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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
codes with Rayleigh fading. . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.8 Average SER Vs. SNR for MMSE/MMSE PIC Detector using WH and CI
codes with Rayleigh fading. . . . . . . . . . . . . . . . . . . . . . . . . . 68
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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