Sharma Anshul

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UNIVERSITY OF CINCINNATI

Date:___________________

I, _________________________________________________________,

hereby submit this work as part of the requirements for the degree of:

in:

It is entitled:

This work and its defense approved by:

Chair: _______________________________

_______________________________

_______________________________

_______________________________

_______________________________

06/21/2007

Anshul Sharma

Master of Science

Electrical Engineering

PERFORMANCE ANALYSIS OF MC-CDMA AND CI/MC-CDMA

USING INTERFERENCE CANCELLATION TECHNIQUES

Dr. James Caffery, Jr., Ph.D

Dr. Howard Fan, Ph.D

Dr. Qing-An Zeng, Ph.D


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PERFORMANCE ANALYSIS OF MC-CDMA AND

CI/MC-CDMA USING INTERFERENCE CANCELLATION

TECHNIQUES

A thesis submitted to the

Division of Graduate Studies and Research

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE

in the Department of

Electrical and Computer Engineering and Computer Science

of the College of Engineering

by

Anshul Sharma

B.Tech., University Of Pondicherry, 1999

Adviser and Committee Chair : Dr. James Caffery, Jr., Ph.D

Committee Members : Dr. Howard Fan, Ph.D

: Dr. Qing-An Zeng, Ph.D


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Abstract

Efficient use of the spectrum is an essential problem in creating any multi-user cellular

mobile system. The bandwidth requirements of the future 4G systems far exceed what the

existing traditional setup can provide. A more creative utilization of the available band-

width is more important now than ever before.

Improved receiver design that utilizes the frequency and code diversity of the MC-

CDMA schemes is one way of increasing the number of users supported at very high bi-

trates. We discuss the MC-CDMA system operating over a frequency selective, slowly

fading channel. We study in detail multiuser Parallel Interference Cancellation detectors

employing the MRC and MMSE detectors. Various configurations of the PIC are studied

and simulated to evaluate and understand the comparative advantages and disadvantages.

In this thesis we offer a review of the literature available on MC-CDMA and CI/MC-

CDMA systems. We study the performance of the MRC-PIC-MMSE system both semi-

analytically and by computer simulations. By means of computer simulations, we also

compare the advantages of using the Carrier Interferometry codes over the Walsh Hadammard

codes under various system configurations.

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Acknowledgements

I would like to thank the following people, without whom this thesis would not have been

possible:

Dr. James J. Caffery, Jr., my guide and mentor, for his profound knowledge, his

constant help, understanding and patience. He has always been a source of support

and motivation. I thank him for taking time out of his busy schedule to provide

invaluable guidance throughout my graduate study at the University of Cincinnati.

Professors Howard Fan and Qing-An Zeng for being on the thesis committee and

providing valuable suggestions.

My parents, Mrs. Pavan and Mr. Vibhakar Sharma, my wife Shrutee and my brother

Vipul for their constant support and encouragement. I am indebted to my family for

always being there for me.

My colleagues and friends at the Wireless Systems Research Lab.

All my friends here at the University of Cincinnati and also elsewhere.

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Contents

1 Introduction 1

1.1 CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 OFDM/COFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 MC-CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 CI/MC-CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 MC-DS-CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6 Contributions of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 System Description 13

2.1 Multipath Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Discrete-Time Baseband Model of MC-CDMA System . . . . . . . . . . . 17

2.3.1 MC-CDMA Transmitter Model . . . . . . . . . . . . . . . . . . . 18

2.3.2 MC-CDMA Receiver Model . . . . . . . . . . . . . . . . . . . . . 20

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Carrier Interferometry and CI/MC-CDMA 24

3.1 Robust CI Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 CI/MC-CDMA Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 System Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 MUD for MC-CDMA and CI/MC-CDMA 31

4.1 Single-user Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.1 Conventional Single User Detector . . . . . . . . . . . . . . . . . . 32

4.2 Linear Multi-user Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Decorrelating Detector . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.2 Maximal Ratio Combining (MRC) Detector . . . . . . . . . . . . . 36

4.2.3 Minimum Mean Square Error (MMSE) Detector . . . . . . . . . . 37

4.3 Interference Cancellation Detectors . . . . . . . . . . . . . . . . . . . . . 37

4.3.1 Successive Interference Cancellation (SIC) Detector . . . . . . . . 38

4.3.2 Parallel Interference Cancellation (PIC) Detector . . . . . . . . . . 39

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4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5 Performance Analysis of A Two Stage MRC/MMSE PIC Detector 42

5.1 Parallel Interference Cancellation . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 MRC as the first stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3 MMSE as second stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6 Simulations and Results 54

6.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.1.1 Simulation Results: Linear Detectors . . . . . . . . . . . . . . . . 57

6.1.2 Simulation Results: Parallel Interference Cancellation Detectors . . 57

7 Conclusion and Future Research 75

7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

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List of Figures

1.1 Multicarrier frequency spectra. (a) 8 subcarriers, = 1 (b) 4 subcarriers, = 1 (c) 4 subcarriers, = 2 . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2 MC-CDMA Scheme: a) Transmitter, b) Power spectrum of transmitted

vector, c) Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 MC-CDMA Transmitter Model . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Simplified MC-CDMA block diagram . . . . . . . . . . . . . . . . . . . . 20

2.3 MC-CDMA Receiver Model . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 CI/MC-CDMA Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 CI/MC-CDMA Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Discrete-time K-dimensional vector of single user matched filter outputs . . 33

4.2 Decorrelating detector block diagram . . . . . . . . . . . . . . . . . . . . 36

4.3 Parallel Interference Cancellation detector block diagram [19] . . . . . . . 40

6.1 Faded envelope generated by using Jakes Fading simulator. . . . . . . . . . 55

6.2 Autocorrelation of the I and Q components generated by the Jakes fading

simulator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.3 Simulated Average SER Vs. SNR for Decorrelating Detector using WH

and CI codes with different number of users. A1 =Aj; uncorrelated Rayleighfading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.4 Simulated Average SER Vs. SNR for MMSE Detector using WH and CI

codes with different number of users. A1 = Aj; uncorrelated Rayleigh fading. 646.5 Simulated Average SER Vs. SNR for a 2 stage MF/MF PIC Detector using

WH and CI codes with different number of users. A1 = Aj; uncorrelated

Rayleigh fading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.6 Average SER Vs. SNR for MMSE/MRC PIC Detector using WH and CI

codes with Rayleigh fading. . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.7 Average SER Vs. SNR for MRC/MMSE PIC Detector using WH and CI


6.8 Average SER Vs. SNR for MMSE/MMSE PIC Detector using WH and CI


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6.9 Average SER Vs. SNR for MRC/MRC PIC Detector using WH codes with

Rayleigh fading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.10 Simulated Average SER Vs. SNR for MMSE/MRC Detector using WH

and CI codes with Nu = 8 and 16. A1 = Aj; uncorrelated Rayleigh fading. . 706.11 Simulated Average SER Vs. SNR for MMSE/MRC and MRC/MMSE

Detectors using WH and CI codes with Nu = 16. A1 = Aj; uncorrelatedRayleigh fading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.12 Simulated Average SER Vs. Number of users for MMSE/MRC and MRC/MMSE

Detectors using WH and CI codes with different number of users. SNR =

0dB; A1 = Aj; uncorrelated Rayleigh fading. . . . . . . . . . . . . . . . . . 726.13 Simulated Average SER Vs. SNR for MMSE/MMSE Detectors using WH

codes with channel estimation errors. Nu = 16A1 =Aj; uncorrelated Rayleighfading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.14 Simulated Average SER Vs. Number of users for MMSE/MRC and MRC/MMSEDetectors using CI codes with different number of users and SNR = 6dB

and 12dB; A1 = Aj; uncorrelated Rayleigh fading. . . . . . . . . . . . . . . 74

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Chapter 1

Introduction

Third Generation (3G) mobile communication systems have already been deployed in sev-

eral markets around the globe and this has enabled new ways to communicate, access in-

formation, conduct business and be entertained. NTT DoCoMo launched the worlds first

commercialized third-generation FOMA mobile communication service on October 1,

2001 [30]. 3G services enable users to make video calls to the office and surf the internet

simultaneously, or play interactive games wherever they may be. Second and third gener-

ation systems like EDGE, IS-95, IMT-2000/UMTS [32], CDMA2000 [31] and WCDMA

[38] can provide nominal data rates of about 50 - 384 Kbps. As 3G deployment con-

tinues around the world, research efforts are looking into systems that can provide even

higher data rates and truly seamless connectivity. In addition to personal wireless commu-

nications, the need for mobile high speed communications for business, government and

the military has also been a driving force toward the interest in the research and devel-

opment of the next generation systems. Fourth Generation (4G) systems are predicted to

provide packet data transmission rates of 5 Mbps in outdoor macro-cellular environments

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and up to 10 Mbps in indoor and microcellular environments [34]. While wide-band sys-

tems could be a natural choice to provide high data rates, the limited spectrum available is

at a premium. Hence, spectrum efficiency is always a factor in the choice of any wireless

technology. For the handsets to be portable, the size and the power consumption of these

handsets becomes another constraint in the design of these systems. Additionally, multi-

path degrades the quality of transmissions which places a serious limitation on the design

of these systems.

Spread spectrum modulation techniques for digital communications were originally

developed and used for military communications either to provide resistance to hostile

jamming or to hide the signal by transmitting it at low power and, thus, making it difficult

for an unintended listener to detect its presence [35]. Today, however, spread spectrum

modulation techniques are being used to provide reliable communications in a variety of

commercial applications. The considerable interest in applying spread spectrum techniques

to multiple access communications is partly due to its multiple access capability, robustness

against fading, and its success in combating interference. CDMA has established itself as a

core wireless technology in 3G and in emerging standards. However, conventional CDMA

systems are fundamentally limited in their ability to deliver high data rates due to ISI and

implementation issues.

Multi Carrier Modulation (MCM), such as Orthogonal Frequency Division Multi-

plexing (OFDM) [33], has attracted considerable interest in both research and industry due

to its ability to support high rates while successfully combating ISI and fading. OFDM-

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based technologies are at the forefront of the competition to provide a physical layer that

would enable very high data capacities. OFDM transforms a frequency-selective fading

channel into a number of parallel flat-fading channels. As we shall see later, from a prac-

tical implementation standpoint, OFDM is especially attractive because modulation and

demodulation can be implemented efficiently by the Fast Fourier Transform (FFT).

Multicarrier CDMA (MC-CDMA) [25], a combination of OFDM and CDMA, has

been subject to much research since being introduced in 1993 [1] and has proven itself to

be a very good candidate to support the high data rates demanded of the next generation

mobile communication systems. MC-CDMA systems are robust to ISI, have an increased

immunity to MAI and exploit frequency selectivity for diversity by using a number of

narrowband subcarriers. There are, however, a number of challenges remaining in achiev-

ing MC-CDMAs full potential for wireless communication systems. Though OFDM, and

hence MC-CDMA, is robust to ISI, its performance and ease of implementation critically

depend on orthogonality between the subcarriers. This orthogonality can be easily de-

stroyed by the non-ideal system characteristics, like frequency offsets, Doppler effects due

to fast fading and phase noise, encountered in practice. Another challenge is the efficient

design of the detector and the choice of orthogonal spreading codes.

1.1 CDMA

FDMA and TDMA were the most prevalent technologies prior to adoption of CDMA by

industry. FDMA (Frequency Division Multiple Access) uses the intuitively obvious ap-

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proach of dividing the available bandwidth into frequency bands - one for each user. Thus,

the receiver which needs to detect the information bits sent by a particular user only needs

to tune to the particular user frequency. In the TDMA (Time Division Multiple Access)

scheme, which was developed much later, each user has the entire bandwidth at his dis-

posal, but is restricted to transmitting in multiplexed time slots. The rigidity of these two

systems is a big disadvantage because each user has to be conscious of the presence of the

other users, whether they are actively transmitting or not. The number of users that can be

supported is limited by the number of slots available, either in frequency or time.

CDMA is a spread spectrum technology, allowing many users to occupy the same

time and frequency allocations in a given band/space [36]. In a world of finite spectrum

resources, CDMA enables many more people to share the airwaves at the same time than

do alternative technologies. In addition, CDMA brings with it the benefits of spread spec-

trum schemes such as robustness against unknown channel distortion and anti-jamming

capabilities.

Direct-sequence CDMA is the most popular of the CDMA techniques. The DS-

CDMA transmitter modulates each users information bits by a distinct code waveform.

There has been a substantial interest in the DS-CDMA technology in recent years because

of its many attractive properties for the wireless medium. The most notable of them is the

increased capacity, which is measured by the number of users that can be supported in a

given frequency band, over TDMA and FDMA systems. This has led to the deployment of

CDMA in the commercial cellular systems.

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Direct sequence code-division multiple access (DS-CDMA) is a method of multi-

plexing wireless users, enabling them to share the same RF channel to transmit data si-

multaneously. The users are assigned specific signature chip sequences (codes) and the

transmitter sends its information bearing signal by modulating it by the appropriate signa-

ture waveform. These sequences, available to the receiver, can be orthogonal or have fairly

low crosscorrelations compared to the signature waveform energies. The receiver receives

the sum of all transmitted signals from its own cell (intracell interference) and adjacent

cells (intercell interference) plus additive white Gaussian noise (AWGN). The receiver, us-

ing the locally generated signature waveforms, despreads the received signal recovers the

data bits belonging to the user of interest by separating them from the data bits of the other

interfering users.

Apart from direct sequence, other spread spectrum signaling formats such as fre-

quency hopping are also very suitable for CDMA. In frequency hopping spread spectrum

(FHSS), the chips are modulated in frequency, rather than in phase as in direct sequence

CDMA. CDMA is susceptible to time-varying channel conditions - channel fading. In the

case of wideband systems like CDMA, the fading is typically frequency-selective.

1.2 OFDM/COFDM

Channel fading causes performance degradation and makes reliable high-data-rate trans-

missions a challenging problem in wireless communications. Researchers have been trying

to address these problems using OFDM based techniques. Since the 1960s, OFDM has

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become well-known as a bandwidth efficient modulation scheme for data communication

[33]. The basic approach of OFDM is grouping serial message symbols and transmitting

each symbol on different frequency domain carriers at a reduced signaling rate. The or-

thogonality of the subcarrier signals is exploited to permit the spectra of the subchannels

to overlap in order to achieve high bandwidth efficiency. As long as the orthogonality be-

tween the subcarriers is not destroyed, the receiver can recover the symbols mapped onto a

given subcarrier.

The OFDM signal can be written in discrete form as

sm = NIDF T(ck) (m = 0,1, . . . ,N1)

where IDFT represents the Inverse Discrete Fourier Transform. Nis the number of message

sequences (c0,c1, . . . ,cN1) and {ci}N1i=0 are the symbols.

One of the major advantages of OFDM is that in case of a deep fade the transmitted

data would still come through with very few or no errors. During an N-symbol duration

period of the conventional serial system, each of the N number of OFDM subchannel mod-

ulators carries only one symbol, each of which has an N times longer duration. Hence,

the channel fade affects only a fraction of the duration of these extended length subcarrier

symbols which are transmitted in parallel.

However, due to the frequency selective nature of the channel each subcarrier has

a different BER and in order to combat this phenomenon several methods have been used.

Coded OFDM is one such technique where error correcting coding in conjunction with

frequency domain interleaving is used to better the probability of error performance of

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OFDM [37].

1.3 MC-CDMA

A number of multicarrier techniques involving a combination of OFDM and spread spec-

trum have been proposed in the literature [1],[2],[3]. The scheme considered here and re-

ferred to as MC-CDMA is the one in which each information bit is spread in the frequency

domain and all its chips are transmitted simultaneously on all the narrowband subcarriers

[1]. Instead of applying the spreading sequences in the time-domain, as in CDMA, we can

apply them in the frequency domain by mapping a different chip of a spreading sequence to

an individual OFDM carrier. Hence, in MC-CDMA each users data symbol is simultane-

ously transmitted over multiple orthogonal narrowband subcarriers with each user assigned

a unique orthogonal spreading code. This provides two levels of orthogonality - the subcar-

rier frequencies are orthogonal and the user spreading codes are orthogonal. By applying

the spreading in the frequency domain, MC-CDMA achieves high frequency diversity. In

a channel with fading, this significantly reduces the probability that all the signal compo-

nents will fade simultaneously. This interesting characteristic is exploited by the Maximal

Ratio Combining (MRC) detectors to better detect the users information.

Each subcarrier has the same data rate as the original input data rate with a wider

spread in the frequency domain. Since each subcarrier is a narrowband carrier, it ex-

periences flat-fading though the entire channel may be frequency selective. As a result,

only a few of the information carrying carriers suffer attenuation while the majority of the

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subcarriers are still available to the receiver for detection. In this sense, the higher the num-

ber of subcarriers, the higher will be the resistance to the frequency-selective nature of the

channel. On the other hand, a large number of subcarriers results in more complicated syn-

chronization issues and the number of subcarriers used becomes crucial in any multicarrier

system design.

To maintain orthogonality, each narrowband subcarrier is at a different frequency

spaced apart by multiples of/Tb at baseband where Tb is the bit duration and is an in-

teger. In Fig. 1.1, we illustrate the frequency domain spectra of three multicarrier systems.

The first two systems are tightly packed with = 1. This corresponds to the closest

possible spacing between the subcarriers, 1/Tb. The structure of the signal is the same as

for OFDM. Having = 1 is most spectrally efficient. Additionally, since the signals are

formed by narrowband sinc() functions, the Since two frequencies lying within the coher-

ence bandwidth are likely to experience correlated fading, we need to ensure that the we do

not place too many subcarriers within the coherence bandwidth of the channel to achieve

frequency diversity. The loss of one sub-carrier in such a scenario could result in the loss of

all subcarriers within the coherence bandwidth. Hence, depending on the physical channel

characteristics, it becomes important to properly choose so that we achieve the goal of

frequency diversity. The spectrum shown in Fig. 1.1 (c) has = 2.

MC-CDMA signals have attractive spectral characteristics. Their spectral energy

is almost entirely confined to the allocated bandwidth. It is robust to multipath fading by

exploiting the inherent frequency diversity built into the scheme. It is also very effective in

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Figure 1.1: Multicarrier frequency spectra. (a) 8 subcarriers, = 1 (b) 4 subcarriers, = 1(c) 4 subcarriers, = 2

narrowband interference suppression by exploiting the orthogonality of the subcarriers and

also has a lower chip rate requirement. Owing to these and other spectral characteristics,

MC-CDMA allows for easier system coexistence and equalization.

However, since MC-CDMA is an OFDM-based technique, it is also vulnerable to

rapid time variations of the channel. The loss in orthogonality between subcarriers due to

frequency offset and timing jitter is a key issue for MC-CDMA [4]. The loss of orthogo-

nality can be between the subcarriers of a particular user or can lead to correlation between

spreading codes of different users causing an increase in ICI and MAI.

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1.4 CI/MC-CDMA

CI/MC-CDMA is a relatively new scheme and is not yet as researched as the technology

that it is based on. CI/MC-CDMA uses complex valued orthogonal spreading codes called

Carrier Interferometry (CI) codes [5]. Additional pseudo-orthogonal users are supported

by assigning, to these users, codes corresponding to CI signals, pseudo-orthogonal to the

original N users CI signals. As we shall see later, CI codes are capable of supporting

twice as many users as MC-CDMA using other codes like Walsh Hadammard codes, thus

doubling the network capacity, without a significant degradation in performance.

1.5 MC-DS-CDMA

In MC-DS-CDMA systems, the original data stream is first converted from serial to paral-

lel, spread by using the user specific spreading code in the time domain and finally, each

of these data streams modulate a subcarrier. In that sense, each frequency band is used to

transmit a narrowband direct sequence signal [25], [26]. As expected, MC-CD-CDMA is

computationally more expensive than DS-CDMA.

1.6 Contributions of this thesis

An analysis of the proposed Parallel Interference Cancellation detector on MC-CDMA has

not been extensively evaluated by other researchers in the field. Maximal Ratio Com-

bining, Equal Gain Combining and Minimum Mean Square Error detection with the PIC is

performed for the MC-CDMA system - this is not thoroughly discussed in literature. Given

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the equivalence of the CDMA and the MC-CDMA systems, the work performed on PIC

detectors for CDMA is extended to the MC-CDMA system. The effect of using CI (Carrier

Interferometry) codes for MC-CDMA when using a PIC detector is studied and evaluated

via simulations and compared with the MC-CDMA system using WH codes.

Chapter two details the MC-CDMA system description that is used throughout the

thesis. The channel model as well as the general receiver and transmitter structures are

described here. The third chapter introduces the Carrier Interferometry concept and its

application to MC-CDMA. Singleuser and Multiuser detectors are studied in chapter four.

A thorough review of the literature and the state of the art in detection techniques for MC-

CDMA is discussed here. Chapter five introduces a two stage interference cancellation

detector for MC-CDMA systems and the system is mathematically analyzed here. Sim-

ulations of the systems using MC-CDMA as well as CI/MC-CDMA for various detector

structures were performed and the results are presented in chapter six. Chapter seven doc-

uments the conclusion and possibilities for future research.

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Figure 1.2: MC-CDMA Scheme: a) Transmitter, b) Power spectrum of transmitted vector,

c) Receiver

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Chapter 2

System Description

In this chapter, we describe the proposed MC-CDMA system. We will first develop the

multi-user MC-CDMA wireless channel model and then elaborate on the design of the

system. The MC-CDMA discrete-time baseband model is presented, with a description of

various parameters used.

2.1 Multipath Channels

Two parameters often used to characterize multipath channels are delay spread and coher-

ence bandwidth. The delay spread, Td, is a measure of the length of the impulse response

of the channel. A large delay spread would lead to intersymbol interference (ISI), thus

degrading the performance of the system. We have assumed that the RMS delay spread for

each subcarrier is comparatively small and hence the ISI is minimal. For channels that have

a large delay spread the ISI can be checked by using a guard interval that is longer than the

maximum delay spread.

Coherence bandwidth is the approximate maximum bandwidth or frequency inter-

val such that any two frequencies lying within this interval are likely to experience corre-

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lated fading. If the average multipath delay spread is Td, then the coherence bandwidth,

Wc, is given as [21]:

Wc =1

2Td. (2.1)

Doppler spread is defined as a measure of the spectral broadening caused by the

temporal rate of change of the mobile channel. A small Doppler spread implies a large co-

herence time or a slowly changing channel. For the purpose of our discussions we consider

a slowly changing wireless channel in which the Doppler shifts are relatively small and the

channel can be assumed to be constant over the bit duration, Tb.

Multipath channels are commonly characterized by Rayleigh or Rician distribu-

tions. These distributions describe the random amplitudes resulting from the multipath

channels. In the absence of a line-of-sight component of the received signal, such as when

the direct path is obstructed by the environment or buildings and the received signal consists

of only scattered components, the channel can be modeled as a Rayleigh faded channel. In

this case, the signal amplitude resulting from the vector addition of all components is mu-

tually uncorrelated Rayleigh distributed with the probability density function (pdf):

f (x) =x

2ex

2/22 x 0 , (2.2)

where 2

is the variance of the in-phase and quadrature components of the received signal

and the phases are mutually independent random variables uniformly distributed over the

interval [0, 2). The nth moment of the Rayleigh random variable is given by

E[()n] = (22)n/2(1 +n

2)

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where, (p) = (p - 1)!, p I, p > 0.

Then, the mean and the variance is given by

E[] =

2

E[ 2] = 22(1 +

4).

In certain environments, like the indoor radio channel, there may be a direct LOS

component present. Here, the signal consists of the LOS component as well as the less

dominant scattered components corresponding to the reflected paths. In such a case, the

received signal amplitude can be characterized by a Rician distribution given by

f (x) =x

2ex2+s2

22 I0

xs2

x 0 , (2.3)

where s2 is the amplitude of the LOS component, I0(x) is the zeroth order modified Bessel

function and 2 is the variance of the in-phase and quadrature components of the received

signal. The envelope distribution is often characterized in terms of the Rice factor K =

s2/(22) which is defined to the be ratio of the power of the LOS component to the power

of the scattered component.

2.2 Channel Model

In this work, we consider the synchronous downlink of a cellular radio system, i.e., the sig-

nals of the different users are transmitted synchronously from the transmitter at the base sta-

tion to the receiver of the mobile unit. This is typically characteristic of the downlink chan-

nel and increasingly, there are communication systems proposed with quasi-synchronous

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uplink channels [23], [24]. The channel is assumed to be a frequency selective channel with

the subcarrier bandwidth much less than the coherence bandwidth, 1/Tb


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transmitting the jth bit can be described by,

Hkj,n = kj,nexp(ikj,n) (2.4)

where, Hkj,n is Rayleigh distributed and k

j,n is uniformly distributed on [0, 2). Inde-

pendent fading between users implies that the fading amplitudes (kj,n : k= 1, . . . ,Nu; n =

1, . . . ,Nc) are a set of mutually independent Rayleigh random variables and phases (k

j,n :

k= 1, . . . ,Nu; n = 1, . . . ,Nc) are a set of mutually independent uniform random variables on

[0, 2).

From the previous section, the mean and variance are given by

m kj,n= E[(j,n)

2] =

2

2kj,n

= E[(j,n)2]E[(j,n)]2 = 22(1

4).

2.3 Discrete-Time Baseband Model of MC-CDMA System

Let Nc be the number of equally spaced subcarriers that divide the entire available band-

width, Wc, into Nc sub-bands. Let Nu be the number of actively transmitting users at the

same time instant t. Let us denote the data vector by B = [bj1,b

j2, . . . ,b

jNu

]T. Let bjk be the

discrete jth bit transmitted by the kth user such that k {1,2, . . . ,Nu} and j {1,2, . . . ,J}.

As mentioned earlier in this chapter, we consider the synchronous downlink of an MC-

CDMA system. The MC-CDMA signal is generated by taking each of the Nu simultaneous

users bits and sequentially replicating the kth users data sequence onto the Nc parallel

branches. Each of these parallel branches is then multiplied by a chip, cik, of the user spe-

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cific spreading sequence ck of length Lc, where, ck = [c1k,c

2k, . . . ,c

Lck ]

T. Consequently, the

entire Lc

Nu code matrix, represented by C, is defined as

C =

c11 c

12 . . . c

1Nu

c21 c22 . . . c

2Nu

......

. . ....

cLc1 c

Lc2 . . . c

LcNu

where the kth column vector corresponds to the kth users spreading code ck. In the system

considered here, the processing gain is assumed equal to the number of subcarriers, i.e., Lc

= Nc.

Each parallel stream is then modulated onto a subcarrier spaced apart from its

neighboring subcarriers by F/Tb where F is an integer and Tb is the bit duration. The

transmitted signal consists of the sum of the output of these branches. This process yields

a multicarrier signal with the subcarrier containing the coded bit.

2.3.1 MC-CDMA Transmitter Model

The continuous-time MC-CDMA transmitter model is shown in Fig. 2.1. The low-pass

equivalent continuous-time waveform for the jth bit transmitted by the kth user can be

written as:

ujk(t) =

Nc

i=1

cikbjkcos(2fct+ 2i

F

Tbt)pTb (t kTb) (2.5)

where pTb (t) is defined as the unit amplitude pulse which has non-zero values in the inter-

val [0,Tb], fc is the center frequency of the subcarrier and F is an integer number which

describes the spacing between the subcarrier frequencies.

From the way the MC-CDMA signal is generated, it is clear that it is similar to the

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Figure 2.1: MC-CDMA Transmitter Model

OFDM signal structure. OFDM transmission can be realized by a discrete-time version of

the OFDM transmitter which is the same as a Discrete Fourier Transform (DFT). Practical

implementations of an OFDM transmission system use Fast Fourier Transforms (FFTs) to

realize the modulation and demodulation of user data signals onto multiple parallel subcar-

riers. Hence, on the transmitter side, the bank of oscillators can be replaced by an IFFT

operation. On the receiver, an Nc-point FFT is performed on the received signal, y(t).

Essentially, the input signal is split into Nc branches and the signal on each branch is

modulated onto one ofNc subcarriers. Each subcarrier is then coded with user ks spreading

code; a recombining and modulation to the passband occurs and the signal is sent out over

the channel. At this point, it should also be noted that though the signal structure of MC-

CDMA is similar to that of Orthogonal Frequency Division Multiplexing (OFDM), the

manner in which the signals are used is very different. A simplified MC-CDMA block

diagram is shown in Fig. 2.2.

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Figure 2.2: Simplified MC-CDMA block diagram

2.3.2 MC-CDMA Receiver Model

The continuous-time MC-CDMA receiver model is shown in Fig. 2.3.

From the figure, the equivalent continuous-time received signal, y(t), can be ex-

pressed as

y(t) =Nu

k=1

Nc

i=1

k,icikb

jkcos(2fct+ 2i

F

Tbt+ k,i) + n(t) (2.6)

where n(t) is the additive white Gaussian noise (AWGN) with zero mean and a one-sided

power spectral density ofN0; k,i and k,i denote the channel effects.

Since we are considering the downlink transmission, it should be noted that the

terminal receives the interfering signals (for users k = 2, 3, ..., Nu) through the same channel

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Figure 2.3: MC-CDMA Receiver Model

as the desired user. Hence, there is only one set of amplitude and phase describing the

channel for all the users. This implies that when the channel correction is applied to the

desired user, the amplitude and phase correction will also apply to the interfering signals.

We also assume perfect front-end filtering so that we are able to perfectly separate the

subcarriers without any distortion.

Consider the ideal single path synchronous downlink system through additive white

Gaussian noise. It is sufficient to consider a single symbol interval [0,T] and hence we can

drop the subscript j for the remainder of the analysis. At the receiver, the received input

can be written as

rk = IFFT{A b s}+ n (2.7)

where s is the normalized code waveform matrix of the k users and n is the additive white

gaussian noise. The IFFT corresponds to the Nu Nc-point IFFT operations for the Nu users.

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We first perform an Nc-point FFT operation on this received signal to obtain

rk = FFT{IF FT{A b s}}+ FFT{n} = A b s + n (2.8)

where n is the colored noise with the same mean and variance as the AWGN. After passing

the received waveform through a bank of matched filters, with each matched filter matched

to the signature waveform of a different user, the discrete-time output of the matched filter

can be expressed in vector form as

y = RAb + n (2.9)

where R is the normalized crosscorrelation matrix with Ri,j given by

Ri,j =T

0si(t)sj(t)dt . (2.10)

The matched filter output vector, y, is

y = [y1,y2, . . . ,yn, . . . ,yNc ]T

where yn is the component on the nth subcarrier. The received noise vector, independent of

b, containing the noise on each carrier is

n = [n1,n2, . . . ,nNc ]T

and A is the received amplitude matrix with Ak the received amplitude of the kth users

signal. As before, b is the transmitted bit vector.

A closer look at equation (2.9) shows that the MC-CDMA received signal has the

same form as the DS-CDMA signal except that the modulation scheme is very different.

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This similarity in form is exploited to derive receiver structures for MC-CDMA later in

this thesis. The discrete-time version of the received signal can also be viewed as the

Discrete Fourier Transform (DFT) of a Direct Sequence Code Division Multiple Access

(DS-CDMA) signal. As we have noted before, this is equivalent to saying that the signal is

CDMA coded in the frequency domain.

2.4 Summary

In this chapter we presented the MC-CDMA system model. We discussed multipath chan-

nels and a mathematical description of the channel model used throughout this thesis was

provided. A mathematical framework for the analysis of the MC-CDMA receiver structures

in subsequent chapters was presented here. We mathematically described the MC-CDMA

signal structure as well as the transmitted and received signal in the presence of channel

effects.

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Chapter 3

Carrier Interferometry and

CI/MC-CDMA

In this chapter, we discuss the concepts involved in Carrier Interferometery and its use

in MC-CDMA systems. We elaborate on Carrier Interferometery (CI) codes and their

applicability to the MC-CDMA. We present the CI/MC-CDMA discrete-time baseband

model, with a brief discussion of the system capacity.

3.1 Robust CI Codes

The Carrier Interferometry (CI) signal is at the heart of the Carrier Interferometry based

technologies. In experimental physics, interferometry refers to the characteristics of in-

terference patterns resulting from the superpositioning of waves. The idea fundamental to

interferometry - distinct peaks and nulls as a result of interfering waves - is particularly

useful to multiple access schemes in wireless communications. For example, by carefully

choosing the initial phases of the transmitted waves, we can ensure that a peak is created

for the desired signal while nulls are created for all the other waves.

In their work [5] Nassar et. al. have applied the principles interferometry to create

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spreading codes that are strongly orthogonal and robust to a number of imperfections in

a wireless channel. Since these spreading codes cause interferometry patterns between

the carriers they are called carrier interferometry codes. By a careful choice of codes, a

main lobe is created in the time domain by the superpositioning of the subcarriers of the

transmitting user. At the same time instant, the other users superpositioned signals at that

time only result in sidelobe activity. Thus, ideally, only one user would have a main lobe at

any given time instant.

The CI signal is composed of a number of narrowband carriers. In the time domain

the signal is narrow enabling an easier separation of the signals at the receiver. The CI

signal is composed of N carriers equally spaced with a frequency separation off. A linear

combination of these in-phase carriers results in the time domain envelope as shown in Fig.

3.1. The periodic signal with a period of 1/f consists of a mainlobe of duration 2/(Ncf)

followed by sidelobe activity each with a duration of 1/(Ncf). Then, a signal positioned

with mainlobe centered at 0 is orthogonal to any signal with its main lobe positioned at time

, where {k/(Ncf)} and k= 1,2,...,N. This important property of CI waveforms is

exploited in creating transmission signals that are resilient to ISI and ICI.

The existing MC-CDMA codes, such as Walsh-Hadammard, Zadoff-Chu, Gold,

Orthogonal Gold, etc., are designed to be orthogonal and support N users or pseudo-

orthogonal and support greater than N users at the cost of degraded performance. Further,

N is limited to 2n or 2n 1, where n is an integer. The CI codes introduced in [4] support

N users orthogonally and, as required, can support upto N 1 additional users pseudo-

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Figure 3.1: CI/MC-CDMA Envelope

orthogonally. Additionally, there are no restrictions for N, i.e., NI.

The MC-CDMA scheme employing Carrier Interferometry complex spreading codes

is called CI/MC-CDMA. A CI signal with a time offset of = k/(Ncf) is equivalent to a

signal having carriers with a phase offset of

{1,2,...,N} = {0,2k/N,2 2k/N,...,(N1) 2k/N} . (3.1)

This can be interpreted as CI signals with carriers using orthogonal complex spread-

ing sequence corresponding to the kth user given by

ej1,ej2,...,ejN

=

0,ej2k/N,ej22k/N,...,ej(N1)2k/N

=

0,ejk,ej2k,...,ej(N1)k

(3.2)

where k =2N

k and k= 1,2,...,N.

The CI codes can also support (N 1) additional users as mentioned above by

resorting to pseudo-orthogonal code sequences. The CI signals are then not orthogonal to

each other but still can exhibit good auto and cross-correlation properties when = /N

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as shown in [4].

With the excellent frequency and time resolution exhibited by the CI signal, it has

been demonstrated via simulations that multicarrier technologies based on this signal per-

form better that when using WH codes.

3.2 CI/MC-CDMA Formulation

To apply carrier interferometry to MC-CDMA, we need to replace the spreading codes

normally used, such as Walsh-Hadammard and Gold codes, with the complex spreading

codes that make up the CI signal. By selecting the spreading codes as given in (3.2) we

can support N users with orthogonal signatures and an additional N1 users with pseudo-

orthogonal signatures.

Figure 3.2: CI/MC-CDMA Transmitter

We consider a CI/MC-CDMA system with Nu users and Nc subcarriers. The kth

users CI/MC-CDMA transmitter is shown in Fig. 3.2. The users data symbols are trans-

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mitted over the Nc narrowband subcarriers each of which is multiplied with the user specific

complex spreading code. With BPSK modulation, i.e., the kth users input symbol in the

nth bit interval bk[n] = 1, the kth users transmitted signal corresponds to

sk(t) =Nc1i=0

bk[n]cos(2fit+ ik) p(tnTb) (3.3)

where fi = fc + if and p(t) is a rectangular pulse with support in [0, T]. The fs are

chosen such that the subcarriers frequencies, fi = 0,1,...,Nc

1, are orthogonal to each

other. As with traditional MC-CDMA and OFDM, f is chosen such that f = 1/Tb

where Tb is the bit duration.

The kth users transmitted signal can also be written as

sk(t) = bk[n] p(t) ck(t) (3.4)

where ck(t) is the superpositioned signal from the N equally spaced subcarriers. ck(t) is

given by

ck(t) =Nc1i=0

cos(2fit+ ik) (3.5)

where k =2Nu

k (k= 0,1, . . . ,Nu1) .

The envelope of the cosine waveform (plotted in Fig. 3.1) with frequency fc +

((Nc 1)/2)f is given by

Ek(t) =

sin( 12Nc(2fit+ ik))sin( 12

(2fit+ ik))

. (3.6)28


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Fig. 3.1 plots the envelope for Nc = 16 carriers, Tb = 1s and k = 0. It is observed

that the code ck(t) is periodic with period 1/f = Tb. Further, the nth period contains a

mainlobe of duration

2

Ncf=

2Tb

Nc

with the mainlobe positioned at time

Tb

n +

k2

.

The Nc1 sidelobes have a duration of TbNc and the maximum amplitude of the lth sidelobe

is given by

1

Nc sin

Nc

l + 1

2

.3.3 System Capacity

The cross-correlation between the jth and the kth user signature waveforms, cj(t) and ck(t)

respectively, can be shown to be

Rk,j() =1

2f

Nc1i=0

cos(2if) (3.7)

=1

2f sin(

12Nc(2f))

sin( 12

(2f))cos

Nc1

22f

(3.8)

where =(kj)

2f .

The Nc 1 equally spaced zeros at = kNcf, k= 1,2, . . . ,Nc 1 indicate that the

CI/MC-CDMA system can simultaneously support Nc orthogonal users by use ofNc codes.

Since depends only on the phase difference kj, introducing a fixed phase

offset to all users phases maintains orthogonality between the the users spreading codes.

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Thus, by replacing k in (3.5) by k+ we can create a set of orthogonal codes given

by (3.5) with

k =2

Nuk+ [0,2]. (3.9)

This second set of codes have a non-zero cross-correlation with the codes in (3.5).

It is shown in [5] that the cross-correlation is minimised by choosing = Nc . Hence, the

system capacity can be increased by selecting a second set of codes with phase offset of

= Nc

with respect to the first set of codes. For 2Nu active users, each user can be assigned

a spreading code {ck(t),k= 0,1, . . . ,2Nu1}, with

ck(t) =Nc1i=0

cos(2fit+ ik) (3.10)

k = 2Nu k k= 0,1, . . . ,Nu12Nu

(kNu) + Nu k= Nu,Nu + 1, . . . ,2Nu1(3.11)

System capacity can effectively be doubled by the use of pseudo-orthogonal CI

codes without an adverse affect on system performance.

3.4 Summary

We introduced the Carrier Interferometry technique and its application to MC-CDMA in

this chapter. We mathematically described the signal structure of the CI/MC-CDMA signal

and explored modifications to support additional users thereby increasing system capacity.

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Chapter 4

MUD for MC-CDMA and

CI/MC-CDMA

4.1 Single-user Detectors

The challenge of detecting a single users bit from a received signal that has been asyn-

chronously transmitted over a time varying multipath channel can be a complicated prob-

lem. MAI due to the non-zero cross correlations of the signature waveforms, Inter Symbol

Interference (ISI) from the memory in the desired users channel, power control and esti-

mation of the channel coefficients are some of the impediments to the proper detection of

the signal that was transmitted.

A simpler problem definition is arrived at by assuming that there is no multipath

and that there is no attenuation of the signal either, thereby eliminating ISI. Further, by

assuming that the transmission is bit-synchronous, k = 0 and the MAI in one bit period is

purely due to the interference due to the bits of the other users transmitted during the same

period. Given these conditions, the problem of sequence estimation reduces to that of one

shot estimation which is independent for each bit period. Then, bk(n) can be estimated for

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all kby considering the received samples in just the nth bit period. Matched filtering y with

the signature waveforms will then yield sufficient statistics.

In conventional single user detection, individual decisions are made based on the

output of the matched filter alone relying entirely on the orthogonality of the user signature

waveforms. The signature waveforms are susceptible to distortion due to channel effects

and lose the orthogonality, leading to MAI. This interference from the other users is treated

as Gaussian noise by a single user detector. The inability of the single-user detectors to

effectively use the structure of the other users signal results in a performance penalty as

the desired users signal is often burried in the entire signal. The situation becomes worse

when the signal energies are very dissimilar even if the cross-correlation is low. Strict

power control becomes necessary to ensure detection of the desired users signal with a

low error probability.

4.1.1 Conventional Single User Detector

Using a single-user matched filter is a natural strategy to demodulate the received signal.

Typically, a bank of matched filters is used as a front end to any subsequent multiuser

detection strategies, as shown in Fig. 4.1. Each matched filter is matched to one of the

signature waveforms. In such a case, each matched filter has responsibility to demodulate

only one user and so the bank of filters does not need to concern itself with users other than

the one of interest as every branch operates independently.

The output of the kth matched filter can be expressed as

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Figure 4.1: Discrete-time K-dimensional vector of single user matched filter outputs

yk = Akbk+j=kAjbjjk+ nk (4.1)

yk = Akbk+MAIk+ nk (4.2)

where, as before, jk is the cross-correlation between the jth and the kth signature wave-

forms. MAIk is the Multiple Access Interference as seen by user k. Defining the cross-

correlation matrix R as

R = jkwe can express the soft output of all users K in vector form as

y = RAb + n (4.3)

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whereE[nnT] = 2R. This matched filter output is then used to drive a single or a multiuser

decision device. The decision is made based on the position of yk in the constellation while

considering MAI to be Gaussion distributed. The bit error probability for BPSK symbol

modulation is given by [20]

Pk() =1

2K1 bi{1,+1}

i=j

Q

Ak+Ki=1i=j

Aiikbi

. (4.4)If the signatures are orthogonal, the conventional single user is optimal as the MAI

vanishes and each user enjoys a single user channel.

4.2 Linear Multi-user Detectors

In multicarrier systems like MC-CDMA, the active users can be transmitted using orthog-

onal codes like WH or CI codes. However, due to the independent scaling of each of the

subcarriers, the code orthogonality between the users is destroyed. A single tap equalizer

has to be used to restore this orthogonality. Linear detectors perform a pseudo-inverse of

the channel matrix, thereby performing a kind of equalization. Multiuser detectors aim

to use the information in the sufficient statistics for all users to obtain the desired users

estimate.

Using the maximum likelihood (ML) criterion, the ML detector is the optimum

detector. However, since the inherent complexity of the optimum detector increases expo-

nentially with the number of users and the length of the users code, this is not a practical

solution when the number of users or the code length can be large. Sub-optimal receivers

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have been the focus of much study under such circumstances.

A general linear multiuser detector can be written as [14]

ak =T

0lk(t)r(t)dt k= 1,2, ,K (4.5)

bk = sgn{ak}where r(t) is the received signal and lk(t) is as described below.

lk forms the kth row of an estimator matrix and as discussed in [9], any interesting

detector has lk span{s1,s2, . . . ,sK}, the vector space spanned by the codes of all users.

Any component outside this subspace will only result in an increase in the background

noise without having any affect on the interference from the other active users of the system.

The general linear multiuser can then also be written as

b = sgnLTy (4.6)where L is the KK estimator matrix.

4.2.1 Decorrelating Detector

Since the input to the decorrelating detector is of the same form as for DS-CDMA, we can

apply the analysis for the decorrelating detector from a CDMA system to the MC-CDMA

system.

For the decorrelating detector, L is R1. Premultiplying the vector of matched filter

outputs by R1, we get

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Figure 4.2: Decorrelating detector block diagram

R1y = Ab + R1n (4.7)

which implies that the kth component is free of MUI and the only source of interference is

the background noise.

4.2.2 Maximal Ratio Combining (MRC) Detector

The motivation for using the MRC detector comes from the observation that it gives best

results in an interference free multipath environment [22] [1]. In a multicarrier system,

the sub-carriers that contain copies of the same information bearing signal can be seen as

different branches that introduce frequency diversity in the system. In such a case, when

replicas of the same signal are available on different sub-carriers, MRC is the most optimum

diversity combining technique with respect to BER. These diversity branches are weighed

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by their respective complex conjugate channel coefficients and combined at the receiver.

4.2.3 Minimum Mean Square Error (MMSE) Detector

For the MMSE detector [27] [28], L, the estimator matrix, is defined asR + 2A2

1.

It can be noted from the above that MMSE detection requires the knowledge of the

noise power 2.

4.3 Interference Cancellation Detectors

An alternative to using linear detectors is to use interference cancellation detectors. The

idea of interference cancellation receivers is to estimate the multiple access and multipath

induced inference and then subtract the interference estimate from the signal that was re-

ceived. Several interference cancellation schemes have been studied in the literature [12]

[13]. Prominent among them are parallel interference cancellation and successive interfer-

ence cancellation. In parallel interference cancellation [29] [11] [14], the bits for all users

are estimated in parallel and the interference is cancelled simultaneously from all users.

In successive interference cancellation [16] [15], it is cancelled on a user-by-user basis.

Also, the interference cancellation principle can be based on utilizing tentative (hard) data

decisions obtained from the composite signal or by utilizing (soft) decisions based on the

signal.

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4.3.1 Successive Interference Cancellation (SIC) Detector

In SIC, as the name suggests, the detection/cancellation process occurs successively. Once

a decision about a users bit has been made, the signal from that user can be recreated and

subtracted from the originally received waveform. Provided a correct decision was made

about the user, this will eliminate the interference from the particular user from the received

signal. This process is iteratively performed until all the users have been detected. On the

other hand, an incorrect decision about the users bit will lead to doubling the interference

from that user. In this successive decoding scheme, since each user is cancelled only once,

a relatively low complexity receiver can be designed. Since the reliability of the successive

decisions is affected by erroneous intermediate decisions, the order of the demodulation of

the users affects the performance of the detector. One popular method ([17], [16], [18])

of ensuring a high probability of a correct bit detection of the users detected towards the

beginning of the process is to rank the users according to their received signal strength.

The strongest user is detected and cancelled first since its is more plausible that the proba-

bility of an error in the detection of this users bit is lower than the others. The process is

repeated until all users have been detected. In this scheme, at the beginning of each loop

the remaining users have to be ranked.

Among the advantages of the scheme is the fact that weak users, which normally

would not be detected reliably using the conventional receiver, can now be detected more

efficiently since most of the interference has been removed by the end of the process. How-

ever, the unequal interference levels seen by users at the beginning and the end of the can-

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cellation process leads to different SINR, and thus BER, for different users. Therefore,

although no strict power control is required, some power control is still essential to ensure

equal SINR ratio for all users. Another issue is the delay required for the completion of

the successive interference cancellation process. This approach can potentially lead to ex-

tended delays when a large number of users are required to be detected. Assuming that

approximately 1 bit delay is required per loop, then for K users we require K - 1 bit de-

lay. This limitation is less of a problem, however, at high bit rates where the bit period

becomes smaller. It should also be pointed out that since the receiver requires amplitude

estimates, any errors in the estimation of received amplitudes directly translate into noise

for succeeding decisions.

Another consideration is that this scheme is suboptimal in the sense that only the

last user experiences complete interference reduction. Additionally, it is also possible that

there is interference that is either incompletely (due to inaccurate channel estimation) or

incorrectly cancelled. This interference accumulates through to the last loop (error propa-

gation) where the final user is detected.

4.3.2 Parallel Interference Cancellation (PIC) Detector

Parallel Interference Cancellation, which involves canceling all users simultaneously, is an

alternative to the successive approach. PIC is considered here for a number of reasons - its

complexity increases linearly with the number of active users, it has a short delay time and

has moderate performance loss compared to the optimal detection. PIC receivers also often

outperform the successive interference cancellation (SIC) receivers.

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Figure 4.3: Parallel Interference Cancellation detector block diagram [19]

The PIC detector (Fig. 4.3) estimates and subtracts out all of the MAI for each user

in parallel. Inputs for this detector are obtained from the matched filter detector (conven-

tional detector) or the MMSE detector, which is referred to as stage 0 of this detector.

These bits are then scaled by the amplitude estimates and re-spread by the codes, which

produces a delayed estimate of the received signal for each user. The partial summer sums

all but one input, creating a complete estimate of the MAI experienced by each user.

In a typical PIC detector, all K users create replicas of their interference contribution

to the other K - 1 users signals. These replicas are then subtracted simultaneously from

the K - 1 users signals. The data estimates from the output of the first stage can be fed

into a second stage to be used as interference replica estimates thus giving better data

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estimates at the output of the second stage. As the number of stages ( m) increases the data

estimates become better. However, increasing the number of stages also makes the system

computationally more intensive as a greater number of operations have to be performed.

4.4 Summary

We discussed single and multiuser detection in the context of MC-CDMA in this chapter.

We explored the concepts for both linear detectors as well as interference cancellation

detectors and briefly reviewed their mathematical representation.

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Chapter 5

Performance Analysis of A Two Stage

MRC/MMSE PIC Detector

We develop and analyze the two stage parallel interference cancellation detector in this

chapter.

5.1 Parallel Interference Cancellation

Varanasi and Aazhang were one of the first to describe the parallel interference cancella-

tion detector in [11]. A multi-stage detector typically consists of successive stages of signal

estimation and cancellation. In a multi-stage PIC detector, tentative decisions from a pre-

vious stage are used to estimate the interference for cancellation. A number of different

configurations of the multi-stage parallel interference cancellation detector are possible by

varying the choice of the initial and subsequent stage detectors.

In this chapter, we examine a two stage PIC detector using Maximal Ratio Com-

bining as its first stage to exploit the frequency diversity provided by the signal structure

of the Multi-carrier CDMA system. This is followed by an interference cancellation stage

where the signal consisting of all the users but the desired user is regenerated using the bit

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estimate of the other users from the first stage. This interference is then subtracted from

the original signal to yield, in an ideal situation, an interference free signal for the desired

user. The output of the IC stage is passed to an MMSE detector to get the final bit estimate.

The algorithm for the conventional PIC employing only matched filters is as fol-

lows. The received signal is fed to a bank of matched filters after conversion to baseband.

Each matched filter correlates the resulting signal with each users known spreading signal

to obtain the initial stage estimates of each users symbols in parallel. Each users estimate

can then be used to recreate the interfering signal. The regenerated signals from all users

but the desired user are summed and subtracted from the original signal. Ideally, this would

result in the elimination of all the interfering signals from the desired users signal and the

desired users signal can be detected without error resulting from any interfering users. The

bit error probability in such an ideal case would tend towards that of a single user system.

Due to errors in the estimation of the users bits, the regenerated signal may not

entirely match the interfering signal. In such cases the subtraction of this regenerated signal

could add to the interfering signal instead of subtracting from it. A proper choice of the

initial stage plays a key role in mitigating this effect. By repeating the entire process over

several stages also helps further refine the estimated bit decision. Ideally, every additional

stage will allow for a further refinement of the signal and better bit estimates corresponding

to each user will be produced, thus allowing for more effective interference cancellation.

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5.2 MRC as the first stage

The underlying goal of any equalization technique should be to mitigate the effect of fad-

ing and interference on the desired signal while not enhancing the noise component of the

received signal. We use the fact that the MC-CDMA signal structure provides frequency

diversity to apply and investigate the performance of a two stage multicarrier parallel inter-

ference cancellation detector. The first stage of this detector is a Maximal Ratio Combining

detector followed by a parallel interference cancellation stage. The output of the PIC stage

is used to drive a MMSE detector stage which gives the final bit decisions.

The transmitted signal for the kth bit of the jth user is given by [3]

sj(t) =Nc1i=0

cj[i]aj[k]cos

2

fc + i

F

Tb

t

pTb (tkTb) (5.1)

where

cj[0]cj[1] . . .cj[Nc1]

represents the signature sequence of the jth user and cj[i]

{+1,1} for Walsh Hadammard codes. In the above equation, Nc is the number of

subcarriers, Tb is the symbol duration, fc is the carrier frequency, and F/Tb is the subcarrier

spacing, where F is an integer. As discussed before, F = 1 makes the most use of the

spectrum and the signal structure is equivalent to the OFDM signal structure. pTb (t) is the

rectangular pulse with support in [0,Tb]. aj[k] is the jth users bit transmitted in the kth bit

interval.

The channel transfer function is given by

Hkj,i = kj,iexp(i

kj,i) (5.2)

where the jth users bit is transmitted in the kth bit interval on the ith subcarrier, kj,i is

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Rayleigh distributed, kj,i is uniformly distributed on [0, 2) and i is1. Independent

fading between users implies that the fading amplitudes (k

j,i: j = 1, . . . ,Nu; i = 1, . . . ,Nc)

will be a set of mutually independent Rayleigh random variables and phases (kj,i : j =

1, . . . ,Nu; i = 1, . . . ,Nc) will be a set of mutually independent uniform random variables on

[0, 2).

Additionally, it is assumed that kj,i and kj,i remain approximately constant over the

symbol duration, Tb. This implies that the channel is not affected by Doppler (slow fading).

Further, for a downlink transmission (i.e., transmissions from the base station to

the user terminals), the terminal receives the interfering signals for the other users (j =

1,2,...Nu 1) via the same channel as the desired users signal (j = 0). As a result, there

will only be one set of amplitudes and phases describing the channel for all the user signals.

If we apply phase or amplitude correction to the desired user signal, then the phase and

amplitude of the interfering signals is also corrected. We can incorporate this information

notationally as below

j,i = 0,i (5.3)

j,i = 0,i . (5.4)

The local mean power at the ith modulated subcarrier of the jth user is given by

pj,i =1

2E[ 2j,i] (5.5)

and from the iid assumption, the local mean power of all the subcarriers is equal, hence,

pj = Ncpj,i . (5.6)

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The continuous-time received signal at the user terminal is given by

r(t) =Nu

1

j=0

Nc

1

i=0

cj[i]aj[k] kj,icos2fc + i FTb t+ kj,i+ n(t) . (5.7)Matched filtering is performed using Nc matched filters, each consisting of an oscil-

lator matched to the corresponding subcarrier frequency and an integrator. A phase offset

is included in the oscillator in order to obtain phase synchronization. Assuming that the

users are synchronized in time, the kth data symbol after despreading and equalization is

given by

0 =Nu1

j=0

Nc1i=0

cj[i]c0[i]aj[k]j,id0,i2

Tb

(k+1)TbkTb

cos

2

fc + i

F

Tb

t+ j,i

cos

2

fc + i

F

Tb

t+ j,i

dt+ (5.8)

where d0,i is the equalization gain for each matched filter branch corresponding to each

subcarrier. This gain depends on the equalization technique employed.

is the additive white Gaussian noise term given by

=Nc1i=0

(k+1)TbkTb

n(t)2

Tbd0,icos

2

fc + i

F

Tb

t+ j,i

dt . (5.9)

Assuming that the phase is perfectly corrected by the bank of matched filters, i.e.,

j,i = 0,i, we have

0 = a0[k]Nc1i=0

0,id0,i +Nu1

j=0

Nc1i=0

cj[i]c0[i]aj[k]j,id0,icosj,i + (5.10)

where j,i = 0,i j,i, denotes the estimate of the phase at the ith subcarrier for the jth

user.

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The decision variable consists of three terms and can be represented as

0 = S+IMAI + (5.11)

where S is the desired users signal, IMAI is the interference from other users and is the

noise term. The bit estimate is obtained by a decision device

b[0] = sign ({0}) . (5.12)

The MRC scheme results in a ML receiver and provides the best possible perfor-

mance among the diversity combining techniques [20]. By using the MRC diversity com-

bining we can exploit all available frequency diversity in the MC-CDMA signal. For the

MRC scheme, the signal from each subcarrier must be weighted by its respective complex

fading amplitude and combined. Thus, the amplitude of each copy of the signal is squared

by using a gain factor for the ith sub-carrier of

d0,i = 0,i . (5.13)

The motivation behind Maximal Ratio Combining is that the components of the

received signal with large amplitudes are likely to contain relatively less noise. Their effect

on the decision process is hence increased by squaring their amplitudes. For the downlink

channel considered, we use (5.4) since the different users arrive at the receiver through one

channel. With MRC used after matched filtering, the decision variable is given by

0 = a0[k]Nc1i=0

20,i +Nu1

j=1

Nc1i=0

cj[i]c0[i]aj[k]20,i + (5.14)

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where the noise can be approximated by a zero-mean Gaussian random variable with the

variance given by

2 = NcN0

TbE[20,i] . (5.15)

Because consists of the sum of(Nu 1)Nc Gaussian random variables, it can be

approximated as a zero mean Gaussian random variable, with the variance given by

Var[IMAI] = (Nu1)Nc20,i

= (Nu1)Nc E[ 40,i] (E[20,i])2=

(Nu1)Nc

4 p02 . (5.16)

Also, since the sum of independent zero mean Gaussian distributions is a zero mean

Gaussian distribution, the variance of can be written as

2

= Var[IMAI] + 2

. (5.17)

With our assumption of aj[k] taking on equi-probable binary antipodal values and

given a0[k] = 1, the probability of making an error conditioned on the amplitude of the

signal and the interference power is given by

Pr (error|0,i) = PrNc1i=

0

20,i < . (5.18)

Since has a Gaussian distribution, we can write the conditional probability of

error as

Pr (error|0,i) =

Nc1i=0

20,i

122

exp

y22

dy . (5.19)48


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Using the complementary error function

erfc(x) =2

x et2 dt (5.20)and (5.17), we can write (5.19) as

Pr (error|0,i) = 12

erfc

12 Nc1i=0 20,i2

Var[IMAI] + 2

. (5.21)Substituting the values ofVar[IMAI] and from equations (5.16) and (5.15) in (5.21) we

have

Pr (error|0,i) = 12

erfc

12

Nc1i=0

20,i

2(Nu1)

Nc4 p0

2 + 2N0

Tbp0

. (5.22)The central limit theorem (CLT) can be employed to obtain an approximation for

finding the distribution of the sum of squared iid Rayleigh random variables for the limiting

case of large Nc. Using the CLT approximation, the probability of error has been found to

be [1]

PMRC 12

erfc

p0Tb

2Nu

Ncp0Tb +N0

. (5.23)

5.3 MMSE as second stage

The signal at the receiver can also be written in vector notation as

r = H C b + (5.24)

r = H s + (5.25)

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where r is the received vector, H isthe[Nc xNc] channel matrix, C is the [Lc xLc] spreading

code matrix for all the users, b is the transmitted bit vector for the users and is the noise

vector.

The signal consisting of all the interfering users is reconstructed by using the bit

estimates of all the users provided by the first stage. In the interference cancellation stage,

this reconstructed signal is subtracted from the received signal

r = rHC b[0] (5.26)where b

[0] is the vector of bits of the interfering users determined at stage [0]. After inter-

ference cancellation and equalization, the output is obtained as

y[1] = G[1]r = G[1]

rHCb[0]

(5.27)

where G is the [Nc x Nc] equalization martix. MMSE minimises the mean square error

between the transmitted and the estimated bits. When using the MMSE SU detector for the

second stage of the PIC, the ith subcarrier equalization coefficient is given by

gi =hi

|hi|2 + 1/c(5.28)

where c is the average signal to noise ratio per subcarrier at the receiver. Diagonal elements

ofG and H, gi,i and hi,i respectively, are written as gi and hi for the sake of brevity. The bit

estimate for the first user, after despreading and thresholding, is given by the scalar product

of the received vector after equalization and the spreading code vector of the user 1

d(1) = sgn(< y[1],c(1) >) (5.29)

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where the superscript [1] denotes the MMSE stage (and [0] denotes the MRC stage), the

superscript (1) denotes the first user and < y[1],c(1) > is given by

< y[1],c(1) >=d(1)

Nc

Nc

i=1

g[1]i hi +

Nc

i=1

Nu

j=2

d(j)[1]d(j)[0]

g

[1]i hic

(1)i c

(j)i +

Nc

i=1

g[1]i c

(1)i i .

(5.30)

The above equation can be written as the sum of three parts as

< y[1],c(1) >= ++ (5.31)

where the first, second and third parts of (5.31) are the useful signal, the residual interfer-

ence and the component due to noise, respectively.

By using the Law of Large Numbers, we can approximate the useful signal energy

in the equation above as

EE

g[1]h2

Eb . (5.32)

By using the Central Limit Theorem, the following approximations can be arrived

at [7]

2 2P[0]bNu1

Nc

E

(g[1])2h2E

g[1]h2

Eb (5.33)

where P[0]b is defined as the probablity of error in the first stage as determined in the previous

section and 2 is the variance of the MUI. The noise variance can be expressed as

2 N0

2E

(g[1])2

. (5.34)

The probability of error can then be written as

Pb = erfc

E

2(2 + 2 )

(5.35)

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where the erfc function is as defined in (5.20).

To evalulate E , 2

and 2

we can use

E{gihi} = E

|hi|2|hi|2 + 1/c

|hi|is rayleigh

= 1 +e1/c

c

1/c

ex

xdx

(5.36)

E|gihi|2 = E |hi|2|hi|2 + 1/c 2

|hi|is rayleigh

= 1 +1

c+

1

2c+

2

c

e1/c

1/c

ex

xdx

(5.37)

E

|gi|2

= E

|hi||hi|2 + 1/c

2|hi|is rayleigh

= 1

1 +1

2c

e1/c

1/c

ex

xdx

(5.38)

.

The exponential integral in the equations above converges for 1/c > 0 and we can

write it as

Ei 1c=

1/c

ex

xdx . (5.39)

Then (5.32) can be written as

E 1 + 12c

e2

c

Ei

1

c

2+

2

ce

1cEi

1

c

Eb . (5.40)

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In a similar fashion, we can write the variance of the MUI in equation (5.33) as

2 2P[1]b Nu1Nc 1 + 1c + 12c + 2ce 1cEi 1cEb 2P[1]b

Nu1Nc

1 +

1

2ce

2c

Ei

1

c

2+

2

ce

1cEi

1

c

Eb

= 2P[1]b

Nu1Nc

1

c+

1

2ce

1cEi

1

c

1e 1cEi

1

c

Eb . (5.41)

Similarly, we can write the variance of the third term in (5.31) as

2 11 + 12c e 1cEi 1cN02 . (5.42)Using (5.40), (5.41) and (5.42) in equation (5.35), we can analytically evaluate the

performance of the two stage detector. Since these approximations are based on the central

limit theorem, we can expect to see an increased accuracy with an increase in the length of

the spreading code.

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Chapter 6

Simulations and Results

The results of the simulations performed are presented in this chapter. First, the simulation

setup is described and then the simulation results are presented with a discussion of each

simulation performed.

6.1 Simulation Setup

The system was simulated using Walsh-Hadamard codes for the MC-CDMA and orthogo-

nal Carrier Interferometry codes for CI/MC-CDMA. The spreading codes of length L = 2,

4, 8 and 16 were considered when using both WH codes and CI codes. The number of ac-

tive users, Nu (i.e., users assumed to be transmitting at a given time) was assumed equal to

the number of sub-carriers (Nc). Hence, a fully loaded system was considered. The system

was simulated for Nc = 2, 4, 8 and 16 subcarriers. The spreading gain was assumed equal

to the number of sub-carriers, L = Nc. The system was assumed free of power loading,

i.e., the average power is the same for all users across all sub-carriers. We assume that the

system transmit power is the same for every user, i.e., that Ak = A.

The fading across users and the subcarriers is considered to be independent, with the

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magnitude of fading following the Rayleigh distribution. Further, we assume that a perfect

estimate of the channel co-efficient matrix H is available to the receiver. In practice, ths

estimation can be made by scattered pilot insertion or insertion of reference symbols [6].

As stated previously, we consider a synchronous system. Based on this, the received vector

is decoded by the receiver to extract a hard bit decision either in a single stage or using two

stages with parallel interference cancellation before the intermediate decision is used for

the next stage. Each data point used to plot the graphs is calculated based on the average

of 200,000 bits of data.

The fading envelope was generated by using the modified Jakes Fading simulator

(Fig. 6.1) [10].

0 2000 4000 6000 8000 1000050

40

30

20

10

0

10

RayleighEnvelopeindB

Time

Figure 6.1: Faded envelope generated by using Jakes Fading simulator.

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To check the properties of the faded envelope the autocorrelation of the I and Q

components generated by the Jakes fading simulator (Fig. 6.2) was plotted.

1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1

x 104

0.4

0.2

0

0.2

0.4

0.6

0.8

1

Time Delay

Au

tocorrelation

Autocorrelation of I and Q components obtained from the Jakes Fading Simulator

Figure 6.2: Autocorrelation of the I and Q components generated by the Jakes fading sim-ulator.

A Binary Phase Shift Keying (BPSK) modulation scheme was considered with the

user bits randomly generated with an equal probability of +1 or -1.

In the absense of interference from other users, the probability of error is determined

by the background Gaussian noise. Since this holds true for every detector, it can be used

as the single user lower bound for any detector. This probablity of error is given by

PSU = Q

A

(6.1)

where Q(x) is given by

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Q(x) = (2)(12 )

x

exp(t2

2)dt . (6.2)

In our simulations, we will use this as the lower bound for the multiuser detectors.

6.1.1 Simulation Results: Linear Detectors

Fig. 6.3 shows the performance of the Decorrelating Detector for a fully loaded MC-

CDMA system using Walsh Hadammard and Carrier Interferometry codes. Here, the num-

ber of users is assumed to be equal to the number of subcarriers, i.e., Nc =Nu. It is observed

that the performance degrades moderately as the system load is increased from Nu = 2 to

Nu = 16. There does not appear to be a substantial difference when using CI codes over

WH codes in the case of the decorrelator.

Next, the system was simulated using the Minimum Mean Square Error (MMSE)

detector (Fig. 6.4) and it was observed that for the two-user case there was no apparent

difference in the BER when using CI codes over WH codes. However, an appreciable

difference was noted when the number of carriers and the number of users were increased.

For an average BER of 103 we note an improvement of 2dB for CI over WH codes with

16 simultaneous users.

6.1.2 Simulation Results: Parallel Interference Cancellation Detec-tors

The two stage Parallel Interference Cancellation (PIC) detector was simulated in a number

of configurations.

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We simulated a two stage version of the matched filter detector (MF/MF Configura-

tion) where the first stage hard decisions were used to regenerate the interfering signal and

was subtracted from the original signal and fed to the second stage. Based of the output of

the second stage the hard decisions were calculated as the received bits. As evidenced from

Fig. 6.5 the 2 stage matched filter detector was found to perform worse than the other PIC

detectors that were simulated. Further, there was no advantage of using CI codes over WH

codes with the matched filter. Similar to previous plots, it was observed that as the number

of users in the system increased, the performance of the MF/MF PIC detector deteriorated.

Fig. 6.6 shows the performance of a two stage PIC detector utilizing MMSE as

its first stage and Maximal Ratio Combining (MRC) as its second stage after interference

cancellation. The performance improved as the number of carriers was increased while

using Carrier Interferometry codes. We also noted that a performance hit compared to

CI codes, similar to the MMSE case, was observed with an increase in the number of

carrier

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