Sharma Anshul

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  • 7/29/2019 Sharma Anshul




    I, _________________________________________________________,

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


    It is entitled:

    This work and its defense approved by:

    Chair: _______________________________






    Anshul Sharma

    Master of Science

    Electrical Engineering



    Dr. James Caffery, Jr., Ph.D

    Dr. Howard Fan, Ph.D

    Dr. Qing-An Zeng, Ph.D

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    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


    in the Department of

    Electrical and Computer Engineering and Computer Science

    of the College of Engineering


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


    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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    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


    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


    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


    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



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

    Then, the mean and the variance is given by

    E[] =


    E[ 2] = 22(1 +


    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


    22 I0


    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] =



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


    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


    ]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


    c21 c22 . . . c



    . . ....

    cLc1 c

    Lc2 . . . c


    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) =



    cikbjkcos(2fct+ 2i


    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





    jkcos(2fct+ 2i


    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



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    Chapter 3

    Carrier Interferometry and


    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







    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





    with the mainlobe positioned at time


    n +



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

    is given by


    Nc sin


    l + 1


    .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



    cos(2if) (3.7)


    2f sin(


    sin( 12





    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


    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}





    . (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


    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


    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


    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



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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


    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



    fc + i




    pTb (tkTb) (5.1)


    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


    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






    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








    fc + i



    t+ j,i



    fc + i



    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






    fc + i



    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



    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



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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



    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=


    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


    = 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=


    20,i < . (5.18)

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

    error as

    Pr (error|0,i) =






    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


    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


    Pr (error|0,i) = 12






    Nc4 p0

    2 + 2N0


    . (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




    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


    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]



    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)




    g[1]i hi +







    [1]i hic

    (1)i c

    (j)i +



    g[1]i c

    (1)i i .


    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



    Eb . (5.32)

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

    at [7]

    2 2P[0]bNu1





    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



    . (5.34)

    The probability of error can then be written as

    Pb = erfc


    2(2 + 2 )



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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






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

    |hi|is rayleigh

    = 1 +1













    = E

    |hi||hi|2 + 1/c

    2|hi|is rayleigh

    = 1

    1 +1








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

    write it as

    Ei 1c=



    xdx . (5.39)

    Then (5.32) can be written as

    E 1 + 12c












    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


    1 +














    = 2P[1]b









    1e 1cEi



    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









    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









    Time Delay



    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



    where Q(x) is given by


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    Q(x) = (2)(12 )



    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