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ABSTRACT

This research work presentsthedevelopment of an improved ergodic capacity of underlay
Cognitive Radio (CR) with imperfect Channel State Information(CSI). An underlay CR
network under a Peak Interference Power (PIP) constraint imposed by a Primary User
(PU) was considered.Aclosed formergodic capacity expression of the Secondary User
(SU)under PIP constraintwas derivedin order to determine the ergodic capacity under
different fading types using Nakagami-m distributions.The m-parameter of the
Nakagami-m fading channel measures the ratio of the Line-of-Sight (LoS) signal power
to that of the multipath component. The improved ergodic capacity expression developed
was validated with the existing ergodic capacity expression at m=1. The results showed
that the ergodic capacity of the SU could be extended to different fading types in the CR
path by adjusting the m-parameter.The impact of channel estimation errors, 2  and
channelcorrelation coefficient,  on the SUergodic capacity was studiedunder different
fading types to provide an insight on the capacity behavior of CR network. The
resultsobtained atdifferent values of m parametersshowedthe ergodic capacity degraded
as a result of increasing 2  and it increases with increasing  .It was observed that at
m=1/2,1,2 and 3, a significant capacity gains of 21.65%, 19.71%, 17.43%, and 15.82%
were achieved, when 3% interference outage   out P was considered for all the m values
from  2 1 to 2   0 . However, a capacity gains of 23.59%, 22.31%, 21.02%, and
20.26% were also achieved respectively at 1% out P . It was also found that at m=1/2,1,2
and 3, a spectral efficiency in (bits/S/Hz) of 0.5007, 0.2888,0.2660, and 0.2596 were
achieved when 3% out P was considered from   0 to  1, while a spectral efficiency
vii
of 0.2548, 0.1771, 0.1211, 0.0931 were also achieved at 1% out P for the respective m
values.

 

 

TABLE OF CONTENTS

DECLARATIONi
CERTIFICATIONii
DEDICATIONiii
ACKNOWLEDGEMENTiv
ABSTRACTvi
TABLE OF CONTENTSvii
LIST OF FIGURESx
LIST OF TABLESxi
LIST OF ABBREVIATIONSxii
CHAPTER ONE: INTRODUCTION
1.1 Background To the Study1
1.2 Problem Statement1
1.3 Significance of Research2
1.4 Aim and Objectives3
1.5 Scope of the Research3
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction4
2.2 Review of Fundamental Concepts4
2.2.1 Cognitive Radio4
2.2.2 Cognitive Tasks5
2.2.3 Cognitive Radio Paradigm7
2.2.4 Cognitive Radio Networks8
2.2.5 Wireless Channel11
2.2.6 Channel State Information17
2.2.7 Channel Capacity19
2.2.8 Ergodic Capacity20
2.3 Review of Similar Works26
CHAPTER THREE: MATERIALS AND METHODS
3.1 Introduction36
viii
3.2 Materials36
3.3 Methodology36
3.4 System and Channel Models37
3.5 Ergodic Capacity40
3.3.1 Ergodic Capacity under the PIP constraint41
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Introduction47
4.2 Impact of 2  on the SU capacity under different m values47
4.3 Impact of 2  on SU Capacity at m=250
4.4 Impact of  on the SU capacity under different m-values52
4.5 Impact of  on the SU Capacity at m=254
4.6 Validation56
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS
5.1 Introduction57
5.2 Conclusion57
5.3 Significant Contributions58
5.4 Recommendations for Further Work59
REFERENCE60
APPENDIX A

 

Project Topics

CHAPTER ONE

 

INTRODUCTION
1.1 Background To the Study
Wireless communications offers a wide range of services like mobile internet, data exchange, location tracking, space communications, etc. In recent years there has been a dramatic increase in the demand for radio spectrum. However, the radio spectrum is a limited natural resource. Access to it is regulated by the government agencies such as the Federal Communications Commission (FCC) in the United Sates, Nigerian Communication Commission (NCC) and Nigerian Broadcasting Commission (NBC). The limited radio spectrum led to the development of the cognitive radio (CR) with a view to exploiting the available spectrum efficiently. This has led to the emergence of a spectrum sharing technique in whichunlicensed/ secondary users (SU’s) can share the spectrum of licensed/ primary users (PU’s) without harming primary communications (Sboui, 2013). The cognitive radio has been studied widely as it provide ways to improve the spectrum efficiency by allowing SU to concurrently access the spectrum band licensed to the PU while causing limited interference to the PU (Haykins, 2005).
1.2 Problem Statement
Capacity analysis is useful in investigating the ultimate performance limits of a CR network. A CR user may coexist with the incumbent PUs on either a non-interfering basis or on an interfering-tolerant basis. The interference-tolerant case works such that the CR users are allowed to operate on the frequency band assigned for the PUs as long
2
as the interference received at the primary user remains below a certain threshold. The channel state information (CSI) between the secondary transmitter (STx) and the primary receiver (PRx) is used by the STx to calculate the appropriate transmit power to limit the interference on the PRx. However, in practical communication systems, the CSI is frequently imperfect for spectrum sharing systems, it is difficult for the SU to perfectly acquire the CSI in the STx to the PRx channel due to channel estimation errors and feedback delay. The cognitive radio channel may also undergoesdifferent fading types, which affects the ergodic capacity. The existing ergodic capacity under imperfect CSI by Xuet al., (2013b) is restricted to study the performance behavior of CR in a Rayleigh fading environment. This work presents the development of an improvedergodic capacity of underlay CRsystem with imperfect CSI under different fading conditions using a Nakagami-m distribution.
1.3 Significance of Research
A number of studies have been conducted on spectrum sharing environments, especially on the secondary link capacity based on using power control to satisfy interference constraints. In most of the works (Ghasemi& Sousa, 2007; Rezki&Alouini, 2012a), the capacity of the secondary link was analyzed under the assumption that the secondary user knows the CSI perfectly between the STx and the PRx. However, the obtained CSI is frequently outdated in practical systems due to channel estimation errors and feedback delay. In a spectrum sharing system the problems caused by this outdated CSI are severe (Kim et al, 2012). The channel estimation errors and feedback delay exist simultaneously, and neglecting either one of them leads to violation of the interference
3
power constraint at the PU. Motivated by the results of Xuet al. (2013b), there is a need
to extend the work in order to consider the fading conditions in the cognitive radio
channel, this is because the cognitive radio path may experience different fading types.
The performance analysis on the behavior CR on the ergodic capacity of the SU under
different fading conditions can be carried out when this fading conditions are considered.
1.4 Aim and Objectives
The aim of this research is to developan improved ergodic capacity of underlay cognitive
radio with an imperfect channel state information. The objectives which was employed to
achieve this aim is as follows:
1. To determine the ergodic capacity under the peak interference power
constraint
2. To examine the impact of channel estimation errors using the estimation
errors variance, 2  and the channel correlation coefficientusing the correlation
coefficient,  on the ergodic capacity
3. To validate the results obtained using the work of Xuet al., ( 2013b)
1.5 Scope of the Research
The scope of this dissertation is to study the performance of CR under different fading
conditions. The study is based on developing an improved ergodic capacity expression
with imperfect CSI using Nakagami-m fading distribution in the cognitive radio path, by
adjusting the m parameter of theNakagami-m fading distribution, the behavior of CR
under different fading conditions can be studied.

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