WILEY Cognitive Radio Networks User Manual
Cognitive Radio Networks
Cognitive Radio Networks Kwang-Cheng Chen and Ramjee Prasad
© 2009 John Wiley & Sons Ltd. ISBN: 978-0-470-69689-7
Cognitive Radio Networks
Professor Kwang-Cheng Chen
National Taiwan University, Taiwan
Professor Ramjee Prasad
Aalborg University, Denmark
This edition first published 2009
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Library of Congress Cataloging-in-Publication Data
Chen, Kwang-Cheng.
Cognitive radio networks / Kwang-Cheng Chen, Ramjee Prasad.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-69689-7 (cloth)
1. Cognitive radio networks. I. Prasad, Ramjee. II. Title.
TK5103.4815.C48 2009
0
81–dc22
621.39
2008055907
A catalogue record for this book is available from the British Library.
ISBN 978-0-470-69689-7
10/12pt Times by Thomson Digital, Noida, India.
Set in
Printed in Great Britain by CPI Anthony Rowe, Chippenham, England
Contents
Preface xi
1 Wireless Communications 1
1.1 Wireless Communications Systems 1
1.2 Orthogonal Frequency Division Multiplexing (OFDM) 3
1.2.1 OFDM Concepts 4
1.2.2 Mathematical Model of OFDM System 5
1.2.3 OFDM Design Issues 9
1.2.4 OFDMA 21
1.3 MIMO 24
1.3.1 Space-Time Codes 24
1.3.2 Spatial Multiplexing Using Adaptive Multiple Antenna Techniques 27
1.3.3 Open-loop MIMO Solutions 27
1.3.4 Closed-loop MIMO Solutions 29
1.3.5 MIMO Receiver Structure 31
1.4 Multi-user Detection (MUD) 34
1.4.1 Multi-user (CDMA) Receiver 34
1.4.2 Suboptimum DS/CDMA Receivers 37
References 40
2 Software Defined Radio 41
2.1 Software Defined Radio Architecture 41
2.2 Digital Signal Processor and SDR Baseband Architecture 43
2.3 Reconfigurable Wireless Comm unication Systems 46
2.3.1 Unified Communication Algorithm 46
2.3.2 Reconfigurable OFDM Implementation 47
2.3.3 Reconfigurable OFDM and CDMA 47
2.4 Digital Radio Processing 48
2.4.1 Conventional RF 48
2.4.2 Digital Radio Processing (DRP) Based System Architecture 52
References 58
3 Wireless Networks 59
3.1 Multiple Access Communications and ALOHA 60
3.1.1 ALOHA Systems and Slotted Multiple Access 61
3.1.2 Slotted ALOHA 61
vi Contents
3.1.3 Stabilised Slotted ALOHA 64
3.1.4 Approximate Delay Analysis 65
3.1.5 Unslotted ALOHA 66
3.2 Splitting Algorithms 66
3.2.1 Tree Algorithms 67
3.2.2 FCFS Splitting Algorithm 68
3.2.3 Analysis of FCFS Splitting Algorithm 69
3.3 Carrier Sensing 71
3.3.1 CSMA Slotted ALOHA 71
3.3.2 Slotted CSMA 76
3.3.3 Carrier Sense Multiple Access with Collision Detec tion (CSMA/CD) 79
3.4 Routing 82
3.4.1 Flooding and Broadcasting 83
3.4.2 Shortest Path Routing 83
3.4.3 Optimal Routing 83
3.4.4 Hot Potato (Reflection) Routing 84
3.4.5 Cut-through Routing 84
3.4.6 Interconnected Network Routing 84
3.4.7 Shortest Path Routing Algorithms 84
3.5 Flow Control 89
3.5.1 Window Flow Control 89
3.5.2 Rate Control Schemes 91
3.5.3 Queuing Analysis of the Leaky Bucket Scheme 92
References 93
4 Cooperative Communications and Networks 95
4.1 Information Theory for Cooperative Communications 96
4.1.1 Fundamental Network Information Theory 96
4.1.2 Multiple-access Channel with Cooperative Diversity 101
4.2 Cooperative Communications 102
4.2.1 Three-Node Cooperative Communi cations 103
4.2.2 Multiple-Node Relay Network 109
4.3 Cooperative Wireless Networks 113
4.3.1 Benefits of Cooperation in Wireless Networks 114
4.3.2 Cooperation in Cluster-Based Ad-hoc Networks 116
References 118
5 Cognitive Radio Communications 121
5.1 Cognitive Radios and Dynamic Spectrum Access 121
5.1.1 The Capability of Cognitive Radios 122
5.1.2 Spectrum Sharing Models of DSA 124
5.1.3 Opportunistic Spectrum Access: Basic Components 126
5.1.4 Networking The Cognitive Radios 126
5.2 Analytical Approach and Algorithms for Dynamic Spectrum Access 126
5.2.1 Dynamic Spectrum Access in Open Spectrum 128
5.2.2 Opportunistic Spectrum Access 130
5.2.3 Opportunistic Power Control 131
5.3 Fundamental Limits of Cognitive Radios 132
Contents vii
5.4 Mathematical Models Toward Networking Cognitive Radios 136
5.4.1 CR Link Model 136
5.4.2 Overlay CR Systems 137
5.4.3 Rate-Distance Nature 140
References 142
6 Cognitive Radio Networks 145
6.1 Network Coding for Cognitive Radio Relay Networks 146
6.1.1 System Model 147
6.1.2 Network Capacity Analysis on Fundamental CRRN Topologies 150
6.1.3 Link Allocation 154
6.1.4 Numerical Results 156
6.2 Cognitive Radio Networks Architecture 159
6.2.1 Network Architecture 159
6.2.2 Links in CRN 161
6.2.3 IP Mobility Management in CRN 163
6.3 Terminal Architecture of CRN 165
6.3.1 Cognitive Radio Device Architecture 165
6.3.2 Re-configurable MAC 168
6.3.3 Radio Access Network Selection 169
6.4 QoS Provisional Diversity Radio Access Networks 171
6.4.1 Cooperative/Collaborative Diversity and Efficient Protocols 172
6.4.2 Statistical QoS Guarantees over Wireless Asymmetry
Collaborative Relay Networks 174
6.5 Scaling Laws of Ad-hoc and Cognitive Radio Networks 177
6.5.1 Network and Channel Models 177
6.5.2 Ad-hoc Networks 178
6.5.3 Cognitive Radio Networks 179
References 180
7 Spectrum Sensing 183
7.1 Spectrum Sensing to Detect Specific Primary System 183
7.1.1 Conventional Spectrum Sensing 183
7.1.2 Power Control 187
7.1.3 Power-Scaling Power Control 188
7.1.4 Cooperative Spectrum Sensing 190
7.2 Spectrum Sensing for Cognitive OFDMA Systems 194
7.2.1 Cognitive Cycle 195
7.2.2 Discrimination of States of the Primary System 197
7.2.3 Spectrum Sensing Procedure 203
7.3 Spectrum Sensing for Cognitive Multi-Radio Networks 206
7.3.1 Multiple System Sensing 207
7.3.2 Radio Resource Sensing 216
References 228
8 Medium Access Control 231
8.1 MAC for Cognitive Radios 231
viii Contents
8.2 Multichannel MAC 232
8.2.1 General Description of Multichannel MAC 235
8.2.2 Multichannel MAC: Collision Avoidance/Resolution 238
8.2.3 Multichannel MAC: Acces s Negotiation 242
8.3 Slotted-ALOHA with Rate-Distance Adaptability 251
8.3.1 System Model 252
8.4 CSMA with AMC 259
8.4.1 Carrier Sense Multiple Access with Spatial-Reuse
Transmissions 261
8.4.2 Analysis of CSMA-ST 263
8.4.3 A Cross-Layer Power-Rate Control Scheme 268
8.4.4 Performance Evaluations 270
References 272
9 Network Layer Design 275
9.1 Routing in Mobile Ad-hoc Networks 275
9.1.1 Routing in Mobile Ad-hoc Networks 275
9.1.2 Features of Routing in CRN 276
9.1.3 Dynamic Source Routing in MANET 278
9.1.4 Ad-hoc On-demand Distance Vector (AODV) 283
9.2 Routing in Cognitive Radio Networks 286
9.2.1 Trusted Cognitive Radio Networking 286
9.2.2 Routing of Dynamic and Unidirectional CR Links in CRN 288
9.3 Control of CRN 291
9.3.1 Flow Control of CRN 291
9.3.2 End-to-End Error Control in CRN 292
9.3.3 Numerical Examples 292
9.4 Network Tomography 296
9.5 Self-organisation in Mobile Communication Networks 298
9.5.1 Self-organised Networks 298
9.5.2 Self-organised Cooperative and Cognitive Networks 299
References 304
10 Trusted Cognitive Radio Networks 307
10.1 Framework of Trust in CRN 308
10.1.1 Mathematical Structure of Trust 308
10.1.2 Trust Model 311
10.2 Trusted Association and Routing 311
10.2.1 Trusted Association 312
10.2.2 Trusted Routing 317
10.3 Trust with Learning 319
10.3.1 Modified Bayesian Learning 319
10.3.2 Learning Experiments for CRN 322
10.4 Security in CRN 328
10.4.1 Security Properties in Cellular Data Networks 328
10.4.2 Dilemma of CRN Security 330
Contents ix
10.4.3 Requirements and Challenges for Preserving User
Privacy in CRNs 331
10.4.4 Implementation of CRN Security 332
References 334
11 Spectrum Management of Cognitive Radio Networks 335
11.1 Spectrum Sharing 337
11.2 Spectrum Pricing 339
11.3 Mobility Management of Heterogeneous Wireless Networks 347
11.4 Regulatory Issues and International Standards 350
11.4.1 Regulatory Issues 351
11.4.2 International Standards 354
References 355
Index 357
Preface
Wireless communications and networks have experienced booming growth in the past few decades,
with billions of new wireless devices in use each year. In the next decade we expect the exponential
growth of wireless devices to result in a challenging shortage of spectrum suitable for wireless
communications. Departing from the traditional approach to increase the spectral efficiency of physical
layer transmission, Dr. Joe Mitola III’s innovative cognitive radio technology derived from software
defined radio will enhance spectrum utilization by leveraging spectrum “holes” or “white spaces”. The
Federal Communication Commission (FCC) in the US quickly identified the potential of cognitive
radio and endorsed the applications of such technology. During the past couples of years, there now
exist more than a thousand research papers regarding cognitive radio technology in the IEEE Xplore
database, which illustrates the importance of this technology. However, researchers have gradually
come to realize that cognitive radio technology, at the link level, is not sufficient to warrant the spectrum
efficiency of wireless networks to transport packets, and networking these cognitive radios which
coexist with primary/legacy radios through cooperative relay functions can further enhance spectrum
utilization. Consequently, in light of this technology direction, we have developed this book on
cognitive radio networks, to introduce state-of-the-art knowledge from cognitive radio to networking
cognitive radios.
During the preparation of the manuscript for this book, we would like to thank t he encourage men t,
discussion, and support from many international researchers and our students, including Mohsen,
Guizani, Fleming Bjerge Frederiksen, Neeli Prasad, Ying- Chang Liang, Sumei Sun, Songyoung
Lee, Albena Mihovska, Feng-Seng Chu, Chi-Cheng Tseng, Shimi Cheng, Lin-Hun g Kung, ChungKai Yu, Shao-Yu L ien, Sheng-Yuan Tu, Bilge Kartal Cetin, Yu-Cheng Peng, Jin Wang, Peng-Yu
Chen, Chu-Shiang Huang, Chin g-Kai Liang, Hong-Bin Chang, Po-Yao Huang, Wei-Hong Liu, I-Han
Chiang, Michael Eckl, Yo-Yu Lin,Weng Chon Ao, Dua Idris, and Joe Mitola III, the father of
cognitive radio. Our thanks also to Inga, Susanne and Keiling who helped with so ma ny aspec ts that
the book could not have be en comple ted without their support.
The first author (K.C. Chen) would especially like to thank Irving T. Ho Foundation who endowed
the chair professorship to National TaiwanUniversity which enabled him to dedicate his time towriting
this book. For the readers’ information, Dr. Irving T. Ho is the founder of Hsin-Chu Science Park in
Taiwan. Our appreciation also goes to the National Science Council and CTiF Aalborg University who
made it possible for KC and Ramjee to work together in Denmark. Last but not the least, KC would like
to thank his wife Christine and his children Chloe´and Danny for their support, especially during his
absence from home in the summer of 2008 while he was completing the manuscript.
Kwang-Cheng Chen, Taipei, Taiwan
Ramjee Prasad, Aalborg, Denmark
1
Wireless Communications
Conventional wireless communication networks use circuit switching, such as the first generation
cellular AMPS adopting Frequency Division Multiple Access (FDMA) and second generation cellular
GSM adopting Time Division Multiple Access (TDMA) or the IS-95 pioneering Code Division
Multiple Access (CDMA). The success of the Internet has caused a demand for wireless broadband
communications and packet switching plays a key role, being adopted in almost every technology.
From the third generation cellular and beyond, packet switching becomes a general consensus in the
development of technology.
The International Standards Organisation (ISO) has defined a large amount of standardsfor computer
networks, including the fundamental architecture of Open System Interconnection (OSI) to partition
computer networks into seven layers. Such a seven-layer partition might not be ideal when optimising
network efficiency, but it is of great value in the implementation of large scale networks via such
a layered-structure. Engineers can implement a portion of software and hardware in a network
independently, even plug-in networks, or replace a portion of network hardware and/or software,
provided that the interfaces among layers and standards are well defined. Considering the nature of
‘stochastic multiplexing’ packet switching networks, the OSI layer structure may promote the quick
progress of computer networks and the wireless broadband communications discussed in this book.
Figure 1.1 depicts the OSI seven-layer structure and its application to the general extension and
interconnection to other portion of networks. The four upper layers are mainly ‘logical’ rather than
‘physical’ in concept in network operation, whereas physical signalling is transmitted, received and
coordinated in the lower two layers: physical layer and data link layer. The physical layer of a wireless
network thus transmits bits and receives bits correctly in the wireless medium, while medium access
control (MAC) coordinates the packet transmission using the medium formed by a number of bits.
When we talk about wireless communications in this book, we sometimes refer it as a physical layer
and the likely MAC of wireless networks, although some people treat it with a larger scope. In this
chapter, we will focus on introducing physical layer transmission of wireless communication systems,
and several key technologies in the narrow-sense of wireless communications, namely orthogonal
frequency division multiplexing (OFDM) and multi-input-multi-output (MIMO) processing.
1.1 Wireless Communications Systems
To support multimedia traffic in state-of-the-art wireless mobile communications networks, digital
communication systemengineering has been used for the physical layer transmission. To allow a smooth
transitioninto laterchapters, we shall brieflyintroduce herethe fundamentals ofdigital communications,
Cognitive Radio Networks Kwang-Cheng Chen and Ramjee Prasad
©
2009 John Wiley & Sons Ltd. ISBN: 978-0-470-69689-7
2 Cognitive Radio Networks
Application
Presentation
Session
Transport
Network
Data Link
Control
Physical
Virtual
Link for
Reliable
Packets
Virtual Bit
Pipe
Virtual Network Service
Virtual Session
Virtual End-to-End Link
(Message)
Virtual End-to-End Link(Packet)
Network
DLC DLC
PHYPHY
DLC DLC
Network
PHYPHY
SubnetSubnet
Application
Presentation
Session
Transport
Network
Data Link
Control
Physical
Figure 1.1 Seven-Layer OSI Network Architecture
assuming some knowledge of undergraduate-level communication systems and signalling. Interested
readers will find references towards more advanced study throughout the chapter.
Following analogue AM and FM radio, digital communication systems have been widely studied
for over half a century. Digital communications have advantages over their analogue counterparts due
to better system performance in links, and digital technology can also make media transmission more
reliable. In the past, most interest focused on conventional narrow-band transmission and it was
assumed that telephone line modems might lead the pace and approach a theoretical limit. Wireless
digital communications were led by major applications such as satellite communications and analogue
cellular. In the last two decades, wireless broadband communications such as code division multiple
access (CDMA) and a special form of narrowband transmission known as orthogonal frequency
division multiplexing (OFDM) were generally adopted in state-of-the-art communication systems for
high data rates and system capacity in complicated communication environments and harsh fading
channels. A digital wireless communication system usually consists of the elements shown in
Figure 1.2, where they are depicted as a block diagram.
Information sources can be either digital, to generate 1s and 0s, or an analogue waveform source.
A source encoder then transforms the source into another stream of 1s and 0s with high entropy. Channel
coding, which proceeds completely differently from source coding, amends extra bits to protect
information from errors caused by the channel. To further randomise error for better information
protection, channel coding usually works with interleaving. In this case, bits are properly modulated,
which is usually a mapping of bits to the appropriate signal constellation. After proper filtering,
in typical radio systems, such baseband signalling is mixed through RF (radio frequency) and likely IF
(intermediate frequency) processing before transmission by antenna. The channel can inevitably
introduce a lot of undesirable effects, including embedded noise, (nonlinear) distortion, multi-path
fading and other impairments. The receiving antenna passes the waveform through RF/IF and an A/D
converter translates the waveform into digital samples in state-of-the-art digital wireless communication systems. Instead of reversing the operation at the transmitter, synchronisation must proceed so that
Wireless Communications 3
Noise
Channel
Coding &
Interleaving
Channel
Decoding &
De-interleaving
Modulation
& Filtering
D/A
RF &
Antenna
Fading
Source
Decoding
Destination
Information
Source
Distortion
RF &
Antenna
A/D
Equalization Demodulation
Channel
Estimation
Source
Coding
Synchronization
Channel
Impairments
Figure 1.2 Block diagram of a typical digital wireless communication system
the right frequency, timing and phase can be recovered. To overcome various channel effects that
disrupt reliable communication, equalisation of these channel distortions is usually adopted. For further
reliable system design and possible pilot signalling, channel estimation to enhance receiver signal
processing can be adopted in many modern systems.
To summarise, the physical layer of wireless networks in wireless digital communications systems is
trying to deal with noise and channel impairments (nonlinear distortions by channel, fading, speed, etc.)
in the form of Inter Symbol Interference (ISI). State-of-the-art digital communication systems are
designed based on the implementation of these functions over hardware (such as integrated circuits) or
software running on top of digital signal processor(s) or micro-processor(s).
In the next section of this chapter, we focus on OFDM and its multiple access, Orthogonal Frequency
Division Multiple Access (OFDMA).
1.2 Orthogonal Frequency Division Multiplexing (OFDM)
In 1960, Chang [1] postulated the principle of transmitting messages simultaneously through a linear
band limited channel without Inter Channel Interference (ICI) and Inter Symbol Interference (ISI).
Shortly afterwards, Saltzberg [2] analysed the performance of such a system and concluded, ‘The
efficient parallel system needs to concentrate more on reducing crosstalk between the adjacent channels
rather than perfecting the individual channel itself because imperfection due to crosstalk tends to
dominate’. This was an important observation and was proven in later years in the case of baseband
digital signal processing.
The major contribution to the OFDM technique came to fruition when Weinstein and Ebert [3]
demonstrated the use of Discrete Fourier Transform (DFT) to perform baseband modulation and
demodulation. The use of DFT immensely increased the efficiency of modulation and demodulation
processing. The use of the guard space and raised-cosine filtering solve the problems of ISI to a great
extent. Although the system envisioned as such did not attain the perfect orthogonality between
subcarriers in a time dispersive channel, nonetheless it was still a major contribution to the evolution
of the OFDM system.
To resolve the challenge of orthogonality over the dispersive (fading) channel, Peled and Ruiz [4]
introduced the notion of the Cyclic Prefix (CP). They suggested filling the guard space with the cyclic
4 Cognitive Radio Networks
extension of the OFDM symbol, which acts like performing the cyclic convolution by the channel
as long as the channel impulse response is shorter than the length of the CP, thus preserving the
orthogonality of subcarriers. Although addition of the CP causes a loss of data rate, this deficiency was
compensated for by the ease of receiver implementation.
1.2.1 OFDM Concepts
The fundamental principle of theOFDM system is to decomposethe high rate data stream(Bandwidth ¼
W)intoN lower rate data streams and then to transmit them simultaneously over a large number
of subcarriers. A sufficiently high value of N makes the individual bandwidth (W/N) of subcarriers
narrowerthan the coherencebandwidth(B
flat fading only and this can be compensated for using a trivial frequency domain single tap equaliser.
The choice of individual subcarrier is such that they are orthogonal to each other, which allows for the
overlapping of subcarriers becausethe orthogonality ensures the separationof subcarriers at the receiver
end. This approach results in a better spectral efficiency compared to FDMA systems, where no spectral
overlap of carriers is allowed.
The spectral efficiency of an OFDM system is shown in Figure 1.3, which illustrates the difference
between the conventional non-overlapping multicarrier technique (such as FDMA) and the overlapping
multicarrier modulation technique (such as DMT, OFDM, etc.). As shown in Figure 1.3 (for illustration
purposes only; a realistic multicarrier technique is shown in Figure 1.5), use of the overlapping
multicarrier modulation technique can achieve superior bandwidth utilisation. Realising the benefits of
the overlapping multicarrier technique, however, requires reduction of crosstalk between subcarriers,
which translates into preserving orthogonality among the modulated subcarriers.
) of the channel. The individual subcarriers as such experience
c
Figure 1.3 Orthogonal multicarrier versus conventional multicarrier
The ‘orthogonal’ dictates a precise mathematical relationship between frequencies of subcarriers
in the OFDM based system. In a normal frequency division multiplex system, many carriers are spaced
Wireless Communications 5
apart in such a way that the signals can be received using conventional filters and demodulators. In such
receivers, guard bands are introduced between the different carriers in the frequency domain, which
results in a waste of the spectrum efficiency. However, it is possible to arrange the carriers in an OFDM
system such that the sidebands of the individual subcarriers overlap and the signals are still received
without adjacent carrier interference. The OFDM receiver can therefore be constructed as a bank of
demodulators, translating each subcarrier down to DC and then integrating over a symbol period to
recover the transmitted data. If all subcarriers down-convert to frequencies that, in the time domain,
have a whole number of cycles in a symbol period T, then the integration process results in zero ICI.
These subcarriers can be made linearly independent (i.e., orthogonal) if the carrier spacing is a multiple
of 1/T, which will be proven later to be the case for OFDM based systems.
Figure 1.4 shows the spectrum of an individual data subcarrier and Figure 1.5 depicts the spectrum
of an OFDM symbol. The OFDM signal multiplexes in the individual spectra with a frequency spacing
equal to the transmission bandwidth of each subcarrier as shown in Figure 1.4. Figure 1.5 shows that at
the centre frequency of each subcarrier there is no crosstalk from other channels. Therefore, if a receiver
performs correlation with the centre frequency of each subcarrier, it can recover the transmitted data
without any crosstalk. In addition, using the DFT based multicarrier technique, frequency-division
multiplexing is achieved by baseband processing rather than the costlier bandpass processing.
Figure 1.4 Spectra of OFDM individual subcarrier
The orthogonality of subcarriers is maintained even in the time-dispersive channel by adding the CP.
The CP is the last part of an OFDM symbol, which is prefixed at the start of the transmitted OFDM
symbol, which aids in mitigating the ICI related degradation. Simplified transmitter and receiver block
diagrams of the OFDM system are shown in Figures 1.6 (a) and (b) respectively.
1.2.2 Mathematical Model of OFDM System
OFDM based communication systems transmit multiple data symbols simultaneously using orthogonal
subcarriers as shown in Figure 1.7. A guard interval is added to mitigate the ISI, which is not shown
6 Cognitive Radio Networks
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–5 –4 –3 –2 –1 0 1 2 3 4 5
Figure 1.5 Spectra of OFDM symbol
in the figure for simplicity. The data symbols (d
then modulated with complex orthonormal (exponential in this book) waveform ff
) are first assembled into a group of block size N and
n,k
k
ðtÞg
N
k¼0
as shown
in Equation (1.1). After modulation they are transmitted simultaneously as transmitter data stream.
The modulator as shown in Figure 1.7 can be easily implemented using an Inverse Fast Frequency
Transform (IFFT) block described by Equation (1.1):
"#
¥
N 1
X
xðtÞ¼
X
n¼¥
k¼0
d
fkðt nTdÞ
n;k
ð1:1Þ
where
j2pfkt
f
ðtÞ¼
k
e
t«½0; Td
0 otherwise
and
¼ foþ
k
; k ¼ 0 ...N 1
T
d
f
k
We use the following notation:
&
d
: symbol transmitted during nth timing interval using kth subcarrier;
n,k
&
Td: symbol duration;
&
N: number of OFDM subcarriers;
&
fk: kth subcarrier frequency, with f0being the lowest.
Wireless Communications 7
Figure 1.6 (a) Transmitter block diagram and (b) receiver block diagram
The simplified block diagram of an OFDM demodulator is shown in Figure 1.8. The demodulation
process is based on the orthogonality of subcarriers {f
ð
*
fkðtÞf
R
d
n,0
d
n,N–1
ðtÞdt ¼ Tddðk lÞ¼
l
tjw
0
e
tjw
N−1
e
(t)}, namely:
k
T
d
0 otherwise
Σ
k ¼ l
x(t)
Figure 1.7 OFDM modulator
x
8 Cognitive Radio Networks
T
d
d
)(
•
∫
T
T
t
−jw
0
e
d
n,0
(t)
T
d
d
)(
•
∫
T
T
t
−jNw
0
e
d
n,N–1
Figure 1.8 OFDM demodulator
Therefore, a demodulator can be implemented digitally by exploiting the orthogonality relationship
of subcarriers yielding a simple Inverse Fast Frequency Transform (IFFT)/Fast Frequency Transform
(FFT) modulation/demodulation of the OFDM signal:
ðn þ 1ÞT
d
ð
1
¼
d
n;k
T
d
nT
xðtÞ*f
d
*
ðtÞdt ð1:2Þ
k
Equation (1.2) can be implemented using the FFT block as shown in Figure 1.8.
The specified OFDM model can also be described as a 2-D lattice representation in time and
frequency plane and this property can be exploited to compensate for channel related impairments
issues. Looking into the modulator implementation of Figure 1.7, a model can be devised to represent
the OFDM transmitted signal as shown in Equation (1.3). In addition, this characteristic may also be
exploited in pulse shaping of the transmitted signal to combat ISI and multipath delay spread. This
interpretation is detailed in Figure 1.8.
X
dkf
xðtÞ¼
k;l
ðtÞð1:3Þ
k;l
The operand fk,l(t), represents the time and frequency displaced replica of basis function f(t)by
and kn0in 2-D time and frequency lattice respectively and as shown in Figure 1.9. Mathematically it
lt
0
τ
0
ν
0
Frequency
Time
Figure 1.9 2-D lattice in time-frequency domain
Wireless Communications 9
can be shown that operand f
Usually the basis function f(t) is chosen as a rectangular pulse of amplitude 1=
t
and the frequency separation are set at y0¼1/t0.Each transmitted signal in the lattice structure
0
(t) is related to the basis function in Equation (1.4) as follows:
k,l
f
ðtÞ¼fðt lt0Þe
k;l
j2pky0t
p
ffiffiffiffiffi
and duration
t
0
ð1:4Þ
experiences the same flat fading during reception, which simplifies channel estimation and the
equalisation process. The channel attenuations are estimated by correlating the received symbols
with a priori known symbols at the lattice points. This technique is frequently used in OFDM based
communication systems to provide the pilot assisted channel estimation.
1.2.3 OFDM Design Issues
Communication systems based on OFDM have advantages in spectral efficiency but at the price of
being sensitive to environment impairments. To build upon the inherent spectral efficiency and simpler
transceiver design factors, these impairment issues must be dealt with to garner potential benefits.
In communication systems, a receiver needs to synchronise with a transmitter in frequency, phase and
time (or frame/slot/packet boundary) to reproduce the transmitted signal faithfully. This is not a trivial
task particularly in a mobile environment, where operating conditions and surroundings vary so
frequently. For example, when a mobile is turned on, it may not have any knowledge of its surroundings
and it must take few steps (based upon agreed protocol/standards) to establish communication with the
base station/access point. This basic process in communication jargon is known as synchronisation and
acquisition. The tasks of synchronisation and acquisition are complex issues anyway, but impairments
make things even harder. Impairment issues are discussed in detail in the following sections.
1.2.3.1 Frequency Offset
Frequency offset in an OFDM system is introduced from two sources: mismatch between transmit and
receive sampling clocks and misalignment between the reference frequency of transmit and receive
stations. Both impairments and their effects on the performance are analysed.
The sampling epoch of the received signal is determined by the receiver A/D sampling clock, which
seldom resumes the exact period matching the transmit sampling clock causing the receiver sampling
instants slowly to drift relative to the transmitter. Many authors have analysed the effect of sampling
clock drift on system performance. The sampling clock error manifests in two ways: first, a slow
variation in the sampling time instant causes rotation of subcarriers and subsequent loss of the SNR
due to ICI, and second, it causes the loss of orthogonality among subcarriers due to energy spread
among adjacent subcarriers. Let us define the normalised sampling error as
T0T
¼
t
D
T
where T and T
DFT, on the received subcarriers R
where l is the OFDM symbol index, k is the subcarrier index, T
the useful duration of thesymbol duration respectively,W
term N
t
approximated by P
0
are transmit and receive sampling periods respectively. Then, the overall effect, after
can be shown as:
l,k
T
s
j2pktDl
T
R
¼ e
l;k
is the additional interference due to the sampling frequency offset.The power of the last term is
D
2
p
ðktDÞ2.
t
D
3
u
X
sin cðpktDÞH
l;k
l;kþWl;kþNt
and Tuare the duration of the total and
s
is additivewhite Gaussian noise and the last
l,k
ðl; kÞ
D
g
10 Cognitive Radio Networks
Hence, the degradation grows as the square of the product of offset tDand the subcarrier index k. This
means that the outermost subcarriers are most severely affected. The degradation can also be expressed
as SNR loss in dB by following expression:
2
p
E
s
10 log101 þ
D
n
3
N
ðktDÞ
0
2
In OFDM systems with a small number of subcarriers and quite small sampling error t
1, the degradation caused by the sampling frequency error can be ignored. The most significant
kt
D
issue is the different value of rotation experienced by the different subcarriers based on the subcarrier
index k and symbol index l; this is evident from the term {e
T
s
j2pktDl
T
u
}. Hence, the rotation angle is the
largest for the outermost subcarrier and increases as a function of symbol index l. The term t
such that
D
D
controlled by the timing loop and usually is very small, but as l increases the rotation eventually
becomes so large that the correct demodulation is no longer possible and this necessitates the tracking
of the sampling frequency in the OFDM receiver. The effect of sampling offset on the SNR degradation
is shown in Figure 1.10.
SNR Degradation Due to Sampling Offset
18
Num Subcarriers = 4
Num Subcarriers = 8
Num Subcarriers = 16
16
Num Subcarriers = 32
Num Subcarriers = 64
14
12
10
Loss
(dB)
8
6
4
is
2
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Normalized Samplin
Offset
Figure 1.10 SNR degradation due to sampling mismatch
1.2.3.2 Carrier Frequency Offset
The OFDM systems are much more sensitive to frequency error compared to the single carrier
frequency systems. The frequency offset is produced at the receiver because of local oscillator
instability and operating condition variability at transmitter and receiver; Doppler shifts caused by
the relative motion between the transmitter and receiver; or the phase noise introduced by other channel
impairments. The degradation results from the reduction in the signal amplitude of the desired
subcarrier and ICI caused by the neighbouring subcarriers. The amplitude loss occurs because
the desired subcarrier is no longer sampled at the peak of the equivalent sinc-function of the DFT.
Wireless Communications 11
Adjacent subcarriers cause interference because they are not sampled at their zero crossings. The
overall effect of carrier frequency offset effect on SNR is analysed by Pollet et al [6] and for relatively
small frequency error, the degradation in dB is approximated by
SNR
ðdBÞ
loss
10
3ln10
ðpTf
E
s
2
Þ
D
N
0
where fDis the frequency offset and is a function of the subcarrier spacing and T is the sampling period.
The performance of the system depends on modulation type. Naturally, the modulation scheme with
large constellation points is more susceptible to the frequency offset than a small constellation modulation scheme, because the SNR requirements for the higher constellation modulation scheme are much
higher for the same BER performance.
It is assumed that two subcarriers of an OFDM system can be represented using the orthogonal
frequency tones at the output of the A/D converter at baseband as
f
k
ðtÞ¼e
j2pfkt=T
and f
k þ m
ðtÞ¼e
j2pðk þmÞt=T
where T is the sampling period. Let us also assume that due to the frequency drift the receive station has
a frequency offset of d from kth tone to (k þ m)th tone, i.e.,
f
d
k þ m
ðtÞ¼e
j2pðk þm þdÞt=T
Due to this frequency offset there is an interference between kth and (k þ m)th channels given by
T
I
ðdÞ¼
m
ð
jk2pt=Tejðk þ m þdÞ2pt=T
e
0
jI
ðdÞj ¼
m
dt ¼
TjsinðpdÞj
pjm þdj
j2pd
Tð1 e
j2pðm þdÞ
Þ
The aggregate loss (power) due to this interference from all N subcarriers can be approximated as
following:
N 1
X
m
2
I
ðdÞðTdÞ
m
X
1
2
m¼1
m
ðTdÞ
2
2
23
14
for N 1
1.2.3.3 Timing Offset
The symbol timing is very important to the receiver for correct demodulation and decoding of the
incoming data sequence. The timing synchronisation is possible with the introduction of the training
sequences in addition to the data symbols in the OFDM systems. The receiver may still not be able to
recover the complete timing reference of the transmitted symbol because of the channel impairments
causing the timing offset between the transmitter and the receiver. A time offset gives rise to the phase
rotation of the subcarriers. The effect of the timing offset is negated with the use of a CP. If the channel
response due to timing offset is limited within the length of the CP the orthogonality across the
subcarriers are maintained. The timing offset can be represented by a phase shift introduced by the
channel and can be estimated from the computation of the channel impulse response. When the receiver
is not time synchronised to the incoming data stream, the SNR of the received symbol is degraded.
12 Cognitive Radio Networks
The degradation can be quantised in terms of the output SNR with respect to an optimal sampling time,
, as shown below:
T
optimal
LðtÞ
z ¼
Lð0Þ
where T
T
optimal
is the autocorrelation function and t is the delay between the optimal sampling instant
optimal
and the received symbol time. The parameter t is treated as a random variable since it is
estimated in the presence of noise and is usually referred as the timing jitter. The two special cases of
interest, baseband time-limited signals and band-limited signals with the normalised autocorrelation
functions, are shown below in mathematical forms:
LðtÞ¼ 1
LðtÞ¼
1NsinðpNWtÞ
tjj
T
symbol
sinðpWtÞ
where W is the bandwidth of the band-limited signal. The single carrier system is best described as the
band-limited signal whereas the OFDM (multicarrier) system is best described as the time-limited
signal. For single carrier systems, the timing jitter manifests as a noisy phase reference of the bandpass
signal. In the case of OFDM systems, pilot tones are transmitted along with the data-bearing carrier to
estimate residual phase errors.
Paez-Borrallo [7]has analysed the loss of orthogonality due to time shift and the result of this analysis
is shown here to quantise its effect on ICI and the resulting loss in orthogonality. Let us assume the
timing offset between the two consecutive symbols is denoted by t, then the received stream at the
receiver can be expressed as follows:
ð
T =2 þt
¼ c
X
i
0
T =2
fkðtÞf
*
ðt tÞdt þc
l
ð
1
T=2
T =2 þt
fkðtÞf
*
ðt tÞdt
l
where
j2pfkt=T
ðtÞ¼e
f
k
Substitute m ¼k l and then the magnitude of the received symbol can be represented as
jX
8
>
sin mp
>
<
2T
j¼
i
>
>
:
0; c0¼ c
mp
t
T
; c
„ c
0
1
1
This can be further simplified for simple analysis if t T:
jXij
T
mp
t
T
¼ 2
T
t
2mp
This is independent of m, for t T.
We can compute the average interfering power as
"#
2
jXij
E
¼ 4
2
T
2
t
1
þ0
T
2
1
¼ 2
2
2
t
T
Wireless Communications 13
The ICI loss in dB is computed as follows:
2
ICI
dB
¼ 10 log102
t
T
1.2.3.4 Carrier Phase Noise
The carrier phase impairment is induced due to the imperfection in the transmitter and the receiver
oscillators. The phase rotation could either be the result of the timing error or the carrier phase offset for
a frequency selective channel. The analysis of the system performance due to carrier phase noise
has been performed by Pollet et al. [8] The carrier phase noise was modelled as the Wiener process u (t)
with E {q (t)} ¼0 and E [{q (t
þ t) q(t0)}2] ¼4pb|t|, where b (in Hz) denotes the single sided
0
line width of the Lorentzian power spectral density of the free running carrier generator. Degradation
in the SNR, i.e., the increase in the SNR needed to compensate for the error, can be approximated by
DðdBÞ
11
6ln10
4pN
b
E
s
W
N
0
where W is the bandwidth and Es/N0is the SNR of the symbol. Note that the degradation increases with
the increase in the number of subcarriers.
1.2.3.5 Multipath Issues
In mobile wireless communications, a receiver collects transmitted signals through various paths, some
arriving directly and some from neighbouring objects because of reflection, and some even arriving
because of diffraction from the nearby obstacles. These arriving paths arriving at the receiver may
interfere with each other and cause distortion to the information-bearing signal. The impairments
caused by multipath effects include delay spread, loss of signal strength and widening of frequency
spectrum. The random nature of the time variation of the channel may be modelled as a narrowband
statistical process. For a large number of signal reflections impinging on the receive antenna, the
distribution of the arriving signal can be modelled as complex-valued Gaussian Random Processes
based on central limit theory. The envelope of the received signal can be decomposed into fast varying
fluctuations superimposed onto slow varying ones. When the average amplitude of envelope suffers
a drastic degradation from the interfering phase from the individual path, the signal is regarded as
fading. Multipath is a term used to describe the reception of multiple copies of the information-bearing
signal by the receive antenna. Such a channel can be described statistically and can be characterised
by the channel correlation function. The baseband-transmitted signal can be accurately modelled as a
narrowband process as follows:
sðtÞ¼xðtÞe
2pfct
Assuming the multipath propagation as Gaussian scatterers, the channel can be characterised by time
varying propagation delays, loss factors and Doppler shifts. The time-varying impulse response of the
channel is given by
X
where c(t
; tÞ¼
cðt
n
, t) is the response of the channel at time t due to an impulse applied at time t tn(t); an(t)
n
anðtn; tÞe
n
is the attenuation factor for the signal received on the nth path; t
nth path; and f
is the Doppler shift for the signal received on the nth path.
D
n
j2pf
tnðtÞ
D
n
d½t tnðtÞ
(t) is the propagation delay for the
n
14 Cognitive Radio Networks
The Doppler shift is introduced because of the relative motion between the transmitter and the
receiver and can be expressed as
v cosðunÞ
¼
f
D
n
l
where v is the relative velocity between transmitter and receiver, l is the wavelength of the carrier and
q
is the phase angle between the transmitter and the receiver.
n
The output of the transmitted signal propagating through channel is given as
; tÞ*sðtÞ
n
ÞtnðtÞ
D
n
xðt tnðtÞÞe
j2pfct
zðtÞ¼
X
an½tnðtÞe
n
zðtÞ¼cðt
j2pðfcþf
where
ðtÞÞ*xðtÞ¼xðt tnðtÞÞ
dðt t
n
dðt t
ðtÞÞ*e
n
bn¼ antnðtÞ½e
j2pfct
j2pfcðt tnðtÞÞ
¼ e
j2pðfcþf
D
ÞtnðtÞ
n
Alternately z(t) can be written as
zðtÞ¼
X
bnxðt tnðtÞÞe
n
j2pfct
where bnis the Gaussian random process. The envelope of the channel response function c(tn, t) has
a Rayleigh distribution function because the channel response is the ensemble of the Gaussian random
process. The density function of a Rayleigh faded channel is given by
2
z
z
2
f
ðzÞ¼
z
2s
e
2
s
A channel without a direct line of sight (LOS) path (i.e., only scattered paths) is typically termed a
Rayleigh fading channel. A channel with a direct LOS path to the receiver is generally characterised
by a Rician density function and is given by
ðzÞ¼
f
z
z
s
I
0
2
zh
s
e
2
2
z2þh
2
2s
where I
is the modified Bessel function of the zeroth order and h and s2are the mean and variance
0
of the direct LOS paths respectively. Proakis [9] has shown the autocorrelation function of c(t, t)as
follows:
ðt; DtÞ¼Efcðt; tÞc*ðt; t þDtÞg
L
c
In addition, it can be measured by transmitting very narrow pulses and cross correlating the received
signal with a conjugate delayed version of itself. The average power of the channel can be found by
setting Dt ¼ 0, i.e., L
intensity profile. The range of values of t over which L
(t, Dt) ¼ Lc(t). The quantity is known as the power delay profile or multipath
c
(t) is essentially nonzero is called the multipath
c
Wireless Communications 15
delay spread of the channel, denoted by tm. The reciprocal of the multipath delay spread is a measure of
the coherence bandwidth of the channel, i.e.,
1
B
m
t
m
The coherence bandwidth of a channel plays a prominent role in communication systems. If the
desired signal bandwidth of a communication system is small compared to the coherence bandwidth
of the channel, the system experiences flat fading (or frequency non-selective fading) and this eases
signal processing requirements of the receiver system because the flat fading can be overcome by
adding the extra margin in the system link budget. Conversely, if the desired signal bandwidth is large
compared to the coherence bandwidth of the channel, the system experiences frequency selective
fading and impairs the ability of the receiver to make the correct decision about the desired signal.
The channels, whose statistics remain constant for more than one symbol interval, are considered a slow
fading channel compared to the channels whose statistics change rapidly during a symbol interval.
In general, broadband wireless channels are usually characterised as slow frequency selective fading.
1.2.3.6 Inter Symbol Interference (ISI) Issues
The output of the modulator as shown in Equation (1.1) is shown here for reference
"#
¥
N 1
X
n¼¥
X
k¼0
d
fkðt nTdÞ
n;k
xðtÞ¼
Equation (1.1) can be re-written in the discrete form for the nth OFDM symbol as follows:
N 1
X
where f
For the n
j2pfkt/T
(t) ¼e
k
th
block of channel symbols, dnP, d
.
x
n
ðkÞ¼
k¼0
d
fkðt nTdÞ
n;k
...d
nP þ 1
nP þ P 1
, the ithsubcarrier signal can be
expressed as follows:
N 1
ðkÞ¼
X
d
k¼0
where l
i
x
n
the index of time complex exponential of length N, i.e., 0 liN -1.
i
These are summed to form the n
nP þ i;k
2p
j
lik
N
e
For i ¼ 0; 1; 2 ...P 1; P ¼ number of subcarriers
th
OFDM symbol given as
ðkÞ
x
n
P 1
X
i¼0
x
0
ðkÞ¼
n
P 1
X
i¼0
d
nP þ i
2p
j
lik
N
e
ð1:5Þ
The transmitted signal at the output of the digital-to-analogue converter can be represented as
follows:
"#
L 1
X
X
sðtÞ
n
xnðkÞdðt ðnL þkÞTdÞ
k¼0
where, L is the length of data symbol larger than N (number of subchannels). Since the sequence length
L is longer than N, only a subset of the OFDM received symbols are needed at thereceiver to demodulate
16 Cognitive Radio Networks
the subcarriers. The additional Q ¼L N symbols are not needed and we will see later that it could be
used as a guard interval to add the CP to mitigate the ICI problem in OFDM systems. In multipath and
additive noise environments, the received OFDM signal is given by
ðkÞ¼
r
n
L 1
X
xnðiÞhðk iÞþ
i¼0
L 1
X
i¼0
x
ðiÞhðk þL iÞþvnðkÞð1:6Þ
n 1
The first term represents the desired information-bearing signal in a multipath environment, whereas
the second part represents the interference from the preceding symbols. The length of the multipath
channel, L
, is assumed much smaller than the length of the OFDM symbol L. This assumption plus the
h
assumption about the causality of the channel implies that the ISI is only from the preceding symbol.
If we assume that the multipath channel is as long as the guard interval, i.e., L
Q, then the received
h
signal can be divided into two time intervals. The first time intervalcontains the desired symbol plus the
ISI from the preceding symbol. The second interval contains only the desired information-bearing
symbol. Mathematically it can be written as follows:
8
ðkÞ¼
r
n
L 1
X
>
>
>
xnðiÞhðk iÞþ
>
<
i¼0
L 1
>
X
>
>
>
xnðiÞhðk iÞþvnðkÞ Q k L 1
:
i¼0
L 1
X
i¼0
x
ðiÞhðk þL iÞþvnðkÞ 0 k Q 1
n 1
ð1:7Þ
We are ready to explore the performance degradation due to ISI. ISI is the effect of the time dispersion
of the information-bearing pulses, which causes symbols to spread out so that they disperse energy
into the adjacent symbol slots. The Nyquist criterion paves the way to achieve ISI-free transmission
with observation at the Nyquist rate samples in a band limited environment, to result in zero-forcing
equalisation. The complexity of the equaliser depends on the severity of the channel distortion.
Degradation occurs due to the receiver’s inability to equalise the channel perfectly, and from the noise
enhancement of the modified receiver structure in the process. The effect of the smearing of energy into
the neighbouring symbol slots is represented by the second term in Equation (1.7). The effect of the ISI
can be viewed in time and frequency domain.
One of the most important properties of the OFDM system is its robustness against multipath delay
spread, ISI mitigation. This is achieved by using spreading bits into a number of parallel subcarriers to
result in a long symbol period, which minimises the inter-symbol interference. The level of robustness
against the multipath delay spread can be increased even further by addition of theguard period between
transmitted symbols. The guard period allows enough time for multipath signals from the previous
symbol to die away before the information from the current symbol is gathered. The most effective use
of guard period is the cyclic extension of the symbol. The end part of the symbol is appended at the start
of the symbol inside the guard period to effectively maintain the orthogonality among subcarriers.
Using the cyclically extended symbol, the samples required for performing the FFT (to decode the
symbol) can be obtained anywhere over the length of the symbol. This provides multipath immunity as
well as symbol time synchronisation tolerance.
As long as the multipath delays stay within the guard period duration, there is strictly no limitation
regarding the signal level of the multipath; they may even exceed the signal level of the shorter path.
The signal energy from all paths just adds at the input of the receiver, and since the FFT is energy
conservative, the total available power from all multipaths feeds the decoder. When the delay spread is
larger than the guard interval, it causes the ISI. However, if the delayed path energies are sufficiently
small then they may not cause any significant problems. This is true most of the time, because path
delays longer than the guard period would have been reflected of very distant objects and thus have been
diminished quite a lot before impinging on the receive antenna.
Wireless Communications 17
Subcarrier # 1
Subcarrier # 1
Part of subcarrier # 2
Part of subcarrier # 2
causing ICI
Missing part of
Missing part of
Sinusoid
Sinusoid
Guard
Guard
Time
Time
causing ICI
FFT Integration Time = 1/Carrier Spacing
FFT Integration Time = 1/Carrier Spacing
OFDM Symbol Time
OFDM Symbol Time
Subcarrier #2
Subcarrier #2
Figure 1.11 Effect of multipath on the ICI
The disaster of OFDM systems is ICI, which is introduced due to the loss of the orthogonality of
subcarriers. The loss of orthogonality may be due to the frequency offset, the phase mismatch or
excessive multipath dispersion. The effect of this is illustrated in Figure 1.11, where subcarrier-1 is
aligned to the symbol integration boundary, whereas subcarrier-2 is delayed. In this case, the receiver
will encounter interference because the number of cycles for the FFT duration is not the exact multiple
of the cycles of subcarrier-2. Fortunately, ICI can be mitigated with intelligent exploitation of the guard
period, which is required to combat the ISI. The frequency offset between the transmitter and the
receiver generates residual frequency error in the received signal. The effect of the frequency offset can
be analysed analytically by expanding upon Equation (1.7) as follows:
8
ðkÞ¼
r
n
L 1
X
>
>
>
xnðiÞhðk iÞþ
>
<
i¼0
L 1
X
>
>
>
xnðiÞhðk iÞþvnðkÞ Q k L 1
>
:
i¼0
L 1
X
i¼0
x
ðiÞhðk þL iÞþvnðkÞ 0 k Q 1
n 1
ð1:8Þ
At the receiverthe guard period isdiscardedand the remainingsignal is defined for k ¼0, 1...N -1as
0
r
ðkÞrnðk þQÞð1:9Þ
n
Substitute Equation (1.5) into Equation (1.9), which after simplification yields the following:
0
r
ðkÞ¼
n
X
a
hðaÞ
X
2p
j
liðk þ Q a Þ
nP þ i
N
e
þvnðkÞ
d
i
or,
0
ðkÞ¼
r
n
X
2p
j
likej
N
d
e
nP þ i
i
X
2p
liQ
N
hðaÞe
a
2p
j
lia
N
þvnðkÞð1:10Þ
Equation (1.10) can be written in a simplified form as
X
0
ðkÞ¼
r
n
0
The (
) is dropped from the equation without the loss of generality
d
fiHðliÞe
nP þ i
i
where
2p
j
liQ
N
f
Hðl
Þ¼
i
X
a
i
¼ e
hðaÞe
Constant phase multiplier
2p
j
lia
N
Fourier Transform of the hðnÞ
2p
j
lik
N
þvnðkÞð1:11Þ
18 Cognitive Radio Networks
The received signal with frequency-offset Df can be plugged into Equation (1.11) to yield the
following:
off
ðkÞrnðkÞe
r
n
j2pDfk
X
¼
d
fiHðliÞe
nP þ i
i
2p
j
kðliþDfN Þ
N
þVnðkÞð1:12Þ
It can be shown from Equation (1.12) that the frequency offset induces ICI as well the loss of
orthogonality between subcarriers, which degrades performance by this ICI. In other words, the symbol
estimate becomes
^
d
nP þ i
2
6
¼ GifHðliÞd
4
nP þ iIDf
ð0Þgþ
8
>
<
>
:
P 1
X
i¼0
i „ m
HðlmÞd
nP þ iIDfðlmli
ÞgþVnðliÞ
3
7
5
ð1:13Þ
where the ICI term is
I
Dfðlmli
Þ¼e
ð1:14Þ
2p
j
kðlmliþDfN Þ
N
Starting from Equation (1.14) it can be shownthat the SNR degradation due to small frequency offset
is approximately
where E
SNR
ðdBÞ
loss
is the SNR in the absence of the frequency offset.
s/N0
10
3ln10
ðpDfNT
E
s
2
Þ
s
N
0
ð1:15Þ
Please recall that ISI is eliminated by introducing a guard period for each OFDM symbol. The guard
period is chosen larger than the expected delay spread such that multipath components from one symbol
do not interfere with adjacent symbols. This guard period could be no signal at all but the problem of ICI
would still exist. To eliminate ICI, the OFDM symbol is cyclically extended in the guard period as
shown in Figure 1.12, bytwo intuitive approaches using cyclic prefix and/or cyclic suffix to facilitate the
guard band. This ensures that the delayed replicas of the OFDM symbols due to multipath will always
have the integer number of cycles within the FFT interval, as long as delay is smaller than the guard
period. As a result, multipath signals with delays smaller than the guard period do not cause ICI.
Cyclic Suffix
tTs0
Tg
Original OFDM
tTs0
Cyclic Prefix
Tg
Figure 1.12 Cyclic prefix in the guard period
tTs0
Wireless Communications 19
Mathematically it can be shown that the cyclic extension of the OFDM symbol in the guard period
makes the OFDM symbol appear periodic at the receiver end even though there might be a delay
because of the multipath environment. In OFDM system the N complex-valued frequency domain
symbols X(n),0 < n < N -1, modulate N orthogonal carriersusing the IDFTproducing domain signal
as follows:
N 1
xðkÞ¼
X
XðnÞe
n¼0
þj2pk
n
N
¼ IDFT XðnÞ
fg
ð1:16Þ
The basic functions of the IDFT are orthogonal. By adding a cyclic prefix, the transmitted signal
appears periodic:
sðkÞ¼
xðk þNÞ 0 k < Q
xðkÞ Q k < L
where Q is the length of the guard period. The received signal now can be written as
yðkÞ¼sðkÞ*hðkÞþwðkÞ 0 k < L ð1:17Þ
If the cyclic prefix added is longer than the impulse response of the channel, the linear convolution
with the channel will appear as a circular convolution from the receiver’s point of view. This is shown
below for any subcarrier l,0l < L:
YðnÞ¼DFTðyðkÞÞ ¼ DFTðIDFT ðXðnÞÞ hðkÞþwð
¼ XðnÞDFTðhðkÞÞ þDFTðwðkÞÞ ¼ XðnÞHðnÞþW ðnÞ; 0 k < N
kÞÞ
ð1:18Þ
where denotes circular convolution and W(n) ¼DFT (w(k)). Examining Equation (1.18) shows that
there is no interference between subcarriers, i.e., zero ICI. Hence, by adding the cyclic prefix, the
orthogonality is maintained through transmission. The obvious drawback of using the cyclic prefix
is that the amount of data that has to be transmitted increases, thus reducing the usable throughput.
1.2.3.7 Peak to Average Power Ratio (PAPR)
Another challenge for OFDM systems (or multicarrier systems) is the accommodation of the large
dynamic range of signal, caused by the peak-to-average power ratio due to the fact that the OFDM
signal has a large variation between the average signal power and the maximum signal power. A large
dynamic range is inherent to multicarrier modulations having essentially independent subcarriers. As a
result, subcarriers can add constructively or destructively, which may contribute to large variation in
signal power. In other words, it is possible for the data sequence to align all subcarriers constructively
and accrue to a very large signal. It is also possible for the data sequence to make all subcarriers align
destructively and diminish to a very small signal. This large variation creates problems for transmitter
and receiver design requiring both to accommodate a large range of signal power with minimum
distortion.
The large dynamic range of the OFDM systems presents a particular challenge for the Power
Amplifier (PA) and the Low Noise Amplifier (LNA) design. The large output drives the PA to nonlinear
regions (i.e., near saturation), which causes severe distortion. To minimise the amount of distortion
and to reduce the amount of out-of-band energy radiation by the transmitter, the OFDM and other
multicarrier modulations alike need to ensure that the operation of a PA is limited as much as possible in
the linear amplification region. With an inherentlylarge dynamic range,this means that the OFDM must
keep its averagepower well below the nonlinear region of PA in order to accommodate the signal power
fluctuations. However, lowering the average power hurts the efficiency and subsequently the range
20 Cognitive Radio Networks
since it corresponds to a lower output power for the majority of the signal in order to accommodate the
infrequent peaks. As a result, OFDM designers must make careful tradeoffs between allowable
distortion and output power. That is, they must choose an average input level that generates sufficient
output power and yet does not introduce too much interference or violate any spectral constraints.
To examine this tradeoff further, consider the IEEE802.11a version of an OFDM system that uses
52 subcarriers. In theory, all 52 subcarriers could add constructively and this would yield a peak power
log(52) ¼34.4 dB above the average power. However, this is an extremely rare event. Instead,
of 20
most simulations show that for real PAs, accommodating a peak that is 3 to 6 dB above average is
sufficient. The exact value is highly dependent on the PA characteristics and other distortions in the
transmitter chain.In other words,the distortions caused by peaks above this rangeare infrequent enough
to allow for low average error rates.
A simple method of handling PAPR is to limit the peak signals by clipping or replacing peaks with
a smooth but lower amplitude pulse. Since this modifies the signal artificially, it does increase the
distortion to some degree. However, if it is done in a controlled fashion then it generally limits the
PA-induced distortion. As a result, it can in many cases improve the overall output power efficiency.
For packet-based networks the receiver can request a retransmission of any packet with error. A
simple but effective technique may be to rely on a scramble sequence to control PAPR on retransmission. In other words, the data is scrambled prior to modulating the subcarriers for retransmission.
This alone does not prevent largepeaks and there may still be occasions when the transmitter introduces
significant distortion due to a large peak power in the packet. However when the distortion is severe, the
receiver will not correctly decode the packet and will request a retransmission. When the data
is retransmitted, however, the scramble sequence is changed. If the first scramble sequence caused
a large PAPR, the second sequence is extremely unlikely to do the same despite the fact that it contains
the same data sequence. Since IEEE 802.11a/g/n networks use packet retransmissions already,
this technique is used to mitigate some of problems with PAPR. The downside to this technique is
that it does impact the network throughput because some of the data sequences must be transmitted
more than once.
To minimise the OFDM system performance degradation due to PAPR, several techniques has been
explored each with varying degrees of complexity and performance enhancements. These schemes
can be divided into three general categories:
&
Signal Distortion Technique:
.
Signal Clipping
.
Peak Windowing
.
Peak Cancellation
&
Coding Technique
&
Symbol Scrambling Technique
The simplest way to mitigate the peak-to-average power ratio problem is to limit (clip) the signal such
that the peak level of the signal is always below the desired maximum level. However, this causes out of
band radiation and signal distortion. The effect of this clipping is analogous to the rectangular
windowing of the sample, which is equivalent to the spectrum of the desired signal being convolved
by the sinc-function (spectrum of the rectangular window) causing the spectrum regrowth in the side
bands and thus causing interference to the neighbouring channels. Simple clipping gives rise to spectral
growth in side bands. Therefore, to tame the spectral growth in adjacent bands, other windowing
functions with narrow bandwidth (such as Gaussian, Kaiser, Hamming and root raised cosine) have
been applied.
The goal of the signal distortion techniques is to reduce the amplitude of the data samples, whose
magnitude exceeds a certain threshold. The undesirable effect of signal distortion due to these can
be avoided by using the peak cancellation technique. In this method, a time-shifted and scaled reference
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