Neural network based multiuser detectors for DS CDMA

List of Symbols k k user’s signal amplitude A diagonal matrix of all users received amplitudes C j th center vector of RBF network E energy function of Hopfield neural network ] ⋅ E e

NEURAL NETWORK BASED MULTIUSER DETECTORS

FOR DS-CDMA

BIJAYA NEPAL

(B Eng., Tianjin University, P R China)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2003

Acknowledgement

August 2003

I would like to express my sincere gratitude towards my supervisor Professor Dr Tjhung Tjeng Thiang for his invaluable guidance and continuous encouragement throughout the course of this research work Especially I thank him for the inspiration he provided to me during the hard time of the research work I will always remember his supports on academic as well as on personal matters I would also like to express my sincere gratitude

to Dr Chew Yong Huat for providing me a lot of suggestions plus showing me the mistakes on my work Finally I would like to thank the National University of Singapore for providing me the research scholarship to pursue my Master of Engineering Degree in this prestigious University

Bijaya Nepal

Acknowledgements i

Table of Contents ii List of Figures vi

List of Symbols ix List of Abbreviations xii Summary xiii

Chapter 1: Introduction 1

1.1 Background ……… 1

1.2 Spread Spectrum Communications Principle ……… 3

1.3 DS-CDMA ……… 5

1.3.1 Multiple Access Interference ……… 7

1.3.2 Performance of DS-CDMA ……… 7

1.3.3 Simple Illustration of Near-far Problem in DS-CDMA … 8 1.3.4 Power Control ……… 10

1.3.5 Multiuser Detection ……… 11

1.4 Motivation ……… 12

1.5 Contribution of this Thesis ……… 13

1.6 Organization of the Thesis ……… 14

Chapter 2: Multiuser Detection Strategies 17

2.1 DS-CDMA Received Signal Model ……… 17

2.1.1 Synchronous Transmission ……… 20

2.1.2 Asynchronous Transmission ……… 21

2.2 Output of Matched Filter Detector - Matrix – Vector Notation … 21 2.2.1 Synchronous System ……… 22

2.2.2 Asynchronous System ……… 24

2.3 Established Multiuser Detectors ……… 28

2.3.1 Conventional Matched Filter Detector (CD) ……… 28

2.3.2 Optimum Multi-user Detector (OMD) ……… 29

2.3.3 Decorrelating Detector ……… 31

2.3.4 Multistage Detector ……… 33

2.3.4 Minimum Mean Square Error (MMSE) Detector ………… 34

2.4 Summary ……… 35

Chapter 3: Hybrid-MGNANN Multiuser Detector for DS-CDMA 37 3.1 Neural Network in DS-CDMA Multiuser Detection ……… 37

3.2 Hopfield Neural Network (HNN) for Multiuser Detection …… 39

3.3 Problems with HNN ……… 43

3.4 Solution of Local Minima Problem ……… 43

3.4.1 Annealed Neural Network Multiuser Detector ……… 43

3.4.2 Matrix Graduated Non-Convexity Technique ……… 44

3.5 Complexity Reduction by Using Reduced Detector ……… 46

3.6.1 Simulation Parameters ……… 53

3.6.1.1 User bits, Phase angle, Delay and Gaussian

noise Generation ……… 54 3.6.1.2 Spreading Codes ……… 54 3.6.1.3 Packet Size ……… 56 3.6.1.4 Gain of the Sigmoid function and Time

Constant value in HNN ……… 57 3.6.1.5 Initial Temperature for Annealing Process … 57 3.6.2 Flowchart of the Simulation Programs for

the Multiuser Detection ……… 58 3.6.2.1 Synchronous Transmission ……… 58 3.6.2.2 Asynchronous Transmission ……… 59 3.6.3 Simulation Results and Discussions for Hybrid-MGNANN

Multiuser Detector ……… 60

3.6.3.1 Synchronous DS-CDMA Simulation Examples … 60 3.6.3.2 Asynchronous DS-CDMA Simulation Examples … 66

3.7 Summary ……… 69

Chapter 4: Hybrid-RBFN Multiuser Detector for DS-CDMA 70

4.1 Radial Basis Function Networks (RBFN) ……… 70 4.2 Bayesian Decision Rule ……… 73

4.3 Complexity Reduction Techniques ……… 74

4.4 Proposed Hybrid Detector ……… 76 4.5 Simulation Results and discussions for Hybrid-RBFN

Multiuser Detector ……… 78

4.5.1 Synchronous DS-CDMA Simulation Examples … 78

4.5.2 Asynchronous DS-CDMA Simulation Examples … 82 4.6 Summary ……… 85

Chapter 5: Conclusions and Future Research Directions 86

5.1 Conclusion ……… 86 5.2 Future Work ……… 88

Chapter 1: Introduction

Figure 1.1 Multiaccess Channel – Signals from K users ……… 3

Figure 1.2 Basic spread spectrum technique ……… 4

Figure 2.1 K asynchronous users over an AWGN channel ……… 19

Figure 2.2 Relative time delays between user bits (assumingτ1 =0) …… 21

Figure 2.3 K - user detector employing matched filter detector at the front end ……… 23

Figure 2.4 The decorrelator for synchronous CDMA ……… 32

Figure 2.7 n stage multistage detector ……… 34

Figure 3.1 Additive model of a neuron ……… 40

Figure 3.2 A simple Hopfield Neural Network of 3 neurons ……… 41

Figure 3.3 Hybrid MUD ……… 47

Figure 3.4 Flowchart for simulation in synchronous transmission …… 58

Figure 3.5 Flowchart for simulation in asynchronous transmission …… 59

Figure 3.6 Cumulative BER versus SNR i (K = L7, =4,NFR=10dB) …… 60

Figure 3.7 Weakest user’s BER versus SNR (K = L7, =4,NFR=6dB) … 61

Figure 3.8 Cumulative BER versus SNR (K= 7 , L= 4,E1 =10,E2 =20,E i =1,i=3, ,7) ……… 62

Figure 3.9 Cumulative BER versus SNR (K= 5 , L= 7Gold CodesE1 =10, E i =1, i=2, ,5) ……… 63

Figure 3.10 Cumulative BER versus number of users

(E1 E i =10dB, SNR i =8dB) ……… 64 Figure 3.11 Weakest user’s BER versus NFR

(K= 5 , L= 4,NFR=E i E1,SNR1 =8dB) ……… 65 Figure 3.12 Weakest user’s BER versus SNR (K= 3 , L= 4,

,8

1 dB E

E NFR= i = i= 2 , 3, delay fixed at [0 ; 0 5T; 0 75T]) …… 66 Figure 3.13 Cumulative BER versus SNR i (K = L5, =7, NFR=10dB,

delay changed at every 300 transmissions) ……… 67 Figure 3.14 Weakest user BER versus SNR (K= 5 , L= 7Gold Codes,

dB

Figure 4.1 A Radial Basis Function Network for DS-CDMA ……… 72

Figure 4.2 Hybrid RBF Receiver with preprocessing stage ……… 76

Figure 4.3 CumulativeBER performance of different

detectors (K = L5, =4) ……… 78 Figure 4.4 Weakest userBER Performance of different

detectors (K =7,L=4) ……… 79 Figure 4.5 Cumulative BER versus number of users

(E1 E i =10dB, SNR i =8dB) ……… 80 Figure 4.6 Cumulative BER versus NFR (K =5,L=7,SNR i =8dB)……… 81

Figure 4.7 Cumulative BER versus SNR (K =3, L=4, dBE1/E i =10 ,

delay fixed at [0;0.5T b;0.75T b]) ……… 82

=

L , 10E1 =1,E2 =6,E3 = , delay fixed at [0;0.5T b;0.75T b] … 83 Figure 4.9 Cumulative BER versus SNR(K =4, L=7, dBE4/E i =10 ) … 84

List of Symbols

k

k user’s signal amplitude

A diagonal matrix of all users received amplitudes

C j th center vector of RBF network

E energy function of Hopfield neural network

]

⋅

E expected value

p

E constraint energy term in matrix graduated nonconvexity

E diagonal matrix with elements as signal energies

F soft output from the RBFN

H cross correlation matrix

H~ cross correlation matrix for asynchronous transmission

rr

H cross-correlation matrix of the determined users (or elements) after

an iteration of reduced algorithm

ww

H cross-correlation matrix of the undetermined users (or elements)

after an iteration of reduced algorithm

rw

H cross-correlation matrix related with the determined and

undetermined users after an iteration of reduced algorithm

j

I externally supplied bias for th

j neuron

K number of transmitting users

k penalty parameter in matrix graduated nonconvexity

L length of spreading sequence (number of chips)

n colored Gaussian noise vector

k

n noise output from matched filter for th

k user )

R partial cross correlation between user i and user j

R normalized cross correlation matrix

R information data rate

)

(t

k user’s transmitted spread spectrum signal

S covariance matrix in Mahalanobis distance measure

SNR signal to noise ratio

ρ cross correlation between signature waveform of user i and user j

α sigmoid gain that controls the slope of the nonlinearity

k

k user’s asymptotic efficiency

φ nonlinear basis function

desired signal vector

j centerspread parameter

τ time constant of the RCcircuit in HNN

AWGN Additive White Gaussian Noise

ANN Annealed Neural Network

ANNMD Annealed Neural Network Multiuser Detector

BER Bit Error Rate

BPSK Binary Phase Shift Keying

CD Conventional Detector

CDMA Code Division Multiple Access

CLB Chip Level Based

DS-CDMA Direct Sequence Code Division Multiple Access

DSP Digital Signal Processing

DS-SS Direct Sequence Spread Spectrum

DSSS-BPSK Direct Sequence Spread Spectrum Binary Phase Shift Keying DECO Decorrelating Detector

FDMA Frequency Division Multiple Access

FH Frequency Hopping

FH-CDMA Frequency Hopping Code Division Multiple Access

HNN Hopfield Neural Network

HNNMD Hopfield Neural Network Multiuser Detector

H-RBFN Hybrid Radial Basis Function Network

H-MGNANN Hybrid Matrix Graduated Non-Convexity Annealed Neural

Network MAI Multiple Access Interference

MAP Maximum a posteriori

MLP Multilayer Perceptron

MLSD Maximum Likelihood Sequence Detection

MRBF Radial Basis Function based on Mahalanobis Distance Measure MSD Multistage Detector

MUD Multi User Detector

NFR Near Far Ratio

OMD Optimum Multiuser Detector

PPB Pre Processing Based

PSK Phase Shift Keying

RBF Radial Basis Function

RBFN Radial Basis Function Network

SNR Signal to Noise Ratio

TDMA Time Division Multiple Access

S Verdu, in his seminal work, proposed the optimal multiuser detector (OMD) Despite the huge performance gains over conventional detector, this detector is not suitable for practical implementation since the complexity of the detector increases exponentially with the increase in the number of users Therefore most of the research thereafter has focused

on finding sub-optimum multiuser detector solutions which give acceptable bit error rate (BER) performance and are more feasible to implement than the OMD

proposed detector is an efficient two stage multiuser detector The first stage is a reduced detector to effectively reduce the size of the optimization process and the second stage is a matrix graduated non-convexity annealed neural network (MGN-ANN) detector Likewise, the second proposed detector is also a two stage detector consisting of a reduced detector at the first stage and radial basis function network (RBFN) at the second stage

By using a first stage reduced detector, the computational complexity in the second stage can be significantly reduced Neural networks were chosen to implement the sub-optimum multiuser detection in our work because they are well suited for the pattern classification problem

We carried out extensive simulations for synchronous and asynchronous DS-CDMA systems with various operating conditions in order to compare the error probability performance of our proposed detectors with other competing multiuser detectors, which are based on conventional matched filter detector (CD), Hopfield Neural Network (HNN), multistage detector (MS-10) and annealed neural network (ANNMD) We also use the optimum multiuser detector (OMD) as comparison benchmark for all the MUDs To have broader view to the proposed detectors’ performances, we vary parameters such as spreading codes, user power ratio, and number of users in the system etc Simulations for the AWGN channel, performed using MATLAB 6.1, have shown that the error probability performances of our proposed detectors are significantly better than other suboptimum MUD’s and approaches the performance of OMD

Chapter 1 Introduction

Mobile communication is one of the fastest growing industries in the world these days

We are experiencing near exponential growth in the number of cellular subscriber in some regions of the world Particularly during the past two decades, the mobile radio communication industries has grown by orders of magnitude, fuelled by digital and RF circuit fabrication improvements, new large scale circuit integration and other miniaturization technologies which make portable radio equipment smaller, cheaper and more reliable [37] Moreover digital switching techniques have made possible the large-scale deployment of affordable and user-friendly radio communication networks We can

be sure that the mobile communication will have an ever increasing impact upon our daily life over the next several decades

In the early 1980s, the first generation cellular systems were introduced which were based

on analog FM technology The system was designed to carry narrow band voice service Later in the early 1990s came the second generation cellular system, which uses digital modulation The second generation cellular system was also designed to carry narrow

band voice and data services In comparison with the first generation, the second generation systems provide a lot of improvements in terms of spectral efficiency and voice quality Now the third generation system is being deployed in some parts of the world that offer voice, high bit rate data and multimedia services In the mean time a lot of works are being carried out to specify the fourth generation cellular system that will provide broadband wireless access with asymmetric bit rates that approach 1 Gb/s [19]

To realize the reliable and affordable wireless communication for everyone, anywhere and anytime, major improvements in the current wireless technology are expected Furthermore, the growing demand for different wireless services have motivated researchers to develop novel techniques to increase channel capacity, data rates and reliability of multimedia applications Efficient use of channel bandwidth is always a top priority and use of multiple access technique is one major step taken in this direction The multi-access channel is used quite extensively in today’s wireless environment In a multi-access environment, the receiver receives the additive sum of all signals present in the channel as shown in the figure 1.1 There are primarily three multiple access techniques: Frequency division multiple access (FDMA), Time division multiple access (TDMA) and Code division multiple access (CDMA) Certain characteristics of spread spectrum waveforms upon which CDMA is based have given some edge to CDMA over FDMA and TDMA Spread spectrum signals are effective in mitigating multi-path and interference from other users due to wide bandwidth The result of these effects is the higher capacity potential compared to that of other non-spread type multiple access methods [21]

Chapter 1: Introduction _

Spread spectrum (SS) signals used for the transmission of digital information are distinguished by the characteristics that their bandwidth W is much greater than the

information bandwidth R The bandwidth expansion of the signal is accomplished by the

use of spreading codes The spreading codes are independent of the data bits The spread signals are generated by linear modulation of narrow band user signal with wideband PN (pseudo noise) sequences that are assigned to individual users as their signature codes This results in wide bandwidth spectrum and highly reduced average power spectral density for the spread signal At the receiver, estimation of the original data is performed

by the inverse process, given knowledge of the desired user’s spreading sequence

As seen from figure 1.2, the bandwidth expansion of the data (narrow band) is performed

by multiplying with the high bandwidth spreading codes The enhancement in the

User 1

User 2 User 3

User K

: : :

performance due to the bandwidth expansion and bandwidth contraction is termed as Processing Gain (PG) and is given by

R

W

BandwidthSignal

Data

BandwidthSignal

Spread

(1.1)

The choice of spreading sequence is an important element in the design of SS signals A second important element employed in the design of SS signals is pseudo-randomness, which makes signals appear similar to random noise and difficult to demodulate by receivers other than the intended ones

The single most important purpose of spread spectrum technique is to protect against jamming signal from intentional or unintentional users Another application of spread spectrum is that of multiple access by numerous users who share the same spectrum using codes, which are distinguishable from those of all other users The third form of interference suppressed by spread spectrum technique is the self interference caused by multipath in which delayed version of the signal, arriving via alternate paths, interfere with the direct path transmission [3]

FilterData signal

Rate R

Spreading

signal

Spread signal Bandwidth

W

Spreading signal

Recovered data signal

Bandwidth R

Figure 1.2 Basic spread spectrum technique

Undesired signal

Chapter 1: Introduction _

There are two main strategies within spread spectrum: Direct Sequence (DS), in which the data bit modulates the spreading sequence to produce the signal to be transmitted and frequency hopping (FH), in which the signature sequence defines the frequency hopping pattern of the signal FH-CDMA is primarily concerned with evading eavesdropping and interception of signal and data, so it is suitable for the military application In our work,

we are only considering DS-CDMA

The performance gain obtained from a Direct Sequence Spread Spectrum (DS-SS) signal through the processing gain can be used to enable many DS-SS signals to occupy the same channel bandwidth, provided that each signal has its own fixed, distinct signature waveform This allows several users to transmit simultaneously over the same channel bandwidth In general, as the performance gain (PG) increases, so does the number of signals that can be accommodated in the system Since all the users transmit over the same channel using DS-SS technique, this type of communication is called Direct Sequence-Code Division Multiple Access (DS-CDMA)

Direct sequence systems are widely used spread spectrum systems because of their relative simplicity from the standpoint that they do not require a high-speed fast-settling frequency synthesizer [20] (as only one carrier frequency has to be generated) DS-CDMA

is one major spread spectrum technology that is gaining popularity these days primarily because of some of its attractive properties such as soft capacity, soft handover and resistance to multipath fading among others This technology has been used in many

military applications for secure communications over the decades However the development of the DS-CDMA cellular system for civilian applications was mainly for its higher spectral efficiency and capacity reasons [14]

In a typical DS-CDMA system, users are assigned unique codes or spreading sequences that are near orthogonal to one another These spreading sequences allow users to spread the information signal across the assigned frequency band Signals from various users are then separated at the receiver by taking correlation of the received signal with each of the possible user spreading sequences

Consider a DS-CDMA channel with K simultaneous users Assuming AWGN channel,

the noise corrupted received signal at the receiving end is the superposition of all the users spread data plus Gaussian noise as follows:

)()()

(

1

t n t S t

k user is given by:

)cos(

)(2

)

k c i

b k i k k

Chapter 1: Introduction _

T t lT

t p a t

c T L

l l k

=

0),

()

(

1 0

1.3.1 Multiple Access Interference (MAI)

In CDMA systems, the capacity of the system is no longer limited by bandwidth, the limiting factor is now interference noise CDMA systems have to deal with a special kind

of interference Since all users transmit at the same carrier frequency, they all interfere with one another This interference is called multiple access interference (MAI) The level

of this interference varies, depending on (i) similarity of signals (ii) the number of users at any given time, and (iii) signal power of each user, if the spreading sequences are not totally orthogonal This interference may cause detrimental effect if the receiver is unable

to perfectly remove the effect of all the interfering signals on the signal of interest

1.3.2 Performance of DS-CDMA

The conventional way of detecting each users data bit in DS-CDMA is to decorrelate the received signal using each users spreading waveforms and simply taking sign of the

output thus obtained In a single user channel, when the signal is corrupted by AWGN only, this conventional way of detection minimizes the probability of error and yields optimum decision, but in multiple access environment, its performance is acceptable only

if the energies of the received signals are not too different and the spreading waveforms have sufficiently low cross correlation properties

In the multiple access environments, due to the non-orthogonality of user spreading codes, there exists multiple access interference, which becomes excessive, if some users are received with more powers than other users (near-far problem) The conventional single user detector treats each user separately and considers the signal from other users simply

as white noise As the number of users increases, the equivalent noise causes the degradation of performance Even in the high SNR scenario, the error probability of the conventional matched filter receiver exhibits a non-zero floor because of the MAI Thus the conventional DS-CDMA is interference limited

1.3.3 Simple Illustration of Near-Far Problem in DS-CDMA

We now present a simple example of a conventional DS/CDMA system consisting of only 2 synchronous users (τ1 =τ2 =0)to elaborate the near far problem faced by such systems As mentioned previously, the received signal is superposition of all the users’ transmitted signal plus the additive white gaussian noise

)()cos(

)(2

a b W t

k

Chapter 1: Introduction _

where W k,b k,a k, are average signal power, data bit and spreading codes of the th

) 1 ) 2

) 1 2

2 1

2 1 1

i i

i

n

n b

b W

W W

W W W

b

)()( 2

Let’s assume user 1 is the desired user As seen from expression (1.6), the matched filter

output for user 1, )

1

i

y consists of three terms: recovered data term )

1 1

i

b W

W ρ and noise term )

1

i

n If the spreading codes are well designed, then the cross-correlation value will be very small

(ρ ≅0) and MAI becomes insignificant In such a case, the conventional matched filter detector yields optimum detection in AWGN On the contrary, if we implement poorly designed spreading codes, then the interference from other user may become excessive if the other user’s received power W2 is significantly higher than the desired user’s received power W1, thus making reliable detection for the desired user almost impossible

The above example shows, the key to avoid MAI is to employ well-designed spreading codes that are orthogonal to each other But in the practical situation, it is never possible

to have totally orthogonal spreading sequences Moreover, the CDMA system operates asynchronously, which means that the transmission time of a user’s data symbols may not coincide with those of the other users This reality complicates the design of good codes for CDMA It is almost impossible to maintain orthogonality between user’s signature waveforms over all possible delays Even if we employ well-designed spreading codes, if the number of active user increases, the multiple access interference will slowly accumulate and eventually cause the receiver to produce a false output The problem may further worsen if the users’ signals arrive at the receiver with different powers (near-far problem) due to the physical location of the users from the receiver or due to fading, badly affecting the overall performance of the system

To ameliorate this problem, stringent power control is implemented in current CDMA system design Multiuser detection is another way to tackle the problem

1.3.4 Power Control

The use of power control ensures that each mobile within the base station coverage area provides the same signal level to the base station receiver This solves the problem of a nearby user overpowering the base station receiver and swamping out the distant weak users Power control is provided by the base station in its coverage area by constantly monitoring the transmitted power level of each user Power control can be implemented in two ways: open loop power control and closed loop power control If the users adjust their

Chapter 1: Introduction _

transmitted power to be inversely proportional to the power level it receives from the base station, then it is called open loop power control, whereas if the base station sends power control instructions to the users based on the power level it receives from the users, then it

is called closed loop power control [32]

Precise power control is difficult to maintain and significantly increases complexity, which is considered one of the serious impediments to the CDMA system Besides, power control can become self-defeating, since it actually decreases the overall multiple access and anti-jamming capabilities of the system [36]

1.3.5 Multiuser Detection

Multi-user detection is a technique to separate different mutually interfering signals transmitted over the same multiple access channel Whereas in conventional single user detection, the other user’s signals are treated as white noise, in multi-user detection, the signal information of multiple users such as spreading sequence, amplitude and phase are used for joint detection Verdu’s seminal work [34] showed that the CDMA systems are inherently neither interference nor near-far limited, but those are actually limitations of the conventional single user receiver By suitable design of multiuser receiver that takes into account the structure of MAI it is possible to increase spectral efficiency, decrease output power and strengthen the system against imbalances in the received powers of various users [33]

1.4 Motivation

Multiuser detection (MUD) technique is a novel approach for joint detection of user’s data

in DS-CDMA The optimal multiuser detector (OMD), proposed by Verdu to jointly decode the signals using the information from all the users, is based on the maximum likelihood sequence detection (MLSD) which is implemented by a dynamic programming algorithm and is not suitable for practical implementation primarily because of it’s high computational complexity that increases exponentially with the number of users On the other hand, the conventional matched filter detector is interference limited It is optimal only in the single user channel corrupted by AWGN So various sub-optimal detectors such as decorrelating detector [22, 23], multistage detector [19], neural networks detectors [5, 10, 35, 38] and adaptive detectors with acceptable bit error rate but moderate complexity have been proposed

The application of Neural Networks (NN) to the demodulation of spread spectrum signals has shown great promise due to their adaptability Neural networks use many simple processing units (nodes), which are interconnected in parallel (via the weights) Through this massively parallel structure, the NN learns by formulating a decision boundary for the problem at hand Moreover, the optimal decision boundary in DS-CDMA is nonlinear in nature, due to this reason, the nonlinear receivers can perform better than the linear receivers as they can approximate the decision boundary more effectively

Azhang et al [5] proposed a multiuser receiver using the multilayer perceptron (MLP) neural network trained by the back propagation algorithm whereas Mitra et al [38]

Chapter 1: Introduction _

proposed a multiuser receiver using a radial basis function (RBF) network Similarly, Ketchriotis et al [10] and Miyajima [35] have proposed Hopfield neural network (HNN) based multiuser receiver Though all these neural network based MUDs’ perform better than the conventional matched filter detector and at par with OMD, they all suffer from one or other problems In the MLP based MUD, the number of units needed grows exponentially with increasing the number of users and so does the training time RBF based MUD performs optimally in AWGN but its complexity in terms of centers (nodes) grows exponentially In the same way HNN based MUD suffers from local minima problem

The main objective of this thesis is to address the need for sub-optimum multiuser detector for DS-CDMA that performs reliably in high bandwidth efficiency situations and

is robust to near far effects and yet require a reasonable computational complexity to ensure their practical implementation For this purpose, we propose hybrid matrix graduated non convexity annealed neural network (Hybrid-MGNANN) and hybrid radial basis function network (Hybrid-RBFN) multiuser detectors and investigate and discuss the performance of these detectors in comparison with other sub-optimal detectors

In this thesis, we investigate the performance of various multi-user detection schemes in the AWGN channel Particularly we are interested in the performance of hybrid matrix graduated non-convexity multi-user detector and hybrid radial basis function multi-user detector We have performed various simulations and the performances of our proposed

detectors have been compared with other sub-optimum detectors as well as with the OMD

• Performance of hybrid matrix graduated non-convexity annealed neural network multi-user detector (Hybrid-MGNANN): This detector is based on digital signal processing as well as Hopfield neural network (HNN) with annealing and matrix graduated non-convexity capabilities Performance of this detector in synchronous and asynchronous AWGN channel is evaluated via simulation experiments in different scenarios such as number of users, near-far ratio and spreading codes This detector has attractive bit error rate performance with low complexity

• Performance of hybrid radial basis function multi-user detector (Hybrid-RBFN): This detector is based on digital signal processing and radial basis function neural network and performs very well in synchronous CDMA with complexity a little higher than the Hybrid-MGNANN But in the asynchronous CDMA, the performance of this detector is comparatively worse and the complexity is also higher than the Hybrid-MGNANN

The primary goal of this work is to introduce a novel sub-optimum multiuser detector that has lower complexity and can achieve near optimum performance Basically we are interested in using some neural network models for this purpose as neural networks are shown to be effective in pattern recognition problem

Chapter 1: Introduction _

The current chapter is chapter 1 and provided a brief introduction of spread spectrum and DS-CDMA systems We reviewed the role of MAI in performance degradation of DS-CDMA The need for multi-user detection as well as sub-optimum multi-user detectors has been mentioned The motivation and objective of our work have been provided

Chapter 2 reviews the system model of DS-CDMA followed by a detailed background of some of the established multiuser detectors such as conventional detector, optimum multi-user detector, decorrelator, multistage detector and their theoretical bit error rate

Chapter 3 provides a brief introduction of neural network, particularly, Hopfield neural network (HNN) We will discuss the shortcomings of this network and measures that are taken to overcome these weaknesses We describe the proposed Hybrid Matrix Graduated Non-convexity Annealed Neural Network (Hybrid-MGNANN) for utilization in a multiuser detection problem We also present simulation parameters and simulation flowcharts for the simulation of our proposed detectors In the end of this chapter, simulation results for proposed Hybrid-MGNANN detector will be given

Chapter 4 deals with the proposed Hybrid Radial Basis Function Network (Hybrid-RBFN) multiuser detector We describe the RBFN, its use in multiuser detection problem, its weakness and measure taken to counteract it In the end of this chapter, we will analyze the results obtained from the simulation experiments for both synchronous and asynchronous DS-CDMA channels Performances of the proposed hybrid RBFN detector will be compared with other multi-user detectors

The report concludes in Chapter 5, where we provide a summary of our research work and possible future research directions

Chapter 2 Multi-user Detection Strategies

In this chapter, we describe the DS-CDMA system model in detail As most of the multiuser detectors employ banks of matched filters at the front end, we derive the output

of the matched filter in matrix-vector form for convenience purpose Finally we introduce some widely discussed multiuser detector models such as conventional matched filter detector (CD), optimum multiuser detector (OMD), decorrelating detector (DECO) and multistage detector (MSD) We also provide the theoretical bit error rate for CD and DECO

Figure 2.1 shows a Direct Sequence Code Division Multiple Access (DS-CDMA) system

model with K active asynchronous users over a stationary additive white Gaussian noise

(AWGN) channel A signature sequence waveform a k (t) with L chips, time limited in

the interval t∈[0,T b], T b =LT c, is assigned to each of the transmitter Here

(

1 0 , T c c L

l l k

k t a p t lT

=



=otherwise0

0for1)

c

T

T t t

The signature sequence waveform is unique for each user and is normalized to have unit power

1)(1

The realization of bandwidth spreading is achieved by multiplying the input data symbol

by the corresponding signature code The spread data symbol u k (t) corresponding to the

th

k user can be written as

K k

iT t a b t

k user Thus the transmitted spread spectrum signal corresponding to the th

k

user is given as:

)cos(

)()

Chapter 2: Multi-user Detection Strategies _

)()cos(

)(

)

1

t n t

w iT

t a b A t

k P

P i K

k

=∑∑− = τ θ (2.6) where θk =φk +w cτk

In (2.6), (2P+1)is the length of the transmitted sequence (packet size), τk ∈[0,T b] are the relative time delays between the users and n (t) is the AWGN Without loss of generality,

it is assumed that the users are numbered such that their delays satisfy0≤τ1 ≤ ≤τK <T b In this type of system, bandwidth efficiency is measured

as the ratio of the number of channel users to spreading factor, K / L[5]

The objective of multiuser detection is the development of strategies for demodulation of information sequences sent by several transmitters sharing a channel In a multiple access

∑

) (

1 t a

) (

2 t a

1 t u

)(

2 t u

)

(t

u K

)(

1 t S

)(

2 t S

)

(t

S K

)cos(

2W1 w c t+φ1

)cos(

2W2 w c t+φ2

)cos(

2W K w c t+φK

communication system, the receiver is capable of matching to all or a subset of the received signals [5] So whatever detection technique we apply, the first step that is taken

to recover the original transmitted sequence is to send the received signal r (t)through the matched filter banks in the case of the uplink or simply through a matched filter matched with a particular users’ signature sequence in the case of the downlink

Before proceeding further it is appropriate to describe the two transmission models: synchronous transmission and asynchronous transmission

as in uplink mobile communications if transmitters are provided with access to a common

clock such as the Global Positioning System [33] As the K users maintain time

synchronism, therefore in the model presented in (2.6), the relative time delays associated with all users are assumed to be zero, i.e., τk = 0∀ k Although synchronous transmission

is unlikely in present uplink mobile communication systems, it is nevertheless useful as it considerably simplifies exposition and analysis and often permits the derivation of closed form expressions [2] It helps us in understanding easily the more complex asynchronous system

Chapter 2: Multi-user Detection Strategies _

2.1.2 Asynchronous Transmission

The detection of users’ bits in the asynchronous channel is more complex than in a synchronous channel There is overlap of bits between different intervals as illustrated in the Figure 2.2 The th

turn must further take into account the effects of bits that overlap them and so on In this way the detection problem is framed over the whole message It can be easily realized that the detection of user data in asynchronous system will be more complex

As already mentioned, multi-user detectors commonly have a bank of matched filters at the front end to convert the continuous time waveform into discrete time process Each of

Figure 2.2 Relative time delays between user bits (assumingτ1 =0)

i

b

) 1 ( 1

−

i

1 +

i

b

) 2

i

2 +

i

b

) 1 ( 2

−

i

b

) 1 (i−

multiuser detection, it is convenient to introduce a matrix-vector system model to describe the output of the matched filter detector Throughout this thesis, vectors and matrices are denoted by bold face letters The symbols ( ) ( )T H

⋅

⋅ , and ( )− 1

⋅ represent matrix transposition, Hermitian and inversion respectively All vectors are defined as column vectors with row vectors represented by transposition

2.2.1 Synchronous System

For reasons of simplicity, let us first consider synchronous transmission (i.e.τk =0, k =1, ,K) In the synchronous case, it is sufficient to restrict attention to the received waveform in an interval of lengthT b, the bit duration [33] Substituting the values of all τk =0, k=1, ,K in equation (2.6), the received signal for a specific bit period T b can be written as:

)()cos(

)

( )

(

1

t n t

w t

a b A t

K

k

k k

y y

b , , ][ 1, 2

=

b given r (t)

)()()cos(

)

(

)()(

c K

k

k k k

b k k

dt t s t n t

w t

a b A

dt t s t r y

φ

Chapter 2: Multi-user Detection Strategies _

Here )s k(t)= A k a k(t)cos(w c t+φk is the th

k user’s code waveform The output from the

bank of matched filter can be conveniently presented using a matrix-vector system as follows:

n Hb

Here for a K user system, y , b and n are all K×1column vectors, which represent respectively matched filter outputs, input data and colored Gaussian noise with mean zero and covariance matrixσ2H, whereas H ∈ RK× Kis the symmetric matrix of signal cross-correlations:

Matched filter user 2

Matched filter user K

: : :

: :

: :

Fig 2.3 K - user detector employing matched filter detector at the front end

)cos(

)(

)()(

2 1 0

k j jk k j

b

k j jk

R E E

dt t s t s h

)(

)(

1

k j k

i L

i

j i k

j E a a E

k user’s energy n is the colored Gaussian noise vector, the individual

component of which is given by

dt t s t n i

n

b i

b iT k

k() ( ) ( )

) 1 (

The discrete time matrix-vector model for the asynchronous channel takes the same form

as for the synchronous channel, but the matrix and vector dimension will be different

] 1

b k b k [P]]

0 [

k

b

]1

b k

Chapter 2: Multi-user Detection Strategies _

Now the equation must encompass the entire message; thus assuming (2P+1)is packet size, the size of the vectors and the order of matrices are (2P+ )1 ×K[32]

In equation (2.6), we have

)()cos(

)(

)

1

t n t

w iT

t a b A t

k P

P i K

k

Here we assume that the delays of the users satisfyτ1≤τ2 ≤ ≤τK

Then the sampled output of the matched filter for the th

)()cos(

)(

)(

)

(

1 )

i k k

i

k

dt iT

t s t n t

w iT

t a b A

dt iT

t s

i bits of th

j user if k < and it is j

interfered by th

i 1)( + and th

i bits of all the th

j user if k> j (j=1, ,K, j ≠k) So the output matrix ( i)

y for asynchronous system is arranged as shown below:

)()1()1()1()1()()0(

)

i i

i i

i

n b

H b

H b H

)

i i

i i

T i

n b

H b H b

H

where the components of cross-correlation matrix H(i), i=−1,0,1can be expressed as [10,11,19]: