performance degrades with higher modulation schemes, especially for

the overload case. Instead, scrambling codes, which have been previously used

for cell separation in WCDMA [77], are adapted here for CRNs. Scrambling has

been also proposed for MIMO-CDMA systems in [87] i.e. Gold codes are used

to distinguish between users and W-H codes for separating different transmit

antennas. However, there are several challenges for their adaptation in CRNs.

One is that the overlay and underlay do not have the same length. In addition,

the code length changes by the results from the spectrum sensing unit. In this


Figure 5.1: Hybrid overload MC-CDMA system model

chapter, we adapt the concept for the application in Hybrid systems in CRNs.

5.3 System Model and Transmitter Structure

The hybrid MC-CDMA system model is shown in Fig. 5.1 where the primary

OFDMA-based system and the Cognitive Radio Network (CRN) coexist in the

same band B. The total bandwidth is divided into M equi-bandwidth subcarriers.

It has been assumed that the spectrum sensing is performed and the available

bands and the interference threshold for the occupied bands are known to the

CRN. Overlay is transmitting through the spectrum holes while underlay users

are overloading the system utilizing the entire spectrum aiming to achieve more

diversity gain and interference suppression with maintaining orthogonality with

the overlay users as much as possible as shown in Fig. 5.1.

The number of subcarriers occupied by the PU system is represented by Mpu

and the number of subcarriers to be used by the overlay CR is shown by Msu

which are known from the spectrum sensing results. The subcarrier availability

for the CR system is shown by an availability vector a in which ai ∈ {0, 1} with 1

indicating the i-th component to be available, and 0 not available for the overlay.

In this model, K overlay users are using the Msu available subcarriers and K¯

underlay users will utilize the whole spectrum while maintaining the interference

threshold of the PU and at the same time keeping the orthogonality with overlay


Figure 5.2: Proposed Transmitter Structure

users. The total number of cognitive users is shown by K. P consecutive symbols

are spread with the spreading factor G and are sent in parallel by each overlay

user, i.e. Msu = GP . Since underlay is utilizing the whole spectrum, the underlay

code length will be M . The spread data of each overlay user is obtained by

multiplying the user’s symbols by its specific signature sequence as

yk = bk ⊗ ck (5.1)

where bk of size P × 1 is the k-th user’s symbol vector and ck of size G× 1 is the

k-th user’s specific spreading code, which the elements are normalized such that

each code has unit energy. The column vector yk is defined as

yk = [b1c1, . . . , b1cG, . . . , bP c1, . . . , bP cG, ]T ∈ CMsu×1. (5.2)

We note x ∈ CM×1 as the equivalent overlay signal y after respective subcarrier

mapping (according to the availability vector a) and summation over all G

overlay users. The overlay spread data is then multiplied by the overlay diagonal


scrambling matrix S of Msu nonzero elements according to the the availability

vector a. The overlay multiplexed symbol vector of G users is then

d = Sx. (5.3)

The transmitter block diagram is shown in Fig. 5.2. The k¯-th underlay user’s

data symbol is represented by b¯k¯

and its M×1 spreading code is c¯k¯

. The underlay

spread signal of K¯

users is

x¯

=

K∑k¯

=1

b¯k¯c¯k¯

(5.4)

It is further multiplied by the underlay diagonal scrambling matrix S¯

of M

elements. Therefore, the transmitted hybrid signal, dh ∈ CM×1, can be shown by

dh =√pcoSx +

√pcuS¯

x¯

=√pcod +

√pcud¯

(5.5)

which is an M × 1 vector consisting of the summation of overlay and underlay

signals.√pco and

√pcu are the overlay and underlay signal energy per subcarrier

respectively. The channel state information is assumed to be known perfectly at

the receiver side, but not at the transmitter. Let

Hss = diag[hss[1],hss[2], ...,hss[M ]] (5.6)

be the diagonal M ×M frequency domain complex channel from the secondary

transmitter to the secondary receiver, where hss[i] is the channel gain on the i-th

subcarrier. Likewise,

Hps = diag[(1− a1)hps[1], (1− a2)hps[2], ..., (1− aM)hps[M ]] (5.7)

is the M ×M frequency domain complex channel from the primary transmitter

to the secondary receiver. Here, the unoccupied subcarriers will be set to zero


by the term (1− ai). The channel is assumed to be frequency selective Rayleigh

fading, with flat fading over each subcarrier. Then, the received signal on the

i-th subcarrier at the secondary receiver is given by

r[i] = hss[i]dh[i] + hps[i]spu[i] + n[i] (5.8)

where

spu = [(1− a1)dpu[1], (1− a2)dpu[2], ..., (1− aM)dpu[M ]]T (5.9)

is theM by 1 PU data matrix. The first part in (5.8) is the secondary user’s hybrid

received signal on the i-th subcarrier with dh[i] representing the multiplexed

MC-CDMA transmitted hybrid signal elaborated in (5.5). The second term is

the interference from PU on the i-th subcarrier and the last part, n[i], is the noise

component on the i-th subcarrier of the received signal and is complex Gaussian.

Clearly, the received signal on the i-th unoccupied subcarrier at secondary receiver

will be

r[i] = hss[i]dh[i] + n[i]. (5.10)

The received signal in (5.8) can be expressed in vector form as

r = Hssdh + Hpsspu + n. (5.11)

Overlay channelization code is Walsh-Hadamard (WH) of length G while

the underlay code are a preferred pair of m-sequence of length M . As WH

codes are orthogonal, G overlay sets of codes keep the orthogonality between the

overlay users and so does the underlay WH codes of length M for underlay users.

However, since the overlay system is already fully loaded, the underlay user is

overloading the system, and thus create interference. It should be mentioned

that overload system concept in cognitive radio has some elemental differences

with the previous overload systems. Firstly, the underlay interference threshold

limit should be concerned at all times. Moreover, the overload user, transmitting


via underlay, does not occupy the same number of subcarriers as overlay users.

Therefore, the scrambling sequences should be updated according to the overlay

available subcarriers from the spectrum sensing unit. The scrambling codes

should be also updated when a new user is being added to the underlay hybrid

system. Therefore, the proposed code allocation algorithm is explained next.

5.4 Code Allocation Algorithm

Since the overlay and underlay are overlapping only in Msu subcarriers, the

scrambling code for underlay should be chosen such that underlay system will

have the least possible correlation with overlay system. However, the systems

will need to update the underlay scrambling with each update from the spectrum

sensing unit or any addition to the number of underlay users. In order to achieve

low crosscorrelation between the overlay and underlay users, the orthogonal Gold

codes are employed [43]. A pair of Gold codes of length M − 1 is chosen. By

appending a zero at the tails of these two codes, two orthogonal Gold codes of

length M are generated, one for overlay and one for underlay. The part of the

overlay scrambling code in which PUs exist is set to zero. The underlay scrambling

code is then cyclic shifted and the one that provides the least crosscorrelation with

overlay users is selected for underlay scrambling. The algorithm can be written

as follows where it is based on the average cross-correlation values than their

maximum values [76]:

1. Generate a pair of orthogonal Gold codes of length M for overlay and

underlay scrambling.

2. Generate the periodic overlay channelization code C for K users i.e. C will

be a K ×Msu matrix, where Msu is obtained from the spectrum sensing

unit.

3. Calculate the combined overlay code for K users as T = CS and at the


same time zero pad at the PU occupied subcarriers (T will be a matrix of

K ×M).

4. For the specific underlay user calculate the combined underlay code as

T¯

[k¯] = c

¯[k¯]S¯

(T¯

will be a 1×M vector).

5. Calculate the k-th underlay user’s correlation with the k-th overlay user

Ψk,k,0 =1

Msu

M∑i=1

T¯

[i]T[k, i] (5.12)

where the last index 0 denotes the number of cyclic shift of the underlay

scrambling code and in this case is 0.

6. Perform chip-wise cyclic-shift of the underlay scrambling code and repeat

steps 3-5. The correlation for each shift is Ψk,k,m where m ∈ {1, ...,M}.

7. Repeat steps 3-6 for all underlay users and overlay users.

8. Choose the amount of shift that has the minimum correlation between the

overlay and underlay users’ scrambling codes

m = arg minm

1

k

K∑i=1

1

k

K∑j=1

Ψi,j,m

. (5.13)

5.5 Receiver

The block diagram of the proposed receiver is shown in Fig. 5.9. The received

signal is descrambled by using the overlay scrambling sequence. The overlay

signal is first detected, due to its relative high power to the underlay signal,

from the received hybrid signal using CL MMSE. There are two main reasons

to use Chip-Level (CL) MMSE for overlay detection. Firstly, CL detector can

maintain the simplicity of the MC-CDMA receiver for overlay users as it does not

require the knowledge of the other users’ sequences. Secondly, since the overlay


Figure 5.3: Overload Receiver Block Diagram

transmission power is considerably higher than that of the underlay and there is

no interference from PU, the CL MMSE exhibits a good performance. The CL

MMSE criterion for the i-th overlay subcarrier is given by

minw[i]

E[|z[i]− d[i]|2] = minw[i]

E[(w[i]r[i]− d[i])(w[i]r[i]− d[i])∗

](5.14)

where zi is the decision variable on the i-th subcarrier. Substituting (5.10) into

the objective function (5.14) and differentiating with respect to w∗ we will have

E[(w[i]r[i]− d[i])r∗[i]

](5.15)

=E[(d∗h[i]h

∗ss[i]w[i] + w[i]n∗[i]− d[i])(d∗h[i]h

∗ss[i] + n∗[i])

]. (5.16)

Assuming the overlay data is detected perfectly and knowing (5.5), the above

expression can be written as

E[w[i]hss[i]d[i]d[i]∗hss[i]

∗ + w[i]hss[i]d[i]d[i]∗hss[i]∗ + wnn∗ − d[i]d[i]∗hss[i]

∗] = 0.

(5.17)

Rearranging the formula for w it can be easily shown that the CL equalization

coefficient for overlay is

w[i] =h∗ss[i]

(1 +pcupco

)hss[i]h∗ss[i] +

N0

pco

(5.18)

where E[d[i]d[i]∗] = pco , E = [d[i]d[i]∗] = pcu and E = [nn∗] = N0.


After overlay CL MMSE equalization, the receiver will then perform the

descrambling and despreading process to obtain the overlay users’ symbols,

ˆb[1], ˆb[2], ..., ˆb[K]. The second step in the receiver is to perform interference

cancellation. With the overlay users’ symbols detected, their contribution to the

received can be removed. Therefore, the detected overlay symbols can then be

re-spread, re-scrambled, and subtracted from the received signal. The modified

received signal hence mainly contains the underlay users’ signal, the PU signals,

and noise. After overlay interference reconstruction and cancellation, the modified

received signal on the i-th subcarrier for underlay detection is

r¯[i] = r[i]−

M∑i=1

ˆx[i]hss[i] (5.19)

where ˆx[i] is the sum of K overlay users’ detected multiplexed data on the i-th

subcarrier. Therefore, the reconstructed received signal component after overlay

signal detection and cancellation corresponds to

rc = Hssd¯

+ Hpsspu + n + Î (5.20)

where Î is the residual interference from overlay due to imperfect cancellation.

It is assumed to be zero in the subsequent derivation due to the relative high

overlay to underlay power and low overlay/underlay crosscorrelation.

In order for the underlay signals to be detected under the high interference

from the PUs, SL equalization is considered for underlay as it has better

performance than CL equalizer. The MMSE criterion for underlay is

minW¯

E[(W¯

r− b¯

)(W¯

r− b¯

)H ]. (5.21)

Substituting reconstructed received signal, rc, from (5.20) into the objective


function of (5.21), knowing d¯

= S¯C¯

b¯

we will have

J =E[((W¯

HssS¯C¯

b¯

+ W¯

Hpsspu + W¯

n)− b¯

) (5.22)

((W¯

HssS¯C¯

b¯

+ W¯

Hpsspu + W¯

n)− b¯

)H ].

= W¯

HssS¯C¯

RbbC¯HS

¯HHH

ssW¯H −RbbW

¯HssS

¯C¯

+ (5.23)

W¯

HpsRppHHpsW¯

H + W¯

RnnW¯H −RbbC

¯HS

¯HHH

ssW¯H + Rbb

where Rbb = E[bbH ] is a K × K diagonal matrix of the underlay users’ symbol

energy. Solving the above equation for minimum value of W¯

, we differentiate

the above expression with respect to W¯H using the properties of the derivative

matrix [88, 89] and set it to 0, i.e dJdW

¯H = 0, we will have

W¯

HssS¯C¯

RbbC¯HS

¯HHH

ss + wHpsRppHHps + W

¯Rnn −RbbC

¯C¯HS

¯HHH

ss = 0. (5.24)

Rearranging for W¯

we obtain

W¯

= RbbC¯HS

¯HHH

ss.(PunHssS¯C¯

RbbC¯HS

¯HHH

ss + HpsRppHHps + Rnn)−1 (5.25)

where Pun is the underlay symbol power1. Assuming the MAI to be negligible,

the underlay SINR can be written as

γSLun =pcuW¯

HssHHssW¯

H

W¯

HpsspusHpuHHpsW¯

H +N0W¯

W¯H

(5.26)

Since several symbols are sent through overlay in each block, any potential

overlay error will not directly propagate and make underlay erroneous. On the

other hand, in case that the overlay performance is poor, the proposed Full-load

method will be preferable.

1Note that underlay signal power (Pun) has been set to be lower than the PU’s interferencethreshold (Ith)



This section presents the simulation results and compares the proposed systems’

performance for different scenarios and with existing systems. The total available

bandwidth is assumed to be 10 MHz and chip duration is 100 ns. Fading

channel from the primary transmitter to the secondary receiver is modelled by

the ITU-Pedestrian B [74] as well as the secondary transmitter to secondary

receiver’s channel. A total of 512 subcarriers in 8 blocks of 64 are available for

the PU system. The primary system uses OFDMA and each user occupies a

block of 64 consecutive subcarriers. If a block is not occupied by the PU, it

will be exploited by the overlay users with a spreading factor of 64. Overlay

uses WH codes of length 64 for spreading. The underlay spreads the data

over the whole 512 subcarriers respecting the interference threshold of the PU.

Underlay uses WH codes of length 512. A pair of orthogonal Gold codes using

the algorithm elaborated in Section 5.4 is used for the scrambling. It is worth

mentioning that underlay and overlay users are orthogonal between themselves.

The proposed overload system’s underlay performance is first compared with

the full-load system previously introduced in Chapter 4 for intermediate PU

interference levels. The overload system’s performance is further examined for

high PU interference level in 5.6.2. Finally, the Multi-User underlay performance

is discussed in 5.6.3.

5.6.1 Medium PU Interference Level

For the Full-load case, there are a total of 64 cognitive users in the system.

Overlay users are utilizing the unoccupied spectrum in chunks of 64 subcarriers.

The last user is transmitting in underlay over the total bandwidth. In this

scenario, the secondary user’s underlay received power is assumed to be -20dB

relative to the received signal power from the PU whilst it is maintained below

the PU interference threshold. Overlay to underlay relative power is also 20dB.


0 5 10 15 20 25

10−4

10−3

10−2

10−1

Underlay Eb/No

BE

R

Mpu=448Mpu=384Mpu=320Mpu=256Mpu=128

Figure 5.4: Proposed full-load and Overload underlay performance comparisonwith relative underlay to PU received interference level of −20dB; Solid linesshow the overload and dashed lines show the full-load results

Fig. 5.4 compares the underlay performance results for the full-load and overload

systems when the relative overlay to underlay and PU to underlay powers

are kept at 20dB [25], as in the previous scenario in Chapter 4. Solid lines

show the overload and dashed lines show the full-load results for different PU

occupancies. It is observed that for high PU occupancy levels the overload

system’s performance diverges more from the full-load case while for low PU

occupancy the performance of the two proposed systems converge.

5.6.2 High PU Interference Level

In this scenario, the interference from the PU is increased to 47dB relative to the

underlay received power while interference threshold is kept at the same level as

in the previous part. It is further assumed that the CR system receives the PU

signal 3dB less due to the path loss. The overlay to underlay power is also 47dB.


0 5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

Underlay Eb/No

BE

R

Mpu=320Mpu=256Mpu=192Mpu=128Mpu=64

Figure 5.5: Underlay performance of the proposed overload hybrid system withdifferent PU occupancy levels. Total number of subcarriers are 512

The underlay BER performance of the proposed overload system is presented

for different number of PU occupancy levels, Mpu = 64, 128, 192, 256 and 320, in

Fig 5.5. The results show that in spite of very high interference level from PU,

the underlay maintains good performance and as the number of available overlay

subcarriers increases, the underlay performance enhances.

The underlay sensitivity of the proposed system due to PU interference power

is shown in Fig. 5.6. In this scenario, the number of overlay subcarriers is

fixed to 256. The PU received power at the secondary receiver is varying while

the interference threshold and hence the underlay power is kept the same. It

is observed that increasing the PU interference power from 37dB to 44dB, the

underlay performance is degraded by 2dB or less. This shows the overloaded

system performs well in high PU interference scenarios.

To evaluate the overlay performance degradation due to underlay transmission

in the proposed hybrid system, its BER performance is compared to that of the


0 2 4 6 8 10 12 14 16 18 20

10−4

10−3

10−2

10−1

100

Underlay Eb/No

BE

R

Ppu=44 dBPpu=40 dBPpu=37 dBBaseline (No PU)

Figure 5.6: Underlay sensitivity of the proposed overload system to PUinterference power level, Mpu = 256

pure overlay system. In this scenario, the worst case for overlay is considered

where the overlay and underlay power levels are equal. This is the worst case

since it is not likely in an underlay cognitive radio system, that is utilizing the

same bandwidth as the primary user and hence has to maintain the interference

threshold of the PU. In the hybrid case, overlay occupancy level is 50% (256

subcarreirs). The overlay BER performance is depicted in Fig. 5.7. It is observed

that even in such scenario, the overlay performance degradation is very small.

Therefore, with the proposed hybrid system the underlay can enhance the spectral

efficiency without disturbing the overlay performance.

Fig. 5.8 compares the NC-MC-CDMA underlay approach [24], with the

proposed overload performance. For the NC-MC-CDMA case, underlay is a single

user sending in the PU occupied parts of the spectrum only, i.e. 256 subcarriers.

The Dashed lines show the CL and solid lines the SL results while the dotted

lines show the proposed systems results. The CL equalization coefficients for the


0 2 4 6 8 10 12 14 16 18 2010

−4

10−3

10−2

10−1

100

Eb/No

BE

R

Hybrid System

Pure Overlay System

Figure 5.7: Overlay performance with and without underlay transmission for theworst case scenario when overlay and underlay power levels are equal


0 2 4 6 8 10 12 14 16 18 2010

−5

10−4

10−3

10−2

10−1

Eb/No

BE

RUnderlay Performance

Baseline (No PU)PU=20 dBPU=44 dB

Figure 5.8: Underlay NC MC-CDMA sensitivity to PU interference power levelfor 256 subcarriers. Dashed lines show the CL and solid lines the symbol-levelwhile the dotted lines show the proposed system’s results with Mpu = 256

NC-MC-CDMA are abtained from

w[i] =h∗ss[i]

hss[i]h∗ss[i] + N0

pcu+ ppu

pcuhps[i]h∗ps[i]

. (5.27)

and symbol-level from

w = PuncHhK

HHss.(HssChRssC

Hh HH

ss + HpsRppHHps + Rnn)−1. (5.28)

It is observed that with increasing the PU interference, the performance of the

NC-MC-CDMA underlay degrades dramatically while the proposed system still

maintains good results. For instance, for PU interference level of 44dB, the

proposed system still shows better result than the previous NC-MC-CDMA of

20dB.


0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Underlay Eb/No

BE

R

Kun=64Kun=48Kun=32Kun=1

Figure 5.9: Underlay performance for increasing number of underlay users whileoverlay is full-loaded with Mpu = 64

5.6.3 Underlay Multi-User Results

In this part, the overload performance is discussed for underlay multi-user case.

It should be mentioned that the proposed system is appropriate for downlink

and the BER results are achieved from a random underlay user. To evaluate the

proposed code assignment algorithm, in this part, the interference threshold is

assumed to increase as the number of underlay users increases. This way the

underlay degradation due to underlay multi access interference can be evaluated.

Fig. 5.9 shows the underlay performance with increasing number of underlay users

while the overlay is full-loaded. It is observed from the figure that the degradation

with increasing number of underlay users is negligible for 50% overload. Indeed

any degradation will be due to the interference threshold limits. Therefore, the

interference threshold determines how many underlay users can be added to the

underlay hybrid system according to the users’ requirements.

Fig. 5.10 for Mpu = 64 investigates the underlay performance degradation


0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Underlay Eb/No

BE

R

Kun=64Kun=48Kun=32

Figure 5.10: Overlay Interference to underlay with Mpu = 64. Solid lines showthe underlay performance with overlay and the dashed lines without overlay

due to overlay. Underlay interference to Overlay is negligible since the overlay

transmission power is considerably higher than the underlay one. On the other

hand, the underlay codes have been chosen meticulously and according to the

number of overlay and underlay overlapping subcarriers to make the least possible

correlation with the overlay system. In Fig. 5.10 the underlay performance is

shown with and without overlay for 64 PU occupancy. Solid lines show the

underlay performance with overlay and the dashed lines without overlay. It is

observed that the underlay performance degradation due to overlay is very small

and negligible for any number of underlay user. This is due to the scrambling code

selection algorithm explained in Section 5.4 which gives the priority to the overlay

users to have less correlation with underlay users and hence better performance.

It is observed that as the length of overlay codes decreases, i.e. PU occupancy

level increases, from 448 to 192, the crosscorrelation between overlay and underlay

increases. For fading and high PU interference the MAI was negligible till 50%


overload. Because the underlay codes are orthogonal to each other, adding further

underlay users should not degrade the performance. It can be inferred that the

reason behind was the fading.

5.7 Summary

In this chapter a hybrid overload MC-CDMA system is proposed to enhance the

spectral efficiency of a cognitive radio network. It consists of a full MC-CDMA

system that uses the full signal dimension for the overlay users for high data

rate. The overload user will utilize the underlay transmission using the two

layered spreading. With maintaining the orthogonality with the overlay, the

underlay can suppress PU’s interference. At the receiver side, the overlay signal

is first detected using chip-level MMSE. The overlay reconstructed signal is then

cancelled from the received signal which is used for the underlay SL detection.

Simulation results show that the proposed overload scheme can achieve good

performance, with only slight degradation comparing to full loaded system. It

is therefore a viable solution to improve spectral efficiency of a cognitive radio

network.

Chapter 6

Hybrid Overlay/Underlay Sum

Rate Optimization

6.1 Introduction

The spectrum sharing is via overlay, underlay, or a hybrid model as previously

elaborated. It was also shown, in Section 3.6, that hybrid case achieves higher

sum rate than overlay or underlay being utilized solely. Now, the question is which

hybrid scheme achieves more sum rate in different scenarios in CR systems.

In [17], authors have considered coexisting primary and secondary in side

by side bands in overlay. Secondary system is assumed to be OFDM-based

single-user. An optimal and suboptimal power allocation is obtained with the

assumption that modulation of primary users bands are known to the cognitive

system. The framework is then extended to the case where different interference

constraints are set by different PUs in [18]. An OFDM-based hybrid system

is proposed in [90]. The hybrid sum rate is compared with the case in which

transmission is performed through either overlay or underlay. An optimal and

suboptimal power loading scheme is proposed. The results show that the hybrid

system (achieved by either of the optimal and suboptimal schemes) outperforms

overlay or underlay being exploited solely. Farhad Arpanaei et al. have developed

110

CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUMRATEOPTIMIZATION111

the hybrid system for a more general case in which sub-carriers side-lobe leakage

is also considered [91]. The system in [90] is further optimized for the joint

subcarrier and power allocation in [23].

In [69] primary system is considered to be utilizing DS-CDMA while underlay

secondary user is employing OFDM. The spreading factor of the primary system

is assumed to be known at the secondary system’s transmitter. Khoshkholgh et

al. have related the two interference constrained problem and power constrained

problem by a critical system parameter and could therefore, eliminate the

interference threshold constraint. It will reduce the system’s complexity by

making secondary system independent of the channel state information between

the secondary transmitter and the primary receiver.

Some works have suggested mixture of overlay/underlay schemes. The authors

in [92] have studied the achievable capacity of the secondary user for three access

strategies: overlay, underlay and mixed. In the mixed strategy the total system

capacity is maximized regarding the secondary service parameter, pa, which can

be adjusted based on the spectrum status. In case the primary user is idle,

overlay is employed and pa = 0. Otherwise, according to the primary system’s

interference level at the secondary receiver, pa will be increased or decreased to

maximize the secondary user’s capacity. Authors in [93] proposed a sensing-based

spectrum sharing model. Based on the first stage result, the spectrum sensing,

secondary user decide the spectrum sharing strategy. The ergodic capacity of the

secondary user is formulated as an optimization problem over the sensing time

and transmit power. The two cases of perfect and imperfect sensing are then

studied.


6.2 Sum Rate Comparison for Different Hybrid

Schemes

In this chapter, the aim is to compare maximum achievable sum rate with different

hybrid access strategies. Four hybrid transmission schemes for CR systems are

compared in AWGN channel. The four systems are namely Full-OFDM, Mixed

OFDM/MC-CDMA system, the proposed Full MC-CDMA introduced in Chapter

4, and the Proposed Overload MC-CDMA system introduced in Chapter 5. The

two leading systems are then chosen, namely the proposed Overload MC-CDMA

and the Full-OFDM, and the systems capacities are examined for fading channels

in Section 6.5. The simulation results for both AWGN and fading channels are

presented in Section 6.6. It also worth mentioning that the results shown in this

chapter consider the worst-case scenario in which all bands are fully occupied

either by overlay or primary user. It is shown in [12] that in case some bands are

vacant, the performance will dramatically improve.

6.3 System Model

System model is shown in Fig. 6.1. The total available bandwidth B is

divided into NB subbands, each subband having Ns unit-bandwidth subcarriers.

Frequency selective downlink channel is considered where the channel is flat over

a subcarrier. Furthermore, the subband size is chosen such that it is less than the

coherence bandwidth of the channel. αj is the j-th sub-band availability which

is assumed to be known from the spectrum sensing unit. αj = 1 if the primary

system is idle in that sub-band and is 0 otherwise. After each update from the

spectrum sensing, the total number of occupied subbands by the primary system

is shown by Npu. The total number of available subbands to be used by overlay

is shown by Nov. Interference threshold of the PU and the PU’s average received

power on each subcarrier, shown by Ith and ppu respectively, are also assumed


Figure 6.1: System model

to be known by the CR transmitter. The total CR power budget, Ptot is to

be allocated to the hybrid system in each case such that the total sum rate is

maximized. Note that a maximum allowable transmission power through overlay

is also considered which is shown by Pov. This is due to the interference leakage

to the adjacent PU bands [83]. However, the constraint is considered to be very

high.

To formulate the optimization problem, sum rate of the sum of overlay and

underlay capacities is maximized with respect to the PU interference threshold

and the CR transmission power budget. The objective is to maximize the total

sum rate of the system:

Cergadic = max E{K∑k=1

Rk +

K∑k¯

=1

Rk¯} (6.1)

where K and K¯

are the number of overlay and underlay users respectively, and

Rk and Rk¯

are the instantaneous rate functions representing transmitted bits per

symbol of overlay and underlay cognitive users. Note that the above maximization

problem is with respect to the allocated power on subbands. Maximizing the

average sum rate in (6.1) can be achieved through maximizing the instantaneous


sum rate [94]:

C inst. = max {K∑k=1

Rk +

K∑k¯

=1

Rk¯}. (6.2)

6.4 AWGN Channels

In this section, the four hybrid transmission schemes for CR systems are

compared in AWGN channels. The four systems are namely full-OFDM, mixed

OFDM/MC-CDMA system, the proposed full MC-CDMA introduced in Chapter

4, and the Proposed overload MC-CDMA system introduced in Chapter 5. The

total Hybrid system’s transmission rate is formulated as an optimization problem

for each case.

6.4.1 Full-OFDM

The total achievable transmission rate for the full-OFDM hybrid system can be

written as an optimization problem (Q1) as follows:

Maximize R = Ns

NB∑j=1

log2

(1 +

pjN0Ns + (1− αj)Nsppu

)(6.3)

subject to

NB∑j=1

pj ≤ Ptot (6.4)

NB∑j=1

(1− αj)pj ≤ Ith (6.5)

NB∑j=1

αjpj ≤ Pov (6.6)

pj ≥ 0 j = 1, 2, ..., NB (6.7)

where pj is the secondary user’s allocated power on j-th sub-band, and ppu is the

average received interference from PU on each subcarrier which is assumed to

be equal for all occupied subchannels. N0 is the two sided noise power spectral


density. It should be mentioned that in this case, a single user is utilizing the

entire bandwidth. Note that the total sum rate formula in (6.3) is multiplied by

Ns. This is due to the fact that pj is assumed to be the allocated power to the

j-th subband and since it is assumed that in each subband the fading will be

flat, pj is then divided by N − s to shown the capacity by each subcarrier in a

subband1. The objective function of Q1 in (6.3) has the following Hessian with

regard to p:

∇2(R) =−Nslog2e

(pj +N0Ns + (1− αj)Nsppu)2≺ 0 ∀ pj (6.8)

and therefore, is strictly concave over p. The problem can be solved for p by

solving the following problems Q11 and Q12 where:

Q11 : Ptot > Pov + Ith and Q12 : Ptot ≤ Pov + Ith.

Also knowing that KKT conditions (2.28) - (2.32) are satisfied for the above

problem, a unique analytical solution can be obtained for each case of Q11 and

Q12. Note that throughout this chapter λ, ν and µ will be Lagrangian multipliers

related to the total power constraint, overlay power constraint and underlay power

constraint respectively.

Solving the problem Q11, the total power constraint (6.4), can be omitted

from the optimization problem and Q1 can be rewritten as

Maximize R = Ns

NB∑j=1

log2

(1 +


)(6.9)

subject to

NB∑j=1

(1− αj)pj ≤ Ith (6.10)

NB∑j=1

αjpj ≤ Pov (6.11)

pj ≥ 0 j = 1, 2, ..., NB. (6.12)

1Here Q1 is written for the case of AWGN. However, the model is applicable to the fadingchannels which will be discussed later


It is straight forward that in the case of AWGN, the allocated power to all

the occupied subbands will be equal. Similarly, the allocated power to all

unoccupied subbands. As a result, the above subband power allocation can

be simplified to pov and pun, the allocated power to the overlay and underlay

subbands respectively. Therefore, considering the constraints 6.11 and 6.10, the

optimized power allocated to the overlay and underlay in Problem Q11 can be

shown to be p∗ov = PovNov

and p∗un = IthNpu

respectively.

For Q12, due to the PU interference in underlay band, the optimum p achieves

with filling overlay first for the case of AWGN. Hence, the underlay power

constraint (6.4), can be omitted from the optimization problem Q1 and reduces

to the Problem Q12 as

Maximize R = Ns

NB∑j=1

log2

(1 +


)(6.13)

subject to

NB∑j=1

pj ≤ Ptot (6.14)

NB∑j=1


pj ≥ 0 j = 1, 2, ..., NB. (6.16)

It is clear that for Problem Q11, water-filling will result in filling the

unoccupied subbands first due to the absence of interference from PU. Therefore,

the optimized power allocated to the overlay and underlay for the Problem Q12

will be p∗ov = PovNov

and p∗un = Ptot−PovNpu

respectively. Clearly, in case that the total

available SU power is less than Pov, only the overlay bands will be utilized and

no data will be transmitted via underlay. So, the optimized allocated power to

overlay will be p∗ov = PtotNov

.


6.4.2 Mixed OFDM/MC-CDMA

In this scheme, overlay is utilizing OFDM through the available spectrum and

underlay utilizing NC-MC-CDMA [25]. In this case, since MC-CDMA is utilizing

the occupied subcarriers only, the underlay system will not benefit much from

the interference rejection capability of the MC-CDMA system. However, all the

codes can be used for transmission to enhance the data rate. It is straight forward

that the maximum sum rate is achieved when all underlay users are active. The

problem for the Mixed OFDM/MC-CDMA scheme is defined in problem Q2 as:

R = Ns

Nov∑n=1

log2

(1 +

pov[n]

N0Ns

)+

K∑k¯

=1

log2

(1 +

pk¯

N0 + ppu

)(6.17)

subject toNov∑n=1

pov[n] +

K∑k¯

=1

pk¯≤ Ptot (6.18)

K∑k¯

=1

pk¯≤ Ith (6.19)

Nov∑n=1

pov[n] ≤ Pov (6.20)

pov[n] ≥ 0 n = 1, 2, ..., Nov (6.21)

pk¯≥ 0 pk

¯= 1, 2, ...,K

¯. (6.22)

Knowing that all underlay users are active, pk¯

= PunK¯

where Pun is the

total alocated power to underlay. We also know that for the AWGN channel

pov[1] = pov[2] = ... = pov[Nov] = pov where pov[n] is the allocated power

to the n-th unoccupied subband. Note that there will be no MAI in AWGN

underlay MC-CDMA. Here again the problem is split into two subproblems when

Q21 : Ptot > Pov + Ith and Q22 : Ptot ≤ Pov + Ith. It is clear that for

Q21 the optimized overlay and underlay powers will be p∗ov = PovNov

and p∗k = IthK

respectively. Note that pov is the allocated power to the overlay subband and pk


is the allocated power to the k-th underlay user using NC-MC-CDMA.

Problem Q22 is similar to the Problem Q12 in the sense that the water-filling

algorithm will allocate power to the overlay first. This is due to the fact that the

PU interference in the occupied parts will degrade the underlay SU performance.

Therefore, the optimum overlay and underlay powers will be p∗ov = PovNov

and

p∗K = Ptot−PovK

(Pun = Kp∗K).

6.4.3 Proposed Full-MC-CDMA

The proposed full-MC-CDMA system sum rate, introduced in Chapter 4, is

considered in this section. Note that there will be no overlay to underlay

interference and vice versa since OVSF codes are utilized. The system sum rate

is defined in Problem Q3 as:

R =Nov∑n=1

Ns−1∑m=1

log2

(1 +

pov[m,n]

N0(Ns − 1)

)+ log2

(1 +

punN0 + ppu

χ

)(6.23)

subject toNov∑n=1

Ns−1∑m=1

pov[m,n] + pun ≤ Ptot (6.24)

pun ≤(NBIthNpu

)(6.25)

Nov∑n=1

pov[n] ≤ Pov (6.26)

pov[m,n] ≥ 0 n = 1, 2, ..., Nov ; m = 1, 2, ..., Ns − 1 (6.27)

pun ≥ 0 (6.28)

where χ = NBNun

is the PU interference suppression factor. Note that unlike the

two previous methods, in the proposed Full-Mc-CDMA method, the optimized

problem will not necessarily fill the overlay portions first since not all parts of the

underlay are affected by the PU interference. Here again, the problem is convex

and the KKT conditions are satisfied. Therefore, the Lagrangian can be used to


achieve the optimal power. Considering λ and µ to be the Lagrangians related to

the total power constraint and Interference threshold respectively, and bearing in

mind the overlay power constraint (6.26), the Lagrangian for Problem Q3 will be

L(pov, pun, λ, µ) = R− λ

(Nov∑n=1

Ns−1∑m=1

pov[m,n] + pun − Ptot

)− µ

(pun −

IthNB

Npu

).

(6.29)

Again, we use the fact that in AWGN channel the optimized power over all

subchannels and for all overlay users will be equal, and also knowing the MAI

between underlay users will not occur. Differentiating (6.29) with respect to the

variables pov and pun we will have

∂L

∂pov=

(Ns − 1)log2e

pov +N0(Ns − 1)− λ (6.30)

∂L

∂pun=

log2e

pun +N0 + ppuχ

− λ− µ. (6.31)

Setting the above formulas to zero, the optimal overlay and underlay powers will

be

p∗ov =

[(Ns − 1)(

log2e

λ−N0)

]+

(6.32)

p∗un =

[log2e

λ+ µ−N0 −

ppuχ

]+

(6.33)

which asserts that pov and pun are positive. λ and µ can then be obtained from

the following iterative algorithm

Initialize µmin = 0 and µmax = µ (µ ∈ [0, µ]).

Repeat

1. Set µ = (µmin + µmax)/2.

2. Find minimum λ from (6.24) for new set of µ (by solving the equation

(Ns − 1)( log2eλ−N0) + log2e

λ+µ−N0 − ppu

χ= Ptot).

3. Substitute in (6.32) and (6.33) to obtain pov and pun.


4. Update the vector µ by bisection method, i.e. if satisfies (6.25) set µ →

µmin, otherwise µ→ µmax.

Until µmax − µmin < δ where δ is a small positive constant.

Check if pov > Pov, set pov to Pov and allocate the rest of the available power

to the underlay with respect to 6.25. This is to ensure that the constraint (6.26)

is not violated.

6.4.4 Proposed Overload MC-CDMA

The sum rate of the overload hybrid MC-CDMA proposed in Chapter 5, is

considered in this section. Due to overloading, MAI will not be zero in this

system. However, assuming AWGN channel and knowing that orthogonal codes

have been used for both overlay and underlay, we can conclude that there is no

interference amongst the overlay users, as well as amongst the underlay users, i.e.

intra overlay/intra underlay interference is zero. On the other hand, the relative

power from overlay to underlay is very high. Thus, the underlay to overlay

interference can be assumed negligible. The overlay signal is detected first, and is

cancelled from the received signal. The underlay data is then detected from this

modified signal. Assuming the overlay signal is detected and cancelled perfectly,


the optimization problem for the overload system, Q4, can be defined as:

R =Nov∑n=1

Ns∑m=1

log2

(1 +

pov[m,n]

N0Ns

)+

K∑k¯

=1

log2

(1 +

pk¯

N0 + ppuχ

)

(6.34)

subject toNov∑n=1

Ns∑m=1

pov[m,n] +

K∑k¯

=1

pk¯≤ Ptot (6.35)

K∑k¯

=1

pk¯≤ IthNB

Npu

(6.36)

Nov∑n=1

pov[n] ≤ Pov (6.37)

pov[m,n] ≥ 0 n = 1, 2, ..., Nov ; m = 1, 2, ..., Ns (6.38)

pk¯≥ 0 k

¯= 1, 2, ...,K

¯(6.39)

where χ = NBNun

is the PU interference suppression factor. The Problem is convex

and the KKT conditions are satisfied. Similarly as in Problem Q3, considering λ

and µ to be the Lagrangians related to the total power constraint and Interference

threshold respectively, and bearing in mind the overlay power constraint (6.38),

the Lagrangian for Problem Q4 will be

L(pov, pk, λ, µ) = R−λ

Nov∑n=1

Ns∑m=1

pov[m,n] +

K∑k¯

=1

pk¯− Ptot

−µ K∑

k¯

=1

pk¯− IthNB

Npu

(6.40)

Assuming downlink, we will have pk¯

= PunK¯

. Differentiating (6.40) with respect

to the variables pov and pun we will have

∂L

∂pov=

Nslog2e

pov +N0Ns

− λ (6.41)

∂L

∂pun=

K¯log2e

pun + K¯

(N0 + ppuχ

)− λ− µ (6.42)


Setting the above formulas to zero, the optimal overlay and underlay powers will

be

p∗ov =

[Ns(

log2e

λ−N0)

]+

(6.43)

p∗un =

[K¯log2e

λ+ µ−K

¯(N0 +

ppuχ

)

]+

. (6.44)

which asserts that each pov and pun are be positive. λ and µ can then be obtained

from the following iterative algorithm


Repeat


2. Find minimum λ from (6.35) for new set of µ (by solving the equation

Ns(log2eλ−N0) + Klog2e

λ+µ−KN0 − Kppu

χ= Ptot).

3. Substitute in (6.43) and (6.44) to obtain pov and pun.




Check if pov > Pov, set pov to Pov and allocate the rest of the available power

to the underlay with respect to (6.36)2.

6.5 Rayleigh Fading Channels

The four hybrid systems’ capacities were studied in AWGN channels in Section

6.4. In this section, the two leading systems in terms of sum rate, namely the

full-OFDM and the proposed overload system, will be investigated in fading

channels. The simulation results for both AWGN and fading channels will be

discussed in Section 6.6.

2This is to ensure that the constraint (6.37) is not violated.


6.5.1 Full-OFDM

The sum rate maximization problem for the Full-OFDM case in fading can be

defined in Q5 as:

R = Ns

NB∑j=1

log2

(1 +

pj|hss[j]|2

N0Ns + (1− αj)Nsppu|hps[j]|2

)(6.45)

subject to

NB∑j=1

pj ≤ Ptot (6.46)

NB∑j=1

(1− αj)pj|hsp[j]|2 ≤ Ith (6.47)

NB∑i=1


pj ≥ 0 j = 1, 2, ..., NB (6.49)

where pj is the power allcoated to each secondary subchannel. The same

procedure is followed as for AWGN case where the problem in Q5 can be split to

two subproblems Q51 and Q52

Q51 : Ptot > Pov + Ith and Q52 : Ptot ≤ Pov + Ith.

For Q51 the total power constraint (6.46) can be omitted from the optimization

problem and Q5 can be rewritten as

Maximize R = Ns

NB∑j=1

log2

(1 +

pj|hss[j]|2

N0Ns + (1− αj)Nsppu|hps[j]|2

)(6.50)

subject to

NB∑j=1

(1− αj) pj|hsp[j]|2 ≤ Ith (6.51)

NB∑j=1


pj ≥ 0 j = 1, 2, ..., NB (6.53)


Due to convexity of the problem (KKT conditions hold), Lagrangian can be

applied to obtain the optimal solution to the problem

L(p, ν, µ) = R− ν

(NB∑j=1

αjpj − Pov

)− µ

(NB∑j=1

(1− αj)pj|hsp[j]|2 − Ith

)(6.54)

where ν and µ are non-negative Lagrangian multipliers corresponding to equations

(6.52) and (6.51) respectively. Differentiating (6.54) with respect to pj we will

have

∂L

∂pb=

Ns|hss[j]|2log2e

pj|hss[j]|2 +N0Ns + (1− αj)Nsppu|hps[j]|2− ναj − µ(1− αj)|hsp[j]|2.

(6.55)

Setting the above formula to zero, the optimal solution to the problem will be:

P ∗j =

[Nslog2e

ναj + µ(1− αj)|hsp[j]|2− N0Ns

|hss[j]|2− (1− αj)Nsppu

|hps[j]|2

|hss[j]|2

]+

(6.56)

which asserts that pj should be positive. ν and µ can then be obtained from the

following iterative algorithm


Repeat


2. Find minimum ν from (6.52) for new set of µ (by solving the equation[α1Nslog2e

να1+µ(1−α1)|hsp[1]|2 −N0Ns|hss[1]|2 − (1− α1)Nsppu

|hps[1]|2|hss[1]|2

]+ ...

+[

αNBNslog2e

ναNB+µ(1−αNB )|hsp[NB ]|2 −N0Ns

|hss[NB ]|2 − (1− αNB)Nsppu|hps[NB ]|2|hss[NB ]|2

]= Pov).

3. Substitute in (6.56) to obtain pj.





In fading channels, omitting interference threshold constraint, (6.47), for the

case Q52 : Ptot ≤ Pov + Ith will not necessarily lead to the optimal solution.

Therefore, for simplicity, we solve the problem with the two constraints, (6.46)

and (6.47), and the Lagrangians λ and µ bearing in mind the constraint (6.48).

The Lagrangian will be

L(λ, µ) = R− λ(

NB∑j=1

pj − Ptot)− µ(

NB∑j=1

(1− αj)pj|hsp[j]|2 − Ith) (6.57)

Differentiating (6.57) with respect to pj we will have:

∂L

∂pb=

Ns|hss[j]|2log2e

pj|hss[j]|2 +N0Ns + (1− αj)Nsppu|hps[j]|2−λ−µ(1−αj)|hsp[j]|2. (6.58)

Setting the above formula to zero, the optimal solution to the problem will be:

P ∗j =

[Nslog2e

λ+ µ(1− αj)|hsp[j]|2− N0Ns

|hss[j]|2− (1− αj)Nsppu

|hps[j]|2

|hss[j]|2

]+

(6.59)

which asserts that each pj should be positive. λ and µ can then be obtained from

the following iterative algorithm


Repeat


2. Find minimum λ from (6.46) for new set of µ (by solving the equation[Nslog2e

λ+µ(1−α1)|hsp[1]|2 −N0Ns|hss[1]|2 − (1− α1)Nsppu

|hps[1]|2|hss[1]|2

]+ ...

+[

Nslog2eλ+µ(1−αNB )|hsp[NB ]|2 −

N0Ns|hss[NB ]|2 − (1− αNB)Nsppu

|hps[NB ]|2|hss[NB ]|2

]).

3. Substitute in (6.59) to obtain pj.





Check if∑NB

i=1 αjpj > Pov, set the overlay subband’s power to PovNov

and allocate

the rest of the available power to the underlay with respect to (6.47)3.

6.5.2 Proposed Overload MC-CDMA

The sum rate maximization problem for the proposed Overload MC-CDMA in

fading channels can be defined in Q6 as:

R =Nov∑n=1

Ns∑m=1

log2

(1 +

pov[m,n]|hss[n]|2

N0Ns

)

+

K∑k¯

=1

log2

(1 + γk

¯

)(6.60)

subject toNov∑n=1

Ns∑m=1

pov[m,n] +

K∑k¯

=1

pk¯≤ Ptot (6.61)

K∑k¯

=1

M∑i=1

pk¯|hss[i]|2 ≤ Ith

NB

Npu

(6.62)

pov[m,n] ≥ 0 n = 1, 2, ..., Nov ; m = 1, 2, ..., Ns (6.63)

pk¯≥ 0 k

¯= 1, 2, ...,K

¯(6.64)

where γ is achieved from (5.26). Due to the complexity of the problem, the

optimal solution could not be achieved and a suboptimal solution is proposed

here. To allocate the overlay and underlay powers, water-filling algorithm is first

applied to the overlay subbands. The remaining power is then allocated to the

underlay overload users. It should be noted that symbol-level equalization is

considered for overlay symbol detection. Therefore, the overlay MAI is assumed

to be negligible

3This is to ensure that the constraint (6.48) is not violated.



Simulation results for sum rate comparison of the four hybrid systems in AWGN

discussed in Section 6.4 is presented in this section. Furthermore, the two leading

systems, namely the full-OFDM and the proposed overload system, are compared

in fading channels. Simulations are performed in MATLAB. Total available

subbands, NB, are assumed to be 8, each having 64 subcarriers (Ns = 64).

For simplicity of simulations, the average PU interference power on all occupied

subbands are assumed to be equal. Noise variance, N0, has been taken to

10−3mw. Interference threshold and PU average interference power are 10−2mw

and 0.5 mw per subcarrier respectively. It should be mentioned that throughout

the simulations in this chapter, sum rate is computed in Nats, base of Natural

Logarithm. It should be also mentioned that no more than 50% overload is

applied to the overload system. This is to ensure that the overlay cancellation is

perfect.

Fig. 6.2 compares the four hybrid systems’ capacities discussed in Section 6.4

versus the maximum transmission power. The occupied bands by PU is assumed

to be 50% of the total bands, i.e. Npu = Nov = 4. The overload system is taken

half-overload, i.e. 64 users transmitting through overlay and 32 users through

underlay. It is observed that the proposed overload system has the highest sum

rate for all transmission power levels, followed by the Full-OFDM and Mixed

Hybrid systems while the Full MC-CDMA is the last with this regard.

Fig. 6.3 shows the four hybrid systems’ total sum rate versus PU interference

level for fixed interference threshold level and total transmission power limit

of 1 mW and 280 mW. It is observed that the overload MC-CDMA system

achieves better sum rate for all PU interference levels exceeding full-OFDM and

Mixed-Hybrid system. On the other hand, the full MC-CDMA shows the least

sensitivity to PU interference level. with 10 dB PU increment degrading very

slightly as compared to the other methods

Fig. 6.4 shows the four systems’ capacities versus PU interference threshold


210 220 230 240 250 260 270 280 290 300 3101690

1700

1710

1720

1730

1740

1750

1760

1770

1780

1790

Maximum Transmission Power

Sum

Rat

e (N

ats)

Overload MC−CDMAFull OFDMMixed HybridFull MC−CDMA

Figure 6.2: Sum rate comparison of the four hybrid systems in AWGN for Npu = 4

1 2 3 4 5 6 7 8 9 10 11

x 10−4

1750

1760

1770

1780

1790

1800

1810

PU Interference Level

Sum

Rat

e (N

ats)

Figure 6.3: Sum rate vs. PU interference power level in AWGN for Npu = 4, andfixed interference threshold level and total transmission power limit of 1 mW and280 mW.


1 2 3 4 5 6 7

x 10−5

1740

1750

1760

1770

1780

1790

1800

1810

1820

Interference Threshold

Sum

Rat

e (N

ats)

Figure 6.4: Sum rate vs. interference threshold in AWGN for Npu = 4, and fixedPU interference and total transmission power of 0.5 and 280 mW.

level for fixed PU interference and total transmission power of 0.5 and 280

mW. It is observed that the overload MC-CDMA reaches its maximum sum

rate with lower interference threshold level in compared with the other three

hybrid schemes. For example, for the interference threshold of 500 mW, the

Overload MC-CDMA can reach the maximum achievable sum rate whereas the

Full-OFDM and the Mixed Hybrid can not achieve such sum rate even with the

interference threshold of 700 mW. This is a key advantage with the proposed

Overload MC-CDMA system as CRNs are mainly limited by the interference

threshold of the PU system.

In Fig. 6.5 the sum rate comparison of the four hybrid systems is shown

for different PU occupancy levels while noise variance, PU interference threshold

and interference per subcarrier is kept as in Fig. 6.2. Similar trend is observed

in Fig. 6.5a and 6.5b where PU occupancy levels are 25% and 75%of the total

bandwidth i.e. 128 and 384 subcarriers respectively. The overload MC-CDMA

is leading for all transmission powers. However, the sum rate difference with


340 350 360 370 380 390 400 410 420 430 4402560

2580

2600

2620

2640

2660

2680


Sum

Rat

e (N

ats)

Overload MC−CDMAFull OFDMMixed HybridFull MC−CDMA

(a) Sum rate comparison of the four hybrid systems in AWGNfor Npu = 2

100 110 120 130 140 150 160 170 180840

850

860

870

880

890

900


Sum

Rat

e (N

ats)

Overload MC−CDMAFull OFDM Mixed HybridFull MC−CDMA

(b) Sum rate comparison of the four hybrid systems in AWGNfor Npu = 6

Figure 6.5: Sum rate comparison of the four hybrid systems in AWGN for differentPU occupancy levels


210 220 230 240 250 260 270 280 290 300 3101600

1620

1640

1660

1680

1700

1720

1740

1760


Sum

Rat

e (N

ats)

Overload MC−CDMA

Full OFDM

Figure 6.6: Sum rate comparison of the two hybrid systems in Fading channel forNpu = 4

.

the second highest rate, Full-OFDM, decreases with increasing PU occupancy

level. This is due to the fact that Overload system treats the PU interference as

narrowband interference. The more the PU occupancy, the less overload system

can suppress the interference. However, the overload has the highest sum rate in

compared with other three methods.

The simulations are also shown for the fading channels. Primary transmitter

to secondary receiver is assumed to be ITU-Pedestrian B channel, as well as

secondary transmitter to secondary receiver. It should be noted that for the case

of full-OFDM, the power allocation is applied for the length of 32 subcarriers to

make sure that the channel is flat over the subband.

Fig. 6.6 compares the overload MC-CDMA and Full-OFDM systems’

capacities for the case of 50% PU occupancy. It is observed that the sum rate of

the proposed scheme significantly outperforms the Full-OFDM system. There is

a sharp sum rate increment observed for the overload case at transmission power


340 350 360 370 380 390 400 410 420 430 4402350

2400

2450

2500

2550

2600

2650

2700


Sum

Rat

e (N

ats)

Overload MC−CDMAFull−OFDM

Figure 6.7: Sum rate comparison of the two hybrid systems in Fading channel forNpu = 2

.

of 250 mW. As mentioned in Section 6.5.2, due to the complexity of the problem,

the sub-optimal algorithm is used for the overload case in fading channels. The

sudden sum rate increment is due to the system shifting from utilizing overlay

only, to the hybrid case. The capacities are also compared for different PU

occupancy level of 25% in Fig. 6.7.

6.7 Summary

In this chapter, four hybrid transmission schemes for CR systems are compared in

AWGN channels in terms of sum rate. The four systems were namely full-OFDM,

mixed OFDM/MC-CDMA system, the proposed full MC-CDMA introduced in

Chapter 4, and the Proposed overload MC-CDMA system introduced in Chapter

5. The optimization problem to maximize the sum rate for each case was defined

and the optimal solution was found. The two leading systems in terms of sum rate


were then chosen, namely the proposed overload MC-CDMA and the Full-OFDM,

to be compared in fading channels. The two systems’ capacities were studied for

fading channels in Section 6.5. The simulation results in Section 6.6 showed that

the proposed overload system exhibits more achievable sum rate in compared

with the other three methods both in AWGN and fading channels.

Chapter 7

Conclusions and Future Work

7.1 Conclusions

The study focuses on the problem of spectrum efficiency using Dynamic

Spectrum Sharing (DSS), specifically in Cognitive Radio Networks (CRNs).

Spectrum sharing in CRNs is mainly through two schemes, overlay and underlay.

By combining the two schemes as a hybrid system, this thesis has shown

the significant capabilities to improve spectral efficiency and underlay BER

performance in CRNs. With this regard, two hybrid systems were proposed

and compared with the available systems in the literature. Two performance

measures, Capacity and BER, were considered to compare the existing and the

proposed schemes.

The first scheme, elaborated in Chapter 4, is a full-load hybrid MC-CDMA

system. Unlike the available schemes that solely use the underutilized parts of

the spectrum for underlay transmission, the proposed scheme uses the whole

bandwidth for underlay. By using a full MC-CDMA system for both overlay and

underlay while keeping orthogonality between them, underlay can benefit from the

interference mitigation capability of MC-CDMA. Two chip-level and symbol-level

MMSE-based equalizers were proposed for underlay data detection. The underlay

performance of the proposed system was next compared with the existing system,

134

CHAPTER 7. CONCLUSIONS AND FUTURE WORK 135

Mixed hybrid scheme. The proposed full-load underlay performance showed to

have better performance for different PU occupancy levels.

To further enhance the spectrum efficiency, an overload MC-CDMA was

proposed in Chapter 5. Overlay transmits through the spectrum holes, utilizing

the full signal dimension, while underlay overloads the system. Two layered

spreading was applied to separate overlay/underlay data. The benefit with the

proposed system is that the overlay detection can be applied independently and

without the knowledge of the underlay spreading and/or scrambling codes, or

even other overlay users’ spreading codes. Therefore, the overloading is applied

without disturbing or adding complexity to the overlay detection. Furthermore,

The underlay performance was shown to maintain good BER performance even in

high PU interference level. The underlay was next extended to a multi-user case

in which the number of underlay users depend upon the interference threshold of

the primary system. To minimize Inter-User-Interference (IUI), a code allocation

algorithm is proposed.

Chapter 6 compared the capacity of the two hybrid schemes proposed in

Chapters 4 and 5, with the two available hybrid schemes in the literature, namely

Full-OFDM and the Mixed hybrid schemes. The proposed overload system

showed to increase capacity significantly in compared with the other 3 methods.

In addition, the proposed full-load scheme showed to have the least sensitivity to

the PU interference level.

In conclusion, the two proposed scheme can highly utilize the MC-CDMA

interference mitigation capability and suppress the PU interference considerably.

The proposed systems are shown to have better BER performance in compared

with the existing schemes in the literature. On the other hand, the overload

system is shown to significantly improve the total capacity in AWGN and Rayleigh

fading channels.

CHAPTER 7. CONCLUSIONS AND FUTURE WORK 136

7.2 Future Work

Several possible research directions in this area is listed below.

• The systems proposed in this work are considered for downlink transmission.

It will be of interest to adapt the system for uplink application.

• In Chapter 5, we proposed an overload MC-CDMA system using W-H

and orthogonal Gold codes for spreading and scrambling respectively.

Both types of codes are a set of binary codes. The performance of the

proposed overload system can be examined with non-binary codes. It is

also interesting to examine the system’s performance with non-binary codes

and in conjugation with higher order modulation techniques.

• In Chapter 6, the sum rate of the systems proposed in Chapters 4 and 5

are calculated and compared with the available systems in the literature.

The optimization problem is considering the interference threshold. In

other words, the received received power from the cognitive user to the

secondary receiver in the PU occupied bands should not be more than a

certain threshold. In this work, the interference leakage from the adjacent

secondary bands (unoccupied bands) to the occupied bands are neglected

as it is small in practice. Similarly, the interference leakage from PU to

overlay bands are also neglected. However, considering these leakages, a

more realistic scenario for the optimization problem can be studied.

• Finally, the proposed systems in Chapters 4 and 5 can be extended for

applications in Femto cell access point [95] and also cognitive cellular

networks [96].

References

[1] S. Inc., “Cisco visual networking index: Forecast and

methodology, 2013-2018,” June 2014. [Online]. Available:

http://www.cisco.com/c/en/us/solutions/collateral/service-provider/

ip-ngn-ip-next-generation-network/white paper c11-481360.html

[2] S. Chen and J. Zhao, “The requirements, challenges, and technologies for

5G of terrestrial mobile telecommunication,” Communications Magazine,

IEEE, vol. 52, no. 5, pp. 36–43, May 2014.

[3] P. Rost, C. Bernardos, A. Domenico, M. Girolamo, M. Lalam, A. Maeder,

D. Sabella, and D. Wbben, “Cloud technologies for flexible 5G radio access

networks,” Communications Magazine, IEEE, vol. 52, no. 5, pp. 68–76,

May 2014.

[4] FCC, “Unlicensed and unshackled: A joint osp-oet white paper on

unlicensed devices and their regulatory issues,” May 2003.

[5] J. Mitola and J. Maguire, G.Q., “Cognitive radio: making software radios

more personal,” Personal Communications, IEEE, vol. 6, no. 4, pp. 13–18,

Aug 1999.

[6] I. Akyildiz, W. Lee, M. Vuran, and S. Mohanty, “Next generation/dynamic

spectrum access/cognitive radio wireless networks: a survey,” Computer

Networks, vol. 50, no. 13, pp. 2127–2159, 2006.

137

REFERENCES 138

[7] K. Ben Letaief and W. Zhang, “Cooperative communications for cognitive

radio networks,” Proceedings of the IEEE, vol. 97, no. 5, pp. 878 –893, may

2009.

[8] J. Mitola, “The software radio architecture,” Communications Magazine,

IEEE, vol. 33, no. 5, pp. 26–38, May 1995.

[9] FCC, “Federal communications commission notice of proposed rule making

and order,” Dec. 2003.

[10] M. Marcus, “The underlay/overlay controversy,” Wireless

Communications, IEEE, vol. 14, no. 5, pp. 4 –5, October 2007.

[11] J. Tadrous, A. Sultan, and M. Nafie, “Admission and power control for

spectrum sharing cognitive radio networks,” Wireless Communications,

IEEE Transactions on, vol. 10, no. 6, pp. 1945–1955, June 2011.

[12] L. B. Le and E. Hossain, “Resource allocation for spectrum underlay in

cognitive radio networks,” Wireless Communications, IEEE Transactions

on, vol. 7, no. 12, pp. 5306–5315, December 2008.

[13] K. Son, B. C. Jung, S. Chong, and D. K. Sung, “Opportunistic underlay

transmission in multi-carrier cognitive radio systems,” in IEEE Wireless

Commun. Net. Conf. (WCNC), April 2009, pp. 1 –6.

[14] Q. Qu, L. Milstein, and D. Vaman, “Cognitive radio based multi-user

resource allocation in mobile ad hoc networks using multi-carrier cdma

modulation,” Selected Areas in Communications, IEEE Journal on, vol. 26,

no. 1, pp. 70–82, Jan 2008.

[15] T. Weiss and F. Jondral, “Spectrum pooling: an innovative strategy for the

enhancement of spectrum efficiency,” IEEE Commun. Mag., vol. 42, no. 3,

pp. S8 – 14, Mar 2004.

REFERENCES 139

[16] B. Farhang-Boroujeny and R. Kempter, “Multicarrier communication

techniques for spectrum sensing and communication in cognitive radios,”

Communications Magazine, IEEE, vol. 46, no. 4, pp. 80–85, April 2008.

[17] G. Bansal, M. Hossain, and V. Bhargava, “Optimal and suboptimal

power allocation schemes for ofdm-based cognitive radio systems,” Wireless

Communications, IEEE Transactions on, vol. 7, no. 11, pp. 4710 –4718,

november 2008.

[18] ——, “Adaptive power loading for ofdm-based cognitive radio systems

with statistical interference constraint,” Wireless Communications, IEEE

Transactions on, vol. 10, no. 9, pp. 2786 –2791, september 2011.

[19] A. Attar, M. Nakhai, and A. Aghvami, “Cognitive radio transmission based

on direct sequence MC-CDMA,” IEEE Trans. Wireless Commun., vol. 7,

no. 4, pp. 1157 –1162, April 2008.

[20] FCC, “Federal communications commission spectrum policy task force:

Report of the spectrum efficiency working group,” Nov. 2002.

[21] S. Haykin, “Cognitive radio: brain-empowered wireless communications,”

IEEE J. Sel. Areas in Commun., vol. 23, no. 2, pp. 201 – 220, Feb. 2005.

[22] L. B. Le and E. Hossain, “Resource allocation for spectrum underlay in

cognitive radio networks,” Wireless Communications, IEEE Transactions

on, vol. 7, no. 12, pp. 5306–5315, December 2008.

[23] G. Bansal, M. Hossain, V. Bhargava, and T. Le-Ngoc, “Subcarrier and

power allocation for OFDMA-based cognitive radio systems with joint

overlay and underlay spectrum access mechanism,” Vehicular Technology,

IEEE Transactions on, vol. 62, no. 3, pp. 1111–1122, 2013.

[24] V. Chakravarthy, X. Li, R. Zhou, Z. Wu, and M. Temple, “Novel

overlay/underlay cognitive radio waveforms using SD-SMSE framework to

REFERENCES 140

enhance spectrum efficiency-part ii: analysis in fading channels,” IEEE

Trans. Commun., vol. 58, no. 6, pp. 1868 –1876, June 2010.

[25] V. Chakravarthy, X. Li, Z. Wu, M. Temple, F. Garber, R. Kannan, and

A. Vasilakos, “Novel overlay/underlay cognitive radio waveforms using

SD-SMSE framework to enhance spectrum efficiency- part i: theoretical

framework and analysis in AWGN channel,” IEEE Trans. Commun.,

vol. 57, no. 12, pp. 3794 –3804, December 2009.

[26] T. Rappaport and S. B. O. (Firme), Wireless communications: principles

and practice. Prentice Hall PTR Upper Saddle River (New Jersey), 1996,

vol. 2.

[27] A. Goldsmith, Wireless communications. Cambridge Univ Pr, 2005.

[28] M. Simon and M. Alouini, Digital communication over fading channels.

Wiley-IEEE Press, 2005, vol. 86.

[29] A. Molisch, Wireless communications. Wiley, 2011.

[30] J. Proakis and D. Manolakis, “Digital signal processing, principles.

algorithms, and applications, printice-hall,” Inc, New Jersey, 1996.

[31] K. Fazel and S. Kaiser, Multi-Carrier and Spread Spectrum systems. John

Wiley and Sons Ltd, 2003.

[32] L. Cimini, “Analysis and simulation of a digital mobile channel using

Orthogonal Frequency Division Multiplexing,” Communications, IEEE

Transactions on, vol. 33, no. 7, pp. 665–675, Jul 1985.

[33] Y. Wu and W. Zou, “Orthogonal Frequency Division Multiplexing:

a multi-carrier modulation scheme,” Consumer Electronics, IEEE

Transactions on, vol. 41, no. 3, pp. 392–399, Aug 1995.

REFERENCES 141

[34] A. Chouly, A. Brajal, and S. Jourdan, “Orthogonal multicarrier

techniques applied to direct sequence spread spectrum cdma systems,” in

Global Telecommunications Conference, 1993, including a Communications

Theory Mini-Conference. Technical Program Conference Record, IEEE in

Houston. GLOBECOM ’93., IEEE, Nov-2 Dec, pp. 1723–1728 vol.3.

[35] S. Hara and R. Prasad, “Overview of multicarrier cdma,” Communications

Magazine, IEEE, vol. 35, no. 12, pp. 126 –133, dec 1997.

[36] K. El-Barbary and H. Alneyadi, “Comparison of the behavior of mmse

detection scheme for ds-cdma and mc-cdma,” in Wireless and Optical

Communications Networks, 2005. WOCN 2005. Second IFIP International

Conference on, March 2005, pp. 490–495.

[37] J.-P. Linnartz, “Performance analysis of synchronous mc-cdma in mobile

rayleigh channel with both delay and doppler spreads,” Vehicular

Technology, IEEE Transactions on, vol. 50, no. 6, pp. 1375–1387, Nov 2001.

[38] E. Sourour and M. Nakagawa, “Performance of orthogonal multicarrier

cdma in a multipath fading channel,” Communications, IEEE Transactions

on, vol. 44, no. 3, pp. 356–367, Mar 1996.

[39] S. Kondo and L. Milstein, “Performance of multicarrier DS-CDMA

systems,” IEEE Trans. Commun., vol. 44, no. 2, pp. 238–246, 1996.

[40] K. Cheun, K. Choi, H. Lim, and K. Lee, “Antijamming performance of

a multicarrier direct-sequence spread-spectrum system,” Communications,

IEEE Transactions on, vol. 47, no. 12, pp. 1781 –1784, dec 1999.

[41] V. Tarokh, New Directions in Wireless Communications Research.

Springer, 2009.

[42] L. Vandendrope, Performance analysis of Multi-tone CDMA wireless

communication system, most secure communication for 4G, April 1993.

REFERENCES 142

[43] L. Hanzo, M. Munster, B. J. Chio, and T. Keller, OFDM and MC-CDMA

for broadband multi-user communication, WLANs and broadcasting. John

Wiley and Sons, 2003.

[44] J. Ahmed, Spectral Efficiency of CDMA-based AD-HOC Networks. school

of Electrical and Electronic Engineering, The University of Manchester,

2010.

[45] S. Haykin, Communication Systems. John Wiley and Sons, Inc., 2001.

[46] H. Poor and S. Verdu, “Probability of error in mmse multiuser detection,”

Information Theory, IEEE Transactions on, vol. 43, no. 3, pp. 858–871,

May 1997.

[47] M. Vehkapera, D. Tujkovic, Z. Li, and M. Juntti, “Receiver design

for spatially layered downlink MC-CDMA system,” IEEE Trans. Vehic.

Technol., vol. 54, no. 3, pp. 1042–1055, 2005.

[48] J.-F. Helard, J.-Y. Baudais, and J. Citerne, “Linear MMSE detection

technique for MC-CDMA,” Electron. Lett., vol. 36, no. 7, pp. 665–666,

2000.

[49] A. Phasouliotis and D. So, “Layered space-time receiver for downlink

multiple-input multiple-output multi-carrier code division multiple access

systems,” Communications, IET, vol. 5, no. 13, pp. 1907–1917, 2011.

[50] D. Mottier, D. Castelain, J.-F. Herlard, and J. Baudais, “Optimum and

sub-optimum linear mmse multi-user detection for multi-carrier cdma

transmission systems,” in Vehicular Technology Conference, 2001. VTC

2001 Fall. IEEE VTS 54th, vol. 2, 2001, pp. 868–872 vol.2.

[51] S. Kaiser, “Analytical performance evaluation of ofdm-cdma mobile radio

systems,” in Proc. 1st European Personal and Mobile Communications

Conf., EPMCC95, 1995, pp. 215–220.

REFERENCES 143

[52] L. Rugini, “Linear equalization for multicode MC-CDMA downlink

channels,” Communications Letters, IEEE, vol. 16, no. 9, pp. 1353–1356,

2012.

[53] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge Univ Pr,

2004.

[54] M. Rajabzadeh and H. Khoshbin, “A novel multicarrier cdma transmission

scheme for cognitive radios with sidelobe supression,” International Journal

of Communication Systems, vol. 26, pp. 1485–1499, Mar. 2012.

[55] ——, “Novel spreading codes for multicarrier code division multiple

access based cognitive radio networks with sidelobe suppression,” Wireless

Communications and Mobile Computing, vol. 14, no. 4, pp. 355–365, Jan.

2012.

[56] E. Hossain and V. K. Bhargama, Cognitive Wireless Communication

Networks. Springer, 2007.

[57] L. Berlemann and S. Mangold, Cognitive Radio and Dynamic Spectrum

Access. Wiley, 2009.

[58] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for

cognitive radio applications,” IEEE Commun. Surveys Tuts., vol. 11, no. 1,

pp. 116 –130, 2009.

[59] G. Salami, O. Durowoju, A. Attar, O. Holland, R. Tafazolli,

and H. Aghvami, “A comparison between the centralized and

distributed approaches for spectrum management,” Communications

Surveys Tutorials, IEEE, vol. 13, no. 2, pp. 274 –290, quarter 2011.

[60] K. C. Chen and R. Prasad, Cognitive radio networks. John Wiley and

Sons, 2009.

[61] B. Fette, Cognitive Radio Technology. Academic Press, Elsevier, 2009.

REFERENCES 144

[62] X. Chen, H. Chen, and W. Meng, “Cooperative communications for

cognitive radio networks; from theory to applications,” pp. 1–13, 2014.

[63] FCC, “Establishment of an interference temperature metric to quantify and

manage interference and to expand available unlicensed operation in certain

fixed, mobile and satellite frequency bands,,” ET Docket No. 03-237, Notice

of Inquiry and Notice of proposed rule making, Nov. 2003.

[64] G. Minden, J. Evans, L. Searl, D. DePardo, R. Rajbanshi, J. Guffey,

Q. Chen, T. Newman, V. Petty, F. Weidling, M. Peck, B. Cordill, D. Datla,

B. Barker, and A. Agah, “Cognitive radios for dynamic spectrum access -

an agile radio for wireless innovation,” Communications Magazine, IEEE,

vol. 45, no. 5, pp. 113–121, May 2007.

[65] R. Rajbanshi, Q. Chen, A. M. Wyglinski, G. J. Minden, and J. B. Evans,

“Quantitative comparison of agile modulation techniques for cognitive radio

transceivers,” in Consumer Communications and Networking Conference,

2007. CCNC 2007. 4th IEEE, jan. 2007, pp. 1144 –1148.

[66] B. Natarajan, C. Nassar, S. Shattil, M. Michelini, and Z. Wu,

“High-performance MC-CDMA via carrier interferometry codes,”

Vehicular Technology, IEEE Transactions on, vol. 50, no. 6, pp. 1344–1353,

2001.

[67] G. Chung, S. Sridharan, S. Vishwanath, and C.-S. Hwang, “On the capacity

of overlay cognitive radios with partial cognition,” Information Theory,

IEEE Transactions on, vol. 58, no. 5, pp. 2935–2949, May 2012.

[68] A. Ghasemi and E. Sousa, “Fundamental limits of spectrum-sharing in

fading environments,” Wireless Communications, IEEE Transactions on,

vol. 6, no. 2, pp. 649–658, Feb 2007.

[69] M. Khoshkholgh, K. Navaie, and H. Yanikomeroglu, “Impact of the

secondary service transmit power constraint on the achievable capacity

REFERENCES 145

of spectrum sharing in rayleigh fading environment,” Communications

Letters, IEEE, vol. 12, no. 12, pp. 865 –867, december 2008.

[70] S. Stotas and A. Nallanathan, “Enhancing the capacity of spectrum sharing

cognitive radio networks,” Vehicular Technology, IEEE Transactions on,

vol. 60, no. 8, pp. 3768–3779, Oct 2011.

[71] C. E. Shannon, “A mathematical theory of communication,” Bell system

technical journal, vol. 27, 1948.

[72] R. Zhang and Y.-C. Liang, “Exploiting multi-antennas for opportunistic

spectrum sharing in cognitive radio networks,” Selected Topics in Signal

Processing, IEEE Journal of, vol. 2, no. 1, pp. 88 –102, feb. 2008.

[73] X. Wang and H. Poor, “Iterative (turbo) soft interference cancellation

and decoding for coded cdma,” Communications, IEEE Transactions on,

vol. 47, no. 7, pp. 1046–1061, Jul 1999.

[74] “Selection procedures for the choice of radio transmission technologies of the

UMTS (UMTS 30.03 version 3.2.0),,” Tech. Rep., 101 112 V3.2.0, 1998-04.

[75] B. Popovic, “Spreading sequences for multicarrier CDMA systems,”

Communications, IEEE Transactions on, vol. 47, no. 6, pp. 918–926, Jun

1999.

[76] I. Oppermann and B. Vucetic, “Complex spreading sequences with a wide

range of correlation properties,” Communications, IEEE Transactions on,

vol. 45, no. 3, pp. 365–375, Mar 1997.

[77] E. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and

wideband CDMA cellular networks,” Commun. Mag., IEEE, vol. 36, no. 9,

pp. 48–54, 1998.

[78] S. I. Park, S. R. Park, I. Song, and N. Suehiro, “Multiple-access interference

reduction for qs-cdma systems with a novel class of polyphase sequences,”

REFERENCES 146

Information Theory, IEEE Transactions on, vol. 46, no. 4, pp. 1448–1458,

Jul 2000.

[79] D. Kedia, M. Duhan, and S. L. Maskara, “Evaluation of correlation

properties of orthogonal spreading codes for cdma wireless mobile

communication,” in Advance Computing Conference (IACC), 2010 IEEE

2nd International, Feb 2010, pp. 325–330.

[80] E. Alsusa and A. ElKalagy, “On the performance of orthogonal

polyphase sequences in asynchronous cdma systems,” in Software,

Telecommunications Computer Networks, 2009. SoftCOM 2009. 17th

International Conference on, Sept 2009, pp. 196–200.

[81] C. Zhang, “Non-continuous carrier-interferometry codes,” in Signal Design

and its Applications in Communications, 2009. IWSDA ’09. Fourth

International Workshop on, Oct. 2009, pp. 134 –137.

[82] C. Nassar, B. Natarajan, and S. Shattil, “Introduction of carrier interference

to spread spectrum multiple access,” in Wireless Communications and

Systems, 2000. 1999 Emerging Technologies Symposium, 1999, pp. 4.1–4.5.

[83] Z. Yuan and A. M. Wyglinski, “On sidelobe suppression for

multicarrier-based transmission in dynamic spectrum access networks,”

Vehicular Technology, IEEE Transactions on, vol. 59, no. 4, pp. 1998–2006,

May 2010.

[84] H. Nguyen and E. Shwedyk, “A new construction of signature waveforms for

synchronous cdma systems,” Broadcasting, IEEE Transactions on, vol. 51,

no. 4, pp. 520–529, Dec 2005.

[85] M. Mukherjee and P. Kumar, “Overloaded WH-spread ci/mc-cdma with

iterative interference cancellation,” Communications Letters, IEEE, vol. 15,

no. 12, pp. 1391–1393, 2011.

REFERENCES 147

[86] N. Taylor, M. A. Cooper, S. M. D. Armour, and J. McGeehan,

“Performance evaluation of carrier interferometry implementations of

mc-cdma over a wideband channel suffering phase noise,” in Vehicular

Technology Conference, 2005. VTC 2005-Spring. 2005 IEEE 61st, vol. 5,

May 2005, pp. 3043–3047 Vol. 5.

[87] C. D’Amours and A.-O. Dahmane, “Permutation spreading for

asynchronous mimo-cdma systems using hadamard codes and gold

scrambling sequences,” in Wireless Communications and Networking

Conference, 2009. WCNC 2009. IEEE, April 2009, pp. 1–6.

[88] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University

Press, 1985.

[89] A. Hjorungnes and D. Gesbert, “Complex-valued matrix differentiation:

Techniques and key results,” Signal Processing, IEEE Transactions on,

vol. 55, no. 6, pp. 2740–2746, 2007.

[90] G. Bansal, O. Duval, and F. Gagnon, “Joint overlay and underlay power

allocation scheme for OFDM-based cognitive radio systems,” in IEEE Veh.

Technol. Conf. (VTC), May 2010, pp. 1–5.

[91] F. Arpanaei, K. Navaie, and S. N. Esfahani, “A hybrid overlay-underlay

strategy for ofdm-based cognitive radio systems and its maximum

achievable capacity,” in Electrical Engineering (ICEE), 2011 19th Iranian

Conference on, may 2011, pp. 1 –6.

[92] M. Khoshkholgh, K. Navaie, and H. Yanikomeroglu, “Access strategies for

spectrum sharing in fading environment: Overlay, underlay, and mixed,”

Mobile Computing, IEEE Transactions on, vol. 9, no. 12, pp. 1780 –1793,

dec. 2010.

[93] X. Kang, Y.-C. Liang, H. Garg, and L. Zhang, “Sensing-based spectrum

REFERENCES 148

sharing in cognitive radio networks,” IEEE Trans. Veh. Technol., vol. 58,

no. 8, pp. 4649 –4654, Oct. 2009.

[94] E. Lo, P. Chan, V. Lau, R. Cheng, K. Letaief, R. Murch, and W.-H.

Mow, “Adaptive resource allocation and capacity comparison of downlink

multiuser mimo-mc-cdma and mimo-ofdma,” Wireless Communications,

IEEE Transactions on, vol. 6, no. 3, pp. 1083–1093, March 2007.

[95] H. Venkataraman and G. Muntean, Cognitive Radio and its Application for

Next Generation Cellular and Wireless Networks. Springer, 2011.

[96] X. Hong, J. Wang, C.-X. Wang, and J. Shi, “Cognitive radio in 5g:

a perspective on energy-spectral efficiency trade-off,” Communications

Magazine, IEEE, vol. 52, no. 7, pp. 46–53, July 2014.

[97] A. Papoulis and P. Unnikrishna, Probability, random variables and

stochastic processes. Mc Graw Hill, 2002.

[98] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products.

San Diego, CA: Acdemic, 1994.

[99] M. Hasna and M.-S. Alouini, “End-to-end performance of transmission

systems with relays over rayleigh-fading channels,” Wireless

Communications, IEEE Transactions on, vol. 2, no. 6, pp. 1126–1131, Nov

2003.

[100] J. Ahmed and K. Hamdi, “Spectral efficiency degradation of multicarrier

cdma due to carrier frequency offset,” in Communications (ICC), 2011

IEEE International Conference on, June 2011, pp. 1–5.

[101] K. Hamdi, “On the statistics of signal-to-interference plus noise ratio

in wireless communications,” Communications, IEEE Transactions on,

vol. 57, no. 11, pp. 3199–3204, Nov 2009.

Appendix A

Underlay Full-Load BER

Performance with ZF

We seek to obtain the average BER, by solving the expression of the form

E[Erfc

(√γ)]

in

Pe = Q(√γ) =

1

2Erfc

√γ

2(A.1)

where Erfc(x) = 2π

∫∞0

exp(−t2)dt is the complementary error function. For

simplicity of notation, γzfun in (4.13) is shown by γ in this section. Using direct

methods, we will require to solve at least M + Mpu integrals to average out the

M +Mpu random variables in (4.13). Moreover, directly obtaining the joint PDF

for γ is a very tedious task. To simplify the problem, we first seek to find out the

baseline BER, i.e. BER without the PU interference. With this regard, we need

to obtain the PDF of the form

Z =M∑i=1

Y =M∑i=1

1

X(A.2)

where X has exponential PDF i.e. fX(x) = λe−λx for λ > 0, and λ is the

parameter of the exponential distribution. Knowing the PDF of y as [97]

fY (y) =λ

y2e(−λ/y) y ≥ 0, (A.3)

149

APPENDIX A. UNDERLAY FULL-LOAD BER PERFORMANCEWITH ZF150

the Moment Generating Function (MGF) of y will be

MY (s) = E[esY ] = λ

∫ ∞0

esY fY (y)dy = λ

∫ ∞0

λ

y2esY e(−λ/y)dy. (A.4)

using [98], eq. (8.486.16) we will have 1

MY (s) = 2√λsK1(2

√λs) (A.5)

where K1(.) is the first order modified Bessel function of the second kind. The

symmetry property of the modified Bessel function, K−1 = K1 , is used in

the above derivation ([98], eq. (8.486.16)). Assuming X1 ,X2, ... , XM to be

independent random variables, MZ(s) can be written as

MZ(s) = (2√λsK1(2

√λs))M . (A.6)

Knowing the BER is given by

BER =

∫ ∞0

Q(γ)fγ(γ)dγ (A.7)

and γ is in the form γ = MpcuzN0

, we can write

BER =

∫ ∞0

Q

(√MpcuzN0

)fz(z)dz (A.8)

where

fz(z) =1

2π

∫ ∞−∞

e−iszφZ(s)ds. (A.9)

It should be mentioned that several direct and indirect methods were

attempted, including [100, 101], to achieve the MGF or the characteristic function

of (A.2) to obtain a closed-form for the problem. However, the result is not yet

achieved due to the unknown pdf of the inverse of the channel frequency response.

1also approved by [99]

Documents

HYBRID OVERLAY/UNDERLAY COGNITIVE RADIO NETWORKS …