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COMMUNICATIONS

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SPACE-TIME CODING AND ITS
APPLICATIONS IN EFFICIENT AND
J AMMING-RESISTANT WIRELESS
COMMUNICATIONS

By

Leonard E. Lightfoot

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR. OF PHILOSOPHY

Electrical Engineering

2010

 

ABSTRACT

SPACE-TIME CODING AND ITS
APPLICATIONS IN EFFICIENT AND
J AMMING—RESISTANT WIRELESS
COMMUNICATIONS

By

Leonard E. Lightfoot

Along with the wide spread of various wireless devices, especially with the advent
of user configurable intelligent devices, such as cognitive radios, the security threats
of malicious jamming, detection, and interception is no longer limited to military
communications. With the majority of today’s transactions and communications
relying heavily on wireless networks, security has become the key enabler for present
and future high speed wireless networks. Patching or add-on security maybe effective
in short term, but is far from adequate for addressing the needs on wireless security
and can greatly complicate the communication systems. In this dissertation, we
focus on the fundamental study of developing a spectrally efficient and secure wireless
system by exploiting multiple diversity techniques.

First, we propose a more efficient space-time coding scheme based on the Alamouti
scheme. Through bit-level inspection, our investigation reveals that the Alamouti
scheme is a low efficient code and there is an opportunity for spectral efficiency
enhancement. Unlike most of the existing methods which are designed to maximize
the diversity or rate for space-time block codes, the proposed spectrally efficient
Alamouti scheme aims to improve the code efficiency of the Alamouti codes, while
achieving excellent transmit diversity and retaining the decoding simplicity. The code
efficiency of the proposed scheme is enhanced by transmitting more information bits
than redundancy bits per Alamouti block. Although the main focus of the proposed

scheme is to improve the code efficiency for two transmit antennas, the same ideas

can be extended in a straightforward way to the Alamouti codes with more than two
transmit antennas.

Second, we propose an innovative spectrally efficient, jamming-resistant wireless
scheme by exploiting the joint space—time and frequency diversity. Recently, the
collision-free frequency hopping (CFFH) system, which is based on the orthogonal
frequency division multiple access (OFDMA) framework and the secure subcarrier
assignment scheme, was proposed as a spectrally efficient anti-jamming system. In
this research, we investigate the security features of the CFFH system and propose to
enhance the inherent security of CFFH through joint space-time and frequency diver-
sity. More specifically, (i) we analyze the limitations of the CFFH system and pr0pose
a new subcarrier assignment scheme based on secure permutation. The new algorithm
is designed to ensure that malicious users cannot predict or repeat the hOpping pattern
of the authorized users and hence cannot launch follower jamming attacks; (ii) We
improve the performance of the CFFH system under random jamming, by enhancing
the system diversity through space-time coding, and introduce the space—time coded
collision-free frequency hOpping (STC-CFFH) system. The proposed STC-CFFH is
found to be particularly powerful in eliminating both channel interference and hostile
jamming interference. Our analysis indicates that the proposed scheme is both highly
efficient and very robust under various jamming scenarios.

Third, we investigate the use of quasi-orthogonal space-time block codes (Q0-
STBCs) to mitigate jamming noise. The combination of constellation rotation Q0-
STBC and OFDM can exploit multipath diversity resulting in excellent performance
under frequency-selective fading. Moreover, such systems must be robust against
jamming interference, especially partial-band noise jamming. Hence, proper analyti-
cal tools are needed to assess the performance of QO-STBC—OFDM in the presence of
jamming. In this research, (i) we derive analytical expressions for the exact pairwise
error probability (PEP) of the QO-STBC-OFDM system using the moment gener-
ating function (MGF); (ii) We calculate the exact PEP under various situations,
and derive the closed-form expressions and union bound for the bit error probability

(BEP). Our simulation results show that the union bound is tight.

Dedicated to my family

iv

ACKNOWLEDGMENTS

I would like to take this opportunity to express my gratitude to my advisor, Dr.
Tongtong Li, for her continuous support, guidance and encouragement throughout
the years. Even before she was my official advisor, she believed in me. Whenever I
hit a road block with research, she gently but firmly pushed me. For these reasons
and many more, I thank you, Dr. Li!!!

I want to also thank Dr. Percy Pierre, Dr. Subir Biswas and Dr. Jonathan Hall for
serving on my PhD committee. I am deeply indebted to them for their guidance and
support. Dr. J ian Ren , thank you for the technical advice on network security. Dr.
Barbara O’Kelly, thank you for your valuable advice and for making my transition
to graduate school a smooth one. Dr. Uche Wejinya, thank you for being a great
mentor and friend.

To all my friends of the Sloan-Rigas program, and the N SBE organization, I thank
you for making my life at Michigan State University an enjoyable experience. I would
also like to thank all my friends around the country, J amin, DeAndre, Chris, Dominic,
Michelle, Kenny, and Ashley for all the fun times and encouraging conversations. I
would like to send a special thank you to my lab mates Lei Zhang, Xiaochen Tang
and Dr. Huahui Wang for our valuable discussions on research.

I would like to thank my parents, my brother, my sisters, my nephew, my nieces
and my extended family for their love and constant support. Finally, I would like
to send a very special thank you to my wife, Tinesha, for her unconditional love,
patience and continuous support throughout the PhD process. Tinesha, you are my

inspiration and I will forever be grateful to have you in my life. Love You!!!

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

1 Introduction

1.1
1.2

1.3

1.4

1.5

Growth of Wireless Communication Networks .............
Vulnerabilities and Security Threats of Wireless Networks .......
1.2.1 Eavesdropping ...........................
1.2.2 Malicious Jamming ........................
Existing Spread-Spectrum Techniques ..................
1.3.1 Spread-Spectrum Systems ....................
1.3.2 The Frequency Hopping Technique and Its Limitations . . . .
Proposed Research Directions ......................
1.4.1 Spectrally Efficient Space—Time Coding .............
1.4.2 Secure Space—Time Coded Collision-Free Ffequency Hopping

System ...............................
1.4.3 Jamming Mitigation Using Quasi-Orthogonal Space-Time

Block Codes ............................
Overview of the Dissertation .......................

2 An Overview of Space-Time Coding

2.1
2.2

2.3

2.4

Introduction ................................
Alamouti Space—Time Coding ......................
2.2.1 Alamouti Encoding ........................
2.2.2 Alamouti Decoding ........................
2.2.3 Performance of the Alamouti Scheme ..............
Orthogonal Space-Time Block Codes ..................
2.3.1 Orthogonal Space-Time Block Codes for Real Signal Constel-

lations ...............................
2.3.2 Orthogonal Space-Time Block Codes for Complex Signal Con—

stellations .............................
2.3.3 Decoding Orthogonal Space-Time Block Codes .........
Quasi-Orthogonal Space—Time Block Codes ...............
2.4.1 Code Structure and Pairwise Decoding of Quasi-Orthogonal

Space-Time Block Codes .....................

vi

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8
9

11
11
13
13
14
17
17

2O
23
25
25

26

2.4.2 Quasi-Orthogonal Space-Time Block Codes with Constellation

Rotation .............................. 30
2.4.3 Performance of Quasi-Orthogonal Space-Time Block Codes . . 31
2.5 Summary ................................. 31
Spectrally Efficient Space-Time Coding 34
3.1 Introduction ................................ 34
3.2 System Model of Alamouti Scheme ................... 36
3.3 Bit-Level Inspection of the Alamouti Code ............... 37
3.3.1 The Alamouti Patterns ...................... 38
3.3.2 Irregular Partitioning of the Alamouti Code .......... 40
3.4 The Spectrally Efficient Alamouti Scheme ............... 41
3.4.1 Encoding Algorithm Design ................... 42
3.4.2 Decoding Algorithm Design ................... 42
3.5 Simulation Examples ........................... 44
3.6 Summary ................................. 48
Secure Space-Time Coded Collision-Free Frequency Hopping Sys-
tem 49
4.1 Introduction ................................ 50
4.2 The Collision-Free Frequency Hopping Scheme ............. 53
4.2.1 Signal Transmission ........................ 53
4.2.2 Signal Detection ......................... 54
4.3 The Subcarrier Assignment Algorithm and Its Limitations ...... 56
4.3.1 The Subcarrier Assignment Algorithm ............. 57
4.3.2 Limitations of The Subcarrier Assignment Algorithm ..... 58
4.4 Secure Subcarrier Assignment Based on Secure Permutation ..... 59
4.4.1 Secure Permutation Index Generation .............. 60
4.4.2 Secure Permutation Algorithm and Subcarrier Assignment . . 61
4.4.3 Secure Subcarrier Assignment Distribution ........... 64
4.5 Secure SpaceTime Coded Collision-Free Frequency Hopping ..... 65
4.5.1 Transmitter Design ........................ 65
4.5.2 Receiver Design .......................... 69
4.6 Performance Analysis of Space-Time Coded Collision-Free Frequency
Hopping System .............................. 71
4.6.1 System Performance in Jamming-Free Case .......... 71
4.6.2 System Performance Under Hostile Jamming .......... 73
4.6.3 Spectral Efficiency ........................ 75
4.7 Simulation Examples ........................... 77
4.8 Summary ................................. 80

vii

5 Jamming Mitigation Using Quasi-Orthogonal Space-Time Block

Codes 84
5.1 Introduction ................................ 84
5.2 System Model ............................... 86

5.3 Quasi-Orthogonal Space-Time Block Codes with Constellation Rotation 88
5.3.1 Quasi-Orthogonal Space-Time Block Code with Constellation

Rotation Code Design ...................... 88

5.3.2 Global Minimum Euclidean Distance .............. 89

5.3.3 Diversity Product ......................... 89

5.4 Analysis of the Pairwise Error Probability ............... 91
5.4.1 Pairwise Error Probability Analysis without Jamming ..... 93

5.4.2 Pairwise Error Probability Analysis with Jamming ...... 94

5.4.3 Overall Pairwise Error Probability Analysis .......... 97

5.5 Closed-Form Expressions of the Pairwise Error Probability ...... 97
5.6 Union Bound of Bit Error Probability .................. 101
5.7 Numerical Evaluations and Simulations ................. 102
5.8 Summary ................................. 107

6 Conclusions and Future Work 108
6.1 Conclusions ................................ 108
6.2 Future Directions ............................. 110
6.2.1 Cognitive Networks ........................ 110

6.2.2 Major Challenges and Future Research Directions ....... 111
BIBLIOGRAPHY 113

viii

3.1
4.1
4.2

5.1

LIST OF TABLES

Comparison of three Alamouti codes. .................. 47
STC—CFFH 'Ii‘ansmitter Example ..................... 68
STC-CFFH Receiver Example. ..................... 70
Distribution of us and us for PF scheme with QPSK ......... 101

ix

2.1
2.2
2.3

2.4
2.5

3.1
I 3.2

3.3
3.4
3.5
4.1

4.2
4.3

4.4

4.5

LIST OF FIGURES

Transmitter for the Alamouti Scheme ..................
Receiver for the Alamouti Scheme ....................
BER performance of Alamouti and MRC schemes ............

BER performance of Alamouti scheme with one receive antenna and
two receive antennas ............................

BER performance of OSTBC vs. QO—STBC schemes with and without
constellation rotation. ..........................

QPSK constellation with Gray mapping. ................
Constellation design for the spectrally efficient Alamouti code. . . . .

The BER performance comparison of the proposed scheme and the
Alamouti code in Rayleigh flat fading, nT = 2, n R = 1. ........

The BER performance comparison of the proposed scheme and the
Alamouti code in Rayleigh fiat fading, nT = 2, n}; = 2. ........

The BER performance comparison of the proposed scheme with nT =
2, m; = 1 and nT = 2, 72}; = 2 in Rayleigh fiat fading .........

Example of the Secure Permutation Algorithm for N628 subcarriers
and M =2 users ...............................

Public/ Private Key Cryptosystem ....................

Block diagram of the STC—CFFH transmitter. .............

Probability of collision (Ph) versus the number of users (starting at the
two-user case) for NC = 64. .......................

BER performance over AWGN channel of the CFFH, FH—OFDMA, and
the conventional FH systems with M=8 users and Nc=128 available
subcarriers. ................................

13

15

18

19

39

43

45

46

47

63

64

66

4.6

4.7

4.8

5.1

5.2

5.3

5.4

5.5

Comparison of the BER over frequency selective fading channel with
partial-band jamming. Number of subcarriers NC = 256, number of
users = 16 and SJR = 0dB. .......................

BER performance with Turbo Coding over frequency selective fading
channel with partial-band jamming. Number of subcarriers NC = 256,
number of users = 16 and SJR = 0dB. .................

BER versus J ammer Occupancy over frequency selective fading channel
with partial—band to full-band jamming. Number of subcarriers NC =
256, number of users = 16, SJR = 0dB and SNR = 10dB. ......

Diversity product C, and the global minimum Euclidean distance d E
versus the rotation angle ()5 ........................

Union bound on the BEP and simulation results for QO-STBC with
constellation rotation in frequency-selective fading (Nr = 2). .....

Union bound on the BEP and simulation results for QO-STBC with
constellation rotation in partial-band noise jamming and frequency-
selective fading (Nr = 2, a = 0.5, SIR=6dB). .............

Union bound on the BEP for QO—STBC with constellation rotation in
partial-band noise jamming and frequency-selective fading (N7. = 2, 0:
= [0.1,0.3,0.5,0.7,0.9], SIR=6dB). ....................

Comparison of OSTBC vs. QO-STBC with constellation rotation in
rayleigh fading and partial-band noise jamming (SIR=6dB), a = 0.5,
and N,- = 2 ................................

“Images in this dissertation are presented in color”

xi

80

81

82

92

103

104

105

106

CHAPTER 1

Introduction

1.1 Growth of Wireless Communication Networks

Wireless communication is one of the most active areas in research today. While
it has been a topic of study since the 19605, the past few decades has seen a surge
of research activities in the area. This is due to the fact that wireless technology
offers organizations and users many benefits such as portability, flexibility, increased
productivity and lower installation cost. Today, the wireless technology covers a broad
range of services such as voice, video, and data services. As a result, there has been an
explosive increase in demand for tetherless connectivity, which is driven by the cellar
telephony and wireless data applications. In 2011, it is projected that the worldwide
cellular telephony subscriber base will be 4.3 billion, roughly 62% of the projected
world population [1—3]. Furthermore, the Internet is also growing tremendously, with
1.1 billion worldwide users as of March 2007 [4]. Based on the current growth trends,
it is projected that global revenues from mobile data-centric applications will exceed
$166 billion by 2010, in comparision to global revenues of $100 billion in 2005 [5].
The growth and technological advancements of wireless communication applica-
tions has accelerated the demand for increased data rates, wider coverage, improved
link reliability and security of the wireless network. However, fulfilling these demands
are challenging because the radio spectrum is limited and the wireless infrastructure
has an inherent security problem. Moreover, the wireless channel is time varying due
to the small-scale effect of multipath fading, as well as larger-scale effects such as
path loss via distance attenuation and shadowing by obstacles. Lastly, unlike the

wired counterpart where each transmitter-receiver pair is free from outside interfer-

ence, wireless users communicate over the air and there is unpredictable interference.
The lack of protective physical boundary increases the potential of adversary inter-
ception and eavesdmpping. Any adversary with the appropriate radio frequency (RF)
equipment within the radio range can intercept the transmitted information. As high-
lighted, wireless networks are inherently unreliable and vulnerable to serious security

threats.

1.2 Vulnerabilities and Security Threats of Wire-
less Networks

Along with the wide spread of various wireless devices, especially with the advent
of user configurable intelligent devices, such as cognitive radios, the security threats
of malicious jamming, detection, and interception are no longer limited to military
communications. With today’s business and social cultures relying heavily on wireless
technologies to execute all day-to-day transactions and communications, security has
become the key enabler for present and future high speed wireless networks.
Incorporating security into the wireless infrastructure has its challenges. First, the
underlying wireless medium is broadcast by nature and more vulnerable to security
attacks due to the lack of physical boundary. Second, the wireless channel is inherently
unreliable, time varying and hard to predict. Lastly, the physical layer of the wireless
network model is generally not equipped with built-in security. In the following
subsections, we discuss two major security threats in wireless networks, eavesdropping

and malicious jamming.

1.2.1 Eavesdropping

Eavesdropping consists of an adversary capturing transmitted information from the
airlink. Eavesdropping is considered an easy attack because the wireless channel is
broadcast by nature. Furthermore, radio signals are not directional, therefore, anyone

with the proper radio receiver can capture the transmitted information.

The lack of built-in security at the physical layer simplifies the adversaries’ job of
discovering the transmitted message even if the message in encrypted. An accurately
received encrypted message means that the only barrier between the adversary and
the original message is the need for correct decryption. Due to the weakness of some
existing encryption algorithms, it is not too difficult for an adversary to decode the
original message. For example, several research groups [6-8] found the 40—bit/ 128-bit
wired equivalent privacy (WEP) [9] thoroughly flawed because of the relatively weak
encryption algorithm it uses.

1.2.2 Malicious Jamming

In wireless networks, one of the most commonly used techniques for limiting the ef-
fectiveness of an opponent’s communication is referred to as jamming. Generally,
intentional jamming, also known as malicious jamming, intends to disable the legiti-
mate transmission by saturating the receiver with noise or false information through
deliberate radiation of radio signals, and thus significantly decreasing the signal-to-
interference-plus-noise ratio (SINR). In other words, malicious jamming can be viewed
as a. denial of service (DoS) attack.

Conventionally, jamming signals are classified into four types: (i) Tone-
jamming [10—12], where the jamming power is concentrated around carrier frequen-
cies; (ii) Partial-time jamming [13—15], where the jamming occurs at certain time
periods during the signal transmission. Partial-time jamming can be considered as a
two-state Markov process. When the jammer is in state 0, it is off; when the jammer
is in state 1, the jammer emits the interfering signal. State 1 occurs with probabil-

ity of p, for which the variance of jamming signals is N where N J is the power

7,1,
spectral density of the jamming signal. State 0 occurs with probability of (1 — p), for
which the variance of jamming signals is 0. (iii) Full-band jamming [16,17], where the
power of the jammer is uniformly distributed over the bandwidth; (iv) Partial-band
jamming [18—20], where the jamming power is characterized by the additive Gaussian

noise interference power 97,51- over a fraction p of the total bandwidth and negligible

interference over the remaining fraction (1 -- p) of the band.

With the increased use and dependence of wireless communications in today’s
society, malicious jamming attacks are no longer only a concern for military appli-
cations. In order for wireless networks to become a reliable information exchange

platform, security must be strengthened.

1.3 Existing Spread-Spectrum Techniques

1.3.1 Spread-Spectrum Systems

The physical layer of the open system interconnection (OSI) model is not equipped
with built-in security and suffers from adversary attacks such as eavesdropping and
malicious jamming. A response to the eavesdropping and jamming threats was the
implementation of the spread-spectrum technology. Spread-spectrum systems encom-
pass modulation techniques in which the signal of interest is spread to occupy a much
larger transmission bandwidth. Spread-spectrum techniques were originally devel—
oped for miliary applications, but have gained interest in commercial applications
due to the promise of greater tolerance to interference. The advantages of spread-

spectrum techniques are [21, 22]:
0 Force adversary to monitor an expanded frequency band.
0 Resistance to unintended or malicious jamming.
-0 Provides location privacy.
0 Low probability of detection or interception.
0 Increased tolerance to multipath.
0 Sharing of a single channel among multiple users.

Two basic multiple access spread-spectrum techniques used in broadband cellular

networks and wireless local area network (WLAN) communications are direct-sequence

code division multiple access (DS—CDMA) and frequency hopping (FH). DS-CDMA
technique may be regarded as a Special case of PH, thus we focus our attention on

FH systems.

1.3.2 The Frequency Hopping Technique and Its Limitations

In traditional FH systems, the transmitter hops in a pseudo-random manner among
available frequencies according to a pre—specified algorithm, the receiver then-operates
in strict synchronization with the transmitter and remains tuned to the same cen—
ter frequency. The pseudo-random hopping of frequencies during radio transmission
minimizes the possibility of hostile jamming and unauthorized interception.

For FH systems, the inherent security relies on the difficulty to follow the de-
sired user’s transmission frequency without the knowledge of the hopping pattern.
Although frequency hopping is designed to minimize the probability of the unautho-
rized interception of telecommunications, the conventional FH scheme has two major
limitations: (i) Strong requirement on frequency acquisition, and (ii) low spectral ef-
ficiency over large bandwidth. Typically, FH systems require large bandwidth, which
is proportional to the product of the hopping rate and the total number of all the
available channels. In conventional frequency hopping multiple access (F HMA), each
user hOps independently based on its own pseudo-random number (PN) sequence,
and a collision occurs whenever there are two users over the same frequency band.
Mainly limited by the collision effect, the spectral efficiency of the conventional FH
system is very low. In the literature, considerable efforts have been devoted to increas-
ing the spectral efficiency of PH systems by applying high-dimensional modulation
schemes [23—29]. However, existing work is far from adequate to address the ever-
increasing demand on inherently secure high data rate wireless communication, thus

new techniques that are more efficient and reliable have to be developed.

1.4 Proposed Research Directions

This dissertation is focused on the fundamental study of deve10ping spectrally efficient
and inherently secure wireless interface by introducing antenna diversity, and inte-
grating advanced signal processing techniques and cryptographic techniques into the
physical layer transceiver design. More specifically, the proposed research directions

are briefly summarized in the following subsections.

1.4.1 Spectrally Efficient Space-Time Coding

The integration of the Internet and multimedia applications in the next generation
of wireless communications has increased the demand for wide-band high data rate
services. Due to the limited radio spectrum, the high data rates can only be achieved
by more efficient signaling techniques. Research in information theory has shown that
large gains in capacity of wireless channels are feasible in multiple-input multiple-
output (MIMO) systems [30—32]. The MIMO system consists of multiple antennas at
both ends of the communication link and increases the channel capacity linearly as
the number of transmit and receive antennas grows simultaneously. An effective and
practical way to approaching the capacity of MIMO wireless channels is to employ
space-time coding. Space—time codes can achieve rich transmit diversity and power
gain over spatially uncoded systems without sacrificing the bandwidth. There are
various approaches in coding structures, including space-time block codes and space-
time trellis codes. Due to the decoding simplicity of space-time block codes, it is
preferred over space-time trellis codes. The Alamouti space-time block code is the
only full-rate full diversity complex orthogonal code, but the code efficiency can be
further improved.

In this dissertation, we aim to: (i) Investigate the efficiency of the Alamouti scheme
from a bit-level perspective by introducing the concepts of Alamouti patterns and
irregular partitioning; (ii) Improve the spectrally efficiency of the Alamouti scheme.
More specifically, we enhance the code efficiency of the Alamouti code by increasing

the number of information bits transmitted in each Alamouti block.

1.4.2 Secure Space-Time Coded Collision-Free Frequency
Hopping System

Originally developed for military communications, frequency hopping (FH) was de-
signed to prevent hostile jamming, interception and detection [33]. However, the con-
ventional FH scheme has two major limitations: (i) Strong requirement on frequency
acquisition, and (ii) low spectral efficiency over large bandwidth. In an effort to pro-
vide anti-jamming communications in OFDMA systems, the combination of the PH
technique and the OFDMA scheme, called FH-OFDMA, has been proposed [34, 35].
However, as the system is based on the conventional FH techniques, the spectral
efficiency is seriously limited by the collision effect. Along with the ever increasing
demand on inherently secure high data-rate wireless communications, new techniques
that are more efficient and reliable have to be developed.

Recently, the collision-free frequency hopping (CFFH) system, which is based on
the orthogonal frequency division multiple access (OFDMA) framework and the se-
cure subcarrier assignment scheme was proposed as a spectrally efficient anti-jamming
system. In this dissertation, we investigate the security features of the CFFH system,
and propose to enhance the inherent security of CFFH through joint space-time and
frequency diversity.

First, we analyze the security limitations of the previously proposed subcarrier
assignment and propose a new subcarrier assignment scheme based on secure permu-
tation. The new algorithm is designed to ensure that: (i) Each user hops to a new
set of subcarriers in a pseudo-random manner at the beginning of each hopping pe-
riod; (ii) Different users always transmit on non-overlapping sets of subcarriers; (iii)
Malicious users cannot predict or repeat the hopping pattern of the authorized users,
and hence cannot launch follower jamming attacks. Moreover, using the fast Fourier
transform (FFT) based OFDMA framework, CFFH has the same high spectral ef-
ficiency as that of OFDM, and at the same time can relax the complex frequency
synchronization problem suffered by conventional FH systems.

Second, we observe that although CFFH is very robust under partial-band jam-

ming, where the jamming interference spans over a fraction of the total bandwidth, it
is still sensitive to random jamming. In this dissertation, we propose to overcome this
drawback through space-time coding and introduce the space-time coded collision-
free frequency hopping (STC—CFFH) system. The proposed STC-CFFH is found to
be particularly powerful in eliminating both channel interference and hostile jamming
interference. Our analysis indicates that the proposed scheme is both highly efficient

and very robust under various jamming environments.

1.4.3 Jamming Mitigation Using Quasi-Orthogonal Space-
Time Block Codes

Full-rate orthogonal space-time block codes with complex elements in its transmission
matrix only exist for two transmit antennas. In an effort to provide full-rate trans-
mission for space-time block codes with more than two transmit antennas, quasi-
orthogonal space-time block codes (QO-STBCS) were pr0posed. With the quasi-
orthogonal structure, the orthogonality of the code is relaxed to provide a higher
symbol transmission rate. Furthermore, by introducing signal constellation rotation
into the QO—STBC design, we can improve the bit error rate performance.

The combination of QO-STBCS with orthogonal frequency division multiplexing
(QO-STBC-OFDM) can exploit multipath diversity and achieve spectrally efficient
communications. However, future wireless communication systems must be robust
against both unintentional and intentional interference. As a result, there is a need
for proper analytical tools to assess the performance of QO-STBC-OFDM in the
presence of partial-band noise jamming. First, we derive analytical expressions for
the exact pairwise error probability (PEP) of the QO—STBC-OFDM system in the
presence of partial-band noise jamming using the moment generating function (MGF).
Second, we calculate the PEP under various situations, and derive the closed-form
expressions and union bound for the bit error probability (BEP). Our numerical

analysis and simulation results show that the union bound is tight.

1.5 Overview of the Dissertation

In the dissertation, we aim to address the following specific problems:

0 How to improve the code efficiency of the conventional Alamouti scheme, while

achieving high transmit diversity and retaining the decoding simplicity?

o How to enhance the spectral efficiency of the conventional frequency hopping

systems, while maintaining the anti-jamming security feature?

0 How to analytically assess the performance of multiple input, multiple output

systems in the presence of partial-band noise jamming?

The dissertation is structured as follows.

Chapter II provides an overview of space-time codes. First, the encoding and
decoding algorithms, and the performance of the classic Alamouti scheme with two
transmit antennas is reviewed. Second, the generalized space-time block codes for
systems with more than two transmit antennas is discussed. The generalized space-
time block codes includes real and complex signal constellation designs. Finally, we
review the code structure and performance of quasi-orthogonal space-time block codes
with four transmit antennas.

Chapter III presents a spectrally efficient Alamouti scheme for high data rate
communications over multiple-antenna channels. Unlike most of the existing methods
which are designed to achieve full-rate and / or full-diversity, the proposed scheme
aims at increasing the spectral efficiency. The prOposed scheme increases the code
efficiency of the traditional Alamouti scheme by increasing the number of information
bits transmitted in each Alamouti block. Furthermore, the proposed scheme achieves
high transmit diversity and retains the decoding simplicity of the maximum likelihood
decoder. Finally, simulation examples are provided to demonstrate the effectiveness
of the proposed scheme.

Chapter IV exploits an encryption based protection mechanism to strengthen

the efficiency and anti-jamming features of the dynamic spectrum access control.

First, we develop a collision-free frequency hopping (CFFH) system based on the or-
thogonal frequency division multiplexing (OFDM) framework. Second, we investigate
the limitations in the subcarrier assignment algorithm and pr0pose a new subcarrier
assignment algorithm based on the secure permutation scheme. The new secure sub-
carrier assignment algorithm is designed to ensure that: (i) Each user hops to a new
set of subcarriers in a pseudo-random manner at the beginning of each hopping pe-
riod; (ii) Different users always transmit on non-overlapping sets of subcarriers, such
that malicious users cannot predict or repeat the hopping pattern of the authorized
users, and hence cannot launch follower jamming attacks. Third, we enhance the anti-
jamming property of the CFFH system by incorporating space-time coding (STC).
The enhanced system is referred to as STC-CFFH. Our analysis indicates that STC-
CFFH is particularly powerful in eliminating channel distortion and hostile jamming
interference, including both random jamming and follower jamming attacks. Simula-
tion examples are provided to illustrate the performance of the proposed schemes.

Chapter V investigates the use of quasi-orthogonal space-time block codes (QO—
STBCs) to mitigate jamming noise. Unlike orthogonal space-time block codes, Q0-
STBCS are capable of providing full diversity and full-rate transmission for codes
designed for more than two transmit antennas. With QO—STBCS, the orthogonal-
ity of the code is relaxed and by introducing signal constellation rotation into the
QO—STBC design, we can improve the bit error rate performance. First, we derive
analytical expressions for the exact pairwise error probability (PEP) of the QO-STBC
orthogonal frequency division multiplexing (QO-STBC—OFDM) system using the mo-
ment generating function (MGF). Second, we calculate the exact PEP, and derive the
closed-form expressions and union bound for the bit error probability (BEP). Finally,
simulations are performed and compared with the theoretical results.

Chapter VI summarizes the contributions of the dissertation. By using space-
time coding, we are able to exploit space diversity in conjunction with time and
frequency diversity, resulting in efficient and jamming-resistant wireless communica-
tions for OFDM systems. For future research, we consider secure communications

and dynamic resource allocation for cognitive radio networks.

10

CHAPTER 2

An Overview of Space-Time

Coding

In this chapter, we provide an overview of space-time codes. We first review the
encoding and decoding algorithms, and the performance of the Alamouti scheme
with two transmit antennas. Second, we discuss generalized space—time block codes
for systems with more than two transmit antennas. The generalized space-time block
codes includes real and complex signal constellation designs. Finally, we review the
code structure and performance of quasi-orthogonal space-time block codes with four

transmit antennas.

2. 1 Introduction

Over the past few decades, the demand for cellular and wireless local area networks
has grown exponentially. Wireless multimedia services such as video conferencing,
mobile computing and high-speed Internet access requires an increase in informa—
tion throughput that is orders of magnitude below the current achievable data rates.
Furthermore, the stringent limitations imposed on the available radio spectrum con-
straints the evolution of high data rate systems. The only way to meet increasing
demand of capacity in wireless networks is to design efficient signaling techniques.
A technological technique that has shown large gains in capacity is a system with
multiple antennas at the transmitter and receiver. A system with multiple trans-
mit and receive antennas is called a multiple-input multiple-output (MIMO) system.

Advances in turbo coding [36], low density parity check codes [37,38], and the compu-

11

tational power of today’s integrated circuits, enables the feasibility of implementing
MIMO systems and the associated signal processing algorithms.

Space-time coding is a signal technique design aimed at approaching the informa-
tion theoretic capacity limit of MIMO systems. Similar to ordinary channel codes,
space-time codes employs redundancy to protect against channel fading, noise and
interference. The transmitted signals of space-time codes are jointly correlated in
space and time domains. Space—time codes are classified into two types: space-time
block codes and space-time trellis codes. Space-time trellis codes [39,40] designed for
2-4 transmit antennas, performs exceptionally well in slow fading environments (in-
door data transmissions). However, the decoding of space-time trellis codes requires
a multidimensional version of the Viterbi algorithm [41], which involves non-linear
processing. Accordingly, for a fixed number of transmit antennas, the decoding com-
plexity of space-time trellis codes increases exponentially with the transmission rate.
On the other hand, space-time block codes resolves the decoding complexity problem
of space-time trellis codes, but does not perform as well. Despite, the performance
penalty, spacetime block codes are preferred because of its decoding simplicity and
satisfactory performance capability.

Space-time block codes was pioneered by Siavash Alamouti. In 1998, Alamouti
developed a full transmit diversity scheme for two transmit antennas. The full diver-
sity scheme is known as the Alamouti code [42], which utilizes a simple maximum
likelihood algorithm to decode the desired signal. Alamouti’s work motivated Vahid
Tarok et al. [30,43—48] to generalize space-time block codes to accommodate the use
of more than two transmit antennas. The generalized space-time block codes includes
real and complex signal constellation designs, and also takes advantage of the simple
maximum likelihood decoding algorithm. However, generalize space-time blocks for
more than two antennas do not provide full-rate transmission.

In an effort to provide full-rate transmission for space-time block codes with more
than two transmit antennas, quasi-orthogonal space-time block codes (QO-STBCS)
[49,50], were proposed. With the quasi-orthogonal structure, the orthogonality of the

code is relaxed to provide a higher symbol transmission.

12

Tx 1
Hit a]

 

 

Bits [x1 x2] Space-Time Encoder TX 2
—’ 32353: ‘—” [Jq x, J“ W £=[ *]
’ x2 x1 x2 x1

 

 

 

 

 

 

Figure 2.1. Transmitter for the Alamouti Scheme

The rest of the chapter is organized as follows: In Section 2.2, we introduce
the encoding and decoding schemes, and the performance of the Alamouti code. In
Section 2.3, we review generalized space-time block codes for systems with more than

two antennas. In Section 2.4, we discuss quasi-orthogonal space-time block codes.

2.2 Alamouti Space-Time Coding

The Alamouti code is the first and only full-rate, full transmit diversity space-time
block code. The key features of the Alamouti code is that it achieves satisfactory per-
formance and only requires the linear processing of the maximum likelihood decoding
algorithm. In this section, we discuss the encoding, decoding and performance of the

Alamouti code.

2.2. 1 Alamouti Encoding

The Alamouti code considers a system with two transmit antennas. In Figure 2.1,
a block diagram of the Alamouti space-time encoder is depicted with two transmit
antennas. Initially, a block of information bits are transformed into a stream of
baseband constellation complex symbols through a mapper. Then, the space-time

encoder takes two complex symbols 2:1 and 2:2 in each encoding Operation and maps

13

them to a transmission code matrix given by

:1: —x*
x = 1 2 , (2.1)

where * is the complex conjugate operator. At the first transmission period t, symbols
x1 and :52 are transmitted from the first and second transmit antennas, respectively.
During the second transmission period t + T, symbols —a:§ and as”; are transmitted
from the first and second transmit antennas, respectively, where T is the symbol
period.

From the transmission code matrix, it is clear that the Alamouti encoding is
done in both space and time domains. In fact, the Alamouti code is orthogonal.
Let us define the transmit sequence from antenna one and two by x1 = [$1, —:r}:;]
and x2 = [23,19]], respectively. The Alamouti code is othogorthonal since the inner

1

product of transmit sequences x and x2 is zero.

2.2.2 Alamouti Decoding

The Alamouti code considers a system with one receive antenna. The receiver design
of the Alamouti scheme is depicted in Figure 2.2. The fading channel coefficients from
the first and second transmit antennas to the receive antenna at time t are denoted
by h1(t) and fig (t), respectively. Assuming that the fading channel coefficients are
constant across two consecutive symbol transmission periods (quasi-static), the fading

coefficients can be expressed as

hl (t) = h1(t + T) = h1 = jhlleiol, (2.2)
h2(t) = h2(t + T) = h2 = Ihzlejgz, (23)

where [hi] and 6;, i = 1,2, are the amplitude gain and phase shift for the path from
transmit antenna i to the receive antenna.

At the receiver, the received signals over two consecutive symbol periods are de-

14

variance 0

 

 

 

 

 

Receive
Antenna
n1, 12, Noise
I ,gl I
Channel A ’ Signal
Estimator h2__, Combiner

 

 

 

 

 

 

 

at It 32.! Isa.
Maximum Likelihood Decoder

I I

 

 

 

 

Figure 2.2. Receiver for the Alamouti Scheme

received signals are expressed as

T1 = h1$1 + h2$2 + 77.1,

7‘2 = —h1$;+ b.2513: + 71.2,

15

noted as r1 and r2 for the first and second transmission periods, respectively. The

(2.4)
(2.5)

where 77.1 and 71.2 are independent additive white Gaussian noise with zero mean and

Assuming ideal channel state information (CSI), and perfect synchronization be-

tween the transmitter and receiver, the desired signals can be recovered by the use of

a signal combiner and a maximum likelihood decoder. The signal combiner generates
two decision statistics 5:1 and :22, by combining the received signals with the fading

channel coefficients. The decision statistics can be expressed as

2:1 = hfr1+h2r§,

532 = hETI—hlt‘g. (2.6)

The decision statistics can be rewritten by substituting r1 and r2 from (2.5) into

(2.6), and expressed as

551 = (Ih1I2 + |h2|2)a:1 + him + h2n3,

532 = (Ihll2 + |h2|2)$2 - ’11"; + hint (2.7)

Note that the decision statistics sir,- is only a function of symbols x;, i = 1, 2, thus
the maximum likelihood decoding rule can be evaluated as two independent decoding
rules. If we use the notation d2(:r, y) = (:1: — y)(:c* - y*) = [11: — yl2 as the squared
Euclidean distance between signals :1: and y, the independent decoding rules for 2:1

and x2 are expressed as,

5‘1 = arg gnielgflhllz + Ih2|2 + 1)|5:1|2 + 612(51, 551), (2-8)
1

5:2 = arg gigglhflz + Ihzl2 + 1)|532I2 + 612052, 532)- (2-9)
2

For phase-shift keying (PSK) signal constellations, the term (Ih1I2 + [h2]2 + 1) is
constant for each estimated symbol, therefore the decsion rule in (2.8) and (2.9) can

be simplified to

5:1 = arg min d2(i1,5f31), (2.10)
@165

5:2 = arg min d2(:i':2,:i72). (2.11)
@265

16

2.2.3 Performance of the Alamouti Scheme

In this subsection, the bit error rate (BER) performance of the Alamouti scheme
on slow Rayleigh fading channels is evaluated by simulation. For comparison, the
BER performance of the maximal ratio combining (MRC) scheme is also simulated
over slow Rayleigh fading channels. Each system transmits binary phase shift keying
(BPSK) symbols. In Figure 2.3, we consider a system with one transmit and one
receive antenna (no diversity), and a MRC system with one transmit antenna and
two receive antennas, and Alamouti system with two transmit antennas and one
receive antenna. From the Figure 2.3, it can be seen that the Alamouti code suffers a
3dB performance penalty. This is due to the fact that the power from each transmit
antenna in the Alamouti code is half of the power from the transmit antenna in the
MRC scheme. If the transmit antennas in the Alamouti code transmit the same
power as the MRC scheme, then the Alamouti code would be equivalent to the MRC
scheme. Also, in Figure 2.3, the Alamouti scheme and the MRC scheme have the
same slope, which indicate that the Alamouti scheme has the same diversity order as
the MRC scheme.

In Figure 2.4, the Alamouti scheme with one and two receive antennas are sim-
ulated over slow Rayleigh fading channels with BPSK modulation. From the figure
we see that increasing the number of receive antenna improves the BER performance

significantly.

2.3 Orthogonal Space-Time Block Codes

The satisfactory performance and decoding simplicity of the Alamouti scheme gener-
ated interest in multi-antenna systems with more than two transmit antennas. The
simple maximum likelihood decoder provides full diversity gain at the receiver. Hence,
a system with two transmit antennas and n R receive antennas guarantees an over-
all diversity gain of 211R, without CSI at the transmitter. The full diversity gain is
achieved by the orthogonality between the sequences generated by the two transmit

antennas. As a result, the Alamouti scheme was generalized to an arbitrary number

17

 

 

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

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

 

. No Diversity (nTx=1,nRx=1) ::
............... MRC(nTx=1n=Rx=2) ,,

 

 

 

Bit Error Rate

 

 

 

 

. SNR(dB)

Figure 2.3. BER performance of Alamouti and MRC schemes.

of transmit antennas by applying the theory of orthogonal designs. The generalized
schemes are referred to as orthogonal space-time block codes. The key features of or-
thogonal space-time codes is its capability of achieving full transmit diversity, while
allowing a very simple maximum likelihood decoding algorithm.

Let nT represent the number of transmit antennas and p represent the number of
time periods for the transmission of one block of coded symbols. In general, a space-
time block code is defined by an nT x p transmission matrix, and k is the number
of symbols the encoder takes as input for each encoding operation. In other words,
during each encoding operation, It symbols are encoded into 3 mp x p transmission
matrix, which is transmitted in p time periods. The rate of the space-time block code
is defined as the ratio between the number of symbols the encoder takes as its input

and the number of space-time coded symbols transmitted from each antenna. The

18

 

 

 

 

 

 

 

 

 

I I
-— e —- Alamouti (nTx=2, nRx=1) '1
-— ale -Alamouti (nTx=2, nRx=2) "
'Z'\ZZIZZZ.’I2ZIZIIZIZZZZZZZIZ.‘22I1122221222232232222ZZlIZII'IZZZZZIIIIIIII'l
22282IIIIIIIIIIIIIIIHIZLZLZIIIIIZZZIIIZILIIIIIIIIIIIIIIIZIIIZIIIIIII..
"""" \"''::::::::::::::::::::::;:::::::::::::::::::::::::::::::::::::1
V; .......................................................... .
........................................................ fl
.................................................................. T
7312ZZZ:Z¥IZZS:ZZIZ$IZTQ\$IZIII:221222222222Ziiiiiiliiii113332123133323331
Q) """"""'IIIIIIIIIIIIIZ\III.IIIIIIIIZZZIIfJIIIZIIIIIIZZIIIIIIIIIIIIIZII:
‘5 Q::::::::::::::::::::::::::::':::::::::::::::
m ................................ \.‘.\ ........................................
'5 ............... X ..... Q ....... ', .............. ‘ .............. .
utJ . . \ . :
-3 : : : :
=10 :‘333333333335ii-Siszsl‘HEEZZEES-EE3333333EIOZXHEEESEEEESEESE3-3533333‘333353‘:
CD IZZIIIZIISICIIIfiIZIIZI\!2322222:2IZIIZIZIIIZZI:Z\IIIIIIZSIICIZRIIIIZZZEIIIIIII
IIZIiiiIIIIIIIiIIIIIIIIiIEIIIZIIIIIIIIIIIIIIICIIbiZIIIIIIIIZIIiiiliiillilil
. ........................ \\ ..........................
........................... \\®
-4 : \k : \ :

10 :‘235323335:2353;323:55553533553:\.25355555333323355533533;33\:*?53€5355553555‘:
:EEEEEEEEEEEEEE’EEEEEEEEEEEEEEE'E:\EEif333353333332333533“3EQE;EEE3”‘33333
................................. \ .........
.................................. \K‘O\
................................................................... \.....
0 5 1O 15 20 25

SNR(dB)

Figure 2.4. BER performance of Alamouti scheme with one receive antenna and two
receive antennas.

19

rate is represented as
k
R = —. (2.12)
P

The orthogonal space-time transmission matrix is constructed such that the rows
and columns of each matrix are orthogonal to each other. In other words, the dot
product of each row with another row is zero. The orthogonality of the transmission
matrix yields full transmit diversity of nT. In addition, orthogonality of the trans-
mission matrix allows the receiver to decouple the signals transmitted from different
antennas with the simple maximum likelihood decoding algorithm, which is based
only on linear processing of the received signals. However, the orthogonality of the
transmission matrix does not translate to full rate (R = 1) of the transmission ma-
trix. In fact, the rate of the code matrix depends on how the code is constructed.
In the following subsections, we show that it is relatively easy to construct full rate
codes with real signal constellations, whereas the choice of full rate code matrices of

complex signal constellations are more restricted.

2.3.1 Orthogonal Space-Time Block Codes for Real Signal

Constellations

Orthogonal space-time block code designs are based on two types of signal constella-
tions: real and complex. In this subsection, we discuss the construction of orthogonal
space-time block codes for real signal constellations. We first introduce orthogonal
space—time block codes with a square transmission matrix, then present orthogonal
space-time block codes with non-square transmission matrix.

Let us denote orthogonal space-time block codes as XnT. Note that, orthogonal
space-time block codes with square transmission matrix have size nT X 127». For any
arbitrary real signal constellation, a square transmission matrix XnT exist only if

the number of transmit antennas nT = 2, 4, or 8 [43]. The transmission matrix for

20

nT = 2 is given by

CC -2?
x2 = 1 2 . (2.13)
1132 $1

The transmission matrix for nT = 4 is given by

$1 —$2 —$3 —$4

$2 $1 $4 -$3 '

X4 = . (2.14)
373 ’34 $1 $2
1'4 $3 ‘332 331

1- d

 

 

The transmission matrix for nT = 8 is given by

p$1 -$2 —$3 —$4 —$5 —$6 —$7 —$8-
$2 $1 -$4 $3 —$5 $5 $8 —$7
3:3 334 x1 —x2 —a:7 -378 1:5 1:5
X8: (r4 —:r3 2:2 2:1 —:r8 2:7 —:r§ $5 . (215)
1:5 536 x7 x8 x1 —:z:2 —:1:3 —:1:4
$6 —$5 $8 -$7 $2 $1 $4 —$3
$7 -$8 -—$5 $6 $3 —$4 $1 $2
_$8 $7 —$6 —$5 $4 $3 -$2 $1 _

 

 

The following codes have full rate (R = 1) and offer full transmit diversity of nT.
For example, if we consider (2.14), we observe that there are four transmit antennas
(corresponding to the number of rows), and there are four transmission periods (cor-
responding to the number of columns). Also, the transmission matrix contains four

symbols (1:1, 2:2, 11:3, 334). As a result, the rate of X4 is given by
k 4
R = _ = _ = 1, 2.16
p 4 < >

Full rate non-square real constellation code matrices also exist. From [43], non-

21

n = 0 WS
f 110
as
ted
truc
ons
e c
ar
7
3 5,6, an
. T
1th
' es w d
atric
de m
e co
ar
squ

$1

$2

$4

 

5'35

$1
$2
$3
$4

175

 

936

$1
$2
$3

_ x4
X7 is

$6

 

337

L.

118
r

31

$4

$6

_$2
$1
$4

-133
$6

_1~2
331
$4

—$3
376

_$5

$1

$2

 

331
372

$7

$1
$2
$7

1'8

_x3
_x4
$1
$2
$7
$8

171

_$4
$3
—$2
$1

$8

_$4
$3
_332
$1
338

—$4
553
—$2
$1
$8
_$7

1'6

the
'on,
struct1

11

co

de

co

$4

$1

$1

-335
‘36
—$7
—-'L'8
331

332

_1-5
’36
—$7
"'38
$1
$2

333

22

‘336
$5
“5’38
337
_$2

$1

_$6
$5
-$8
$7
{52
$1

 

$8

$5

_$7
$8
$5

‘136

—$3

$4

—$7
378
$5

‘36

-333
$4

331

’338
—$7
$6
335

—:r:4

 

 

—$8
-337
$6
135
-:r4

 

5’32

(2.17)

(2.18)

(2.19)

(2.20)

rate. For example, if we consider transmission matrix X5, we observe a total of eight
symbols ( = 8) and eight transmission periods (p = 8). As a result, transmission

matrix X6 has a rate of

k 8
R_;_§_r am)

2.3.2 Orthogonal Space-Time Block Codes for Complex Sig-

nal Constellations

In the previous subsection, we observed that constructing full transmit diversity,
full rate orthogonal space-time block codes for real signal constellations is relatively
easy. However, symbol constellations used in wireless communication typically con-
tains complex constellations. Complex orthogonal design matrices have size nT X p
with entries of 2:1, 2:2, - - - , 22p and their conjugates. Such matrices have full transmit
diversity of nT with code rate k/ p.

The Alamouti code is a complex orthogonal design matrix for two transmit an-

tennas and is expressed as

$1 —$5

3: * an)

The Alamouti code is the only full transmit diversity, full rate space—time block code
with complex constellation [43]. Consequently, the design goal of complex orthogonal
matrices for more than two transmit antennas is to provide full transmit diversity
and minimize the value of p to minimize the decoding delay.

For an arbitrary complex signal constellation, there are orthogonal space-time
block codes that can achieve code rates of 1 / 2 and 3/ 4. Complex transmission ma—
trices X5 and X2 are orthogonal designs for space-time block codes with three and

four transmit antennas, respectivel . Matrices X6 and K“ have a code rate of 1 2
y 3 4

23

and are expressed as [43]

x1 —:c2 —x3 —:r4 2:1 —:1:2 —x3 —:1:4
xg: $2 1'1 1'4 —x3 :6; x; x; -x;; . ($23)

$3 —$4 x1 x2 x3 —a:4 11:1 11:;

_

 

 

 

r 1
11:1 —:r2 —:c3 —:c4 x’i‘ —:c§ —:r§ —:1:2
:1:
X i = 2:2 1:1 2:4 -—1:3 11:; x”; :13: —:1:3 (2 24)
1:3 —x4 3:1 2:2 33;, —:1:Z :r’f a);
_:I:4 2:3 —:1:2 3:1 :52 x; —:r; xi

 

Tfansmission matrix X§ consist of four complex symbols, which are transmitted in
eight time periods via three transmit antenna; hence the code rate is 1 / 2. Similarly,
transmission matrix Xi has a code rate of 1 / 2.

Transmission matrices X3 and X2 are complex generalized orthogonal designs for

space-time block codes with rate 3 / 4. These codes are expressed as [43]

 

 

 

 

' _ * £11 £3 1
h m —x
X3 = $2 I; {/35 '7§3' 1 (2'25)
£3- 21 —:1:1—a:1 +32 ~33 $2+$§+$1 —:1:’i
-x/2 fl 2 2 .
— * * -
_ * £3. :3.
$1: 21 “—353
x5; = 1/5 1/5 . (2.26)

”1'1 gang-x; z2+x§ +x1 -$1
2 2

 

 

I
a

3 —z2—$§+x1—x’£ —:c1—:r:—:r2+:c§
\f2- 2 2 _

 

 

SB 8!? s
SIS

Transmission matrix X3 consist of three complex symbols, which are transmitted in
eight four periods via three transmit antenna, hence the code rate is 3/ 4. Similarly,

transmission matrix Xi has a code rate of 3/ 4.

24

2.3.3 Decoding Orthogonal Space-Time Block Codes

Decoding orthogonal space-time block codes with more than two antennas is similar to
decoding the Alamouti scheme. Assuming the channel coefficients hj,,-(t) are constant

over p symbol periods, such that
hj,z'(t) = hjfl', t = I, 2, : ° - ,p, (2.27)

where i and j represent the transmit and receive antenna, respectively. The max-
imum likelihood decoding algorithm is used to construct the decision statistics for
the transmitted signal sci. As an example, we calculate the decision statistics for the
space-time block code Kg. The decision statistics for the other codes can be found

in [43]. The decision statistics for X§ are

"R . . . . . .

~ 203,211, + rghh + 137,111,, + (7-57,)*h,-,1 + (atria-,2 +(1-;)*h,-,3), (2.28)
j=1
"R . . . . . .

i2 = Evihis - ffhia + 721"},3 + (7%)*hj,2 - (Rifles + (7%)“st (2'29)
j=1
"R . . . . . .

$3 = :(l‘ihls — fifth — ”ibis + (7‘3)*hj,3 - (T‘Whjn — (7%)*hj,2), (2-30)
j=1
"R . . . . . .

$4 = Z(-7§hj,3 + 723/612 — Filth - (7'2;st + (7‘31)*hj,2 - (7%)*hj,1)-(2-31)

i=1

H
I—l
II

2.4 Quasi-Orthogonal Space-Time Block Codes

Although, orthogonal space-time block codes are attractive for its full transmit diver-
sity and linear maximum likelihood (ML) decoding prOperties, the full-rate orthogonal
space-time block code for complex signal constellations only exist for two transmit an-
tennas. In an effort to provide full-rate transmission for space-time block codes with
more than two transmit antennas, quasi-orthogonal space-time codes (QO-STBCS)
were preposed by three groups of researchers from three major telecommunication

laboratories around the same time. Jafarkhani from the AT&T Laboratory named

25

his code QO—STBC [49], Tirkkonen, Boariu and Hottinen from N okia Research named
their code ABBA [50] for the code structure, and Papadias and Foschini from Lucent
Technology Bell Laboratory did not name their code [51].

With the quasi-orthogonal structure, the orthogonality of the code is relaxed to
provide a higher symbol transmission rate. Specifically, the data symbols in the Q0-
STBC are separable into groups after match filtering. The maximum likelihood (ML)
decoding of QO-STBC is performed by jointly detecting symbols group by group,
separately and in parallel. Whereas, in orthogonal STBCS, the decoding is performed
by detecting single symbols. As a result, the decoding complexity of the QO-STBC
is slightly higher than orthogonal STBC, but lower than a general non-orthogonal
STBC.

2.4.1 Code Structure and Pairwise Decoding of Quasi-

Orthogonal Space-Time Block Codes
Code Structure of Quasi-Orthogonal Space-Time Block Codes

The main advantages of codes from orthogonal designs are simple separate decoding
and full diversity. However, orthogonal STBCs for more than two transmit antennas
suffer from bandwidth inefficiency. In an effort to provide full diversity without the
penalty in bandwidth efficiency, three independent research groups proposed Q0-
STBCs [49—51].

The first example of the QO-STBC is designed by J afarkhani, which is denoted

as J4 and has the following code structure:

x... = _ = , (2.32)
B

 

 

26

where

13 CC (1: :17
A: 1 2 andB= 3 4, (2.33)

* * III =I=
‘32 $1 ‘334 $3

and A and B are the complex conjugate of A and B, respectively.
A second example of the QO-STBC is known as the ABBA code and is proposed

by Tirkkonen, Boariu, and Hottinen [50], which we denote as the TBH scheme. The
TBH scheme has the following code structure

151 372 $3 134

A B —:1:3 as; —:r:'1' at};
XTBH = = , (2.34)
B A 2:3 3:4 :01 11:2

=I= * * it
_-$4 $3 ’32 $1

 

 

where A, and B are the same as those in (2.33).
A third example of the QO-STBC code is proposed by Papadias and Foschini,
and is denoted as PF. The code structure of the PF code is

I- q

131 172 $3 $4

$5? __x* 33* _x*
KIT: 2 1 4 3 . (2.35)
$3 —-$4 “$1 $2

 

 

372 $3 -$3 -$i_
Pairwise Decoding of Quasi-Orthogonal Space-Time Block Codes

For each of the three QO-STBCS, the four transmitted data symbols contained in
the codeword can be separated into two groups. As a result, the ML decoding can
be performed by jointly detecting two complex symbols in each group separately. To
illustrate the ML decoding of the QO—STBC, we consider the J4 code in (2.32) as an

example.

At the receiver, the maximum likelihood decision metric can be calculated as the

27

sum of two terms f14(:c1 , 1:4)+ f23(x2, :13), where f14(a:1 , $4) is independent of symbols
11:2 and 11:3, and f23($2, x3) is independent of symbols 1:1 and 1:4. The minimization
of the maximum likelihood decision metric is equivalent to the minimizing these two
terms independently. After simple manipulation of the maximum likelihood decision

metric, f14(:r:1,:r4) and f23(:1:2,a:3) can be express as

"R 4
f14($1,$4) = Z[(Zlh',il2)(I$1I2+I$4I2l

j=1 i=1
+ 2Re (x1(—hj,1r[3)* — 1233,27»? — r1134“ — 11,4143”)

+ $4(—hj,47‘§‘7)* + h;,31'£]) + hizréj) — hj,1r,(1])*)

+ $1$Z X 2Re(hj,1h;,4 — hj,2h;,3)):| , (2.36)

"R 4
f23($2,$3) = Z[( Ih',z‘I2)(I$2|2+I$3|2)
1

+ 2R8 ($2(-hj,27‘§])* - hilrgj) - h;’4T:(;,J) — hj,37",(1])*)

+ $3(—hj,3r[j)* + (13‘3"?) + hilrgj) — hj’gréj)*)

+ $223; X 2Re(hj,1h;,4 — hj,2hf’3)):| , (2.37)

where Re{-} denotes the real part of {}.

Although the decoding complexity of the QO-STBC is less than of non-orthogonal
designs, the QO-STBCS provided in this subsection do not achieve full diversity.
Using the PF code (2.35) as an example, we show that QO-STBCs do not provide
full diversity.

First we define codeword difference matrix B as

B=X—X, as)

28

where X is the estimated codeword matrix, and calculate the codeword distance

matrix A as

 

 

A = a” B _
a 0 0 b
0 a —b 0
= , (2.39)
0 —b a 0
b 0 0 a
where
4
a = Z Ix,- — m2 (2.40)
i=1
and
b = 2Re(($1 - $1)($4 - $4)* — ($2 - $2)($3 - $3)*)- (2-41)

The determinant of codeword distant matrix is

Det(BHB) = (a + b)2(a — b)2
= (I41 + A4|2 + |A2 - A3I2) (IA1 — A4|2 + lAz + A3|2).(2-42)

where A, = x,- -— 5%,.

From (2.42), the minimum value occurs when half of the symbols have error, i.e.
either A1 = A4 = 0 (while A2 and A3 are non-zero) or A2 = A3 = 0 (while A1 and
A1 are non-zero). Hence, the minimum determinant value in (2.42), can be simplified

as

Min [Det(BHB)] = [[A1 + A4[2[A1 - A4I2], (2.43)

29

assuming that A2 = A3 = 0.

From (2.43), when A1 = :l:A4, the determinant value of the codeword distance
matrix would become zero, which implies the codeword distance matrix does not have
full rank and cannot achieve full diversity. For example, if a conventional symmetric
constellation sets such as phase shift keying (PSK) or quadrature amplitude modula-
tion (QAM) is used, it is easy to see that the determinant of the codeword distance
matrix will be zero. If a binary phase shift keying (BPSK) constellation set {—1, 1}
for all symbols, the possible values of A,- are {0, 2, -2} for all value of 2', therefore

A1 = :l:A4 can easily be zero.

2.4.2 Quasi-Orthogonal Space-Time Block Codes with Con-

stellation Rotation

Although QO-STBC can achieve higher code rates than orthogonal ST BC, (20-
STBCs generally does not provide full diversity. As a result, QO—STBC suffer from
poor bit-error rate (BER) performance in high SNR levels. In an interest of achiev-
ing full diversity, QO—STBCS with constellation rotation were proposed in [52—56].
Specifically, the constellation rotation QO-STBC [55,56] proposes that half of the
symbols in the quasi-orthogonal design be chosen from a signal constellation .A and
the other half of the symbols be chosen from a rotated constellation ej¢A.

Considering the BPSK and the PF code (2.35) as an example, it can be shown
that the rotated constellation achieves full diversity. If 2:1 is chosen from signal
constellation A (hence A1 takes values {0,2, —2}), while symbol 2:4 is chosen from
a rotated signal constellation ej‘f’A (hence A4 takes {0, 2exp(j¢), —2exp(j¢)}), then
a non-zero value for [Al :I: A4| can always be obtained, assuming A2 = A3 = 0.
Similarly, the constellation rotation can be applied to symbols pair (x2, $3).

In addition to providing full diversity, the constellation rotation gives an extra
degree to maximize the minimum determinant value in (2.43) to achieve maximum

coding gain for QO-STBC. Again, using the PF code (2.35) as an example, we illus-

30

trate constellation rotation code structure as follows

 

 

- :01 2:2 ej¢$3 ej¢x4 1
XPFcr = I; Rm; (ej¢x4)* (ej¢x3)* (2.44)
eJ¢x3 —eJ¢:r4 —a:1 x2
L(ej‘f’2:4)"‘ (ej¢x3)* —:I:§ —a:’{ _

2.4.3 Performance of Quasi-Orthogonal Space-Time Block
Codes

In this subsection, the BER performance of the QO—STBC with and without con-
stellation rotation on Rayleigh fading channels are evaluated by simulation. For
comparison, the BER performance of the OSTBC is also simulated over Rayleigh
fading channels. Each system is equipped with four transmit antennas and one re-
ceive antenna. The OSTBC scheme is rate% and the QO-STBCs are rate-1. In order
to for all schemes to have the same spectral efficiency of 2 bps / Hz for fair comparison,
the rate-% transmits 16-QAM systems, while the rate-1 QO-STBCS transmits QPSK
symbols. It can be seen from Figure 2.5 that both QO-STBCS perform better than
the OSTBC scheme at low SNR levels. This is due to the fact that QO-STBCs have
a higher code rate and the QPSK constellation that has a larger Euclidean distance
than 16-QAM constellation. However, as the SNR increases, the OSTBC scheme
begins to outperform the QO-STBC without constellation rotation due to the lack of
full diversity. On the other hand, the QO-STBC with constellation rotation performs
consistently better than OSTBC.

2.5 Summary

In summary, space-time coding is a signal technique design aimed at approaching the
information theoretic capacity limit of MIMO systems. Space-time block codes were
pioneered by Siavash Alamouti, who developed a full transmit diversity scheme for

two transmit antennas. Alamouti’s work motivated Vahid Tarok et al. to generalize

31

 

 

   
 

1O .............. 1 .............. . .............. 1 .............. I ..............

‘ 3 i 1 i i 3 + OSTBC: Simulation I3
- —e— QOSTBC w/ CR: Simulation :-
—B— QOSTBC: Simulation “

   

 

 

 

  

Bit Error Rate

 

 

 

o 5 1o 15 20 25
SNR (dB)

Figure 2.5. BER performance of OSTBC vs. QO—STBC schemes with and without

constellation rotation.

32

space-time block codes to accommodate the use of more than two transmit antennas.
However, generalize space-time block codes for more than two antennas do not provide
full-rate transmission. In an effort to provide full-rate transmission for space-time
block codes with more than two transmit antennas, quasi-orthogonal space-time block
codes were proposed, where the orthogonality of the code is relaxed to provide a higher

symbol transmission.

33

CHAPTER 3

Spectrally Efficient Space-Time
Coding

In this chapter, we introduce a spectrally efficient Alamouti scheme. First, we in-
vestigate the code efficiency of the Alamouti code from a bit-level perspective by
introducing the concepts of Alamouti patterns and irregular partitioning. Our inves-
tigation reveals the possibility of spectral efficiency enhancement. Second, we propose
a novel spectrally efficient Alamouti code. The proposed scheme improves the code
efficiency of the traditional Alamouti scheme by increasing the number of information
bits transmitted in each Alamouti block. Finally, we provide simulation examples to

demonstrate the effectiveness of the pr0posed spectrally efficient Alamouti code.

3. 1 Introduction

Theoretical and experimental results of multiple-input multiple- output (MIMO) sys-
tems promise dramatic improvements in spectral efficiency. Pioneering research of
Foschini and Telatar [30,31] shows that the channel capacity grows linearly as the
number of transmit and receive antennas grow simultaneously. As a result, multiple
transmit and receive antennas with space-time coding has been the subject of many
works [30,39,42,43,48, 57—65] to achieve high data rates.

Schemes such as BLAST [30] and V—BLAST [48] have been proposed to exploit
the spatial multiplexing to transmit independent data streams over MIMO channels.
Although BLAST can handle high data rates, there are some drawbacks against its

use for downlink communications. First, the data stream suffers from deep fades

34

during the transmission due to the lack of spatial coding. Second, the receiver relies
on powerful signal processing techniques, e.g., a sequence of nulling and canceling
steps, to detect the desired signals. Third, the performance is subject to degradation
for the V-BLAST decoding scheme, when the number of receive antennas is less than
the number of transmit antennas.

Space-time codes that use algebraic designs have recently been proposed to simul-
taneously achieve full rate and maximum diversity [62,63]. The full diversity of these
codes are achieved by extending the block length. Consequently, more data symbols
need to be jointly decoded than with V-BLAST, leading to a dramatic increase in
complexity.

Unlike most of the existing methods which are designed to maximize the diversity
or rate for space-time block codes, the proposed scheme aims to improve the code
efficiency of the Alamouti codes, while achieving full transmit diversity and retaining
the decoding simplicity. For example, even the so—called full-rate orthogonal codes [39,
42,43] are low-efficient codes. Defining the code efficiency as the ratio of information
bits to the total number of bits transmitted in a space-time block, we find out that
the full-rate Alamouti code, only achieves a code efficiency of 0.5. As a matter of
fact, all other full-rate space-time block codes have a code efficiency of 0.5, and non
full—rate space-time block codes have a code efficiency less than 0.5.

As an effort to increase the code efficiency of space-time block codes, we investigate
the traditional Alamouti space-time code from a bit-level perspective and propose a
spectrally efficient Alamouti scheme. The proposed scheme enhances the spectral
efficiency by increasing the number of information bits transmitted in each Alamouti
block. Furthermore, the proposed scheme achieves high transmit diversity and retains
the decoding simplicity of the maximum likelihood decoder.

The rest of the chapter is organized as follows: In Section 3.2 we review the system
model for the Alamouti code. In Section 3.3, we investigate the code efficiency of the
Alamouti code from a bit-level perspective by introducing the concepts of Alamouti
patterns and irregular partitioning. In Section 3.4, we propose a spectrally efficient

Alamout code design. We provide illustrative simulation examples of the proposed

35

scheme in Section 3.5. Finally, in Section 3.6, we provide a summary.

3.2 System Model of Alamouti Scheme

In this section, we briefly review the Alamouti code and investigate the Alamouti
code from a symbol-level perspective. Our investigation reveals that the traditional
Alamouti scheme has a low code efficiency.

Recall, the Alamouti scheme is a full-rate full-diversity orthogonal code for a
system with two transmit antennas and one receive antenna. From a symbol-level
perspective, the input binary stream is first mapped into symbols based on a particular
constellation A. In each encoding Operation, two symbols x1 and 222 are encoded into

the Alamouti matrix, which is expressed as

Time
"I * (3.1)
3121 —a:2 I Space,
11:2 13’]
where the complex scalars 2:1 and 32 are chosen from a particular (M-PSK or M-QAM)
constellation, and x’i‘ and as; are the complex conjugates of 2:1 and 1:2, respectively.
The bits related to {:r’f, ~23} depends only on {2:1, 2:2} once the signal constellation
is fixed. As a matter of fact, only the bits corresponding to {3:1, 2:2} carry the useful
information and the others are redundancy bits. In other words, there is room for
spectral efficiency enhancement.
Assuming that one receive antenna is employed at the receiver and the fading

coeflicients, i.e., {h1, h2}, are invariant across two consecutive symbols, the received

signals can then be expressed as,

[T1T2]=[h1h2] +[n1n2], (3.2)

x2 31‘

36

where r1 and r2 are the received signals at time t and t+T and n1 and n2 are complex

random variables representing receiver noise. Rewrite (3.2) as

7’1 h1 h2 $1 n1

* = * * + * . (33)
7‘2 hz — 1 $2 "2
1% 2 ex 2N

Note that HHH = HH’H = (|h1|2 + |h2|2)12, where 12 is 2 x 2 identity matrix

and ’H is the Hermitian conjugate. It follows that

Z
z = 1 2 HHR = (Ihll2 + |h2|2)12X + H’HN, (3.4)
22

therefore, maximum—likelihood decoding of 3:1 and 2:2 can be decoupled:

a = arg min {Izl — xklz + (Ihll2 + Ihzl2 ‘1)lxkl2}a (3.5)
$k€A

572 = arg min {lzz - $k|2 + (lhil2 + lhzl2 - 1)|$k|2}- (3.5)
:L’kEA

For PSK signals, the decision rule in (3.5) and (3.6) can be further simplified as

follows:

A _ ' 2
:c = ar mm z — a: , 3.7
1 aka“ 1 kl } ( >
5:2 = arg min {'22 — xk|2}. (3.8)
xkEA

3.3 Bit-Level Inspection of the Alamouti Code

In this section, we introduce the concepts of Alamouti patterns and irregular par-
titioning to investigate the code efficiency of the Alamouti scheme from a bit-level

perspective.

37

3.3.1 The Alamouti Patterns

Assume that all the symbols in the Alamouti transmission matrix (3.1) are drawn
from a quadrature phase shift keying (QPSK) constellation with Gray code mapping,
as shown in Figure 3.1.

Define Alamouti patterns to be all possible matrices with bit representation of

. 0'") 0'3") .. 0'7") :1:
(3.1). For example, if 2:1 = e I and 2:2 = e T , then 3:1 = e T and —z2 =
-1r

e01). The corresponding bit representations of the four signals are 00, 01, 10 and

00, respectively. If we replace each symbol with its bit representation in (3.1) we get
0000

0110
By computing all combinations of {1:1, 2:2} through the constellation points, we

an Alamouti pattern,

find all Alamouti patterns, which are listed in (3.9). Obviously, bits in each Alamouti
pattern are not independent. Define crucial bits to be the necessary bits uniquely
determining the Alamouti pattern, and auxiliary bits to be the bits totally dependent
on crucial bits. In fact, only crucial bits contain useful information and auxiliary
bits are redundant in some sense. In this case, crucial bits can be chosen to be bit
representations of 2:1 and 2:2, i.e., the first two columns of each Alamouti pattern.
Define the code efficiency (77) as the ratio of the number of crucial bits to the
total number of bits in each Alamouti pattern, such that 77 is bounded by 0 S 17 S 1.
Due to the use of auxiliary bits, in this particular case, 17 = 0.5. In fact, for all the
other full-rate space-time block codes, the efficiency is also 0.5, and even worse for

non full-rate codes.

 

"0001‘ '0000"0011"0010‘ ‘
_0010"_0110_ _1010"_1110"

' 0101 ‘ ' 0100 ' ' 0111 ‘ ' 0110 7
Alamouti patterns < _ 0011 . _ 0111 _ _ 1011 _ _ 1111 j >

for QPSK‘ F 1001 ' ' 1000 ‘ F 1011 ‘ l 1010 '
.0000.’.0100.’.1000_’l1100.’

 

U

 

 

 

 

 

 

 

(3.9)

 

 

 

 

 

 

 

 

“1101' ”1100' "1111‘ [1110‘
.0001.’.0101..1001..1101.°

M
H

 

 

 

 

 

 

 

 

 

 

38

01

Figure 3.1. QPSK constellation with Gray mapping.

11

 

00

10

39

V

On the other hand, if we partition the original bit stream into groups of size 2 x 4
like the Alamouti patterns, and each group consists of one Alamouti pattern, then no
extra bits need to be inserted into data stream in order to form the Alamouti matrix
before transmission. In other words, the data rate is really “full” in this situation and
the efficiency is at its maximum, i.e., 77 = 1. However, since the original data stream is
random, the probability of each group being a Alamouti pattern is only g; = 6.25%.
Suppose that the number of groups is N and the groups are independent of one
another, it turns out that the probability of achieving 17 = 1 for the random data
stream is (6.25%)N , which is a very small number if N > 2. In other words, practical

systems using the Alamouti code achieves 77 = 1 with nearly zero probability.

3.3.2 Irregular Partitioning of the Alamouti Code

To generalize the concept of grouping Alamouti patterns, we introduce irregular par-
titioning. Assume that the original bit stream is partitioned into groups of size 2 x M
matrix, denoted by B.

In irregular partitioning, the input bit stream is first partitioned into a 2 x 4
matrix. If the 2 x 4 matrix matches a valid Alamouti pattern, then the corresponding
matrix has maximum efficiency. In the case that the 2 x 4 matrix does not match
any valid Alamouti patterns, the matrix is reduced to a 2 x 3 matrix. If the 2 x 3
matrix matches the prefix of a valid Alamouti pattern, then a suffix auxiliary bits are
appended to the 2 x 3 matrix, yielding a full 2 x 4 Alamouti pattern. Note, a 2 x 3
partition has 77 = 0.75. In the case that the 2 X 3 partition does not match the prefix
of any valid Alamouti patterns, the partition is reduced to a 2 x 2 matrix. At this
point, there is always a 2 x 2 partition prefix match of a valid Alamouti pattern. As a
result, the 2 x 2 partition has 77 = 0.5. The pseudo-code of this irregular partitioning
is listed as follows:

According to the above irregular partitioning, the probabilities of resulting 2 x 4
matrix, 2 x 3 matrix or 2 x 2 matix, in theory, are %; = 6.25%, (1—6.25%)%:r = 23.44%
and (1 — 6.25% - 23'44%)§—: = 68.75%, respectively. Assuming that the receiver has

40

 

Irregular Partitioning
Initialize i = 1, j = 4.

While i < M
If B(:,i : j) doasn’t match any Alamouti patterns
j=j—1

If B(:,i : j) doesn’t match any Alamouti patterns’
first three columns
1 = j - 1
End if
End if
Record 3'
i=j+1
j = j + 4
End while

 

 

 

the knowledge of the partitioning strategy, the theoretical code efficiency is given by
77 = 1 - 6.25% + 0.75 - 23.44% + 0.5 - 68.75% = 0.5820, (3.9)

which is pretty close to the simulation results, 77 = 0.5796.

On the other hand, the Alamouti code can be regarded as a regular partitioning
of the input. Each partitioned block is always a 2 x 2 matrix, which are treated as
crucial bits. The other 2 x 2 matrix of auxiliary bits are appended to crucial bits in
each block. Thus, 77 = 0.5.

Although the code efficiency is slightly improved by the irregular partitioning
scheme, it introduces extra complexity to the transmitter. Furthermore, it is not
realistic to assume that the knowledge of the data-dependent partitioning strategy is

available at the receiver.

3.4 The Spectrally Efficient Alamouti Scheme

Our goal is to enhance the efficiency of the Alamouti code, and at the same time

achieve high transmit diversity and retain the decoding simplicity.

41

3.4.1 Encoding Algorithm Design

Starting with Alamouti patterns of QPSK, we try to increase the number of crucial
bits by one. Since there are 16 valid Alamouti patterns, each pattern can be uniquely
determined by four crucial bits. How do we increase the number of crucial bits I
by one? We propose to use dual constellations, and the fifth crucial bit can be
utilized to indicate a specific constellation for transmission. In this particular case,
two constellations, A0 and A1 are illustrated in Figure 3.2, where A1 is obtained by
rotating A0 clockwise by 7r / 4. The constellations are coded for minimum BER by
minimizing the number of nearest neighbors.

At the transmitter, the binary data stream is first divided into 5-bit groups. The
first four bits are used to select one of the Alamouti pattern from (3.9). The fifth bit
chooses one of two constellations, which are depicted in Figure 3.2. In particular, the
fifth bit equal to “0” indicates the use of A0 constellation, while the fifth bit equal
to “1” indicates the use of A1 constellation as an alternative. It turns out that the
transmission matrix has the same format of the Alamouti matrix, but each Alamouti
block now contains 5 information bits rather than 4 bits in the original Alamouti
code.

Let b5 6 {0, 1} denote the fifth bit. The transmission matrix can be represented

—' b --'7rb
mm ”3'83“ (310)

-7r “71'
$2 . e-szs x; . e—szs

3.4.2 Decoding Algorithm Design

Assuming the receiver is equipped with one receive antenna and the channel coeffi-
cients are invariant across two consecutive symbols, it follows that the received signal

in (3.3) becomes

h. h “351:55

7'1 1 2 331 6 n1

* = * * —j7rb5 + * 3 (3.11)
T2 h2 -h1 I2 ' C Z n2

2 211 2 e

42

 

0 A0
A A1
01
01 00
o o
00
./_\. .4:
11': ‘
o, o"
11
A 10
10

 

Figure 3.2. Constellation design for the spectrally efficient Alamouti code.

and (3.4) becomes

2 HHR = (will? + 02,212)sz + HHN. (3.12)

 

The fifth bit b5 is decided by the locations of zl and .32. Assuming that all the

signals in the A0 and A1 constellations are equiprobable, the signals 21 and :32 are

43

chosen from the constellations to minimize the distance metric

21 = arg 21 622,131,,1 (2% (W + |h2I2)21) + 22(22, (I211? +Ih2|2)21))

=arg min

216/10, A1

22 = arg min (d2(31(Ih1I2+Ihzlzlzz)+d2(22,(Ih1I2+Ih2I2)22)

I21- (121:2 + lh2|2)21|2 +122 - (W + 122:2)2 H2) (3 13)
216240,}11)
(3.14)

= min Izl- (IhlI2 + Ih2I2)22I2 + IZ2 - (Ih1I2 + Ih2I2)Z I22)

argzléAo,A1

over all possible values of 21 and 22. If 21 < 22, then b5 = 0, else if, :21 > 22, then
b5==1.
Once b5 is determined, maximum-likelihood decoding of 11:1 and x2 can still be

decoupled as:

- . —j“b 2

x1 = arg min {lzl — 2:16 1 5| }, (3.15)
2: EAb5

A _ u —j7rb5 2

1:2 — arg min {'22—2326 1 I }. (3.16)
$2€Ab5

Discussions: It can be seen that the proposed scheme increases the spectral
efficiency in systems with two transmit antennas and QPSK modulation. Modulation
schemes other than QPSK will produce different Alamouti patterns, thus yielding
different performance. Furthermore, the proposed scheme does not change the code
structure, therefore the same idea can be extended to space-time block codes for more

than two transmit antennas.

3.5 Simulation Examples

In this section, simulation results are provided to demonstrate the performance of
the proposed spectrally efficient Alamouti code. The proposed scheme with QPSK
modulation is compared with Alamouti codes with QPSK and 8PSK modulations.
Note that the traditional Alamouti codes with QPSK modulation (Alamouti- QPSK)

44

I
U

 

Bit Error Rate
8

 

   

 

 

 

 

 

 

_4' - + —AIamouti-8PSK, n = 1/2
1° E— an —Alamouti-QPSK,n= 1/2 .
E+P'°p°5°d'BER(b5)!=°'“=5’8ififffffffffffiijif:liffffif'ffl
10.55"+Pr°P°sed'BER(b5)=°v“=5’3 \\\
E—a—BERofbs
10‘6 i l i i
5 1o 15 20 25 30

SNR (dB)

Figure 3.3. The BER performance comparison of the proposed scheme and the Alam-
outi code in Rayleigh flat fading, nT = 2, n R = 1.

and 8PSK modulation (Alamouti-8PSK) are considered full-rate space-time block
codes. As a result, their code efficiency is only 0.5. On the other hand, the proposed
scheme, increases the number of information bits by one per Alamouti block, resulting
in an increase of code efficiency to 0.625. In Figure 3.3, the bit error rate (BER)
performance of the three schemes are evaluated in Rayleigh flat fading and equipped
with W; = 2 and n R = 1 antennas. In addition, we plot the BER performance of the
fifth bit b5 and the proposed scheme with perfect recovery of b5 i.e., the number of
errors related to b5 is zero (BE R(b5) = O). The minimum Euclidean distance between
two QPSK constellations in Figure 3.2 is the same as that of a 8PSK constellation.
Therefore, in the worst case, the BER performance of the proposed scheme will be

slightly worse than Alamouti-8PSK, due to additional b5 errors. On the contrary,

45

if the recovery of b5 is perfect, then the selection of the QPSK constellation at the
receiver is always correct. Correspondingly, the minimum Euclidean distance turns
out to be the same as that of a QPSK constellation. Thus, in the best case (perfect
recovery of b5), the BER performance of the proposed scheme will outperform the

Alamouti-QPSK due to the perfect reconstruction of b5.

Alamouti 2x2

— + — Alamouti-8PSK, n = 1/2
— 2* - Alamouti-QPSK, n = 1/2
———a— Proposed, BER(b5)!=0. n = 5/8

 

  
 
 
 
 

 

 

 

 

 

 

: —9— Proposed, BER(b5)=O, n = 5/8
+BEROfb5

2 @5333?ffffffifgfffftf:33157::Tz'\:::::::::::::::::::::;::::::::::::::
L52 ,......:'XII:CELLS...3:..3'25.::.::.:::.ICI:Z:I:ZI:ZKKK:
21° xx
“J :::::::::::::::.::::::.:'2:::::::\::::::::.:':..':::'\::::::::.:::::::::::::::
H

E Ii:33:3:I:2:2,:CHRIS)".IIICKIIIELi'..3.3.3:::..::::.:::.i::::

-4 i .

10 Ex
::::::::iiiiiii'Iiiiliiiiiiliifi::::~.."::::_.\::::::..':'::::::::::\:<iiii:
:.:::.:I:::::::::::Z:I:IIIZ:ILZi2::i:::::.:"".1::iI::::.:.'i::::::::.ii>}-.::
................................................ \

10 FEESSEEEEESiziiiiiffiii353335Eififfiiiiffififffiff.‘ ....... 2...sssssssssa‘-
:iiliiiiiiiliiiiiziiiiii3::Iif::::::::i:::::;i:l:ifi°:.\::::Z IIIIIIIIIZIIE
:2::::::::::::::::::::::::::::::::::::::2:::.::::::::..:::.\:.::":::::::::::
iiiiiiiji221222.11ZZZ22112212jLiiiIiI222:1:Iiijiijiiiiiijiiffiiiiiiiiiiii

10-6 l L 4 l
5 1O 15 20 25 30

SNR (dB)

Figure 3.4. The BER performance comparison of the proposed scheme and the Alam-
outi code in Rayleigh flat fading, nT = 2, n R = 2.

In Figure 3.4, we consider the BER performance of the three schemes with nT = 2
and n R = 2 antennas. From the figure, it is shown that the additional antenna at the
receiver significantly improves the performance proposed scheme with perfect recovery
of b5. At 10‘3 the proposed scheme with perfect recovery outperforms the Alamouti-
QPSK by 4dB. In Figure 3.5, performance of the proposed scheme with 72.71 = 2,

n R = 1 and 72:; = 2, n R = 2 antennas is shown to demonstrate the effectiveness of

46

 

 

 

 

 

Bit Error Rate
8

I
h

.3
O

10’

 

 

 

 

1o
SNR (dB)

Figure 3.5. The BER performance comparison of the proposed scheme with nT = 2,
72.3 = 1 and nT = 2, 72.3 = 2 in Rayleigh flat fading

additional receive antenna.

In Table 3.1, a comparison of the three Alamouti codes is provided in terms of
code efficiency, bit-rate and BER.

Table 3.1. Comparison of three Alamouti codes.

 

 

Schemes 7) R (bit / s / H 2) BER
Alamouti-QPSK 0.5 2 low
Proposed-Alamouti 0.625 2.5 l
Alamouti-8PSK 0.5 3 high

 

 

 

 

 

 

47

3.6 Summary

In summary, we investigated the efficiency of the Alamouti code from a bit level
perspective, and introduced a spectrally efficient Alamouti scheme. The proposed
scheme enhances the spectral efficiency by transmitting more information bits than
redundancy bits per Alamouti block. Moreover, the proposed scheme preserves the
high transmit diversity and simple receiver design of the Alamouti code. Finally,
the proposed scheme has no specific constraints, therefore can be directly extended
to any space-time block codes with more than two transmit antennas. Simulation

results verify the effectiveness of the pr0posed scheme.

48

CHAPTER 4

Secure Space-Time Coded
Collision-Free Frequency Hopping
. System

In this chapter, we propose an innovative spectrally efficient, jamming-resistant wire-
less scheme by exploiting the joint space—time and frequency diversity. First, we
develop a collision-free frequency hopping (CFFH) system based on the orthogonal
frequency division multiplexing (OFDM) framework. Second, we investigate the limi-
tations of the recently proposed subcarrier assignment algorithm [66,67] and propose a
new subcarrier assignment algorithm based on the secure permutation scheme [68,69].
The new secure subcarrier assignment algorithm is designed to ensure that: (i) Each
user hops to a new set of subcarriers in a pseudo-random manner at the beginning
of each hopping period; (ii) Different users always transmit on non-overlapping sets
of subcarriers; (iii) Malicious users cannot predict or repeat the hopping pattern of
the authorized users, and hence cannot launch follower jamming attacks. Third, we
enhance the anti-jamming prOperty of the CFFH scheme by incorporating space-time
coding. Our analysis indicates that the enhanced system, referred to as STC—CFF H,
is particularly powerful in eliminating channel interference and hostile jamming in-
terference, especially random jamming. Finally, simulation examples are provided to

illustrate the performance of the proposed schemes.

49

4. 1 Introduction

Mainly due to the lack of a protective physical boundary, wireless communication
is facing much more serious security challenges than its wirelined counterpart. In
addition to the time and frequency dispersions caused by multipath pr0pagation and
Doppler shift, wireless signals are subjected to hostile jamming, interference and
interception.

Existing anti-jamming and anti-interception systems, including both code-division
multiple access (CDMA) systems and frequency hopping (FH) systems, rely heavily
on rich time—frequency diversity over large, spread spectrum. Mainly limited by mul-
tiuser interference (caused by multipath propagation and asynchronization in CDMA
systems and by collision effects in FH systems), the spectral efficiency of existing
jamming resistant systems are very low due to inefficient use of the large bandwidth.
While these systems work reasonably well for voice centric communications which
only requires relatively narrow bandwidth, their low spectral efficiency can no longer
provide sufficient capacity for today’s high speed multimedia wireless services. This
turns out to be the most significant obstacle in developing anti-jamming features
for high speed wireless communication systems, for which spectrum is one of the
most precious resources. On the other hand, along with the development of wireless
communications, especially cognitive radios, hostile jamming and interception are no
longer limited to military applications. Therefore, a major challenge in today’s wire-
less communications is: how to design wireless systems which are highly efficient but
at the same time have excellent jamming resistance properties?

As an effort to address this problem, we propose to integrate the frequency hop-
ping technique into highly efficient communication systems through a network-centric

perspective. Our approach is motivated by the following observations:

0 Orthogonal frequency division multiple access (OFDMA) is an efficient multiple
user scheme that divides the entire channel into mutually orthogonal parallel
sub-channels. The OFDMA technique transforms a frequency-selective fading
channel into parallel flat fading channels. As a result, OFDMA can effectively

50

eliminate the intersymbol interference (ISI) caused by the multipath environ—
ment and can achieve high spectral efficiency. For this reason, OF DMA has
emerged as one of the prime multiple access schemes for broadband wireless
networks [70,71]. However, OFDMA does not posses any inherent security

features and is fragile to hostile jamming.

FH is originally designed for jamming resistant communications. In traditional
FH systems, the transmitter hops in a pseudo—random manner among available
frequencies according to a pre—specified algorithm, the receiver then operates in
a strict synchronization with the transmitter and remains tuned to the same
center frequency. Two major limitations with the conventional FH scheme
are: (i) Strong requirement on frequency acquisition. In existing FH systems,
exact frequency synchronization has to be kept between the transmitter and
the receiver. The strict requirement on synchronization directly influencas the
complexity, design and performance of the system [72], and turns out to be a
significant challenge in fast hopping system design. (ii) Low spectral efliciency
over large bandwidth. Typically, FH systems require large bandwidth, which
is proportional to the hopping rate and the number of all the available chan-
nels. In conventional frequency hopping multiple access (FHMA), each user
hops independently based on its own pseudo-random number (PN) sequence,
a collision occurs whenever there are two users over the same frequency band.
Mainly limited by the collision effect, the spectral efficiency of conventional F H

systems is very low.

In literature, considerable efforts have been devoted to increasing the spectral
efficiency of PH systems by applying high-dimensional modulation schemes [23-
29]. More recently, a combination of the PH technique and the OF DMA system,
called FH-OFDMA, has been proposed [34,35]. However, as the system is based
on the conventional FH techniques, the spectral efficiency is seriously limited
by the collision effect. Along with the ever increasing demand on inherently

secure high data-rate wireless communications, new techniques that are more

51

efficient and reliable have to be developed.

We consider highly efficient anti-jamming system design using secure dynamic
spectrum access control. First, we deve10p a collision-free frequency hOpping (CFFH)
system based on the orthogonal frequency division multiplexing (OFDM) framework.
Second, we investigate the limitations of the recently proposed subcarrier assignment
algorithm and propose a new subcarrier assignment algorithm based on the secure
permutation scheme. The new secure subcarrier assignment is achieved through an
advanced encryption standard (AES) [73] based secure permutation algorithm, which
is designed to ensure that: (i) Each user hops to a new set of subcarriers in a pseudo-
random manner at the beginning of each hopping period; (ii) Different users always
transmit on non-overlapping sets of subcarriers; (iii) Malicious users cannot determine
the hopping pattern of the authorized users, and hence cannot launch follower jam-
ming attacks.1 Moreover, using the fast Fourier transform (FFT) based OFDMA
framework, CFFH has the same high spectral efficiency as that of OFDM, and at
the same time can relax the complex frequency synchronization problem suffered by
conventional FH systems. Third, we observe that CF FH is sensitive to random jam-
ming and propose an enhanced CFFH scheme by incorporating space-time coding.
Space-time block coding, which was first proposed by Alamouti [42] and refined by
Tarokh et al. [43,45], is a technique that exploits antenna array spatial diversity
to provide gains against fading environments. When incorporated with OFDM, the
space-time diversity in space-time coding is then converted to space-frequency diver-
sity. The enhanced scheme, referred to as space—time coded collision-free frequency
hopping (STC—CFFH), is found to be particularly powerful in eliminating both chan-
nel interference and hostile jamming interference, especially random jamming. In this
chapter, we analyze the performance of the proposed STC—CFFH system through the
following aspects: (i) Comparing the spectral efficiency of the proposed scheme with

that of the conventional FH-OFDMA system; (ii) Investigating the performance of

 

1Follower jamming is the worst jamming scenario, in which the attacker is aware of the car-
rier frequency or the frequency hopping pattern of an authorized user, and can destroy the user’s
communication by launching jamming interference over the same frequency bands.

52

the STC—CFFH system under Rayleigh fading with hostile jamming. Our analysis
indicates that the proposed system is both highly eficient and very robust under
various jamming environments.

The rest of the chapter is organized as follows: In Section 4.2, the proposed CFF H
system is discussed. In Section 4.3, the limitations of the recently proposed subcar-
rier assignment algorithm is investigated. In Section 4.4, the new secure subcarrier
assignment algorithm based on the secure permutation scheme is introduced. The
anti-jamming features of the new CFFH scheme is enhanced with space-time cod-
ing in Section 4.5. The spectral efficiency and jamming resistant properties of the
proposed systems are analyzed in Section 4.6. Simulation examples are provided in

Section 4.7. Finally, a summary is provided in Section 4.8.

4.2 The Collision-Free Frequency HOpping
Scheme

The CFFH system is essentially an OFDMA system equipped with secure FH-based
dynamic spectrum access control, where the hopping pattern is determined by the

secure subcarrier assignment algorithm described in Section 4.4.

4.2.1 Signal Transmission

Consider a system with M users, utilizing an OFDM system with No subcarriers,
{f03 ' '° ,ch_1}. At each hOpping period, each user is assigned a specific subset of
the total available subcarriers. One hopping period may last one or more OFDM
symbol periods. Assuming that at the nth symbol, user i has been assigned a set
of sub-carriers C,”- = {fn:i0’ - -- , fn’iNfi—IL that is, user i will transmit and only
transmit on these subcarriers. Here N; is the total number of subcarrier assigned to

user i. Note that for any n,
Cm,- flow- = (2), if i 9e j. (4.1)

53

That is, users transmit on non-overlapping subcarriers. In other words, there is no

collision between the users. Ideally, for full capacity of the OFDM system,
M—l '
U Cn,i : {an ° ' ° 1 ch—l}‘ (4'2)
.=0

For the ith user, if N3, > 1, then the ith users information symbols are first fed

into a serial-to-parallel converter. Assuming that at the nth symbol period, user i

transmits the information symbols {ufpm - -- ,u(i)N1. 1} (which are generally QAM
, n, “—
symbols) through the subcarrier set Cmi = {fn,,;0, - -- , fW-Ni 1}. User i’s transmit-
u-

ted signal at the nth OFDM symbol can then be written as:

i

5%): Z ufi,lej2”f""l‘- (4.3)
[=0

Note that each user does not transmit on subcarriers which are not assigned to them,
by setting the symbols to zeros over thase subcarriers. This process ensures collision~

free transmission among the users.

4.2.2 Signal Detection

At the receiver, the received signal is a superposition of the signals transmitted from

all users
M—l .
r(t) = Z r5905) + n(t), (4.4)
where
rile) = stile) * not). (4.5)

and n(t) is the additive noise. In (4.5), h,(t) is the channel impulse response corre-
sponding to user i. Note that in OFDM systems, guard intervals are inserted between
symbols to eliminate intersymbol interference (181), so it is reasonable to study the
signals in a symbol-by-symbol manner. Equations (4.3)-(4.5) represent an uplink

system. The downlink system can be formulated in a similar manner.

54

As is well known, the OFDM transmitter and receiver is implemented through
IFFT and FFT, respectively. Denote the NC x 1 symbol vector corresponding to user
i’s nth OFDM symbol as 1152 ), we have

7. . .
Ufa)” IE {20,--- ”Nil-'1}.

“$100): { 0,. l¢ {i0,. .. ,iN&_1} (4.6)

Let Ts denote the OFDM symbol period. The discrete form of the transmitted signal
3g)(t) (sampled at $3) is
52') = Fug), (4.7)

where F is the IFFT matrix defined as

 

00 0(Nc-1)
1 WNc WNc
F: - -. '
N . . 3
V c WIch-im Wch—nmc—i)
C C

with WE]; = ejzmk/NC. As we only consider one OFDM symbol at a time, for
notation simplification, here we omit the insertion of the guard interval (i.e. the

cyclic prefix which is used to ensure that there is no 181 between two successive
OFDM symbols).
Let h, = [hi(0), - - - ,hz-(Nc — 1)] be the discrete channel impulse response vector,
and let ‘
H,- = th- (4.8)

be the Fourier transform of h. Then the received signal corresponding to user i is

149(1) = ufi)<z)H.-<z). (4.9)

55

The overall received signal is then given by
rn(l) = 1:: rn (”(1) + Nn( (z) (4.10)

M..—
= 231W" H,,,-(l)+N (l). (4.11)
2':
where Nn(l) is the Fourier transform of the noise corresponding to the nth OFDM
symbol.

Note that due to the collision-free subcarrier assignment, for each I, there is at
most one non-zero item in the sum Mil u(2)(l l).H,-(l) As a result, standard channel
estimation algorithms and signal detegtion algorithms for OFDM systems can be
implemented. In fact, each user can send pilot symbols on its subcarrier set to
perform channel estimation. It should be pointed out that instead of estimating the
whole frequency domain channel vector Hi, for signal recovery, user i only need to
estimate the entries corresponding to its subcarrier set, that is the values of Hi(l) for
l 6 {i0, - -- ,i N13. _1}. After channel estimation, user i’s information symbols can be

estimated from

 

. (i)
(i) _ rn (l) . .
“11 (l) .- H2(l) 1 le {20’ . . . ,2N3_1}' (4'12)

It is also interesting to note that we can obtain adequate channel information from
all the users simultaneously, which can be exploited for dynamic resource reallocation

to achieve better BER performance and real-time jamming prevention.

4.3 The Subcarrier Assignment Algorithm and Its
Limitations

In this section, we briefly discuss the recently proposed subcarrier assignment algo-

rithm [66, 67].

56

4.3.1 The Subcarrier Assignment Algorithm

The secure subcarrier assignment is described in the following steps.
Step 1 A pseudo-random binary sequence is generated using a 42-bit linear
feedback shift register (LFSR), which is initialized by an initialization vector to ensure

randomness. The LFSR has the following characteristic polynomial:

$42 +$35 +$33 + $31 +3227 + $26 +1.25

+$22 +3:21 +2:19 +$18 + $17 + 11:16

+xm+x7+x6+x5+x3+$2+x+L (4.13)

Assuming that the total number of subcarriers is K = 128, the sequence output
is grouped into blocks of length 128 bits. The kth block is denoted as X k and is used
to generate the subcarrier index for the kth OFDM symbol.

Step 2 The AES algorithm is used to encrypt the plaintext X k with a specify
128-bit key. The resulting 128-bit ciphertext is denoted as {pc0,pc1, - -- ,pc127}.

Step 3 Each subcarrier position is represented by log2(128) = 7 bits. A 1 x 134
vector is formed by cyclic padding [pc0,pc1, - -- ,pc127,pc0,pc1, - - - , pC5]. The vector
is then divided into 128 7-bit groups:

[pco,p61.--- ,pcsl.[p61.p02,--- .pC7]--- ,[P0127.pco.-~ .1965]-

Step 4 For i = O, 1, - -- , 127, denote P(i) as the decimal number corresponding
to the ith 7-bit vector, such that

P(i)

6 5
pci ' 2 +chi—l mod 128) ' 2

4 3
PC(2'+2 mod 128) '2 +PC(2'+3 mod 128) '2

2 1
PC(z'+4 mod 128) '2 +PC(z'+5 mod 128) '2

+++

0
pc(i+6 mod 128) '2 -

Note that vector P = [P(0) P(1)--- P(127)] does not necessarily contain all the

57

numbers from O to 127 and may contain repeated numbers. To replace the repeated

numbers with the missing numbers:

a) Stack all of the M missing numbers in matrix P from 0, 1, - -- ,127 into a vector

A such that A = [A(O),A(1), - ~ ,A(M —1)].

b) Find the index of each repeated number in P and stack them to formulate a vector
B, such that B = [B(O),B(1), - - - ,B(M — 1)]. Note, the length of A is equal
to B.

c) For j = O, 1, - - - ,M — 1, substitute A(j) for the B(j)’s entry in P. The updated
vector P contains all the numbers from 0 to 127 and each number occurs only

once.

Finally, assign the subcarriers with indexes {P(O), P(l), - ~- ,P(N1 — 1)} to user
0, assign the subcarriers with indexes {P(Nl), - -- , P(N1 + N2 — 1)} to user 1 and so
on. Recall that, for user i = 0,1 - -- ,U — 1, the total number of subcarriers assigned

to the ith user is N,-.

4.3.2 Limitations of The Subcarrier Assignment Algorithm

Although the concept of the recently proposed subcarrier assignment algorithm is
innovative, the recently proposed scheme has numerous limitations. The primary
drawback of the recently proposed scheme materializes in Step 3 of the secure sub-
carrier assignment algorithm, where additional bits are appended to the ciphertext
bit vector via cyclic padding. The cyclic padding operation introduces bit redundancy
and eliminates bit independence and the strong security properties of the ciphertext
bit vector. Furthermore, in Step 3 the overlapping partition of the ciphertext bit
vector creates strong correlation between partitions.

Another limitation of the recently proposed subcarrier assignment scheme is the
replacement algorithm in Step 4. Simply replacing the repeated numbers with the

missing numbers does not guarantee a secure subcarrier assignment. For example,

58

the strong correlation between the partitions in Step 3 can result in many repeated
numbers, leading to a sequential non-random subcarrier allocation.

In all, the secure subcarrier assignment algorithm recently proposed is clever, but
lacks strong security properties due to the cyclic padding and overlapping partition
of the ciphertext bit vector. Furthermore, the replacement algorithm in Step 4 can
lead to non-random subcarrier allocation.

In the following section, we introduce a new subcarrier assignment scheme based
on the secure permutation algorithm. The new subcarrier assigmnent scheme en-
hances the security features of the previous subcarrier assignment algorithm and

possess strong cryptographic properties.

4.4 Secure Subcarrier Assignment Based on Se-
cure Permutation

In this section, we present the proposed secure subcarrier assignment scheme [68,69],
for which the major component is an AES based secure permutation algorithm. AES
is chosen because of its simplicity of design, variable block and key sizes, feasibility
in both hardware and software, and resistance against all known attacks [74]. Note
that, the secure subcarrier assignment is not limited to any particular cryptographic
algorithm, but is highly recommended that only thoroughly analyzed cryptographic
algorithms be applied.

The ABS-based permutation algorithm is used to securely select the frequency
hopping pattern for each user so that: (1) Different users always transmit on non-
overlapping sets of subcarriers; (ii) Malicious users cannot determine the frequency
hopping pattern and therefore cannot launch follower jamming attacks.

We assume there is a total of NC available subcarriers and there are M users in

the system. For i = 0,1,--- , M — 1, the number of subcarriers assigned to user i is

denoted as N3. We assume that different users transmit over non-overlapping set of
M —1

subcarriers and we have 2: N; = NC. The secure subcarrier algorithm is described
i=0

59

in the following subsections.

4.4.1 Secure Permutation Index Generation

A pseudo-random binary sequence is generated using a 32-bit linear feedback shift
register (LFSR), which is initialized by a secret sequence chosen by the base station.
The LFSR has the following characteristic polynomial:

$32 +$26 +2:23 +1.22 +$16 +2712 +2:11

+rlo+18+x7+15+x4+xz+x+L (4.14)

Use the pseudo-random binary sequence generated by the LFSR as the plaintext.
Encrypt the plaintext using the AES algorithm and a secure key. The key size can
be 128, 192, or 256. The encrypted plaintext is known as the ciphertext. Assume
Nc is a power of 2, pick an integer L 6 [9,25, NC]. Note that a total of Nb = logch
bits are required to represent each subcarrier, let q = Llogch. Take q bits from the
ciphertext and place them in a q—bit vector e = [61, 62, - - - , eq].

Partition the ciphertext sequence e into L groups, such that each group contains
Nb bits. For k = 1, 2, - - - , L, the partition of the ciphertext is as follows

pk : [B(k—I)*Nb+1’ e(k—1)*Nb+21 ' ° ' v e(k—1)*Nb+Nb]a (4-15)

where pk corresponds to the kth Nb-bit vector.
For k = 1,2, - - - ,L, denote Pk as the decimal number corresponding to pk, such

that

__ N—l N—2
Pk — C(k—1)*Nb+1'2 b +e(k—1)*Nb+2'2 b
l
+ "‘+e(k—1)*Nb+Nb—1'2

O
+ 6(k_1)*Nb+Nb ° 2 . (4.16)

Finally, we denote P = [P1, P2, - -- ,PL] as the permutation index vector. Here

60

the largest number in P is NC — 1. In the following subsection, we will discuss the

secure permutation algorithm.

4.4.2 Secure Permutation Algorithm and Subcarrier Assign-

ment

For k = 0, 1,2, . - - , L, denote 1k = [Ik(0), Ik(1), - -- , Ik(NC— 1)] as the index vector at
the kth step. The secure permutation scheme of the index vector is achieved through

the following steps:

0. Initially, the index vector is Io = [10(0), 10(1), - - - ,IO(NC — 1)] and the permu-
tation index is P = [P1,P2, - -- , PL]. We start with IO = [0,1, - -- ,Nc -1].

1. For k = 1, switch 10(0) and I0(P1) in index vector ID to obtain 11. In other
words, 11 = [11(0),11(1), ,11(Nc-1)l, where 11(0) = 10(1’1). 11(P1) = 10(0),
and 11(m) = [0(m) for m 75 0, P1.

2. Repeat the previous step for k = 2,3, - -- ,L. In general, if we already
have Ik_1 = [Ik_1(0),Ik_1(1),--- , Ik_1(Nc - 1)], then we can obtain Ik =
[Ik(0),Ik(1), - -- , Ik(Nc — 1)] through the permutation defined as Ik(k — 1) =
Ik—1(Pk),1k(Pk)-'= Ik—1(k - 1), and Ik(m) = Ire-1071) for m 79 ’6 -1,Pk-

3. After L steps, we obtain the subcarrier frequency vector as F L = [fIL(0)’
fIL(1)» ' " ,fIL(NC—1)l-

4. The subcarrier frequency vector F L is used to assign subcarriers to the users.
Recall, for user i = 0, 1 - - - ,M — 1, the total number of subcarriers assigned to

the ith user is N3. We assign subcarriers {fIL(0) ,fIL(1),--- ’fIL(N0—1)} to
u

user 0; Ass1gn {fIL(N,9)’ fIL(N29+1)’ . .. ’fIL(N3+Nzi-1)} to user 1, and so on.

Proposition 1 The proposed secure subcarrier assignment scheme ensures non-

ouerlapping transmission among all the users in the system.

61

Proof: In fact, after L steps, we obtain the subcarrier frequency vector as

FL = [fIL(0)’ fIL(1),-~ ’fIL(Nc-1)]' We can rewrite the subcarrier frequency
vector FL as FL = [FL(0),FL(1),--- ,FL(NC — 1)] by defining FL(j) = fILU)
for j = 0,1, - -- ,Nc — 1, where NC is the total number of subcarriers. Assume

that we have M users in the system, and for i = 0,1--- ,M - 1, the total num-
ber of subcarriers assigned to the ith user is N5. The subcarrier assignment pro-
cess described in step 4 of the secure subcarrier algorithm above is equivalent to
assigning subcarriers {FL(0),FL(1),--- ,FL(N3 — 1)} to user 0, and subcarriers
{FL(N3),FL(N3 + 1), - -- ,FL(N3 + N,] — 1)} to user 1, and so on.

Because each frequency index appears in FL once and only once, the proposed
algorithm ensures that: (i) All the users are transmitting on non-overlapping sets of
subcarriers; (ii) No subcarrier is left idle. That is, all the subcarriers are active. [3

The secure permutation algorithm is performed at the base station. The base
station sends encrypted channel assignment information to each user periodically
through the control channels. Details of how the base station transmits the channel
assignments to each user is provided in Section 4.4.3.

The proposed scheme addresses the problem of securely allocating subcarriers
in the presence of hostile jamming. This algorithm can be combined with existing
resource allocation techniques. First, the number of subcarriers assigned to each
user can be determined through power and bandwidth optimization, see [34, 75], for
example. Then, we use the secure subcarrier assignment algorithm to select the group
of subcarriers for each user at each hOpping period. In the following, we illustrate the
secure subcarrier assignment algorithm though a simple example.

Example: Assume the total number of available subcarriers is Nc=8, to be
equally divided among M =2 users; the permutation index vector P = [4, 7, 4, 0], and
the initial index vector 10 = [0, 1, 2,3,4, 5, 6,7], as shown in Fig. 4.1. Note that, the
initial index vector 10 can contain any random permutation of the sequence {0, 1, - . -
,NC — 1}, and L E [N20,NC]. In this example, we choose L = 9,29.

At Step 1, k = 1, and Pk = 4, thus we switch 10(Pk) and 10(k — 1) of the index

vector IO. After the switching, we obtain a new index vector 11 = [4, 1, 2, 3, 0, 5, 6, 7].

62

Step 0:

Step 1:

Step 2:

Step 3:

Step 4:

l2-

l3-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o1|2|3|4 5 6|7

A4

L11[2]3 o 5 5|7
‘\. /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:7 2|3|o 5 6|‘1_]
j\_—/’/
- "if/K}
4|7 o 3 2|5|51
5. ,/
,_ \w/
/ \‘a -
3 7 o 4|2 5 6|1|
>\ / *’

remaining index vectors for k = 3, 4:

Figure 4.1. Example of the Secure Permutation Algorithm for NC=8 subcarriers and
M =2 users.

At Step 2, k = 2, and Pk = 7, thus we switch [1(Pk) and 11(k — 1) of the index
vector I1. We obtain the new index vector 12 = [4, 7,2, 3,0, 5,6, 1]. Below are the

[3 = [4, 7,0, 3,2,5,6, 1], I4 = [3, 7,0, 4, 2,5,6, 1].

63

The subcarrier frequency vector is F4 = lfI4(O)v fI4(1)1 - -- , fI4(Nc—1)l- Frequencies
{ f3, f7, f0, f4} are assigned to user 0 and frequencies {f2, f5, f5, f1} are assigned to

 

 

 

Assifgrhngt X Encryption Y Encryption Z Decryption Y Decryption X SuhcarrierrIt
Information Algorithm Algorithm Algonthm Algonthm Information

 

 

 

 

 

 

 

 

 

 

PRU ]*

  

 

 

 

Figure 4.2. Public/Private Key Cryptosystem

4.4.3 Secure Subcarrier Assignment Distribution

In this subsection, we will discuss how the subcarriers assignments are distributed to
the users. Recall that the secure permutation algorithm is performed at the based sta-
tion and the subcarrier assignment information is encrypted then transmitted through
a control channel to the users.

The channel assignment information is securely transmitted to each user through
a public/private key cryptosystem. The public/private key cryptosystem is known
as an asymmetric algorithm, where one key is used for encryption and a different,
but related key is used for decryption. Typically, the public key (stored at a public
register) is used to encrypt messages, and the private key is used to decrypt the
message. The public and private key pair are generated by a cryptographic algorithm
developed by Ron Rivest, Adi Shamir, and Len Adleman, which is known as the RSA
algorithm [76].

Figure 4.2 is a depiction of the secure public/ private key cryptosystem algorithm
for the subcarrier assignment distribution. First, the subcarrier assignment infor-

mation (X) is encrypted with the private key of the base station denoted as PRbs.

64

Second, the following ciphertext (Y) is encrypted again using the public key of the
user denoted as PUu. Third, the ciphertext generated from the second encryption
(Z) is transmitted through the control channel to the appropriate user. Fourth, the
transmitted ciphertext Z is decrypted with the user’s private key (PR/u), resulting in
ciphertext Y. Fifth, the ciphertext Y is decrypted with the base station’s public key
(PUbs), resulting in the original subcarrier assignment information.

Note that in the secure public/ private key cryptosystem algorithm, the first en-
cryption process provides a digital signature (ensures subcarrier assignment infor-
mation is from authorized base station) and the second encryption process provides
confidentiality. Also, the transmitted ciphertext Z can only be decrypted by the in-
tended user who has the matching private key. Finally, the encryption algorithm in
the public / private cryptosystem is not limited to any particular encryption algorithm,
but is highly recommended that only thoroughly analyzed cryptographic algorithms
be applied.

4.5 Secure Space-Time Coded Collision-Free Fre-
quency Hopping

In this section, we enhance the anti-jamming features of the CFF H scheme by using
space-time coding. Here we present the transmitter and receiver design of the pro-
posed STC—CFF H system from the downlink perspective. The uplink can be designed

in a similar manner.

4.5.1 Transmitter Design

We assume that during each hopping period, the number of subcarriers assigned to
each user in the CFFH system is fixed. Recall that one hopping period may contain
one or more OFDM symbol periods. In the following we illustrate the transmitter
design over one OFDM symbol.

Assume the transmitter at the base station has nT antennas and there are M

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Input Bits Symbol SPace'
—-> Mapper—7 Time
Encoder
Secure
—’ Subcarrier *
Key Assignment

 

 

Figure 4.3. Block diagram of the STC—CFFH transmitter.

users in the system. Over each OFDM symbol period, the ith user is assigned N3,
subcarriers, which do not need to be contiguous. The transmitter structure at the
base station is illustrated in Fig.4.3.

Initially, the input bit stream corresponding to each user is mapped to symbols
based on a selected constellation. The constellation could be different for different
users based on the channel condition and user data-rate [77,78]. Assume the base
station uses a nT x nT space-time block code (STBC). Note that non-square STBC
codes [43,45] exists, but for notation simplicity, here we adopt the nT x w; square
code. For each user, divide the N3, subcarriers into G,- = g}: groups, where each
group contains nT subcarriers, which is of the same length as that of the STBC. For
simplicity, we assume G,- is an integer, that is, each user transmits G,- space-time
blocks in one OFDM symbol period. (Otherwise, if G,- is not an integer, the symbols
can be broken down and transmitted over two successive OFDM symbol periods.)

For each n 6 {1,2, - - . ,Gi}, the base station takes a block of nT complex symbols

and maps them to a nT x nT STBC code matrix X;(n). In other words, for n =

66

1,2,--- ,Gi, m = 1,2,--- ,nT, the mth row of the code matrix Xi(n) is merged
with the corresponding symbols from other users and transmitted through the mth
transmit antenna, and all symbols within each column (m = 1, 2, - - - , nT) of the code

matrix X ,- (n) is transmitted over the same subcarrier. The code matrix Xi(n) is given

by

Subcarrier —->

"5.1 n 1.1 n
"1] ) ”"74 ) (4.17)

X;(n) = , ; l Antenna ,
913%) 42W-

 

 

where $2; (n) is the tth symbol of the nth block for user i in transmit antenna m.

Note that, since each user is assigned multiple frequency bands, we are transmit-
ting symbols over multiple subcarriers instead of multiple time slots. Thus the time
diversity of the space-time coder is converted to frequency diversity and this structure
is referred to as space-frequency coding [7 9].

STC-CFFH Transmitter Design Example: We provide an example to illus-
trate the transmitter structure of STC-CFFH, in which the subcarrier assignment is
based on the example in Section 4.4. Assume an Alamouti space—time coded system
with nT=2 and we have M =2 users. A total of Nc=8 subcarriers are available and
each user is assigned N3 = N3 = 4 subcarriers. For this example, each user transmit
G,- = {71411: = 2 code matrices in one OFDM symbol period. Consider the nth block
for the ith user, where n = 1, 2 in this case. The space-time encoder takes nT=2
complex symbols x;,1(n), $27.2 (n) in each encoding operation and maps them to the
code matrix X;(n). In this example, the first and second column of X;(n) will be
sent from the first and second transmit antenna, respectively.

In this example, we can drop the superscript m in 2:3 (n) by representing X,- (n)

with the Alamouti space-time code block structure [42]. Then the code matrices

67

Table 4.1. STC—CFFH Transmitter Example.

 

 

 

 

 

T, fie" f0 f1 f2 f3 f4 f5 f6 f7
1 $0,1(1) $1,1(1) -$I,2(1) —$B,2(1) 3301(2) 171,1(2) -$i,2(2) -$6,2(2)
2 442(1) 442(1) 411(1) 45,10) 442(2) 242(2) 411(2) 4332)

 

X;(n) are given by

Subcarrier —>
$4,1(n) —x;{2(n) (4.18)

Xi(n) = l Antenna,
3:32 (n) 517:1(77')

where * is the complex conjugate Operator. Specifically, User 0’s two code matrices
are represented as

$0,1(1) ’13,2(1) X0(2)= 3011(2) —a:5,2(2) (4.19)

X00) =
3302(1) 136,10) 5502(2) 1364(2)

and user 1’s two code matrices are represented as

$1,1(1) “5512(1) X1(2)= 1313(2) —:1:’1‘,2(2) .
$1,2(1) $i,1(1) 2312(2) ati,1(2)

X1(1) = (4.20)

Recall that the secure subcarrier assignment from the example in Section 4.4.
User 0 is assigned to subcarriers {f0, f3, f4, f7}. User 1 is assigned to subcarriers
{f1, f2, f5, f6}. A depiction of the subcarrier allocation for this example is provided
in Table 4.1.

For user 0, [$0,1(1),—x3’2(1),x0,1(2),—x6’2(2)] is transmitted through antenna 1
over subcarriers {f0, f3, f4, f7}, respectively; [$0,2(1)v$3,1(1)1 $0,2(2),x5,1(2)] is trans-
mitted through antenna 2 over the same group of subcarriers. User 1’s subcarrier

allocation can be achieved in the same manner as User 0.

68

4.5.2 Receiver Design

Assuming user i has n R antennas. Recall that the secure permutation index gener-
ation is performed at the base station and the base station sends encrypted channel
assignment information to each user periodically through the control channels. Af-
ter cyclic prefix removal and FFT, the receiver will only extract the symbols on the
subcarriers assigned to itself and discard the symbols on the rest of subcarriers. The
extracted symbols are reorganized into a n R x nT matrix R,- (n), which corresponds to
the transmitted code matrix X; (n) Thus the space-time decoding can be performed
for each symbol matrix R,-(n) individually and the estimated symbols are mapped
back into bits by the symbol de-mapper.

Here we consider the space-time decoding algorithm for a single symbol matrix

R;(n) given as

Subcarrier —>

' 1 .1 '
74,102) ri,nT(n) , (421)
R;(n) = E E J, Antenna
n
12%) 4.5.471)-

 

 

where r: t(n) is the tth symbol of group n for user i from jth receive antenna. Each
symbol in the matrix R;(n) can be obtained as
. "T . .
737$(n) = Z Hg,’tm(n)let(n) + ng,t(n), (4.22)

m=1

where H 23, ’tm (n) is the channel frequency response for the path from the mth transmit
antenna to the jth receive antenna corresponding to tth symbol of group n for user
i. It is assumed that the channels between the different antennas are uncorrelated.
Here, "it (n) is the OFDM demodulated version of the additive white Gaussian noise
(AWGN) at the jth receive antenna for tth symbol of the nth group for ith user. The

noise is assumed to be zero—mean with variance 012V:

69

Table 4.2. STC-CFFH Receiver Example.

 

 

 

 

R1 freq. f0 f1 f2 f3 f4 f5 f6 f7
1 r6,1(l) r],1(l) r1,2(l) r620) 111,1(2) r],1(2) r],2(2) 162(2)
2 rg,1( 1) rilfl) rig 1) r312( l) r3119) Til (2) ri2(2) r3129)

 

 

The space-time ML decoder is obtained as

. "R "T
X4(n)=arg)r{rijg)zz r}.(n)- f: 11me (n) . (4.23)
z j=1

t=1
where X,(n) denotes the recovered symbols of group n for user i. Note that the
minimization is performed over all possible space-time codewords.
STC-CFFH Receiver Design Example: We continue with the transmitter
example in the previous subsection. Assuming each user is equipped with n R = 2
receive antenna, the received symbols are illustrated in Table 4.2. Arranging the

extracted symbols according to the users and the groups, the extracted symbol matrix

R;(n) is given as

Subcarrier —>

1 1
T2101) r;,2(n) [Antenna (4.24)
73,101) Ti,2(")

111-(n) =

Specifically, User 0’s two extracted symbol matrices can be represented as

7‘1 (1) 7‘1 (1) T1 (2) 7’1 (2)
RO(1) = 0,1 0,2 , R0(2) = 0,1 0,2 , (4.25)
rg,1(1) r330) r(2)’1(2) r8,2(2)

70

 

and User 1’s two extracted symbol matrices can be represented as

r],1(1) r],2(1) 121(2): r],1(2) r],2(2)

R1(1)= T¥1(1) T¥2(1) , T%1(2) 7%2(2)

(4.26)
Then, the ML space-time decoding is performed for each R,(n).

Remark: In the discussion above, we focused on STC-CFFH system for the
downlink case, where the information is transmitted from base station to the multiple
users. In the uplink case, the secure permutation index is encrypted and transmitted
from base station to each user, prior to the user transmission. Then during the
transmission, each user only transmits on the subcarriers assigned to them. The
receiver at the base station separates each user’s transmitted data. In order for the

user to use space-time coding, each user needs to have at least two antennas.

4.6 Performance Analysis of Space-Time Coded
Collision-Free Frequency HOpping System

In this section, we investigate the spectral efficiency and the performance of the
proposed schemes under jamming interference over frequency selective fading envi-
ronments. First, the system performance in jamming-free case is analyzed. Second,
the system performance under hostile jamming is investigated. Finally, the spec-
tral efficiency comparison of the proposed schemes and the conventional FH-OFDMA

system is performed.

4.6.1 System Performance in J amming-Free Case

First, we analyze the pairwise error probability of the STC—CFFH system under
Rayleigh fading. Assume ideal channel state information (CSI) and perfect synchro-
nization between transmitter and receiver. Recall that the ML space-time decoding

rule for the extracted symbol matrix R,(n) is given by (4.23).

71

 

 

Denote the pairwise error probability of transmitting X,- (n) and deciding in favor
of another codeword X,(n), given the realizations of the fading channel Hi’tm (n), as
P(X,-(n),X,-(n)|HzJ,’tm(n)). This pairwise error probability is bounded by [80] (see
page 255)

P(X.(n)X “.-(n)IH3;.’" (n>> < exp(—d (X. (n) X.- (71))5’33) (4.27)

where E, is the average symbol energy, N0 is the noise power spectral density, and
d2 (X,- (n), X,(n)) is a modified Euclidean distance between the two space-time code
words X,(n) and X,(n), and is given by

2
, (4.28)

nTnR

d2(X,-( (n), X,(n )=ZZ

t=1j=1

2H {73;an ($th 7“) $301))

m=l

 

 

where 533m) is the estimated version of xzun).
Let us define a codeword difference matrix C (X,- (n), X,- (n)) = X,(n) — X,(n) and
define a codeword distance matrix B(X,(n), X,(n)) with rank r3 as

B(X.(n>.X.-(n)) = C(X.(n). X.(n>) -C(X.-(n). X.(n>)H. (4.29)

where H denotes the Hermitian operator. Since the matrix B(X,(n),)f,-(n)) is a
nonnegative definite Hermitian matrix, the eigenvalues of B(X,(n),X,-(n)) are non-
negative real numbers, denoted as A1, A2, - - ~ ,ATB.

After averaging with respect to the Rayleigh fading coefficients, the upper bound

of pairwise error probability can be obtained as [39]

TB —nR
P(X,(n),X 31101)] g’thl) S (H (1+Aj4%i0))

j=1
TB —nR —anR
(1131 A3“) (560) . (4.30)

In the case of low signal-to—noise ratio (SNR), the upper bound in (4.30) can be

l/\

72

expressed as [80],

. r -"R
P(X.(n>,X.-(n)IH3;.’"(n» s (Ha-335:3.) . (4.31)

4.6.2 System Performance Under Hostile Jamming

In this subsection, we will first introduce the jamming models, and then analyze the

system performance under both full-band jamming and partial-band jamming.

J amming Models

J amming interference in the OFDM framework can severely degrade the system per-
formance [81]. Each extracted symbol in the matrix R,(n) that experiences jamming
interference is given as
. "T . . .
1,7,0.) = Z Hg’}m(n)x$(n) + n{,t(n) + 13,03), (4.32)

m=1

where Jijt(n) is the jamming interference at the jth receive antenna for tth symbol
of the nth group for ith user. Assume all jamming interference Jijt(n) has the same
power spectral density N J, then the signal-to-jamming plus noise ratio (SJNR) at
the receiver is represented by SJ NR = fl. When the noise is dominated by

J
jamming, the SJNR can be represented as the signal-to-jamming ratio (SJR) where
_ E
SJR — NJ'

Partial-band jamming [18—20] is generally characterized by the additive Gaussian
noise interference with flat power spectral density 9—2-1 over a fraction p of the total
bandwidth and negligible interference over the remaining fraction (1— p) of the band.

p is also referred to as the jammer occupancy and is given as

W J
= —- < o

73

where W J is the jamming bandwidth and W3 is the total signal bandwidth. For
CFFH, partial-band jamming means that the jamming power is concentrated on a
certain group of subcarriers. Let n J denotes the number of jammed subcarriers, then
the jamming ratio p is given by p- — 51' For a particular code matrix X,-(n), this
means that on average, pnT subcarriers are jammed out of nT subcarriers used by
X,- (n)

When p = 1, the jamming power is uniformly distributed over the entire band-
width. In this case, the partial-band jamming becomes full-band jamming [16, 17].
For a CF FH system, full-band jamming means that the jamming power is uniformly
distributed over all NC.

System Performance Under Rayleigh Fading and Full-Band Jamming

In the presence of Rayleigh fading and full-band jamming, the pairwise error probabil-
ity can be expressed in terms of the jamming power spectral density N J and average
signal power E3. In the case of high SNR, the upper bound in (4.30) can be expressed

as
._nR

. TB
p(x.(n),X.(n>(H3,3"(n»s HA4 (4%)
j=1

'—T n
B R. (4.34)

From (4.31), the upper bound in the presence of Rayleigh fading and full-band

jamming can be expressed as

P(X,(n),X ,(n)|Hgm(n))< 1+Z—(N—qu—SZM. (4.35)

As will be confirmed in Section 5.7: For the STC—CFFH system, at low SJNR, the
space-frequency diversity gain is low; however, at high SJ NR, the diversity gain be-

comes noticeable.

Under Rayleigh Fading and Partial-Band Jamming

Recall that each column of the received symbol matrix R,(n) is obtained from the

same subcarrier in all received antennas. When we have partial-band jamming, most

74

likely not all columns of R;(n) are jammed, since each column is transmitted though
different subcarriers. Thus the receiver may be able to recover the transmitted signal
relying on the jamming-free columns.

Orthogonal space-time codes (OSTC) are capable of perfectly decoding the trans-
mitted symbols under partial-band jamming and noise-free environments when at
least one frequency band is not jammed. We consider a nT = 4 space-time orthog-
onal block code design as an example. Following the same notation convention in
the STC—CFFH transmitter example in Section 4.5, the code matrix with transmit
symbols xi,t(n) for t = 1, 2, 3, 4, is represented as
r $4,101) $4,200 $4,300 $4,4(n) -
-$i,2(n) $4,1(n) -$i,4(n) $47,301)
--’Di,3(n) $4,400 $4,101) -$i,2(n)

(

_-$i,4 n) -$i,3(n) $4,201) $4,1(nld

(4.36)

 

 

Due to the orthogonality of the code design, each frequency band contains full in-
formation about the transmitted symbols. As a result, the transmitted symbols are
recovered perfectly when there is at least one un-jammed frequency band.

In this case, the average probability of error Pe can be expressed as

4
P6 = ZPCJ Pr{z' out of 4 bands are jammed}, (4.37)
i=0

where P6,,- is the probability of error when 2' out of 4 bands are jammed.

4.6.3 Spectral Efficiency

One major challenge in the current FH-OFDMA system is collision. In FH—OFDMA,
multiple users hop their subcarrier frequencies independently. If two users transmit
simultaneously in the same frequency band, a collision, or hit occurs. In this case,
the probability of bit error is generally assumed to be 0.5 [82].

If there are NC available channels and M active users (i.e., M — 1 possible inter-

75

fering users), assuming that all NC channels are equally probable and all users are
independent. Even if each user only transmit over a single carrier, then the probability

that a collision occurs is given by

1 M—1
- - 1 when NC is large. (4.39)

 

C

Taking NC = 64 as an example, the relationship between the probability of collision
and the number of active users is shown in Figure 4.4. The high collision probability

severely limits the number of users that can be simultaneously supported by an FH-

OFDMA system.

 

 

 

 

 

 

 

 

 

10 . , ‘ . 1
C
.9
g
8
'5 -1 _
3.? 10 :
IE .
(O
In .
2 l
a

+ Empirical results
2 —9— Theoretical values
1 0- l l l l l
0 10 20 30 4O 50 50

Number of users

Figure 4.4. Probability of collision (Ph) versus the number of users (starting at the
two—user case) for NC = 64.

76

In this example, NC = 64, for a required BER of 0.04, only 6 users can be sup-
ported. That is only 6 out of 64 subcarriers can be used simultaneously, the carrier
efficiency is 6%— = 9.38%. On the other hand, due to the collision-free design, CFFH
has the same spectral efficiency and BER performance as that of OFDM. For CFFH,
the carrier efficiency is 100% with a much better BER performance. In this particular
case, CFFH is approximately 10.67 times more efficient than the conventional FH-
OFDMA system. This fact is further illustrated in simulation example 1 of Section
4.7.

4.7 Simulation Examples

In this section, we provide simulation examplas to demonstrate the performance of the
proposed schemes. First, the bit—error performance of the proposed CFF H scheme,
the conventional FH and FH—OFDMA systems is performed under AWGN channels.
Second, the bit-error performance of the proposed CFFH and STC-CFFH schemes,
and the STC-OFDM system is performed over a frequency selective fading channel
with partial-band jamming.

Simulation Example 1: We consider the conventional FH, the FH-OFDMA
and the proposed CFFH systems, each with M=8 users and Nc=128 available sub—
carriers. The conventional FH system uses four frequency shift keying (4—FSK) mod-
ulation, where each user transmits over a single carrier. Both the proposed CFFH
and FH—OFDMA systems transmits 16-QAM symbols, and each user is assigned 16
subcarriers. The average bit error rate (BER) versus the signal-to-noise ratio (SNR)
performance over AWGN channels of the systems is illustrated in Fig. 4.5. As can be
seen, the proposed CFF H scheme delivers excellent results since the multi—user access
interference (MAI) is avoided. The conventional FH and FH-OFDMA schemes, on
the other hand, is severely limited by collision effect among users.

Simulation Example 2: The BER performance of the STC-OFDM scheme and
the proposed STC—CFFH and CFFH schemes are evaluated by simulations. The

simulations are carried out over a frequency selective Rayleigh fading channel with

77

 

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

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

Bit Error Rate

    

 

i I i . . —9— Conventional FH ' I :

—5 —9— FH-OFDMA

 

 

 

 

 

 

4 6
SNR (dB)

Figure 4.5. BER performance over AWGN channel of the CFFH, FH—OFDMA, and
the conventional FH systems with M=8 users and N62128 available subcarriers.

partial-band jamming. An Alamouti space-time coding system with two transmit
and receive antennas is applied to the proposed STC-CFFH system. We assume
perfect timing and frequency synchronization, as well as uncorrelated channels for
each antenna. The total number of available subcarriers is Nc=256 and the number
of users is M=16; therefore each user is assigned 16 subcarriers.

We consider the performance of three systems that transmits 16—QAM symbols:
(i) The proposed CFFH system; (ii) An STC—OFDM system; (iii) The proposed STC-
CFFH system. For system (ii), each user transmits on 16 fixed subcarriers. In systems
(i), and (iii), each user transmits on 16 pseudo-random secure subcarriers. We assume
the jammer intentionally interferes 16 subcarriers out of the whole band.

Figure 4.6 depicts the BER versus SNR over frequency selective fading with

78

SJ R=0dB. The STC—OFDM system outperforms the CFFH scheme due to the lack
of space—time diversity. Incorporating space-time coding into CFFH significantly in-
creases the BER performance. The combination of the secure subcarrier assignment
and space-time diversity lead to the proposed STC-CFFH system outperforming the
STC—OFDM system. The pseudo-random secure subcarrier assignment randomizes
each users’ channel occupancy at a given time, therefore allowing for multiple ac-
cess over a wide range of frequencies. We also noticed that at high SN R levels, the
performance limiting factor for all systems is the partial-band jamming.

One method of improving the BER performance is incorporating turbo coding
into the system design. In Figure 4.7, a rate—% turbo code is utilized for forward error
control. The generation matrix of the constituent code is given by [1, (gig—2h where
(7 )octal and (5)0ctal are the feedback and feedforward polynomials with memory
length 2, respectively. At the receiver, tentative soft decisions are made by the symbol
demodulation, and then the resulting log-likelihood ratios (LLRs) of the code bits are
fed into a turbo decoder. There is no iteration between the demodulator and the
turbo decoder. The decoding algorithm is the canonical log-MAP. The number of
decoding iterations is 5 and no early termination scheme is applied. From Figure
4.7, we observe a significant BER improvement for each system. Furthermore, the
performance limiting of the partial-band jamming is eliminated.

In Figure 4.8, the BER versus the jammer occupancy (p) is evaluated with
SN R=10dB and SJR=0dB for the three systems. Recall the jammer occupancy is
the fraction of subcarriers that experience interference. We can see that the STC-
CFFH system outperforms the other systems for all p < 1. This example shows that
STC—CFFH is very robust under jamming interference.

We also observed that due to the randomness in the frequency hopping pattern, as
well as the fact that the system ensures collision—free transmission among the users,
the performance of the proposed system remains the same as the number of users

varies in the system.

79

2x2. PBJ, SJR = 0dB

 

10 .......... l ............ l ........................ r ............ I ..........
‘ ' ' + STC-CFFH ;:
—{>— STC-OFDM :-

 

 

 

 

Bit Error Rate

 

 

 

 

Figure 4.6. Comparison of the BER over frequency selective fading channel with
partial-band jamming. Number of subcarriers NC = 256, number of users = 16 and
SJR = 0dB.

4.8 Summary

In summary, we introduced a secure collision—free frequency hopping scheme. Based
on the OF DMA framework and the new secure subcarrier assignment algorithm, the
proposed CFF H system can achieve high spectral efficiency through collision-free
multiple access. While keeping the inherent anti-jamming, anti-interception security
features of the PH system, CFFH can achieve the same spectral efficiency as that of
OFDM, and can relax the strict synchronization requirement suffered by the conven-
tional FH systems. Furthermore, we enhanced the jamming resistance of the CFFH
scheme, by incorporating space-time coding to the proposed scheme. Our simulation

experiments demonstrated the superior performance of the proposed schemes in terms

80

 

 

Bit Error Rate

 

    

—>— STC-OFDM --------
CFFH ........

—il(—-- STC-CFFHrl'urbo] ...

>—>—- STC-OFDMrl'urbo]
—l— , CFFHlTurbo]

'5 1 . r r l
5 10 15

 

 

 

 

 

 

 

0
SNR (dB)

Figure 4.7. BER performance with Turbo Coding over frequency selective fading
channel with partial-band jamming. Number of subcarriers NC = 256, number of
users = 16 and SJR = 0dB.

81

 

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

Bit Error Rate

 

  

+ STC—CFFH Ii.
—-A— STC-OFDM ~ ~

 

 

 

 

 

 

'4 1 i 1 1

0 0.2 0.4 0.6 0.8 1

 

Figure 4.8. BER versus Jammer Occupancy over frequency selective fading channel
with partial-band to full-band jamming. Number of subcarriers NC = 256, number of
users = 16, SJR = 0dB and SNR = 10dB.

82

of both spectral efficiency and jamming resistance.

83

CHAPTER 5

Jamming Mitigation Using
Quasi-Orthogonal Space-Time
Block Codes

In this chapter, we investigate the use of quasi—orthogonal space-time block codes
(QO—STBCs) to mitigate jamming noise. Unlike orthogonal space—time block codes,
QO-STBCs are capable of providing full diversity and full-rate transmission for codes
designed for more than two transmit antennas. With QO-STBCs, the orthogonal-
ity of the code is relaxed and by introducing signal constellation rotation into the
QO-STBC design, we can improve the bit error rate performance. First, we derive
analytical expressions for the exact pairwise error probability (PEP) of the QO—STBC
orthogonal frequency division multiplexing (QO—STBC—OFDM) system using the mo-
ment generating function (MGF). Second, we calculate the exact PEP under various
situations, and derive the closed-form expressions and union bound for the bit er-
ror probability (BEP). Third, we compare the numerical results with the simulation
results. Our numerical analysis and simulation results show that union bound is
tight and the QO-STBC—OFDM system is effective in mitigating partial-band noise

jamming.

5. 1 Introduction

Space-time coding [42,43] is an attractive technique to achieve both highly reliable and

spectrally efficient communications. Space-time block codes from orthogonal designs

84

 

 

provide full diversity and simple single symbol decoding at the receiver. However,
full-rate orthogonal space-time block codes (OSTBCs) with complex elements in its
transmission matrix only exist for two transmit antennas, which is the Alamouti
scheme [42].

In an effort to provide full—rate transmission for space—time block codes with
more than two transmit antennas, quasi-orthogonal space-time block codes (QO-
STBCs) [49, 50] were proposed. With the quasi-orthogonal structure, the orthogo-
nality of the code is relaxed to provide a higher symbol transmission rate and the
maximum likelihood (ML) decoding can be done by searching pairs of symbols in-
stead of searching single'symbols in orthogonal designs. The tradeoff for the higher
transmission rate of QO-STBCs is the inability to achieve full diversity. The perfor-
mance of QO—STBCs is better than OSTBCs at low signal-to—noise ratio (SNR), but
worse at high SNR. In other words, the slope of the QO-STBC is not as steep as the
OSTBC because the QO-STBC does not provide full diversity.

In [53,55,56], the authors improve the QO-STBC bit error rate (BER) performance
by introducing signal constellation rotation into the QO-STBC design. In particular,
the constellation rotation QO-STBC [55, 56] proposes that half of the symbols in the
quasi-orthogonal design be chosen from a signal constellation .A and the other half of
the symbols be chosen from a rotated constellation ej‘bA. The constellation rotation
QO—STBC can achieve full diversity and fast ML decoding.

We consider the combination of constellation rotation QO—STBC with orthogonal
frequency division multiplexing (QO-STBC-OFDM) to exploit multipath diversity
and achieve high speed high quality transmissions. However, such systems must
co-exist with various forms of interference to provide reliable communication [83].
Therefore, there is a need for pr0per analytical tools to assess the performance of
QO-STBC-OFDM systems in the presence of partial-band noise jamming. In partial-
band noise (PBN) jamming, the jammer’s total power Jtot is distributed over T
randomly jammed symbol blocks, which are not necessarily contiguous. We define
the jammer occupancy a = T / S as the ratio of the symbol blocks jammed, where S is

the total number of symbol blocks. We assume there is an integer number of symbol

85

 

blocks 8 = Nc/no, where NC is the total number of subcarriers and no is the number
of subcarriers required to transmit one encoded symbol block. The PBN jamming
acts like a Gaussian noise source with zero—mean and the effective jamming power in
any symbol block is J3.

In this chapter, we consider multiple-input multiple-output (MIMO) communica—
tion system that employs a constellation rotated QO—STBC—OFDM and evaluate its
performance under frequency-selective fading and partial-band noise jamming [84].
The exact pairwise error probability (PEP) of the constellation rotated QO-STBC
with quadrature phase—shift keying (QPSK) modulation is derived by using the mo-
ment generating function (MGF). Furthermore, we calculate the PEP under various
situations, and derive the closed-form expressions and union bound for the bit error
probability (BEP). Our numerical analysis and simulation results show that union
bound is tight and the QO-STBC—OFDM system is effective in mitigating partial-
band noise jamming.

This chapter is organized as follows. In Section 5.2, the QO—STBC-OFDM system
model is outlined. In Section 5.3, the code design of the QO-STBC with constellation
rotation is briefly reviewed, and the global minimum Euclidean distance and the
diversity product is analyzed. The pairwise error probability of the QO-STBC—OFDM
system with and without partial-band noise jamming is derived in Section 5.4. The
closed form expressions and the union bound are derived in Section 5.5 and Section
5.6, respectively. Simulation results are provided in Section 5.7. Finally, a summary

is provided in Section 5.8.

5.2 System Model

We consider a QO-STBC-OFDM system with Nt transmit antennas and N,- receive
antennas, which are assumed to be uncorrelated. The total number of subcarriers
NC are distributed over the U = Nc/Nu users such that each user is assigned Nu
subcarriers. Note that each users’ subcarriers need not be contiguous. The data

symbols are modulated with quadrature phase-shift keying (QPSK).

86

Initially, a block of L9 information bits are partitioned into groups of 4 bits which
are transformed into a stream of complex symbols from the QPSK alphabet A. The
resulting complex symbol sequence with elements ak for k = 1, - - - ,L, is parsed into S
blocks of length k0 where La = koS. For 3 = 1, 2, - ~ - , S, we can represent each symbol
block in vector form as as = [ak0(3_1)+1, ak0(3_1)+2, - -- , ak0(s—1)+k0lT- Each block
as is then encoded by a QO-STBC encoder, resulting in a Nt x no block matrix X,
with rate-kO/no. The block matrix X3 = [xm,xm+1, - - - ,xm4_n0_1], where xm =
[$1,m,$2,m, - - - ,ert,m]T and T is the transpose operation. In matrix form, X3 is

represented as

 

X3 = .x'" xm+1 xm+(no-1)l
$1,m $1,m+1 "° $1,m+(n0—1)
$2,m 1‘2,m+1 ' ' ° $2, —1
= . . . "”Fno > , (51>
_th,m thJn-f-l ° . ' th,m+(n0—1)d

 

where rim, is the symbol transmitted from the mth subcarrier of the ith transmitter,

and m = n0(s - 1) + 1 for each S block. Finally, each symbol block X 3 is OFDM

modulated with the no subcarriers and transmitted over independent channels.
After OFDM demodulation with perfect channel state information (CSI), the re-

ceived symbol at the jth receive antenna and mth subcarrier is

Nt
11m = Z $i,mhj,i,m + "yum + Pj.ij,mv (5-2)
i=1
for m = 0, 1, - - - ,Nc — 1, and where hj,i,m is the channel fading coefficient of the mth

subcarrier of the channel between the jth receive antenna and ith transmit antenna,
$2“,m is the symbol transmitted from mth subcarrier of the ith transmit antenna, n M,

is the zero-mean, complex, additive white Gaussian noise (AWGN) with variance 0,2,,

87

 

pj,m is the jammer indicator function defined as

0, No jamming on the mth subcarrier of the jth receive antenna;
pj,m =
1, Jamming on the mth subcarrier of the jth receive antenna,

and 2.73m is the zero—mean, complex, jamming Gaussian noise with variance J3. We
denote the set of symbol blocks that experience jamming as I and the set of symbol

blocks that do not experience jamming as 1".

5.3 Quasi-Orthogonal Space-Time Block Codes
with Constellation Rotation

In this section, we discuss the code design of the QO—STBC with constellation rotation
scheme. In addition, we analyze the performance criteria, namely the global minimum

Euclidean distance d E and the diversity product C.

5.3.1 Quasi-Orthogonal Space-Time Block Code with Con-

stellation Rotation Code Design

We consider the Papadias and Foschini (PF) [51, 53] scheme in our analysis of the
BEP performance in the presence of partial-band noise jamming. The first class of
QO—STBCs [49,50] provides full-rate transmission and outperforms OSTBC at low
SNR levels, but is outperformed by the OSTBC at high SNR levels. The loss in
performance at the high SNR levels is due to QO—STBC’S lack of full diversity. As a
result, the constellation rotation (CR) class of QO-STBCS [53,55,56] were proposed
to provide full-rate and full diversity. Specifically, the constellation rotation scheme
proposes that half of the symbols (3:1 and 2:2) in the quasi-orthogonal design be
selected from a signal constellation set A and the other half of the symbols (x3 and
3:4) be selected from signal constellation ej¢A, where ¢ is the rotation angle. The

PF scheme with rotation angle has the following. code structure

88

 

 

 

:51 11:2 ej¢x3 ej¢x4
X m; -rv‘i‘ (8,3,4)... (€j¢$3)*
PF = . . . (5.3)
63¢:L‘3 —eJ¢x4 —:1:1 2:2
B(ej¢x4)* (ejfx3)* —:c§ —:c’]‘ .

A natural question which arises is what is the optimal rotation angle? In the follow-
ing subsection, we discuss the performance criteria, specifically the global minimum

Euclidean distance and the diversity product.

5.3.2 Global Minimum Euclidean Distance

The first performance criteria for optimizing rotation angle for the QO—STBC with
constellation rotation scheme is the global minimum Euclidean distance.

Lets consider the symbols 9:1 and :33 which are selected from constellation A and
ej¢A, respectively. Furthermore, let us denote the minimum Euclidean distance in
A and 42ij from the pair (231,223) to all other pairs of symbols as dém and diff,

respectively. Denoting the global minimum Euclidean distance as

. j¢
dE : mm [d dminidfninAl (5'4)
in- constellations A and ej¢A. The objective is to maximize d E by choosing the

optimum angle 9b.

5.3.3 Diversity Product

The second performance criteria for optimizing the rotation angle for the QO—STBC
with constellation rotation scheme is the diversity product.

The diversity product is important because it determines the SIOpe of the perfor-
mance curve. In order to achieve the maximum diversity, the difference matrix X —- X

has to be full rank for any distinct codewords X and X [56]. The diversity product

89

is denoted as

. 1
g = —1— min |det[X — xnno. (5.5)
¢x

thX

Note that the diversity product is normalized by the factor 7117, resulting in 0 S
t

C S 1. When all codewords are square matrices (no = Nt), the diversity product can

be simplified as

__1_ - _~ it
§_m§1§|det[(x X)]| 4. (5-6)

Considering QPSK modulation and (5.3), the diversity product can be rewritten as

A 1
c = lmiqldetKX—sz
4x¢x

1 I
= -— mil} Ia2 — W. (5.7)
4x¢x
where,
4
a = Z Ix. — a: 2. (5.8)
i=1
and
b = 2Im{($1,m " i1,m)*(x3,m _ ~'%3,m)ejqS
+ ($2,m "' 552,m)*($4,m —' i4,m)e_j¢}' (5'9)

Due to the fact that (5.9) decreases monotonically with respect to |b|2, C is upper
bounded at [b]2 = 0 by

C S Cub 2 mill 0’2
x¢x

= M, (5.10)

90

 

where, dmin is the minimum Euclidean distance. For the case of |b|2 ; 0, a achieves
the minimum value am,” = dfm-n. This occurs if all but one of the code symbols of
two distinct codewords X 79 X are identical [85].

For a M -PSK constellation (M>2), the diversity product of QO—STBC as a func-

tion of the rotation angle (1) is given as

 

_é7_n_'ifl_ min(\/2|sin(¢—%fi7i)],1), for¢=qb1;

C“ 4 _{min(\/2|Sin(¢"gyfil+W-D£)l’l)’ f°r¢=¢2’

where, 31,61"- 3 (b1 < (2162-11)", fill/{1H S 452 < W, and k is an integer. Note that,

for QPSK constellation, dmz-n = J2.

 

(5.11)

 

If the diversity product is nonzero, the code has full diversity. Note that, maximiz-
ing the diversity product is different from maximizing the Euclidean distance. Two
signals with a large Euclidean distance does not translate to a large diversity product.
In other words, it is possible for two signals to have a large Euclidean distance, but
have a small diversity product.

Figure 5.1 depicts the diversity product C and global minimum Euclidean distance
d E for QPSK constellation. From the figure, we observe that for QPSK constellation,
C achieves the upper bound dmz-n / 4 between 45 = 7r/ 6 and 7r/ 3 and d E is maximized

at (b = 7r / 4. Therefore, the optimal rotation angle for QPSK constellation is (15 = 7r / 4.

5.4 Analysis of the Pairwise Error Probability

In this section, we discuss and derive the PEP performance of QO-STBC-OFDM sys—
tem with and without partial-band noise jamming. We assume the jammer interferes
all subcarriers transmitted in the sth QO-STBC—OFDM symbol block if the symbol

block is jammed.

91

 

 

 

 

 

 

 

 

 

 

 

0.8 I I T l l l l l
: ‘ C.QPSK j . 3

o.e—-- -

05-. . _ .....
‘3. 0.4- ..... _
U

0.3- _

0.1

"o 20 4o 60 so ' 100 120 140 160 mo

odegree

Figure 5.1. Diversity product C, and the global minimum Euclidean distance (15
versus the rotation angle qi

92

5.4.1 Pairwise Error Probability Analysis without Jamming

The authors in [86] derived the exact PEP of various QO-STBCs without interference.
In this subsection, we adopt the result in [86] and derive the exact PEP for the QO-
STBC-OFDM system.

The received signal without jamming can be expressed as
Y. = (1N. ® Xs)hs + ns, (5.12)

where (X) denotes the matrix Kronecker product, I Nr is the N,- x N,- identity matrix,

h, is defined as

118 = [h1,1,m1° ' ' a h1,Nt,m:h2,l,ma ' ° ' a h2,Nt,mv

th,1,m1"' ath,Nt,mlTa (5-13)

and n3 is defined as

ns = [721,m, ’ ' ' anNr,ma n1,m+1a ' ‘ ' anNr,m+la

T
n1,m+(n0_1), . . . , nNr,m+(n0—‘1)] . (5.14)

Assuming channel state information is available at the receiver, then the maximum

likelihood (ML) decoding metric becomes
m(ys,Xs) =ll Ys _ Xshs ”2:“ 3’s — (IN,- ® Xs)hs ”2 (5-15)

We denote the PEP of the 3th symbol block that does not experience jamming as
PI/(Xs, X3|h3), which is averaged over Rayleigh fading.
The probability that the ML decoder decodes the correct X9 into the incorrect

X3 79 X3 is given as

PI;(X3, xslhs) = Pr{m(ys,Xs) — m(y3, x.) 2 Olhs} (5.15)

93

 

After substituting (5.15) into (5.16) and performing some calculations, we obtain

PI’(X3aXslhs) 2 PTny 2 flslhs}

= 3(5)
P Q( 4113,), (5.17)

0n

where 773 = |I[IN,. (8 (X3 — XslthIIZ, and CI; = 2Re{nf[INr 69 (X3 — X3)]hs} is
a zero mean real Gaussian random variable with variance 021, = 403,173. Note that

(-)H denotes the complex conjugate transpose, and Q() is the Gaussian Q—function
7r
2
defined as Q($) = %f0-2 exp(—§:’—mg)d6 [87].

5.4.2 Pairwise Error Probability Analysis with Jamming

In this subsection, we derive the PEP of QO—STBC-OFDM system in the presence of
partial-band noise jamming.

The received signal that experience jamming can be expressed as

ys = (1N7. ® Xs)hs + H3 + Z3, (5.18)
where zs is defined as
ZS : [ZLma ' ° ° 1 ZNr,m7 zl,m+13 ' ° ' a ZNr,m+lv
T
Z1,m+(n0—1)’ ' ' ' 1 ZNr,m+(n0—1)l ° (5°19)

We denote PI(X3,Xs|hs) as the PEP of the sth symbol block that experience
jamming. Similarly to the jamming-free case we can derive the PEP of the jammed

symbol blocks as
PI(X3, Xslhs) : Q (153—)

= Q (fig—3), (5.20)

 

 

where, 173 is defined in Section 5.4.1, and CI = 2Re{(nf,Er + z§)[INr <8) (X3 — X3)]h3}

is zero mean real Gaussian random variable with variance 031 = 4(02, + GEMS.

If we normalize the average transmit symbol energy from each antenna i.e
Elan-ml2 = 1, then the noise variance 0,2, = 112% and jamming variance 0% = 9%,
where 7 is the average signal—to—noise ratio (SN R) and w is the average signal-to-
interference—ratio (SIR). Using Craig’s representation of the Gaussian Q-function [87],

the conditional PEP of (5.20) can be rewritten as

W. I

. 1 ‘Z —23§—2—_

PI(X3,X3|h3) = F/O exp 4(an+orz[]d6
2sin 0

1r .
_ 1 2 "Us
_ ;/0 exP _8(0,21+a%)sin20] d6 (5.21)

 

 

Substituting 0,2, = 122‘ and 03 = 9% into (5.21), we can obtain

7r
.. 1 2
P1(X3,X3|h3) = F/O exp [—,6—17-2—Sin3 9] d0, (5.22)
where, ,6 — —N——N-1 .
“771+?”

To evaluate the exact PEP, we need to average over the channel. Due to the inde-
pendence of the channel gain vectorsassociated with the receivers, the unconditional
PEP can be expressed in terms of a single integral whose integrand is the MGF’s

associated with each of the receivers

7r
- 1 2 _
P1(X3,X3) = E [0 Mgs (717)) d6 (5.23)

sin

where {S = flhfflNr <8 (X3 - X3)]H[INT (8) (X3 — 5(3)]h3 is a quadratic form of
complex variables with MGF M63“) 2 E63 {exp(lC3)}.

Assuming the channel is Rayleigh distributed, we can make use of a result due

95

 

 

to Mn [88] to evaluate the MGF M€s (l). Furthermore, assuming that the channel
gains have identical statistics and making use of the block diagonal structure of [I Nr (8)
(X3 — X3)]H [I N1, (8) (X3 — 5(3)], it is then straightforward to show that

71’
. 1 ’z 1
_N,.
x (X3 — X3)H(Xs — X30] - (5°24)
Using (5.24), we will find the closed-form expression for the exact PEP of constel-

lation rotation QO—STBC (5.3) under partial-band noise jamming.
In order to find the exact PEP of the PF scheme with Nt = 4 transmit an-

 

 

 

tennas, we have to calculate the determinant in (5.24). Defining as = (I4 +
(Xs-Xslflocs-Xs)
'6 sin29 )as
"' "l
1 + as O jbs 0
0 1 + a 0 — 'b
det [r33] = det s J s
_jb3 0 1 + as 0
[- 0 jbs 0 1 + as
= [(1+as)2 — b312, (5.25)

where as = 551-125 23:1 Ix... — 22ml? and b. = asi—Ijfimmuxtm - e1,m)*(zs,m -
e3,m)ef¢+ (em —e2,m)*(e4,m —- e4,m)e-J'¢}. Recall that the ML decoding of the PF
scheme is done pair by pair i.e., symbol pairs (2:1,m, x3,m) are jointly decoded and
(22’1", 334,7”) are jointly decoded, but each pair is decoded independently. Hence, we
consider only symbol pair (xlm, x3,m) to derive the PEP and use the notations X 3 =
(x1,m,a:3,m) and X3 = (5:1,m,§:3,m). Substituting (5.25) into (5.24) and performing

some algebraic simplification, we can express the exact PEP of the PF scheme as

96

'i

 

7r
A A . ’ A 2
Pz(X.,Xs) = i [of [1+ p'(“m-$1.m>+JeJ¢<x3,m—xe,m)l

—2Nr
sin? 0 l

 

x [1+,3“(Elem—5:1,m)“je‘7¢($3,m—§33,m)l2

—2Nr
sin2 0 l

d0. (5.26)

Note that the interference—free case PI/(Xs, 5(3) can be derived in a similar matter.

For the interference-free case, replace )6 with 6 = 1X7?

5.4.3 Overall Pairwise Error Probability Analysis

The average PEP of a QO-STBC—OFDM system over S blocks can be written as

PQO-STBC-OFDM 2 P1" (X3: Xslhs)

$61"

 

l
S
+ Z P1(X3, Xslhsl]

sEI

1 3 ~
2 E Z [(1— a)Pl-I(Xs,xslhs)

s=1

+ aPI(X3,X3|hs) (5.27)

 

where, a = T/ S is the fraction of symbol blocks that experience jamming.

5.5 Closed-Form Expressions of the Pairwise Error

Probability

In this section, we present the closed-form expressions of the PEP for the sth symbol
block of the PF scheme with Nt transmit antennas and N,» receive antennas. In
our calculations of the closed-form expressions we consider the PEP of the jammed
symbol blocks P1(Xs, Xslhs), and only consider the symbol pair ($1,m,x3,m). The
exact PEP expression (5.26) can be simplified by defining variables us and 123 as

97

 

 

u. = l(:c1,m - e1,m)+je3¢(x3,m — 4:3,...)I2.

vs = |($1,m - 531m) - jei¢($3,m - 53,m)l2-

Substituting the variables us and vs, (5.26) can be rewritten as

7T

2N7-
. . 2
PI(X3,Xs) = lf(—3—"—)

7r sin 0+,6u3

2N
—2——8in2 9 r d0 (5 28)
sin 0+flv3 ° '

Depending on the values of us and vs, the exact PEP in (5.28) can be classified into
three types. Note that both us and v3 cannot be zero because we are considering
PEP.

Type I is the case when either us or '03 is equal to zero. The exact PEP of Type

I can be expressed as

 

" 1 22r- sin2 0 2Nr
PI(X3, XS) = ;/0 (3E2 fifl(u3+vs)) (19. (5.29)

Note that the PF scheme with constellation rotation does not have a Type I
closed-form expression because symbols 11:1,m and 11:3,m are selected from different
signal constellations. As a result, neither us or '03 can equal to zero. In others words,
the PF scheme with constellation rotation has full diversity.

Type II is the case when us 2 v3 75 0. The exact PEP of Type II can be expressed

as
7r 4N
“ __ 1 2 sin2l9 r

Type III is the case when us and 123 are nonzero and distinct. The exact PEP of

98

 

 

Type III can be expressed as (5.28),
PIIICXSaXS) = PI(X3,X3). (5.31)

Table 5.1 shows the distribution of us and Us and the corresponding PEP types for
the PF scheme using QPSK modulation, where b,- is the number of i—bit error cases.
From the Table 5.1, it can be easily seen that there are 1-bit, 2-bit or 3—bit errors
between X3 and X; for Type II and there are 2—bit, 3-bit or 4-bit errors between
X, and X, for Type III. Note that when applying QPSK modulation, there are a
total of 256 possible (123,223) pairs. Recall, that if (143,123) = (0,0), then there is no
error between X3 and X3. Thus, the 16 (113,113) pairs resulting in (us, 123) = (0, 0) are
excluded from the analysis, and there are a total of 240 possible (123,123) pairs.

Following the results in [89], the closed-form expressions of the PEPs in the pres-
ence of partial-band noise jamming for QO—STBC-OFDM can be derived as

 

 

PI(X3,X3) ._._ 1[1_\/ 5(u3+vs)

 

 

2 1 + Mus + vs)
2Nr—1 fl(u +12 2 k

x E: (2k) (1_1+[3 25+; ) ], (5.32)

k 4
k=0
. 1 u
PII(X37X3) = '2‘[1 _ lf-flsus
4Nr—1 k

X [CZ—0 (2:) (1-1+uis) :I, (5.33)

99

 

 

 

 

(J)2Nr_1 2Nr—1 k
PIII(XstX8)= v3 [ Z (Bi-1)

4N —1
2(1-33) " “s
u 2Nr—1 k
XBka(fivs)-v—: 2 (1—5-3) Ck1k(fius)]. (5.34)
k=0

where,

2N k (Mr—1) 2M
Ak = (—1) r—1+ m H (4Nr—n),
n=1,n¢k+1

 

 

Ak
Bk (4N2—1)’
2Nr—1 (k)
Ck Z (4N2—1)An’
n=0 n
[(t) __ 1 t [1 Z": (2n—1)!!]
k T _ 1+t +n=1n!2n(1+t)n'

Note (215 - 1)!! denotes the product of only odd integers from 1 to 2k - 1.

Using the closed-form expressions (5.32), (5.33), and (5.34), we can rewrite
PI(xs,x,) as

100

 

Table 5.1. Distribution of us and vs for PF scheme with QPSK

 

 

 

Type us 2)., b1 b2 b3 b4
II 2 2 64 0 0 0

4 4 0 32 0 0

6 6 0 0 32 0

III 0.343 11.657 0 0 16 0
1.172 6.828 O 32 0 0

2.343 13.657 0 0 0 8

6.828 1.172 0 32 0 0

11.657 0.343 0 0 16 0

13.657 2.343 0 0 0 8

PI(X3,X3) = Z PI(X81X3) + Z PII(XSaXS)
x3,xserype I x3,xserype II
+ Z: PIII(X3. 5(3) (5-35)

x3,xseType III
5.6 Union Bound of Bit Error Probability

In this section we will derive the union bound of the bit error probability (BEP) for
the PF scheme in the presence of partial-band jamming. The union bound technique
consists of computing an upper bound of the PF scheme error probability, which
sums the contributions of the of the pairwise error probabilities over all error events.

The BEP of the PF scheme in the presence of partial-band jamming is expressed as

BEP: s 5— 2 [ . Z Px<xs,xs)]p(xs), (536)
Kg Xs7éxs

where nb is the number of bits of X3, and p(X3) is the probability that X, is trans-
mitted.
For simplicity, we only consider symbol pair Xm = ($1.7m 11:3,m) and assume that

each QPSK symbol is equiprobable, such that nb = 4 and p(X3) = 116' The union

101

bound in terms of symbol pair ($1.7m 223,7”) can be expressed as

BEP; g 514 Z [ZPI(X,X)], (5.37)

:1: l,mvx3,m V

where V é (f1,m,§:3,m) 76 (zl,m,x3,m). Similarly, the union bound can be derived

for the BEP for symbols 31:2,m and $4,"?

5.7 Numerical Evaluations and Simulations

In this section, we provide the numerical and the simulation results of the QO-STBC-
OFDM system in the presence of partial-band noise jamming and frequency-selective
fading.

We consider the QO—STBC with constellation rotation (CR) scheme (5.3),
equipped with Nt = 4 transmit antennas and Nr = 2 receive antennas. QPSK
modulation is used for symbol transmissions and 45 = 7r / 4 is the rotation angle. In all
simulations, the channels among different transmit and receive antenna pairs are as-
sumed to be uncorrelated and the channel state information (CSI) of the transmitters
and jamming power are perfectly known at the receivers. The channel coefficients are
constant during one block of code transmission and independent from block to block.
The total number of available subcarriers is N; = 256 and the number of users is 16;
therefore each user is assigned 16 subcarriers.

Figures 5.2 and 5.3 shows the BEP versus SNR performance of the numerical
results and the simulation results of the QO-STBC with CR scheme. In Figure 5.2,
the performance is evaluated in Rayleigh fading. From the figure, we observe that
the theoretical performance is very close to the simulation results and serves as an
upper bound. '

In Figure 5.3, the QO-STBC with CR scheme is evaluated in Rayleigh fading and
partial-band noise jamming with SIR=6dB, and a = 0.5. Recall that jammer occu-
pancy (a) is the fraction of symbol blocks that experience jamming. From the figure

we can see that the performance limiting factor is the partial-band noise jamming and

102

 

QO-STBC w/ CR

 

 

§ +Qo— STBC w/CR Theoretical: g
——*—- QO- STBC w/ CR. Simulation .

 

 

 

 

 

a 1
SNR (dB)

Figure 5.2. Union bound on the BEP and simulation results for QO-STBC with
constellation rotation in frequency-selective fading (N, = 2).

the union bound is tight. In Figure 5.4, the performance for various (1 is evaluated.
From the figure, we observed that as a increases the BEP performance degrades
Finally, in Figure 5.5, we compare the OSTBC scheme and the QO—STBC with
constellation rotation scheme. Each scheme is equipped with 4 transmit antennas
and 2 receive antennas. The BER performance is evaluated under Rayleigh fading
and partial-band jamming with SIR=6dB and a = 0.5. As shown in the figure, the
QO—STBC with constellation rotation scheme significantly outperforms the OSTBC

scheme.

103

QO-STBC wl CR. PBJ. SIR = 6dB a = 0. 5

 

 

 

10° .............. . .............. . ..........................................
£3363;35233223723333333332333313?+00-STBCw/CR Theoretical}?
-------------- +Qo— STBCw/CR: Simulation-

 

 

 

 

SNR (dB)

Figure 5.3. Union bound on the BEP and simulation results for QO-STBC with
constellation rotation in partial-band noise jamming and frequency-selective fading

(N. = 2, a = 0.5, SIR=6dB).

104

 

 

—e—a=0.1
--+-a=0.3 :.
+a=0.5 .

 

 

 

 

 

 

 

 

SNR (as)

Figure 5.4. Union bound on the BEP for QO-STBC with constellation rota-
tion in partial-band noise jamming and frequency-selective fading (Nr : 2, a =
[0.1,0.3,0.5,0.7,0.9], SIR=6dB).

105

OSTBC vs. QO-STBC w/ CR, PBJ, SIR = 6dB a = 0.5
10 .............. . .............. 1 ............. 1 .............. . ..............

uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu

.......... +OSTBC:SimU'afion

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

............... -—*—QO—STBCw/CR:Simulation:

 

 

 

 

 

BEP

 

 

 

 

10‘3 . . . I.
0 5 10 15 20 25
SNR (dB)

Figure 5.5. Comparison of OSTBC vs. QO-STBC with constellation rotation in
rayleigh fading and partial-band noise jamming (SIR=6dB), a = 0.5, and Nr = 2

106

5.8 Summary

In summary, the combination of QO-STBCs with OFDM can exploit multipath di-
versity and achieve spectrally efficient communications. However, future wireless
communication systems must be robust against both unintentional and intentional
interference. As a result, there is a need for pr0per analytical tools to assess the
performance of QO-STBC—OFDM in the presence of partial-band noise jamming. In
this chapter, we derived analytical expressions for the exact PEP of the QO-STBC-
OFDM system using the moment generating function. We calculated the exact PEP
under various situations, and derived the closed-form expressions and union bound
for the bit error probability. Our numerical analysis and simulation results show
that union bound is tight and the QO-STBC—OFDM system is effective in mitigating

partial-band noise jamming.

107

 

 

CHAPTER 6

Conclusions and Future Work

6. 1 Conclusions

In this dissertation, we investigated the efficiency and security of existing work,
and enhanced the spectral efficiency and strengthened the inherent security of wire-
less systems by integrating advanced signal processing techniques and cryptographic
techniques into the transmitter—receiver design. In summary, our spectrally efficient
Alamouti scheme improves the code efficiency of the traditional Alamouti scheme by
increasing the number of information bits transmitted in each Alamouti block; Our
highly efficient anti-jamming system design for secure dynamic spectrum access con-
trol breaks through the bottleneck in developing high-capacity anti-jamming wireless
communication systems.

On spectrally efficient Alamouti scheme:

0 The code efficiency of the traditional Alamouti code is investigated from a bit-
level perspective by introducing the concepts of Alamouti patterns and irregular
partitioning. The investigation reveals room for spectrally efficiency enhance-

ment.

0 A novel spectrally efficient Alamouti scheme is proposed to improve the code
‘ efficiency of the traditional Alamouti scheme by transmitting more information
bits than redundancy bits per Alamouti block, while achieving high transmit di-
versity. The receiver design of the proposed system allows maximum likelihood

decoding for signal decoupling.

0 There are no specific constraints of the spectrally efficient Alamouti scheme,

108

therefore the proposed scheme can be directly extended to any space—time block

codes with more than two transmit antennas.

On highly efficient anti- j amming system design for secure dynamic spectrum access

control:

0 We developed a collision-free frequency hopping (CFFH) system, which is based
on the orthogonal frequency division multiple access (OFDMA) framework and
a new secure subcarrier assignment scheme, and proposed to enhance the anti-

jamming properties of CFFH through joint space-time and frequency diversity.

0 First, we analyzed the limitations in the recently proposed subcarrier assign-
ment algorithm, and pr0posed a new subcarrier assignment scheme based on
secure permutation algorithm. From a security perspective, the subcarrier as-
signment scheme based on secure permutation protects users against follower
jamming attacks by preventing adversaries from determining the frequency hop-

ping patterns.

0 Second, we observed that although CF F H is very robust under partial-band
jamming, it is still sensitive to random jamming. We propose to overcome
this deficiency through space-time coding and introduce the space-time coded
collision-free frequency h0pping (STC-CFFH) system. The pr0posed STC-
CFFH is found to be particularly powerful in eliminating both channel interfer-

ence and hostile jamming interference.

0 Finally, our analysis indicates that the proposed STC—CFFH scheme is both

highly efficient and very robust under various jamming scenarios.
On quasi-orthogonal space-time block codes for jamming mitigation:

o The combination of quasi-orthogonal space-time block coding (QO-STBC) with
constellation rotation exploits multipath diversity and achieves high speed high
quality transmissions. However, such systems must co-exist with various forms

of interference to provide reliable communication. Therefore, there is a need

109

for proper analytical tools to assess the performance of the QO-STBC with

constellation rotation scheme in the presence of partial-band noise jamming.

0 First, we derived analytical expressions for the exact pairwise error probability
(PEP) of the QO—STBC orthogonal frequency division multiplexing (QO—STBC—
OFDM) system using the moment generating function (MGF).

0 Second, we calculated the exact PEP under various situations, and derived the

closed-form expressions and union bound for the bit error probability (BEP).

0 Our numerical analysis and simulation results show that the union bound is
tight and the QO-STBC—OFDM system is effective in mitigating partial-band

noise jamming.

6.2 Future Directions

For future research, we will look at secure communications and dynamic resource

allocation in cognitive radio networks.

6.2.1 Cognitive Networks

The rapid increase of wireless networks have led to a shortage of a precious natural re-
source, radio electromagnetic spectrum. The shortage of spectrum has become more
severe due to the outdated way the spectrum is managed. The Federal Communica-
tions Commission (FCC) allocates static spectrum to primary users for a fee. The
use of static allocations causes spectrum holes. A spectrum hole is defined as a band
of frequencies assigned to a primary user, but at a particular time and specific geo-
graphic location, the band is not utilized by the user [90]. This inefficient utilization
of the spectrum has led to the rise of 802.11-based technologies that uses unlicensed
spectrum. However, these unlicensed frequency bands have become over populated
and interference among the different networks is the major deployment constraint.

All of these factors have led to the need to make dramatic changes in the spectrum

110

 

management process, as existing policies are not capable of scaling with demand [91].
Furthermore, these factors have led to the concept of cognitive radio networks.
Cognitive radio network is an intelligent multiuser wireless communication sys-
tem that is aware of its environment and uses the methodology of understanding-by-
building to learn from the environment and adapt to statistical variations in the input
stimuli with two primary objectives: (i) highly reliable communications; (ii) efficient
utilization of the radio spectrum [92]. In other words, cognitive radio networks im-
prove the spectrum utilization by making it possible for a secondary (unlicensed) user
to access spectrum holes unoccupied by the primary users. Furthermore, cognitive
radio networks are able to sense and predict interference patterns and adapt their

spectrum access accordingly [93].

6.2.2 Major Challenges and Future Research Directions

The major challenges in existing cognitive radio networks are:

0 Spectral Inefficiency Due To Traffic Collisions: The lack of network-
centric scheduling on secondary users may cause collisions between other sec-
ondary users as well as collisions between primary users, leading to low efficiency

and low system capacity.

0 Security Fragility: Spectrum sensing enables the secondary user to perform
legitimate traffic analysis of the primary user, including spectrum occupation,
traffic volume, traffic patterns, and even traffic routing paths. Hostile jamming
and privacy compromise can raise serious security problems in cognitive radio

networks.

0 High Terminal Cost: In cognitive radio, every individual terminal needs to
perform continuous spectrum sensing, and be able to adapt to the unpredictable,
ever changing environment. These operations require expensive hardware and

software, which implies that the cost of each radio terminal will be high.

The future research directions are:

111

 

0 Architecture And Protocol Design For More Efficient Cognitive N et-
works: We propose to increase spectral efficiency and system reliability through
network-centric collision-free spectrum sharing, and to increase system flexibil-

ity and scalability through both fixed and dynamic base station deployment.

e Cross-Layer Jamming Mitigation Techniques In Cognitive Networks:
We will consider jamming-resistant system design for both centralized as well
as ad hoc networks consisting of cognitive radios. The jamming mitigation
techniques will be investigated from both physical layer transceiver design as

well as higher layer protocol development.

112

BIBLIOGRAPHY

113

BIBLIOGRAPHY

[1] I. Wong and B. Evans, Resource Allocation in Multiuser Multicarrier Wireless
Systems. Springer Science'Business Media, New York, NY, 2008.

[2] 3GAmericas, World Cellular Technology Forecast 2006-2011, 2007. [Online].
Available: http: / / www.3gamericas.org / English / Statistics / 17 .cfrn

[3] Total Midyear Population for the World. 1950-2050, 2007. [Online]. Available:
http: / /www census. gov/1pc/www/worldpop html

[4] WORLD INTERNET USA GE AND POPULA TION STA TISTICS, 2007.
[Online] . Available: http: / /www. Intemetworldstats.com/stats.htm

[5] P. Rysavy, Mobile Broadband: EDGE, HSPA, and LTE, 2006. [Online].
Available: http: //3gamericas.org/pdfs/white.papers/2006_Rysavy_Data_Paper-
FINAL_09.15.06.pdf

[6] N. Borisov, I. Goldberg, and D. Wagner, “Intercepting mobile communications:
The insecurity of 802.11,” in Proceedings of the Seventh Annual International
Conference on Mobile Computing and Networking. Rome, Italy: ACM Press,
July 2001, pp. 180—188.

[7] S. Fluhrer, I. Mantin, and A. Shamir, “Weaknesses in the key scheduling algo—
rithm of RC4,” in Proceedings of the Eighth Annual Workshop on Selected Areas
in Cryptography, Aug. 2001, pp. 1—24.

[8] A. Stubblefield, J. Ioannidis, and A. Rubin, “Using the F luhrer, Mantin, and
Shamir attack to break WEP,” in Proceedings of Network and Distributed
System Security Symposium (NDSS). Internet Society, 2002. [Online]. Available:
http: / / www.1soc.org / isoc / conferences / ndss / 02 / proceedings / papers / stubbl.pdf

[9] IEEE Standard for Wireless LAN Medium Access Control (MAC) and Physical
Layer (PHY) Specifications, IEEE Std. 802.11.

[10] S. Houston, “Tone and noise jamming performance of a spread spectrum M-ary
FSK and 2, 4-ary DPSK waveforms,” in Proceedings of IEEE National Aeorspace

and Electronics Conference, Dayton, Ohio, June 1975, pp. 51—58.

[11] L. Milstein, S. Davidovici, and D. Schilling, “The effect of multiple—tone interfer-
ing signals on a direct sequence spread spectrum communication system,” IEEE
Transactions on Communications, vol. 30, pp. 436—446, March 1982.

114

[12]

[13]

[14]

[15]

[15]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

 

K. Raju, T. Ristaniemi, J. Karhunen, and E. Oja, “Jammer suppression in DS-
CDMA arrays using independent component analysis,” IEEE Transactions on
Wireless Communications, vol. 5, pp. 1—6, Jan. 2006.

J .-W. Moon, J. Shea, and T. Wong, “J amming estimation on block-fading chan-
nels,” in IEEE Military Communications Conference, vol. 3, Nov. 2004, pp. 1310—
1316.

J. Tan and G. Stuber, “Multicarrier spread spectrum system with constant enve-
10pe: Antijamming, jamming estimation, multiuser access,” IEEE Transactions
on Wireless Communications, vol. 4, pp. 1527- 1538, July 2005.

J .-W. Moon, J. Shea, and T. Wong, “Collaborative mitigation of partial-time
jamming on nonfading channels,” IEEE Transactions on Wireless Communica-
tions, vol. 5, pp. 1371—1381, June 2006.

R. Pickholtz, D. Schilling, and L.B.Mi1stein, “Theory of spread spectrum com-
munications - a tutorial,” IEEE Transactions on Communications, vol. 30, pp.
855—884, May 1982.

C. Cook and H. Marsh, “An introduction to spread spectrum,” IEEE Commu-
nications Magazine, vol. 21, pp. 8—16, Mar. 1983.

P. Crepeau, “Performance of FH/BFSK with generalized fading in worst case
partial-band gaussian interference,” IEEE Journal on Selected Areas in Commu-
nications, vol. 8, pp. 884—886, June 1980.

M. Pursley and W. Stark, “Performance of Reed-Solomon coded frequency-hop
spread—spectrum communications in partial-band interference,” IEEE T ransac-
tions on Communications, vol. 33, pp. 767—774, Aug. 1985.

W. Stark, “Coding for frequency-hopped spread-spectrum communication with
partial-band interference-Part II: Coded performance,” IEEE Transactions on
Communications, vol. 33, pp. 1045—1057, Oct. 1985.

D. Nicholson, Spread Spectrum Signal Design: LPE and AJ Systems, ser. Com-
puter Science Press. Maryland: Rockville, 1988.

L. Milstein, D. Schilling, R. Pickholtz, V. Erceg, M. Kullback, E. Kanterakis,
D. Fishman, W. Biederman, and D. Salerno, “On the feasibility of a CDMA over-
lay for personal communication networks,” IEEE JOURNAL 0N SELECTED
AREAS IN COMMUNICATIONS, vol. 10, pp. 655—668, May 1992.

M. Simon, G. Huth, and A. Polydoros, “Differentially coherent detection of
QASK for frequency-hopping systems-Part I: Performance in the presence of

115

 

 

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

a gaussian noise environment,” IEEE Transactions on Communications, vol. 30,
pp. 158-164, Jan. 1982.

Y. Lam and P. Wittke, “Frequency-hopped spread-spectrum transmission with
band-efficient modulations and simplified noncoherent sequence estimation,”
IEEE Transactions on Communications, vol. 38, pp. 2184—2196, Dec. 1990.

J. Cho, Y. Kim, and K. Cheun, “A novel FHSS multiple-access network using
M-ary orthogonal Walsh modulation,” in Proc. 52nd IEEE Veh. Technol. Conf.,
vol. 3, Sept. 2000, pp. 1134—1141.

S. Glisic, Z. Nikolic, N. Milosevic, and A. Pouttu, “Advanced frequency hopping
modulation for spread spectrum WLAN,” IEEE Journal on Selected Areas in
Communications, vol. 18, pp. 16—29, Jan. 2000.

K. Choi and K. Cheun, “Maximum throughput of FHSS multiple-access networks
using MFSK modulation,” IEEE Transactions on Communications, vol. 52, pp.
426—434, Mar. 2004.

K.-C. Peng, C.-H. Huang, C.-J. Li, and T.-S. Horng, “High-performance
frequency-hopping transmitters using two-point delta-sigma modulation,” IEEE
Transactions on Microwave Theory and Techniques, vol. 52, pp. 2529—2535, Nov.
2004.

K. Choi and K. Cheun, “Optimum parameters for maximum throughput of
FHMA system with multilevel FSK,” IEEE Transactions on Vehicular Tech-
nology, vol. 55, pp. 1485—1492, Sept. 2006.

G. Foschini, “Layered space—time architecture for wireless communication in a
fading environment when using multi-element antennas,” Bell labs. Tech. J.,
vol. 1, pp. 41—59, 1996.

I. Telatar, “Capacity of multi-antenna Gaussian channels,” Europ. Trans.
Telecommun, pp. 585-595, Nov. 1999.

G. Foschini and M. Gans, “On limits of wireless communicationss in a fading en-
vironment when using multiple antennas,” Wireless Personal Communications,
pp. 311—335, 1998.

Y. Tsai and J. Chang, “Using frequency h0pping spread spectrum technique to
combat multipath interference in a multiaccessing environmen ,” IEEE Trans-
actions on Vehicular Technology, May 1994.

C. Wong, R. Cheng, K. Letaief, and R. Murch, “Multiuser OFDM with'adap-
tive subcarrier, bit and power allocatioin,” IEEE Journal of Selective Areas on
Communications, Oct 1999.

116

 

[35] H. Sari, Orthogonal frequency-division multiple access with frequency hopping
and diversity. in Multi-Carrier Spread Spectrum, K. Fazel and G. P. Fettweis,
Editors, Norwell, USA: Kluwer, 1997, pp. 57—68.

[36] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-
correcting coding and decoding: Turbo codes,” in Proc. 1993 International Con-
ference of Communications, pp. 1064—1070, 1993.

[37] R. Gallager, Low Density Parity Check Codes. MIT Press, Cambridge, Mas-
sachusets, p. 1963.

[38] D. MacKay, “Near Shannon limit performance of low density parity check codes,”
Electronics Letters, pp. 1645—1646, August 1966.

[39] V. Tarokh, N. Seshadri, and A. Calderbank, “Space-time codes for high data rate
wireless communication: Performance criterion and code construction,” IEEE
Trans. Information Theory, pp. 744-765, March 1998.

[40] V. Tarokh, A. Naguib, N. Seshadri, and A. Calderbank, “Spacetime codes for
high data rate wireless communication: performance criteria in the presence of
channel estimation errors, mobility, and multiple paths,” IEEE Tfansactions on
Communications, p. 199207, February 1999.

[41] A. Viterbi, “Error bounds for convolutional codes and an asymptotically op-
timum decoding algorithm,” IEEE Transactions on Information Theory, p.
260269, April 1967.

[42] S. Alamouti, “A simple transmit diversity technique for wireless communica-
tions,” IEEE Journal on Selected Areas in Communications, pp. 1451—1458, Oc-
tober 1998.

[43] V. Tarokh, H. Jafarkhani, and A. Calderbank, “Space-time block code from
orthogonal designs,” IEEE Trans. Information Theory, July 1999.

[44] H. Jafarkhani and F. Taherkhani, “Pseudo orghogonal designs as space-time
block codes,” in Proc. Int. Symp. Advances in Wireless Communications, Victo—
ria, BC, Canada, September 2002.

[45] V. Tarokh, H. Jafarkhani, and A. Calderbank, “Space-time codes for high data
rate wireless communication: Performance results,” IEEE Journal on Select Ar-
eas Communication, pp. 451—460, March 1999.

[46] L. Dalton and C. Georghiades, “A full-rate, full-diversity four-antenna quasi-
orthogonal space-time block code,” IEEE Transactions on Wireless Communi-
cations, vol. 4, pp. 363—366, March 2005.

117

[47] G. Wang and X.-G. Xia, “On optimal multilayer cyclotomic space-time code
designs,” IEEE Transactions on Information Theory, vol. 51, pp. 1102—1135,
March 2005.

[48] G. Golden, G. Foschini, R. Valenzuela, and P. Wolniansky, “Detection algorithm
and initial laboratory results using V-BLAST space-time communication archi-
tecture,” Electron. Lett., vol. 35, pp. 14—16, January 1999.

[49] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEE Transactions
on Communications, January 2001.

[50] O. Tirkkonen, A. Boariu, and A. Hottinen, “Minimal nonorthogonal rate 1 space-
tirne block code for 3+ tx antennas,” IEEE International Symposium on Spread-
Spectrum Techniques and Applications (ISSS TA ), September 2000.

[51] C. Papadias and G. Foschini, “Capacity-approaching space-time codes for sys-
tems employing four transmitter antennas,” IEEE Transactions on Information
Theory, pp. 726—733, March 2003.

[52] O. Tirkkonen, “Optimizing space-time block codes by constellation rotations,”
Finnish Wireless Communication Workshop, pp. 59—60, 2001.

[53] N. Sharma and C. Papadias, “Improved quasi-orthogonal codes through constel-
lation rotation,” IEEE Transactions on Communications, pp. 332—335, March
2003.

[54] D. Dao and C. Tellambura, “Optimal rotations for quasi-orthogonal codes
through constellation rotation,” IEEE Global Telecommunications Conference
(Globecom), pp. 2317—2321, 2005.

[55] W. Su and X. Xia, “Quasi-orthogonal space-time block codes with full diversity,”
IEEE Global Telecommunication Conference (Globecom), pp. 1098—1102, 2002.

[56] —, “Signal constellations for quasi-orthogonal space-time block codes with full
diversity,” IEEE Transactions on Information Theory, pp. 2331—2347, October
2004.

[57] B. Hassibi and B. Hochwald, “High-rate codes that are linear in space and time,”
IEEE Transactions on Information Theory, pp. 1804—1824, July 2002.

[58] G. Golden, G. Foschini, R. Valenzuela, and P. Wolniansky, “Detection algorithm
and initial laboratory results using V-BLAST space-time communication archi-
tecture,” Electron. Lett., pp. 14—16, Jan. 1999.

118

 

[59]

[60]

[51]

[62]

[53]

[54]

[65]

[66]

[67]

[68]

[69]

 

G. Foschini, G. Golden, R. Valenzuela, and P. Wolniansky, “Simplified process-
ing for high spectral efficiency wireless communication employing multi-element

arrays,” IEEE Journal on Selected Areas in Communications, pp. 1841-1852,
Nov. 1999.

V. Tarokh and H. J afarkhani, “A differntial detection scheme for transmit diver-
sity,” IEEE Journal on Selected Areas in Communications, pp. 1169—1174, July
2000.

H. J afarkhani and V. Tarokh, “Multiple transmit antenna differential detection
from generalized orthogonal designs,” IEEE Transactions on Information The-
ory, pp. 2626—2631, Sept. 2001.

M. Damen, A. Tewfik, and J. Belfiore, “A construction of space-time code based

on number theory,” IEEE Transactions on Information Theory, pp. 753—760,
March 2002.

J. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: A 2 x 2 full-rate space-
time code with non-vanishing determinants,” IEEE Transactions on Information
Theory, pp. 1432—1436, April 2005.

H. E. Gamal and M. Damen, “Univeral space-time coding,” IEEE Transactions
on Information Theory, pp. 1097—1119, May 2003.

Z. Chen, J. Yuan, and B. Vucetic, “Improved space-time trellis coded modula-
tion scheme on slow rayleigh fading channels,” Electronics Letters, pp. 440—441,
March 2001.

L. Lightfoot, L. Zhang, and T. Li, “Space-time coded collision-free frequency
hopping in hostile jamming,” IEEE Military Communications Conference (MIL-
COM), November 2008.

L. Lightfoot and T. Li, “Jamming mitigation using space—time coded collision-
free frequency hopping,” IEEE International Conference on Acoustics, Speech
and Signal Processing (ICASSP), pp. 2717 — 2720, April 2009.

L. Lightfoot, L. Zhang, J. Ren, and T. Li, “Secure collision-free frequency h0p—
ping for ofdma based wireless networks,” European Association for Signal Pro—
cessing ( E URASIP) Journal on Advances in Signal Processing, August 2009.

L. Lightfoot, J. Ren, L. Zhang, and T. Li, “Jamming-resilient subcarrier assign-
ment for OF DMA based space-time coded systems,” IEEE Electra/Information
Technology (EI T) Conference, June 2009.

119

 

 

[70] C. Martin, E. Lemois, F. Buda, and D. Merel, “Description of a complete multi—
carrier spread spectrum transmission chain for robust and discrete tactical com-
munications,” IEEE Military Communication Conference, pp. 942—946, October
2000.

[71] J. Nilsson and T. Giles, “Wideband multi-carrier transmission for military HF
communication,” IEEE Military Communication Conference, pp. 1046-1051,
Nov. 1997.

[72] F. Dominique and J. Reed, “Robust frequency hop synchronisation algorithm,”
Electronics Letters, vol. 32, pp. 1450—1451, Aug. 1996.

[73] U. N. I. of Standards and Technology, Federal Information Processing Standards
Publication 197—Announcing the ADVANCE EN CRYPTION STANDARD
(AES), 2001. [Online]. Available: http://csrc.nist.gov/publications/fips/
fipsl97/fips-197.pdf

[74] W. Burr, “Selecting the advance encryption standard,” IEEE Security and Pri-
vacy, pp. 43-52, April 2003.

[75] J. Jang and K. Lee, “Transmit power adaptation for multiuser ofdm systems,”
IEEE Journal of Selective Areas on Communications, Feb. 2003.

[76] R. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signa-
tures and public key cryptosystems,” Communications of the ACM, Feb. 1978.

[77] M. Ergen, S. Coleri, and P. Varaiya, “QoS aware adaptive resource allocation
techniques for fair scheduling in OFDMA based broadband wireless access sys-
tems,” in Proceedings of IEEE Transactions on Broadcasting, pp. 362-370, Dec.
2003.

[78] S. Elayoubi and B. Fourestie, “Performance evaluation of admission control and
adaptive modulation in OFDMA WiMax systems,” in Proceedings of IEEE/A CM
Transactions on Networking, pp. 1200—1211, Oct. 2008.

[79] K. Lee and D. Williams, “A space-frequency transmitter diversity technique for
ofdm systems,” in Proceedings of IEEE Global Communications Conference, pp.
1473—1477, Nov. 2000.

[80] B. Vucetic and J. Yuan, Space Time Coding. John Wiley and Sons, Ltd., ch.
Space Time Coding Peformance Analysis and Code Design, p. 2003.

[81] J. Park, D. Kim, C. Kang, and D. Hong, “Effect of partial band jamming on
ODFM-based WLAN in 802.11g,” IEEE International Conference on Acous-
tics, Speech, and Signal Processing, pp. 560—563, April 2003.

120

 

[82] T. Rappaport, Wireless Communications, 2nd ed. Prentice Hall, 2002.

[83] C. Esli and H. Delic, “Antijamming performance of space-frequency coding in
partial-band noise,” IEEE Transactions on Vehicular Technology, pp. 466—476,
March 2006. ,

[84] L. Lightfoot, L. Zhang, and T. Li, “Performance of qo-stbc-ofdm in partial-band
noise jamming,” Conference on Information Science and Systems (CISS), March
2010.

[85] A. Sezgin, E. Jorswieck, and H. Boche, “Performance criteria analysis and fur-
ther performance results for quasi-orthogonal space-time block codes,” IEEE
International Symposium on Signal Processing and Information Technology, pp.

102—105, December 2003.

[86] J. Yang, X. J in, J. No, and D. Shin, “On the error probability of quasi-orthogonal
space-time block codes,” International Journal Of Communication Systems, pp.
1033—1045, May 2008.

[87] J. Craig, “A new, simple and exact result for calculating the probability of er-
ror for two-dimensional signal constellations,” IEEE Military Communication
Conference, pp. 571—575, October 1991.

[88] G. Turin, “The characteristic function of hermitain quadratic forms in complex
normal variables,” Biometrika Trust, pp. 199—201, 1960.

[89] M. Simon and M. Alouini, Digital Communication over Fading Channels. John
Wiley and Sons, Ltd., 2005, ch. Appendix 5A.

[90] P. Kolodzy, “Next generation communications: Kickoff meeting,” in Proc.
DARPA, October 2001.

[91] J. Burbank, “Security in cognitive radio networks: The required evolution in ap-
proaches to wireless network security,” IEEE Cognitive Radio Oriented Wireless
Networks and Communications, pp. 1—7, May 2008.

[92] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE
Journal on Selected Areas in Communications, pp. 201—220, February 2005.

[93] S. Geirhofer, J. Sun, L. Tong, and B. M. Sadler, “Cognitive frequency hop-
ping based on interference prediction: theory and experimental results,” ACM
SIGMOBILE Mobile Computing and Communications Review, pp. 49—61, April
2009.

121