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
1.1 Cognitive Radio . . .
1.2 Motivations . . . . .
1.3 Contributions . . . .
1.4 Thesis Organization .
1.5 List of Publications .
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2 Theoretical Background
2.1 Introduction . . . . . . . . . . . . . . .
2.2 Large-Scale Path Loss and Shadowing .
2.3 Small-Scale Fading and Multipath . . .
2.4 Multipath Channel Model . . . . . . .
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2.5
Fading Channel Characteristics and Types . . . . . . . . . . . . .
2.5.1 RMS Delay Spread and Mean Excess Delay . . . . . . . .
2.5.2 Coherence Bandwidth . . . . . . . . . . . . . . . . . . . .
2.5.3 Doppler Spread . . . . . . . . . . . . . . . . . . . . . . . .
2.5.4 Coherence Time . . . . . . . . . . . . . . . . . . . . . . . .
2.5.5 Small-Scale Fading Types . . . . . . . . . . . . . . . . . .
2.6 Multi-Carrier Transmission . . . . . . . . . . . . . . . . . . . . . .
2.6.1 OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Multi-Carrier CDMA . . . . . . . . . . . . . . . . . . . . .
2.7 Diversity Techniques . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Equalization Techniques . . . . . . . . . . . . . . . . . . . . . . .
2.8.1 Zero Forcing Equalizer . . . . . . . . . . . . . . . . . . . .
2.8.2 Minimum Mean-Square Error Equalizer . . . . . . . . . . .
2.8.3 Chip and Symbol Level Equalization for MC-CDMA System
2.9 Basics of Convex Optimization . . . . . . . . . . . . . . . . . . . .
2.10 Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Cognitive Radio
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Dynamic Spectrum Access . . . . . . . . . . . . . . . .
3.2.1 Horizontal Spectrum Sharing . . . . . . . . . .
3.2.2 Vertical Spectrum Sharing . . . . . . . . . . . .
3.3 CR Definition and Main Functions . . . . . . . . . . .
3.4 Underlay Transmission and the Interference Threshold
3.5 Non-Contiguous (NC) Transmission . . . . . . . . . . .
3.5.1 Overlay Multi-User NC-MC-CDMA . . . . . . .
3.5.2 Underlay NC-MC-CDMA . . . . . . . . . . . .
3.6 Overlay/Underlay/Hybrid Capacity Comparison . . . .
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . .
4 Full-Load Hybrid System
4.1 Introduction . . . . . . . . . . . .
4.2 Hybrid Systems in the Literature
4.3 Full-Load Hybrid System Model .
4.4 Receiver . . . . . . . . . . . . . .
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4.5
4.6
4.4.1 ZF Receiver . . . . . . . . . . . . . .
4.4.2 Chip-Level MMSE-Based Receiver .
4.4.3 Symbol-Level MMSE Based-Receiver
Simulation Results . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . .
5 Overload Hybrid System
5.1 Introduction . . . . . . . . . . . . . . . .
5.2 Code Selection and Adaptation in CRNs
5.3 System Model and Transmitter Structure
5.4 Code Allocation Algorithm . . . . . . . .
5.5 Receiver . . . . . . . . . . . . . . . . . .
5.6 Simulation Results . . . . . . . . . . . .
5.6.1 Medium PU Interference Level . .
5.6.2 High PU Interference Level . . .
5.6.3 Underlay Multi-User Results . . .
5.7 Summary . . . . . . . . . . . . . . . . .
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6 Hybrid Overlay/Underlay Sum Rate Optimization
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
6.2 Sum Rate Comparison for Different Hybrid Schemes .
6.3 System Model . . . . . . . . . . . . . . . . . . . . . .
6.4 AWGN Channels . . . . . . . . . . . . . . . . . . . .
6.4.1 Full-OFDM . . . . . . . . . . . . . . . . . . .
6.4.2 Mixed OFDM/MC-CDMA . . . . . . . . . . .
6.4.3 Proposed Full-MC-CDMA . . . . . . . . . . .
6.4.4 Proposed Overload MC-CDMA . . . . . . . .
6.5 Rayleigh Fading Channels . . . . . . . . . . . . . . .
6.5.1 Full-OFDM . . . . . . . . . . . . . . . . . . .
6.5.2 Proposed Overload MC-CDMA . . . . . . . .
6.6 Simulation Results . . . . . . . . . . . . . . . . . . .
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . .
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7 Conclusions and Future Work
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7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4
Appendix A Underlay Full-Load BER Performance with ZF
5
149
List of Tables
2.1
2.2
Small Scale Fading Types . . . . . . . . . . . . . . . . . . . . . .
Main system and channel parameters of a W-ATM system [43] . .
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4.1
ITU Pedestrian B channel PDP . . . . . . . . . . . . . . . . . . .
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6
List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.1
4.2
4.3
Tap Delay Line model . . . . . . . . . . . . . . . . . . . . . . . .
OFDM signal spectrum [33] . . . . . . . . . . . . . . . . . . . . .
OFDM with FFT/IFFT implementation [27] . . . . . . . . . . . .
Block Diagram of a Multi-User MC-CDMA Transmitter . . . . . .
Block Diagram of a Multi-User MC-DS-CDMA Transmitter . . .
Block Diagram of a Multi-User MC-MT-CDMA Transmitter . . .
W-ATM Channel Impulse Response [43] . . . . . . . . . . . . . .
Synchronous MC-CDMA for downlink over W-ATM channel with
MRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Dynamic Spectrum Access classifications [56] . . . . . . . . . . . .
Horizontal and vertical spectrum sharing regulatory concept [57] .
Underlay spectrum opportunity and the interference threshold concept [63] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Frequency spectra of NC-OFDM subcarriers [56] . . . . . . . . . .
Overlay Multi-User NC-MC-CDMA in AWGN . . . . . . . . . . .
Overlay NC-MC-CDMA in fading channel with different spreading
and MMSE-FDE . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theoretical vs simulation underlay performance with different spreading in AWGN (SU to PU relative power −30 dB) . . . . . . . . .
Theoretical vs simulation underlay performance with different PU
occupancy levels in AWGN (SU to PU relative power −20 dB) . .
Capacity comparison of overlay, underlay and hybrid scenarios . .
56
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Cognitive Radio System . . . . . . . . . . . . . . . . . . . . . . .
Hybrid MC-CDMA system model . . . . . . . . . . . . . . . . . .
Underlay performance of the proposed full-load hybrid system with
ZF and CL MMSE equalizers for different PU occupancy levels . .
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4.4
4.5
4.6
4.7
Simulation and Numerical underlay BER performance comparison
for ZF. Dashed and solid lines represent simulation and numerical
results respectively . . . . . . . . . . . . . . . . . . . . . . . . . .
Chip and symbol level MMSE comparison. Dashed and solid lines
represent CL and SL MMSE performance respectively. . . . . . .
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) . . . . .
NC-MC-CDMA vs proposed hybrid MC-CDMA underlay performance with ZF and MMSE . . . . . . . . . . . . . . . . . . . . .
5.1
5.2
5.3
5.4
Hybrid overload MC-CDMA system model . . . . . . . . . . . . .
Proposed Transmitter Structure . . . . . . . . . . . . . . . . . . .
Overload Receiver Block Diagram . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Underlay performance of the proposed overload hybrid system with
different PU occupancy levels. Total number of subcarriers are 512
5.6 Underlay sensitivity of the proposed overload system to PU interference power level, Mpu = 256 . . . . . . . . . . . . . . . . . . . .
5.7 Overlay performance with and without underlay transmission for
the worst case scenario when overlay and underlay power levels are
equal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Underlay performance for increasing number of underlay users
while overlay is full-loaded with Mpu = 64 . . . . . . . . . . . . .
5.10 Overlay Interference to underlay with Mpu = 64. Solid lines show
the underlay performance with overlay and the dashed lines without overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1
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System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8
6.2
6.3
6.4
6.5
6.6
6.7
Sum rate comparison of the four hybrid systems in AWGN for
Npu = 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . . . . . . . . . . . . .
Sum rate vs. interference threshold in AWGN for Npu = 4, and
fixed PU interference and total transmission power of 0.5 and 280
mW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sum rate comparison of the four hybrid systems in AWGN for
different PU occupancy levels . . . . . . . . . . . . . . . . . . . .
Sum rate comparison of the two hybrid systems in Fading channel
for Npu = 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sum rate comparison of the two hybrid systems in Fading channel
for Npu = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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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-toMachine (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, frequencies 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 interference and benefit from the frequency diversity. To maximize data rate, overlay
10
utilizes the available bands while keeping orthogonality with underlay using Orthogonal 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 underlay 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 underlay 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 interference 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 University 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 accordance with the regulations of the John Rylands University Library of Manchester. 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 intellectual 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 supervisor, 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, motivation 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
b̄k̄
k-th overlay user’s data vector
bk
¯¯
Ch
k-th underlay user’s data vector
d̄k̄
k-th overlay user’s multiplexed data vector
dk
¯¯
dh
k-th underlay user’s multiplexed 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
on the j-th sub-band
gps [j]
Primary transmitter to secondary receiver’s channel power
on the j-th sub-band
Hss
Secondary transmitter to secondary receiver channel matrix
Hsp
Iˆ¯
Secondary transmitter to primary receiver channel mtrix
Ith
Interference threshold of the primary system
K
Number of secondary users
K̄
Number of overlay secondary users
K
¯
Number of underlay secondary users
Hybrid spreading code matrix
Hybrid data vector
Residual interference from overlay
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
p co
Overlay power per subcarrier
p cu
Underlay power per subcarrier
ppu
Average primary user received power per subcarrier
pj
Allocated power to the j-th subband
ps o
Overlay symbol power
Ptot
Total cognitive radio power budget
r
Received signal vector
r̂c
Reconstructed received signal vector
S̄
Overlay scrambling matrix
S
¯
spu
Underlay scrambling matrix
Ts
Symbol duration
τi
i-th excess delay
w
Equalizer’s coefficient
Primary user data vector containing availability vector a
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
k·k
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
∇2 f (x)
Hessian matrix of function f
Generalized inequality, i.e. component-wise inequality between 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.
1
Different regulatory status for DSA will be discussed further in Section 3.2.
CHAPTER 1. INTRODUCTION
24
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
CHAPTER 1. INTRODUCTION
25
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.
CHAPTER 1. INTRODUCTION
1.3
26
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.
CHAPTER 1. INTRODUCTION
1.4
27
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.
CHAPTER 1. INTRODUCTION
1.5
28
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
2.2
30
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
P L(d)[dB] = P L(d0 ) + 10n log(
d
) + Xσ
d0
(2.1)
where d0 denotes a reference distance, P L(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 P L
mean and standard deviation σ.
CHAPTER 2. THEORETICAL BACKGROUND
2.3
31
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,
CHAPTER 2. THEORETICAL BACKGROUND
32
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
X
ai (t, τ )exp[j(2πfc τi (t)) + φi (t, τ )]δ(τ − τi (t))
(2.2)
i=0
where ai (t, τ ), τi (t) and (2πfc τi (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.
1
A Wide-Sense Stationary channel assumes that the autocorrelation function depends on
time differences only. For the case of a flat Rayleigh fading channel, the mean power and
the 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 autocorrelation
function can be shown as: E[h∗ (τ1 , t)h(τ2 , t + ∆t)] = Rh (τ1 ; ∆t)δ(τ2 − τ1 )[29] and [30]
CHAPTER 2. THEORETICAL BACKGROUND
2.5
33
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
Z∞
p(τ ) =
|h(t; τ )|2 dt = 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
2
Relative delay compared to the first arriving path
CHAPTER 2. THEORETICAL BACKGROUND
34
threshold. For frequency correlation above 0.9 the coherence bandwidth will be
approximately Bc ≈
1
50στ
[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 ≈
9
,
16πfd−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
CHAPTER 2. THEORETICAL BACKGROUND
Fading Type
Flat - Slow
Flat - Fast
Frequency Selective - Slow
Frequency Selective - Fast
Bc
Bc
Bc
Bc
35
Characteristic
> Bs ; Tc > Ts
> Bs ; Tc < Ts
< Bs ; Tc > Ts
< 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
CHAPTER 2. THEORETICAL BACKGROUND
36
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
M −1
1 X
x[m] = √
X[i]ej2πmi/M ,
M i=0
0 ≤ m ≤ M − 1.
(2.5)
The multiplication is identical to taking the IDFT of the signal. The size M
CHAPTER 2. THEORETICAL BACKGROUND
(a) OFDM Transmitter
(b) OFDM Receiver
Figure 2.3: OFDM with FFT/IFFT implementation [27]
37
CHAPTER 2. THEORETICAL BACKGROUND
38
square matrix of IDFT coefficients is given by matrix

1
1
1


2.2π
2π
1
ej M
ej M
M =

...
...
...

(M −1)2π
2(M −1)2π
1 ej M
ej M

...
1
...
(M −1)2π
j
M
e
...
...
... e
(M −1)2 2π
j
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

1
1
1


2π
2.2π
1
e−j M
e−j M
M =

...
...
...

(M −1)2π
2(M −1)2π
1 e−j M
e−j M
...
1
...
(M −1)2π
−j
M
e
...
... e−j
...
(M −1)2 2π
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,
CHAPTER 2. THEORETICAL BACKGROUND
39
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
CHAPTER 2. THEORETICAL BACKGROUND
40
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
CHAPTER 2. THEORETICAL BACKGROUND
Figure 2.5: Block Diagram of a Multi-User MC-DS-CDMA Transmitter
41
CHAPTER 2. THEORETICAL BACKGROUND
42
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
3
Some references, e.g. [31], refer to the scheme as a special case of MC DS-CDMA
CHAPTER 2. THEORETICAL BACKGROUND
43
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.
CHAPTER 2. THEORETICAL BACKGROUND
44
Parameters
Shortened W-ATM
Carrier frequency
60 GHz
Sampling rate
225 MHz
Bpsk data rate
155 Mbps
Max speed of mobile
50 Km/h
Max delay
11 samples
RMS delay spread
15.3 ns
Coherence bandwidth
65.4 MHz
No. of subcarriers
512
No. 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,
4
Wireless Asynchronous Transfer Mode channel is used here to compare the frequency
selective fading results with the results in the reference [43]. However, the ITU PedestrianB channels is used for the rest of this thesis.
CHAPTER 2. THEORETICAL BACKGROUND
45
0.9
0.8
0.7
Magnitide
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
Time Delay ns
70
80
90
100
Figure 2.7: W-ATM Channel Impulse Response [43]
0
10
SF=1
SF=2
SF=4
SF=8
Theoretical
−1
10
L=1, Rayleigh
−2
BER
10
−3
10
−4
10
−5
L=3, Theory
L=2, Theory
L=4, Theory
10
−6
10
0
5
10
15
20
25
SNR
30
35
40
45
50
Figure 2.8: Synchronous MC-CDMA for downlink over W-ATM channel with
MRC
CHAPTER 2. THEORETICAL BACKGROUND
46
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]:
1
Pb = (1 − µ)
2
L X
L−1 k=0
L−1+k
k
1
(1 + µ)
2
k
(2.6)
where L is the diversity order and µ is defined as
r
µ=
γ̄b
.
L + γ̄b
(2.7)
In the above definition, γ̄b 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. γ̄c = γ̄b /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
CHAPTER 2. THEORETICAL BACKGROUND
47
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
x0 [i] = w[i]y[i].
(2.11)
Taking the IFFT of the equalized signal, the original signal is then detected.
CHAPTER 2. THEORETICAL BACKGROUND
2.8.1
48
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 min E[|x[i] − x̂[i]|2 ].
(2.13)
w[i]
Substituting x̂[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
CHAPTER 2. THEORETICAL BACKGROUND
49
[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 MCCDMA 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)
CHAPTER 2. THEORETICAL BACKGROUND
50
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:
∇2 f (x) 0
Note that Hessian: ∇2 f (x)ij =
for all x ∈ dom f
∂ 2 f (x)
∂xi ∂xj
(2.17)
i, j = 1, ..., n. Clearly, if f is convex
then −f is concave.
Some frequently used convex functions are: Negative entropy (xlog(x) on
n
1/p
P
R++ ), all norms kxkp =
|xi |p
for p ≥ 1 (where p = 2 represents Euclidean
i=1
n
P
norm) and logo-sum-exp (log
exp xk ).
k=1
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 ∇2 f (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
subject to
f0 (x)
(2.18)
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
CHAPTER 2. THEORETICAL BACKGROUND
51
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
X
λi fi (x) +
p
X
νi hi (x)
(2.22)
i=1
i=1
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
X
λi fi (x) +
i=1
p
X
!
νi hi (x) .
(2.23)
i=1
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)
CHAPTER 2. THEORETICAL BACKGROUND
52
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 x̃, λ̃, ν̃ to be primal and dual optimal with zero duality gap. The
CHAPTER 2. THEORETICAL BACKGROUND
53
KKT conditions are:
fi (x̃) ≤ 0,
i = 1, ..., m
(2.28)
hi (x̃) = 0,
i = 1, ..., p
(2.29)
λ̃i ≥ 0
i = 1, ..., m
λ̃i fi (x̃) = 0,
∇f0 (x̃) +
m
X
(2.30)
i = 1, ..., m
λ̃i ∇fi (x̃) +
i=1
p
X
(2.31)
ν̃i ∇hi (x̃) = 0
(2.32)
i=1
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.
CHAPTER 2. THEORETICAL BACKGROUND
54
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.
CHAPTER 3. COGNITIVE RADIO
57
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.
CHAPTER 3. COGNITIVE RADIO
3.2.2
58
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.
CHAPTER 3. COGNITIVE RADIO
3.3
59
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.
CHAPTER 3. COGNITIVE RADIO
60
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.
about new opportunistic access.
All these new dimensions bring
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
CHAPTER 3. COGNITIVE RADIO
61
Figure 3.3: Underlay spectrum opportunity and the interference threshold
concept [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.
CHAPTER 3. COGNITIVE RADIO
62
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
CHAPTER 3. COGNITIVE RADIO
63
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
1
The term ”hybrid techniques” used here is different from the concept of the hybrid
overlay/underlay systems proposed for CR systems. However, in the proposed systems the
hybrid multi-carrier techniques have been utilized.
2
No data is being transmitted through the deactivated subcarriers
CHAPTER 3. COGNITIVE RADIO
64
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
CHAPTER 3. COGNITIVE RADIO
65
−1
10
−2
10
−3
BER
10
−4
10
−5
10
Theory
Simulation
−6
10
0
2
4
6
8
10
Eb/No
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
q 2Eb
Pb = Q
[30].
N0
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
CHAPTER 3. COGNITIVE RADIO
66
−1
10
−2
BER
10
M=32
−3
10
M=64
M=128
−4
10
0
1
2
3
4
Eb/No
5
6
7
8
Figure 3.6: Overlay NC-MC-CDMA in fading channel with different spreading
and 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]
SIN R = PKpu
kpu =1
M E bk
Mkpu Ebkpu + M N20
(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
CHAPTER 3. COGNITIVE RADIO
67
user’s bit energy, the underlay BER performance will be
s
P (e) = Q
!
M E bk
PKpu
Note that Gaussian approximation
N0
kpu =1 Mkpu Ebkpu + M 2
3
.
(3.2)
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:
s
P (e) = Q
where Mpu =
PKpu
kpu =1
2Ebk
2Mpu Ebp
M
!
(3.3)
+ N0
Mkpu , 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
3
The approximation is valid for pure Gaussian noise . However, since the PU signal and
thermal noise are independent, the assumption will be still valid for (3.2).
CHAPTER 3. COGNITIVE RADIO
68
0
10
M=32
M=256
−1
10
BER
M=512
−2
10
M=1024
−3
10
Simulation
Theory
Baseline
−4
10
0
1
2
3
4
Eb/No
5
6
7
8
Figure 3.7: Theoretical vs simulation underlay performance with different
spreading 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
CHAPTER 3. COGNITIVE RADIO
69
−1
10
Mpu= 256, 128, 64, 32
−2
BER
10
−3
10
Simulation
Theory
Baseline
−4
10
0
1
2
3
4
Eb/No
5
6
7
8
Figure 3.8: Theoretical vs simulation underlay performance with different PU
occupancy 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.
CHAPTER 3. COGNITIVE RADIO
70
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.
CHAPTER 3. COGNITIVE RADIO
71
300
System Capacity (bits/s)
250
Overlay
Hybrid
Underlay
200
150
100
50
0
−10
−5
0
5
Underlay SNR in dB
10
15
20
(a) Relative overlay to underlay power is 20 dB
300
System Capacity (bits/s)
250
Overlay
Hybrid
Underlay
200
150
100
50
0
−10
−5
0
5
Underlay SNR in dB
10
15
20
(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
4.2
73
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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
74
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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
75
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 K̄ = 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
ȳ[k] = b̄[k] ⊗ c[k]
(4.1)
where ⊗ denotes the Kronecker product and b̄[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 ȳ[k] is defined as
ȳ[k] = [b1 c1 , . . . , b1 cG , . . . , bP c1 , . . . , bP cG , ]T ∈ CMsu ×1 .
(4.2)
d̄ ∈ CM ×1 is the equivalent overlay signal ȳ 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 = bcK .
¯ ¯
(4.3)
The transmitted hybrid signal, dh ∈ CM ×1 , can be shown by
dh =
√
√
pco d̄ + pcu d
¯
(4.4)
which is an M × 1 vector consisting of the summation of overlay and underlay
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
signals.
√
pco and
√
76
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)
spu = [(1 − a1 )dpu [1], (1 − a2 )dpu [2], ..., (1 − aM )dpu [M ]]T
(4.8)
where
is an M by 1 data matrix of the PU. The SU’s received signal in vector form can
be expressed as
r = Hss dh + Hps spu + n.
(4.9)
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
4.4
77
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 k̄-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
ZT
M
X
1
w[i]Ch [i, K]e−j2πfi t r(t)dt.
T
i=1
(4.11)
0
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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
78
the desired signal, PU interference and noise which can be shown as
ZF
zun
=b+
¯
M
X
(1 − ai )wZF [i]hps [i]Ch [i, K]spu [i]+
i=1
M
X
wZF [i]Ch [i, K]n[i] (4.12)
i=1
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
ZF
instantaneous SINR for ZF (γun
) can be written as
ZF
=
γun
N0
M p su
PMpu
2
2
i=1 |wZF [i]hps [i]|
i=1 |wZF [i]| + ppu
PM
(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
Z
BER =
∞
Q(γ)fγ (γ)dγ
(4.14)
0
where fγ (γ) is the joint pdf of γ which includes M + Mpu random variables. For
ZF
is shown by γ in (4.14). The underlay Full-Load BER
simplicity of notation, γun
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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
79
method. The MMSE criterion for an individual subcarrier is
arg min E(wCL [i]r[i] − d[i]|2 )(wCL [i]r[i] − d[i]|2 )∗ .
wCL [i]
¯
¯
(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).
¯
∗
∗
∗
∗
∗
(dh hss [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.
dJ
dWCL
= 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
h∗ss [i]
wCL [i] =
hss [i]h∗ss [i]
N0
pc
ppu
+
+ o ai hss [i]h∗ss [i] +
(1 − ai )hps [i]h∗ps [i]
p cu p cu
pcu
(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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
80
B, the underlay signals’ decision variable with Chip-Level MMSE (CL-MMSE)
is
CL−M M SE
=b
zun
¯
M
X
wCL [i]hss [i] +
i=1
+
M
X
K̄−1
X
i
β (k,K) b̄[d e, k]
G
k=1
{wCL [i]hps [i]Ch [i, K]spu [i] + wCL [i]Ch [i, K]n[i]}
(4.19)
i=1
where β (k,K) =
PM
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 σI2tot =
σI2pu + σI2¯ + σI2n . The variance of the AWGN corresponds to
σI2n
M
N0 X
=
|wCL [i]|2
M i=1
(4.20)
The variance of the PU interference will be
σI2pu
M
ppu X
=
|wpu [i]hps [i]|2
M i=1
(4.21)
where PU to SU channel coefficients are weighted by wpu
wpu [i] =
1
(1 − ai )h∗ss [i]
.
N0
ppu
∗
∗
+ hss [i]hss [i] +
hps [i]hps [i]
p cu
p cu
(4.22)
Note that the variances are all conditional variances to channel coefficients (Hss and Hps )
which is not shown here for notational simplicity
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
81
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
σI2¯ = var[
=
K̄−1
X
M
X
i
wCL [i]hss [i]Ch [i, k]Ch [i, K]]
b̄[b c, k]
G
i=1
k=1
P (K̄ − 1)pso 2
√
σwsu hss
M.G
(4.23)
where pco is the overlay symbol power and
σw2 CL hss = E[w2CL h2ss ] − E2 [wCL hss ]
(4.24)
is the variance of the SU to SU channel coefficients
wsu [i] =
ai h∗ss [i]
.
N0
p co
∗
+ (1 +
)hss [i]hss [i]
p cu
p cu
(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
min E[(z − b)(z − b)H ] = min E[(wSL r − b)(wSL r − b)H ].
w
w
¯
¯
¯
¯
(4.26)
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
82
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 (wSL r − b)rH
¯
H
H
H
H
=E (wSL (Hss dh + Hps spu + n) − b) dH
h Hss + spu Hps + n
H H
H
H
H
H
=E wHss dh dH
h Hss + wHps spu spu Hps + wnn − bdh Hss = 0
(4.27)
(4.28)
(4.29)
Rearranging the formula, the optimal vector can be shown as2
H
H H
H
−1
wSL = Pun cH
hK Hss .(Hss Ch Rdh Ch Hss + Hps Rpp Hps + Rnn )
(4.30)
where Rdh = E[dh dH
h ] 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),
H
Rpp = E[spu sH
pu ] and Rnn = E[nn ] = N0 IM . 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
SL−M M SE
zun
= wSL r = wSL Hss s + wSL Hps spu + wSL n
(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
SL
γun
=
H
pcu wSL Hss HH
ss wSL
.
H H
H
wSL Hps spu sH
pu Hps wSL + N0 wSL wSL
(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
2
The optimal solotion can also be achieved through Wiener solution [48]
M
.
Mpu
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
Relative delay (ns)
0
Average Power (dB) 0
83
200 800 1200 2300 3700
-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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
84
0
10
ZF
−1
10
−2
BER
10
−3
10
−4
10
Chip−level
MMSE
Mpu=448
Mpu=384
Mpu=320
Mpu=256
Mpu=128
Mpu=64
No PU
−5
10
0
5
10
15
Underlay Eb/No
20
25
Figure 4.3: Underlay performance of the proposed full-load hybrid system with
ZF 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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
85
0
10
−1
BER
10
−2
10
−3
10
Mpu=480
Mpu=352
Mpu=256
Mpu=128
Mpu=32
no PU interf.
−4
10
0
5
10
15
Eb/No
20
25
30
Figure 4.4: Simulation and Numerical underlay BER performance comparison for
ZF. 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
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
86
Mpu=448
Mpu=320
Mpu=256
Mpu=128
Mpu=64
No PU
−1
10
−2
BER
10
−3
10
−4
10
5
10
15
Underlay Eb/No
20
25
Figure 4.5: Chip and symbol level MMSE comparison. Dashed and solid lines
represent 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.
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
10
10
BER
10
10
10
10
87
0
ZF
Chip−level MMSE
Symbol−level MMSE
−1
−2
−3
−4
−5
5
10
15
Number of Users
20
25
30
Figure 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)
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.
CHAPTER 4. FULL-LOAD HYBRID SYSTEM
88
0
10
−1
10
−2
BER
10
−3
10
−4
10
−5
NC, Mpu=128
NC, Mpu=256
NC, Mpu=512
Mpu= 480
Mpu=256
Mpu=128
10
0
5
10
15
Eb/No
20
25
30
Figure 4.7:
NC-MC-CDMA vs proposed hybrid MC-CDMA underlay
performance 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
5.2
90
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.
CHAPTER 5. OVERLOAD HYBRID SYSTEM
91
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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
92
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, K̄ 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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
93
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
ȳk̄ = b̄k̄ ⊗ c̄k̄
(5.1)
where b̄k̄ of size P × 1 is the k̄-th user’s symbol vector and c̄k̄ of size G × 1 is the
k̄-th user’s specific spreading code, which the elements are normalized such that
each code has unit energy. The column vector ȳk̄ is defined as
ȳk̄ = [b1 c1 , . . . , b1 cG , . . . , bP c1 , . . . , bP cG , ]T ∈ CMsu ×1 .
(5.2)
We note x̄ ∈ CM ×1 as the equivalent overlay signal ȳ 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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
94
scrambling matrix S̄ of Msu nonzero elements according to the the availability
vector a. The overlay multiplexed symbol vector of G users is then
d̄ = S̄x̄.
(5.3)
The transmitter block diagram is shown in Fig. 5.2. The k-th underlay user’s
¯
data symbol is represented by bk and its M ×1 spreading code is ck . The underlay
¯¯
¯¯
spread signal of K users is
¯
K
X
¯
x=
bk ck
(5.4)
¯
¯ ¯ ¯¯
k=1
¯
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 =
√
pco S̄x̄ +
√
√
√
pcu Sx = pco d̄ + pcu d
¯¯
¯
(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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
95
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)
spu = [(1 − a1 )dpu [1], (1 − a2 )dpu [2], ..., (1 − aM )dpu [M ]]T
(5.9)
where
is the M 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 = Hss dh + Hps spu + 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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
96
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 C̄ for K̄ users i.e. C̄ will
be a K̄ × Msu matrix, where Msu is obtained from the spectrum sensing
unit.
3. Calculate the combined overlay code for K̄ users as T̄ = C̄S̄ and at the
CHAPTER 5. OVERLOAD HYBRID SYSTEM
97
same time zero pad at the PU occupied subcarriers (T̄ will be a matrix of
K̄ × 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 k̄-th overlay user
Ψk,k,0
M
1 X
=
T[i]T̄[k̄, i]
Msu i=1 ¯
(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
m̂ = arg min
m
5.5
K
1X

k

i=1
K
1X
k

Ψi,j,m  .
(5.13)
j=1
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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
98
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
min E[|z[i] − d̄[i]|2 ] = min E (w[i]r[i] − d̄[i])(w[i]r[i] − d̄[i])∗
(5.14)
w̄[i]
w̄[i]
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 w̄∗ we will have
E (w[i]r[i] − d̄[i])r∗ [i]
=E (d∗h [i]h∗ss [i]w[i] + w[i]n∗ [i] − d[i])(d∗h [i]h∗ss [i] + n∗ [i]) .
(5.15)
(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
w̄[i] =
h∗ss [i]
pc
N0
(1 + u )hss [i]h∗ss [i] +
p co
p co
where E[d[i]d[i]∗ ] = pco , E = [d[i]d[i]∗ ] = pcu and E = [nn∗ ] = N0 .
(5.18)
CHAPTER 5. OVERLOAD HYBRID SYSTEM
99
After overlay CL MMSE equalization, the receiver will then perform the
descrambling and despreading process to obtain the overlay users’ symbols,
ˆb̄[1], ˆb̄[2], ..., ˆb̄[K̄]. 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
r̂[i] = r[i] −
¯
M
X
ˆ [i]hss [i]
x̄
(5.19)
i=1
ˆ [i] is the sum of K̄ overlay users’ detected multiplexed data on the i-th
where x̄
subcarrier. Therefore, the reconstructed received signal component after overlay
signal detection and cancellation corresponds to
r̂c = Hss d + Hps spu + n + ˆĪ
¯
(5.20)
where ˆĪ 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
min E[(Wr − b)(Wr − b)H ].
W
¯ ¯
¯
¯
¯
(5.21)
Substituting reconstructed received signal, r̂c , from (5.20) into the objective
CHAPTER 5. OVERLOAD HYBRID SYSTEM
100
function of (5.21), knowing d = SCb we will have
¯ ¯¯¯
J =E[((WHss SCb + WHps spu + Wn) − b)
¯¯¯
¯
¯
¯
¯
H
((WHss SCb + WHps spu + Wn) − b) ].
¯¯¯
¯
¯
¯
¯
H H H
H
= WHss SCRbb C S Hss W − Rbb WHss SC+
¯ ¯
¯¯
¯¯
¯
¯
¯
H
H
H
H H H
WHps Rpp Hps W + WRnn W − Rbb C S Hss WH + Rbb
¯ ¯
¯
¯
¯
¯
¯
(5.22)
(5.23)
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
¯
H
the above expression with respect to W using the properties of the derivative
¯
dJ
matrix [88, 89] and set it to 0, i.e dW
H = 0, we will have
¯
H
H H H
WHss SCRbb CH SH HH
ss + wHps Rpp Hps + WRnn − Rbb CC S Hss = 0. (5.24)
¯ ¯
¯¯ ¯
¯¯
¯
¯
Rearranging for W we obtain
¯
H H H
H
−1
W = Rbb CH SH HH
ss .(Pun Hss SCRbb C S Hss + Hps Rpp Hps + Rnn )
¯ ¯
¯ ¯
¯¯
¯
(5.25)
where Pun is the underlay symbol power1 . Assuming the MAI to be negligible,
the underlay SINR can be written as
SL
γun
=
H
pcu WHss HH
ss W
¯
¯
H
H
H
WHps spu sH
pu Hps W + N0 WW
¯
¯
¯ ¯
(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.
1
Note that underlay signal power (Pun ) has been set to be lower than the PU’s interference
threshold (Ith )
CHAPTER 5. OVERLOAD HYBRID SYSTEM
5.6
101
Simulation Results
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.
CHAPTER 5. OVERLOAD HYBRID SYSTEM
102
−1
10
Mpu=448
Mpu=384
Mpu=320
Mpu=256
Mpu=128
−2
BER
10
−3
10
−4
10
0
5
10
15
Underlay Eb/No
20
25
Figure 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
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.
CHAPTER 5. OVERLOAD HYBRID SYSTEM
103
0
10
Mpu=320
Mpu=256
Mpu=192
Mpu=128
Mpu=64
−1
10
−2
BER
10
−3
10
−4
10
0
5
10
15
Underlay Eb/No
20
25
30
Figure 5.5: Underlay performance of the proposed overload hybrid system with
different 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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
104
0
10
Ppu=44 dB
Ppu=40 dB
Ppu=37 dB
Baseline (No PU)
−1
10
BER
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Underlay Eb/No
14
16
18
20
Figure 5.6: Underlay sensitivity of the proposed overload system to PU
interference 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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
105
0
10
Hybrid System
Pure Overlay System
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
Eb/No
12
14
16
18
20
Figure 5.7: Overlay performance with and without underlay transmission for the
worst case scenario when overlay and underlay power levels are equal
CHAPTER 5. OVERLOAD HYBRID SYSTEM
106
Underlay Performance
−1
10
−2
BER
10
−3
10
Baseline (No PU)
PU=20 dB
PU=44 dB
−4
10
−5
10
0
2
4
6
8
10
Eb/No
12
14
16
18
20
Figure 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
NC-MC-CDMA are abtained from
w[i] =
h∗ss [i]
.
∗ [i]
hss [i]h∗ss [i] + pNc0 + pppu
h
[i]h
ps
ps
c
u
(5.27)
u
and symbol-level from
H
H H
H
−1
w = Pun cH
hK Hss .(Hss Ch Rss Ch Hss + Hps Rpp Hps + Rnn ) .
(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.
CHAPTER 5. OVERLOAD HYBRID SYSTEM
107
0
10
Kun=64
Kun=48
Kun=32
Kun=1
−1
10
−2
10
−3
BER
10
−4
10
−5
10
−6
10
−7
10
0
2
4
6
8
10
12
Underlay Eb/No
14
16
18
20
Figure 5.9: Underlay performance for increasing number of underlay users while
overlay 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
CHAPTER 5. OVERLOAD HYBRID SYSTEM
108
0
10
−1
Kun=64
Kun=48
Kun=32
10
−2
10
−3
BER
10
−4
10
−5
10
−6
10
−7
10
0
2
4
6
8
10
12
Underlay Eb/No
14
16
18
20
Figure 5.10: Overlay Interference to underlay with Mpu = 64. Solid lines show
the 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%
CHAPTER 5. OVERLOAD HYBRID SYSTEM
109
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 SUM RATE OPTIMIZATION111
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.
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION112
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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION113
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:
C
ergadic
K
K̄
X
X
¯
= max E{
Rk̄ +
Rk }
k̄=1
k =1 ¯
¯
(6.1)
where K̄ and K are the number of overlay and underlay users respectively, and
¯
Rk̄ 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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION114
sum rate [94]:
C
6.4
inst.
K
K̄
X
X
¯
= max {
Rk̄ +
Rk }.
k̄=1
k =1 ¯
¯
(6.2)
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
X
log2 1 +
j=1
subject to
NB
X
pj
N0 Ns + (1 − αj )Ns ppu
(6.3)
pj ≤ Ptot
(6.4)
(1 − αj )pj ≤ Ith
(6.5)
αj pj ≤ Pov
(6.6)
j=1
NB
X
j=1
NB
X
j=1
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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION115
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) =
−Ns log2 e
≺ 0
(pj + N0 Ns + (1 − αj )Ns ppu )2
∀ 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
Q12 : Ptot ≤ Pov + Ith .
and
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
X
log2 1 +
j=1
subject to
NB
X
pj
N0 Ns + (1 − αj )Ns ppu
(6.9)
(1 − αj )pj ≤ Ith
(6.10)
αj pj ≤ Pov
(6.11)
j=1
NB
X
j=1
pj ≥ 0
1
j = 1, 2, ..., NB .
(6.12)
Here Q1 is written for the case of AWGN. However, the model is applicable to the fading
channels which will be discussed later
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION116
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 =
and p∗un =
Pov
Nov
Ith
Npu
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
X
log2
j=1
NB
X
subject to
pj
1+
N0 Ns + (1 − αj )Ns ppu
(6.13)
pj ≤ Ptot
(6.14)
αj pj ≤ Pov
(6.15)
j=1
NB
X
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 =
Pov
Nov
and p∗un =
Ptot −Pov
Npu
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 =
Ptot
.
Nov
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION117
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:
X
K
pk
¯
pov [n]
+
log2 1 +
log2 1 +
R = Ns
¯
N0 Ns
N0 + ppu
n=1
k =1
¯
K
N
ov
X
X
¯
pov [n] +
pk ≤ Ptot
n=1
k =1 ¯
¯
K
X
¯
pk ≤ Ith
k =1 ¯
¯
Nov
X
pov [n] ≤ Pov
Nov
X
subject to
(6.17)
(6.18)
(6.19)
(6.20)
n=1
pov [n] ≥ 0
pk ≥ 0
¯
n = 1, 2, ..., Nov
(6.21)
pk = 1, 2, ..., K .
¯
¯
(6.22)
Knowing that all underlay users are active, pk = PKun 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 =
Pov
Nov
and p∗k =
Ith
K
respectively. Note that pov is the allocated power to the overlay subband and pk
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION118
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 =
p∗K =
Ptot −Pov
K
6.4.3
Pov
Nov
and
(Pun = Kp∗K ).
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
s −1
X
X
n=1 m=1
pov [m, n]
log2 1 +
+ log2
N0 (Ns − 1)
pun
1+
N0 + pχpu
!
(6.23)
subject to
Nov N
s −1
X
X
pov [m, n] + pun ≤ Ptot
(6.24)
n=1 m=1
pun ≤
Nov
X
NB Ith
Npu
(6.25)
pov [n] ≤ Pov
(6.26)
n=1
pov [m, n] ≥ 0
pun ≥ 0
where χ =
NB
Nun
n = 1, 2, ..., Nov ; m = 1, 2, ..., Ns − 1
(6.27)
(6.28)
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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION119
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
s −1
X
X
!
pov [m, n] + pun − Ptot
n=1 m=1
Ith NB
.
− µ pun −
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
(Ns − 1)log2 e
−λ
=
∂pov
pov + N0 (Ns − 1)
log2 e
∂L
=
∂pun
pun + N0 +
ppu
χ
− λ − µ.
(6.30)
(6.31)
Setting the above formulas to zero, the optimal overlay and underlay powers will
be
+
log2 e
− N0 )
= (Ns − 1)(
λ
+
log2 e
ppu
∗
pun =
− N0 −
λ+µ
χ
p∗ov
(6.32)
(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 = µ̂ (µ ∈ [0, µ̂]).
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)( logλ2 e − N0 ) +
log2 e
λ+µ
− N0 −
ppu
χ
= Ptot ).
3. Substitute in (6.32) and (6.33) to obtain pov and pun .
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION120
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,
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION121
the optimization problem for the overload system, Q4 , can be defined as:
!
X
K
pk
¯
pov [m, n]
+
log2 1 +
R=
log2 1 +
¯
N
N
N0 + pχpu
0
s
n=1 m=1
k =1
¯
(6.34)
Nov X
Ns
X
subject to
Nov X
Ns
X
pov [m, n] +
n=1 m=1
K
X
¯
K
X
¯
pk ≤ Ptot
k =1 ¯
¯
(6.35)
Ith NB
pk ≤
Npu
k =1 ¯
¯
Nov
X
pov [n] ≤ Pov
(6.36)
(6.37)
n=1
pov [m, n] ≥ 0
pk ≥ 0
¯
where χ =
NB
Nun
n = 1, 2, ..., Nov ; m = 1, 2, ..., Ns
k = 1, 2, ..., K
¯
¯
(6.38)
(6.39)
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 X
Ns
X
n=1 m=1
pov [m, n] +

K
X
¯
pk − Ptot −µ
k =1 ¯
¯

K
X
 ¯

Ith NB 
pk −
Npu
k =1 ¯
¯
(6.40)
Assuming downlink, we will have pk = PKun . Differentiating (6.40) with respect
¯
¯
to the variables pov and pun we will have
∂L
Ns log2 e
=
−λ
∂pov
pov + N0 Ns
∂L
K log2 e
¯
=
∂pun
pun + K (N0 +
¯
ppu
)
χ
−λ−µ
(6.41)
(6.42)
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION122
Setting the above formulas to zero, the optimal overlay and underlay powers will
be
p∗ov
p∗un
+
log2 e
− N0 )
= Ns (
λ
K log2 e
ppu
= ¯
− K (N0 +
)
¯
λ+µ
χ
(6.43)
+
.
(6.44)
which asserts that each pov and pun are be positive. λ and µ can then be obtained
from the following iterative algorithm
Initialize µmin = 0 and µmax = µ̂ (µ ∈ [0, µ̂]).
Repeat
1. Set µ = (µmin + µmax )/2.
2. Find minimum λ from (6.35) for new set of µ (by solving the equation
Ns ( logλ2 e − N0 ) +
Klog2 e
λ+µ
− KN0 −
Kppu
χ
= Ptot ).
3. Substitute in (6.43) and (6.44) to obtain pov and pun .
4. Update the vector µ by bisection method, i.e. if satisfies (6.36) 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 (6.36)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.
2
This is to ensure that the constraint (6.37) is not violated.
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION123
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
X
log2
j=1
subject to
NB
X
pj |hss [j]|2
1+
N0 Ns + (1 − αj )Ns ppu |hps [j]|2
(6.45)
pj ≤ Ptot
(6.46)
(1 − αj )pj |hsp [j]|2 ≤ Ith
(6.47)
αj pj ≤ Pov
(6.48)
j=1
NB
X
j=1
NB
X
i=1
pj ≥ 0
j = 1, 2, ..., NB
where pj is the power allcoated to each secondary subchannel.
(6.49)
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
Q52 : Ptot ≤ Pov + Ith .
and
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
X
log2
j=1
subject to
NB
X
pj |hss [j]|2
1+
N0 Ns + (1 − αj )Ns ppu |hps [j]|2
(6.50)
(1 − αj ) pj |hsp [j]|2 ≤ Ith
(6.51)
αj pj ≤ Pov
(6.52)
j=1
NB
X
j=1
pj ≥ 0
j = 1, 2, ..., NB
(6.53)
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION124
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
X
!
αj pj − Pov
NB
X
−µ
(1 − αj )pj |hsp [j]|2 − Ith
j=1
!
(6.54)
j=1
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
Ns |hss [j]|2 log2 e
∂L
=
− ναj − µ(1 − αj )|hsp [j]|2 .
∂pb
pj |hss [j]|2 + N0 Ns + (1 − αj )Ns ppu |hps [j]|2
(6.55)
Setting the above formula to zero, the optimal solution to the problem will be:
Pj∗
N0 Ns
|hps [j]|2
Ns log2 e
−
−
(1
−
α
)N
p
=
j
s pu
ναj + µ(1 − αj )|hsp [j]|2 |hss [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
Initialize µmin = 0 and µmax = µ̂ (µ ∈ [0, µ̂]).
Repeat
1. Set µ = (µmin + µmax )/2.
2. Find minimum ν from (6.52) for new set of µ (by solving the equation
h
i
|hps [1]|2
α1 Ns log2 e
N0 Ns
−
−
(1
−
α
)N
p
1
s pu |hss [1]|2 + ...
να1 +µ(1−α1 )|hsp [1]|2
|hss [1]|2
h
i
αNB Ns log2 e
|hps [NB ]|2
N0 Ns
+ ναN +µ(1−αN )|hsp [NB ]|2 − |hss [NB ]|2 − (1 − αNB )Ns ppu |hss [NB ]|2 = Pov ).
B
B
3. Substitute in (6.56) to obtain pj .
4. Update the vector µ by bisection method, i.e. if satisfies (6.51) set µ →
µmin , otherwise µ → µmax .
Until µmax − µmin < δ where δ is a small positive constant.
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION125
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
X
NB
X
pj − Ptot ) − µ( (1 − αj )pj |hsp [j]|2 − Ith )
j=1
(6.57)
j=1
Differentiating (6.57) with respect to pj we will have:
∂L
Ns |hss [j]|2 log2 e
=
−λ−µ(1−αj )|hsp [j]|2 . (6.58)
∂pb
pj |hss [j]|2 + N0 Ns + (1 − αj )Ns ppu |hps [j]|2
Setting the above formula to zero, the optimal solution to the problem will be:
Pj∗
Ns log2 e
N0 Ns
|hps [j]|2
=
−
−
(1
−
α
)N
p
j
s
pu
λ + µ(1 − αj )|hsp [j]|2 |hss [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
Initialize µmin = 0 and µmax = µ̂ (µ ∈ [0, µ̂]).
Repeat
1. Set µ = (µmin + µmax )/2.
2. Find minimum λ from (6.46) for new set of µ (by solving the equation
h
i
|hps [1]|2
Ns log2 e
N0 Ns
− |hss [1]|2 − (1 − α1 )Ns ppu |hss [1]|2 + ...
λ+µ(1−α1 )|hsp [1]|2
h
i
|hps [NB ]|2
N0 Ns
2e
−
−
(1
−
α
)N
p
+ λ+µ(1−αNNs log)|h
).
N
s
pu
2
2
2
B
|hss [NB ]|
|hss [NB ]|
sp [NB ]|
B
3. Substitute in (6.59) to obtain pj .
4. Update the vector µ by bisection method, i.e. if satisfies (6.47) set µ →
µmin , otherwise µ → µmax .
Until µmax − µmin < δ where δ is a small positive constant.
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION126
Check if
PNB
i=1
αj pj > Pov , set the overlay subband’s power to
Pov
Nov
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:
Nov X
Ns
X
pov [m, n]|hss [n]|2
R=
log2 1 +
N0 Ns
n=1 m=1
log2 1 + γk
¯
k =1
¯
K
Ns
Nov X
X
X
¯
pov [m, n] +
pk ≤ Ptot
n=1 m=1
k =1 ¯
¯
K
M
X
¯ X
NB
pk |hss [i]|2 ≤ Ith
Npu
k =1 i=1 ¯
¯
pov [m, n] ≥ 0
n = 1, 2, ..., Nov ; m = 1, 2, ..., Ns
+
subject to
K
X
¯
pk ≥ 0
¯
k = 1, 2, ..., K
¯
¯
(6.60)
(6.61)
(6.62)
(6.63)
(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
3
This is to ensure that the constraint (6.48) is not violated.
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION127
6.6
Simulation Results
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
10−3 mw. Interference threshold and PU average interference power are 10−2 mw
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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION128
1790
1780
1770
Sum Rate (Nats)
1760
1750
1740
1730
1720
Overload MC−CDMA
Full OFDM
Mixed Hybrid
Full MC−CDMA
1710
1700
1690
210
220
230
240
250
260
270
280
Maximum Transmission Power
290
300
310
Figure 6.2: Sum rate comparison of the four hybrid systems in AWGN for Npu = 4
1810
Sum Rate (Nats)
1800
1790
1780
1770
1760
1750
1
2
3
4
5
6
7
PU Interference Level
8
9
10
11
−4
x 10
Figure 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.
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION129
1820
1810
Sum Rate (Nats)
1800
1790
1780
1770
1760
1750
1740
1
2
3
4
Interference Threshold
5
6
7
−5
x 10
Figure 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.
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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION130
2680
Sum Rate (Nats)
2660
2640
2620
2600
Overload MC−CDMA
Full OFDM
Mixed Hybrid
Full MC−CDMA
2580
2560
340
350
360
370
380
390
400
410
Maximum Transmission Power
420
430
440
(a) Sum rate comparison of the four hybrid systems in AWGN
for Npu = 2
900
890
Sum Rate (Nats)
880
870
860
Overload MC−CDMA
Full OFDM
Mixed Hybrid
Full MC−CDMA
850
840
100
110
120
130
140
150
Maximum Transmission Power
160
170
180
(b) Sum rate comparison of the four hybrid systems in AWGN
for Npu = 6
Figure 6.5: Sum rate comparison of the four hybrid systems in AWGN for different
PU occupancy levels
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION131
1760
Overload MC−CDMA
1740
Full OFDM
Sum Rate (Nats)
1720
1700
1680
1660
1640
1620
1600
210
220
230
240
250
260
270
280
Maximum Transmission Power
290
300
310
Figure 6.6: Sum rate comparison of the two hybrid systems in Fading channel for
Npu = 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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION132
2700
2650
Sum Rate (Nats)
2600
2550
2500
2450
Overload MC−CDMA
Full−OFDM
2400
2350
340
350
360
370
380
390
400
410
Maximum Transmission Power
420
430
440
Figure 6.7: Sum rate comparison of the two hybrid systems in Fading channel for
Npu = 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
CHAPTER 6. HYBRID OVERLAY/UNDERLAY SUM RATE OPTIMIZATION133
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
7.2
136
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].
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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
r
1
γ
√
(A.1)
Pe = Q( γ) = Erfc
2
2
R∞
where Erfc(x) = π2 0 exp(−t2 )dt is the complementary error function. For
zf
in (4.13) is shown by γ in this section. Using direct
simplicity of notation, γun
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
X
i=1
M
X
1
Y =
X
i=1
(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 (−λ/y)
e
y2
149
y ≥ 0,
(A.3)
APPENDIX A. UNDERLAY FULL-LOAD BER PERFORMANCE WITH ZF150
the Moment Generating Function (MGF) of y will be
Z
sY
∞
∞
Z
sY
e fY (y)dy = λ
MY (s) = E[e ] = λ
0
0
λ sY (−λ/y)
e e
dy.
y2
(A.4)
1
using [98], eq. (8.486.16) we will have
√
√
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
Z
∞
Q(γ)fγ (γ)dγ
BER =
(A.7)
0
and γ is in the form γ =
M pcu
,
zN0
we can write
Z
∞
r
Q
BER =
0
M p cu
zN0
!
fz (z)dz
(A.8)
where
1
fz (z) =
2π
Z
∞
e−isz φZ (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.
1
also approved by [99]