RAKE Thesis

Bachelor of Engineering (Hons) Electrical Engineering

Thesis CDMA Detection Guided RAKE Receiver

CDMA Detection Guided RAKE Receiver

Prepared By: Siang Pin Gan

School of Information Technology and Electrical Engineering

The University of Queensland

Supervisor: Dr. John Homer

Oct 2002

Siang Pin Gan

Unit 1, 242 Carmody Road,

St. Lucia, Queensland 4067

Australia

18 October 2002

Head of School

School of Information Technology and Electrical Engineering

The University of Queensland

St. Lucia, Queensland 4072

Dear Professor Simon Kaplan,

In accordance with the requirements of the degree for Bachelor of Engineering (Honours) in

the division of Electrical Engineering, I present the following thesis entitled ‘CDMA Detection Guided RAKE Receiver’. This work was performed under the supervision and

guidance of Dr. John Homer.

I declare that the work submitted in this thesis is my own, except as acknowledged in the

text, and has not been previously submitted for a degree at the University of Queensland or

any other institution.

Yours sincerely,

Siang Pin Gan

i

ACKNOWLEDGMENTS

The author wishes to express sincere appreciation to the following individuals who have

helped to make the completion of this thesis possible:

• Dr. John Homer - for his invaluable assistance and guidance in preparation of this

manuscript. John has always been approachable, patient and encouraging in his

supervision.

• Mum and Dad - for their selfless love and financial support to allow him in his

pursue to becoming a professional engineer. Both of them have been inspirational

especially during the writing of the thesis.

• Pei Lin - for the long night chats to advice on the improvements that can be made to

the thesis. She has been exceptionally understanding and always the mental support

in times of difficulties.

• Finally to the nine ‘Tuscan’ brothers, for their friendship and the strong bond that

kept them together over these two years where they had fun, peace, laughter and joy

that will always be deeply remembered.

Once again, thank you all…J

ii

TABLE OF CONTENTS

Acknowledgement i

Table of Contents ii

List of Figures vi

List of Tables viii

Abstract ix

CHAPTER 1: INTRODUCTION 1

1.1 Background.........................................................................................................1

1.2 Motivation and Objectives .................................................................................2

1.3 Scope ...................................................................................................................2

1.4 Organization of the Report ................................................................................2

CHAPTER 2: CDMA SYSTEM CONCEPTS 4

2.1 Spread Spectrum Multiple Access .....................................................................4

2.2 Direct-Sequence Spread Spectrum (DS-SS) ......................................................5

2.3 PN Sequence.......................................................................................................7

2.4 Walsh Code Matrix .............................................................................................8

2.5 Quadrature Phase-Shift Keying (QPSK) Modulation .......................................9

2.6 RAKE Receiver ................................................................................................. 11

Table of Contents iii

CHAPTER 3: SIGNAL PROPAGATION CHARACTERISTICS FOR WIRELESS COMMUNICATION 13 3.1 Reflection .......................................................................................................... 14

3.2 Diffraction ......................................................................................................... 15

3.3 Scattering .......................................................................................................... 15

3.4 Large-scale Fading ........................................................................................... 16

3.5 Small-scale Fading............................................................................................ 17

CHAPTER 4: ADAPTIVE FILTERS - THE LMS ALGORITHM 18

4.1 Overview of the LMS Adaptive Filter .............................................................. 18

4.2 Fundamentals of the LMS Algorithm.............................................................. 19

4.2.1 Derivation of the Standard LMS Algorithm......................................... 19

4.2.2 Convergence and Stability of the Standard LMS Algorithm...............21

4.3 Activity Detection Algorithm ...........................................................................21

4.3.1 Activity Measure ...................................................................................22

4.3.2 Activity Threshold.................................................................................22

CHAPTER 5: MATLAB® MODEL 24

5.1 Overview............................................................................................................24

5.1.1 Three-Model Simulation.......................................................................25

5.1.2 GUI Implementation ............................................................................26

Table of Contents iv

5.2 Bit Streams ........................................................................................................29

5.2.1 Training Sequence................................................................................29

5.2.2 Input Bit Sequence ...............................................................................30

5.3 Walsh Code .......................................................................................................30

5.4 PN Sequence.....................................................................................................32

5.5 Complex Baseband Signal................................................................................32

5.6 Channel Impulse Response..............................................................................33

5.7 Thermal Noise ..................................................................................................34

5.8 Channel Estimate .............................................................................................35

5.9 RAKE Receiver .................................................................................................37

5.10 Decision Device ................................................................................................38

CHAPTER 6: FINDINDS AND DISCUSSION 39

6.1 Effects on Increasing the Noise Factor...........................................................40

6.1.1 Noise Factor = 2.0 ................................................................................41

6.1.2 Noise Factor = 8.0 ................................................................................43

6.1.3 Noise Factor = 9.0 ................................................................................45

6.2 Effects on Increasing the Threshold Factor....................................................47

6.2.1 Threshold Factor = 3.0 .........................................................................48

6.2.2 Threshold Factor = 6.0 .........................................................................50

6.3 SNR performance for the Three Models .........................................................51

6.4 Comparison on the Asymptotic Multipath Estimation Error Asymptotic ....51

Table of Contents v

CHAPTER 7: CONCLUSION 52

7.1 Summary of the Findings .................................................................................52

7.2 Suggestions to Possible Future Work..............................................................53

Reference List 534

APPENDICES

Appendix A.1: Current RAKE Receiver Model................Error! Bookmark not defined.

Appendix A.2: Standard LMS Based RAKE Receiver ModelError! Bookmark not defined.

Appendix A.3: CDMA Detection Guided RAKE Receiver ModelError! Bookmark not defined.

Appendix B: Three-Model CDMA RAKE Receiver Simulation with GUI .....Error! Bookmark not defined.

vi

LIST OF FIGURES

Figure 2.1 Basic model of the direct-sequence spread spectrum communications system................................................................................................................................... 5

Figure 2.2 Generation of a DS-SS signal with processing gain = 7 ............................................ 6

Figure 2.3 Transmitter of the DS-SS system ................................................................................... 7

Figure 2.4 Constellation diagram for QPSK.................................................................................... 9

Figure 2.5 Generalized transmitter using QPSK modulations on IQ-channel....................... 10

Figure 2.6 An implementation of a RAKE receiver with 3 correlators.................................... 12

Figure 3.1 The three mechanisms in signal propagation in a multipath channel.................... 12

Figure 3.2 Reflection of a wave........................................................................................................ 14

Figure 3.3 Diffraction of a wave ...................................................................................................... 15

Figure 3.4 Scattering of waves.......................................................................................................... 15

Figure 3.5 Signal strength decays as the path distance increases ............................................... 16

Figure 3.6 Large-scale and small-scale fading ................................................................................ 16

Figure 3.7 Tapped delay line model of a multipath fading channel .......................................... 17

Figure 4.1 LMS adaptive FIR filter in parallel with the time invariant unknown channel............................................................................................................................... 19

Figure 5.1 Flowchart of the simulation........................................................................................... 27

Figure 5.2 Flowchart of the GUI..................................................................................................... 28

Figure 5.3 Screenshot of the GUI ................................................................................................... 29

Figure 5.4 An example of the input verus output bit plot where bits 7 and 8 have errors .................................................................................................................................. 30

Figure 5.5 The Walsh code for the 10th row of the matrix function ....................................... 31

Figure 5.6 System model showing the transformation of the input bit steam to the complex baseband signal................................................................................................ 33

Figure 5.7 Channel impulse response of a multipath channel.................................................... 34

Figure 5.8 Taps below the activity threshold are detected as zero taps in the channel estimate .............................................................................................................................. 36

List of Figures vii

Figure 6.1 Simulated results for the current RAKE receiver on the channel estimate and the input verus output bit plot for noise factor = 2.0....................................... 41

Figure 6.2 Simulated results for the standard LMS based RAKE receiver on the channel estimate and the input verus output bit plot for noise factor = 2.0 ....... 42

Figure 6.3 Simulated results for the detection guided RAKE receiver on the channel estimate and the input verus output bit plot for noise factor = 2.0....................... 42







Figure 6.10 Simulated results for the current RAKE receiver on the channel estimate and the input verus output bit plot for threshold factor = 3.0............................... 48

Figure 6.11 Simulated results for the standard LMS RAKE receiver on the channel estimate and the input verus output bit plot for threshold factor = 3.0............... 49

Figure 6.12 Simulated results for the detection guided RAKE receiver on the channel estimate and the input verus output bit plot for threshold factor = 3.0............... 49

Figure 6.13 Simulated results for the detection guided RAKE receiver on the channel estimate for threshold factor = 6.0............................................................................... 50

Figure 6.14 Simulated results for the detection guided RAKE receiver on the asymptotic error and active taps detection for threshold factor = 6.0.................. 50

Figure 6.15 SNR comparison among the three models derived................................................. 51

Figure 6.16 Asymptotic multipath estimation error comparison between the LMS algorithm and the activity detection algorithm .......................................................... 51

viii

LIST OF TABLES

Table 6.1 Effects on varying the noise factor to 2.0................................................................... 41



Table 6.4 Effects on varying the threshold factor to 3.0 ........................................................... 48

Table 6.5 Effects on varying the threshold factor to 6.0 ........................................................... 50

ix

ABSTRACT

In the radio environment, transmitted signals arrive at the receiver via a direct,

unobstructed path, or via multiple paths from the reflection, diffraction and scattering of

surrounding objects such as buildings and trees. This multipath propagation causes the signal

at the receiver to distort and fade significantly, leading to inter-symbol interference (ISI).

Spread spectrum mobile communication systems use RAKE receivers to minimize these

communication errors resulting from multipath effects. Ideally, the number of correlators in

the RAKE receiver should match the number of multipath signals. In general, however the

number of multipath signals is unknown and consequently RAKE receivers either contain an

excessive number of correlators or the receiver performs sub optimally.

The aim of this thesis is to incorporate a new signal detection technique within the

RAKE receiver of the Code Division Multiple Access (CDMA) system, which is able to

identify every ‘important’ multipath in the unknown channel using the Least Mean Square

(LMS) algorithm. This detection technique involves an activity measure and an activity

threshold. A multipath signal whose activity measure exceeds the threshold is deemed as an

‘important’ tap. The threshold has a theoretical basis, but may be increased to reduce the

number of detected active multipath components resulting in a lower computational cost.

Simulations demonstrate that the CDMA Detection Guided RAKE Receiver has a significant

improvement in the signal-to-noise ratio (SNR), subsequently leading to a lower bit error rate

than the current RAKE receiver with three correlators.

Index Terms – Activity measure, activity threshold, asymptotic error, CDMA system, least mean

square (LMS) algorithm, multipath effects, RAKE receiver.

1

C h a p t e r 1

1. INTRODUCTION

With the technology advancement in today’s society, the ability to communicate with

people on the move has evolved remarkably [1]. However, the transmission quality of the

signal has deteriorated due to the modernization of the urban cities with skyscrapers and

other manmade obstacles. This results in the transmitted signal having to take multiple paths

before reaching the intended receiver. Through the multipath transmissions, the signal is

severely distorted and attenuated. Methods have to be developed to improve on the signal

quality.

1.1 Background

Code Division Multiple Access (CDMA) systems use the spread spectrum technology

and the RAKE receiver concept to minimise communication errors resulting from multipath

effects. In general, the number of multipath signals in the wireless channel is unknown and

difficult to predict. The spread spectrum technology aims to spread the information signal

over a wider bandwidth to make jamming and interception more difficult [2]. A RAKE

receiver allows each arriving multipath signal to be individually demodulated and then

combined to produce a stronger and more accurate signal [1].

The RAKE receiver in the IS-95A CDMA system uses three correlators and a searcher,

while the TIA/EIA-95B CDMA system limits the number of correlators in the RAKE

receiver to six [3]. The searcher receives pilot signals for synchronizing the spreading code.

Both of these systems have a fix number of correlators and leads to the RAKE receivers

either containing an excessive number of correlators or that the receiver performs sub

optimally.

Chapter 1 • Overview 2

1.2 Motivation and Objectives

The ideal approach is to match the number of multipath signals with the number of

correlators, but this would be a waste of resources and add unnecessary expense to the

manufacture of the phone. This thesis aims to incorporate a new signal detection technique

within the RAKE receiver, where the detection technique is used to determine the number of

correlators required for demodulating the ‘important’ multipath signals. This technique is

unlike the method use in the current CDMA system, which has a fix number of correlators

despite the number of multipath signals in the channel.

The objective of this thesis is to develop a RAKE receiver through MATLAB®

simulation that is able to increase the signal-to-noise ratio (SNR) performance with a

minimum number of correlators.

1.3 Scope

This thesis revolves around the least mean square (LMS) algorithm [1], which is used to

obtain a close representation of the channel impulse response via the implementation of an

adaptive filter. A detection technique, better known as the activity detection algorithm is used

to select the necessary multipath signals for demodulation. It requires an activity measure and

an activity threshold to discriminate the ‘important’ multipath signals from the weak and

negligible ones.

1.4 Organization of the Report

This thesis report consists of seven chapters and two appendices in total. The

framework for the thesis is described as follows:

Chapter 1 provides a brief introduction about the CDMA system and the need for an

implementation of this thesis.

Chapter 2 explains the basic concept and principles of the CDMA system. It describes

the spread spectrum technology and the functionality of the RAKE receiver.

Chapter 3 discusses the signal propagation characteristics in a wireless radio channel and

how the resultant waveform at the receiver can be severely distorted by the three propagation

mechanisms.

Chapter 1 • Overview 3

Chapter 4 contains the concept of the LMS algorithm and the activity detection

algorithm, which constitutes to the new signal detection technique incorporated within the

RAKE receiver. This signal detection technique forms the basis for the development of this

thesis.

Chapter 5 presents the methodology behind the foundation of this software simulation

programme created using MATLAB®. Each component of the simulated CDMA

environment is described in details in this chapter. The three RAKE receiver models

developed: (1) Current RAKE receiver; (2) Standard LMS based RAKE receiver; and (3)

Detection guided RAKE receiver, are used to show comparisons for the SNR performance

and output bit errors.

Chapter 6 includes the simulation results obtain from the software simulation

programme in chapter 5. The effects on increasing the noise factor and threshold factor are

investigated and the findings are recorded and discussed.

Finally, chapter 7 gives the reader an overall summary on the collated results. This

chapter concludes with recommendations and improvements for any future research work in

this topic.

4

C h a p t e r 2

2. CDMA SYSTEM CONCEPTS

The rapid worldwide growth in cellular telephone subscribers over the past decade has

evidently showed that the wireless communication is an effective means for transferring

information in today’s society. Time Division Multiple Access (TDMA) and Frequency

Division Multiple Access (FDMA) are two approaches that have contributed to this

advancement in the telecommunications industry. However, the widespread success of these

communications systems has led to the development for newer and higher technology

techniques and standards in order to facilitate high-speed communication for multimedia,

data and video in addition to voice transmissions [1]. Code Division Multiple Access

(CDMA) is today’s dominant technology for the evolution of third generation (3G) mobile

communications systems [4] with the development of two major schemes: Wideband

CDMA (W-CDMA) and CDMA2000.

The W-CDMA technology otherwise known as the Universal Mobile

Telecommunications System (UMTS) is designed with the intention of providing an upgrade

path for the existing Global System for Mobile Communications (GSM) [5] while

CDMA2000 is based on the fundamental technologies of IS-95, IS-95A (cdmaOne) as well as

the 2.5G IS-95B systems [6]. These two schemes are similar for their ability to provide high

data rates and the efficient use of bandwidth but are incompatible as they use different chip

rates. The following sections of this chapter will describe and explain the basic concepts

behind the CDMA technology.

2.1 Spread Spectrum Multiple Access

The spread spectrum modulation techniques are originally developed for use in the

military and intelligence communications systems due to their resistance against jamming

signals and low probability of interception (LPI) [2]. They are immune to various kinds of

noise and multipath distortion. Apart from these advantages, spread spectrum signals also

Chapter 2 • CDMA System Concepts 5

have the capability to support multiple users at the same time by assigning each user with an

orthogonal spreading code. This will be further discussed in section 2.2.

A number of modulation techniques have been developed to generate spread spectrum

signals. These can be generally classified as direct-sequence spread spectrum (DS-SS),

frequency-hopping spread spectrum (FH-SS), time-hopping spread spectrum (TH-SS), chirp

modulation and the hybrid combination modulation [2]. We will look into the functionality

of the DS-SS and how this modulation technique is incorporated to the CDMA system.

2.2 Direct-Sequence Spread Spectrum (DS-SS)

The DS-SS technique is one of the most popular forms of spread spectrum. This is

probably due to the simplicity with which direct sequencing can be implemented. Figure 2.1

shows the basic model and the key characteristics that make up the DS-SS communications

system [7]. In this form of modulation, a pseudo-random noise generator creates a spreading

code or better known as the pseudo-noise (PN) code sequence. Each bit of the original input

data is directly modulated with this PN sequence and is represented by multiple bits in the

transmitted signal. On the receiving end, only the same PN sequence is capable of

demodulating the spread spectrum signal to successfully recover the input data [2].

Figure 2.1 Basic model of the direct-sequence spread spectrum communications system

The bandwidth of the transmitted signal is directly proportional to the number of bits

used for the PN sequence. A 7-bit code sequence spreads the signal across a wider frequency

band that is seven times greater than a 1-bit code sequence, otherwise termed as having a

Input data Spreading code /PN sequence

Channel Encoder

Modulator Channel De- Modulator

Pseudo-random Noise

Generator

Pseudo-random Noise

Generator

Channel Decoder

De-spreading code /PN sequence

m(t) s(t)

c(t) c(t)

s’(t) m’(t)

Output data


processing gain of seven. Figure 2.2 illustrates the generation of a DS-SS signal using an

exclusive-OR (XOR) operation. The XOR obeys the following rules:

000 =⊕ 110 =⊕ 101 =⊕ 011 =⊕

Figure 2.2 Generation of a DS-SS signal with processing gain = 7

Note that an input data bit of zero causes the PN sequence coding bits to be transmitted

without inversion, while an input data bit of one inverts the coding bits. Rather than to

represent the binary data with bits 0’s and 1’s, the input data and PN sequence are converted

into a bipolar waveform with amplitude values of ±1. This is further illustrated in figure 2.3.

0 1 0 1 1

Input data m(t)

0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1

PN sequence c(t)

1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0

Transmitted signal

s(t)

Tc = chip interval

+1

-1

+1

-1

+1

-1


Figure 2.3 Transmitter of the DS-SS system

From Figure 2.3, we are also able to identify two criteria that need to be met in order to

be considered as a DS-SS system [8]: (1) The bandwidth of the transmitted signal s(t) is much

wider as compared to the input data m(t); and (2) This wide bandwidth is caused by the

modulation of the spreading signal c(t) and the intended receiver requires this identical signal

for retrieving the message signal m(t). In the next few sections, we will look into the

functionality of the various components for a Direct-Sequence Code Division Multiple

Access (DS-CDMA) system.

2.3 PN Sequence

The DS-CDMA system uses two general categories of spreading sequences: PN

sequences and orthogonal codes. As mentioned in section 2.2, the PN sequence is produced

by the pseudo-random noise generator that is simply a binary linear feedback shift register,

consisting of XOR gates and a shift register. This PN generator has the ability to create an

identical sequence for both the transmitter and the receiver, and yet retaining the desirable

properties of a noise-like randomness bit sequence. A PN sequence has many characteristics

such as having a nearly equal number of zeros and ones, very low correlation between shifted

versions of the sequence and very low cross correlation with any other signals such as

interference and noise [8]. However, it is able to correlate very well with itself and its inverse.

Another important aspect is the autocorrelation of the sequence as it decides the ability to

s(t) = m(t).c(t) Polar NRZ

Polar NRZ

m(t) Input data

DS-SS

PN Sequence of period N

c(t) B ≈ Rb = 1/Tb

B ≈ NRb = 1/Tc where B = Bandwidth of signal Rb = Bit rate for m(t) Tb = Bit interval for m(t) Tc = Chip interval for c(t)

Polar NRZ waveform


synchronize and lock the spreading code to the received signal [2]. This effectively combats

the effects of multipath interference and improves the SNR. M-sequences, Gold codes and

Kasami sequences are examples of this class of sequences.

2.4 Walsh Code Matrix

Walsh codes are the most common orthogonal codes used in CDMA applications [1]. These codes correspond to the rows of a special square matrix known as the Hadamard

matrix. For a set of Walsh codes of length n, there consists of n rows to form an n x n Walsh

code square matrix. The IS-95 system uses a 64 by 64 Walsh function matrix. The first row

of this matrix contains a string of all zeros with each of the subsequent rows containing

different combinations of bit 0’s and 1’s. Every row is orthogonal and has an equal

occurrence for the binary bits. When implemented with the CDMA system, each mobile user

uses one of the 64 row sequences in the matrix as a spreading code, providing zero cross

correlation among all other users [7]. This matrix is defined recursively as follows:

[ ]01 =W

=

WWWWW

nn

nnn2

where n is a power of 2 indicating the various dimensions of the matrix and nW denotes the

logical NOT operation on all bits in that matrix. The three matrices W2, W4 and W8, show the

Walsh function for dimension 2, 4 and 8 respectively.

=

1000

2W

=

0110110010100000

4W

=

1001011000111100010110101111000001100110110011001010101000000000

8W

Each row in the 64 by 64 Walsh matrix corresponds to a channel number. Channel

number 0 is mapped to the first row of the Walsh matrix, which is the all zeros code. This

channel is also known as the pilot channel and is used to train and estimate the impulse

response of the mobile radio channel.


To compute the cross correlation between the sequences, we will need to convert the

bits in the matrix to the antipodal form of values ±1. Shifted versions of the Walsh sequence

can result in a high cross correlation thus requiring tight synchronization to be implemented.

However, all users of the same CDMA channel can be synchronized to an accuracy of one

chip interval with the use of a common long PN sequence that also functions as a data

scrambler.

2.5 Quadrature Phase-Shift Keying (QPSK) Modulation

In Phase-Shift Keying (PSK) [8], the phase of the carrier signal is shifted to represent

data. For M-ary PSK, the number of bits to represent one symbol is given as:

mn 2log= (2.1)

where n is the number of bits per symbol and m is the number of possible levels to represent

the signal. From the equation (2.1), we determine that the QPSK uses two bits to represent

any one of its four-phasor symbols. Figure 2.4 shows the constellation diagram for QPSK

and how these four levels of signal correspond to carrier phases, θ of 45°, 135°, 225° and

315°.

Figure 2.4 Constellation diagram for QPSK

Q - Imaginary (quadrature)

I - Real (in phase)

(0, 1)

(0, 0)

(1, 1)

(1, 0)

θ = phase angle

Bit A

Bit B

θ I

0 0 225° -1 -1 0 1 135° -1 1 1 0 315° 1 -1

Q

1 1 45° 1 1


Figure 2.5 shows a generalized transmitter using the QPSK modulation technique. The

modulating signal m(t) is a stream of binary bits with a data rate of R = 1/Tb , where Tb is the

width of each bit. This input stream is divided into two separate bit streams known as the I

(in-phase) and Q (quadrature phase) channel [8]. The odd bits of the input stream are

processed by the I-channel while the even bits are processed by the Q-channel. Both

channels are modulated on the same carrier frequency, fc and have a bit rate of R/2 bits-per-

second. However, the carrier signal in the Q-channel is shifted by 90° to achieve a sine

waveform. The difference between these two modulated signals is obtained for transmission

over the radio channel.

Figure 2.5 Generalized transmitter using QPSK modulations on IQ-channel

From figure 2.5, QPSK is generated by using two quadrature carriers and its transmitted

signal s(t) can be defined as:

tftQAtftIAts cccc ππ 2sin)(2cos)()( −= (2.2)

where the complex envelope

)()()()( tjceAtjQtItg θ=+= (2.3)

is a function of the modulating signal m(t). Ac is a positive constant that specify the power

level of the signal and θ is the phase angle of the signal.

tf cπ2cos

2-bit serial-to-parallel converter

I-channel I(t)

∑

Q-channel Q(t)

Transmitted signal

s(t)

Oscillator f = fc

Modulating signal m(t)

R/2 bps

R/2 bps

Odd bit An = ±1

Even bit Bn = ±1

R = 1/Tb

tf cπ2sin

+

- -90°

Phase shift


2.6 RAKE Receiver

CDMA systems use the spread spectrum technique with spreading codes designed to

provide very low correlation between successive chips (see section 2.2). Due to the signal

propagation characteristics of the wireless communications channel, the receiver may receive

one direct line-of-sight (LOS) wave and many multiple versions of the transmitted signal at a

spread of arrival times. If these multipath signals are delayed in time by more than one chip

interval, the despreading process will make the uncorrelated noise appear as negligible at the

receiver. This leads to the implementation of a RAKE receiver [1] within a CDMA system,

as it is able to recover each multipath signal and combine them with the correct delays to

achieve a significant improvement in the SNR of the output signal. The RAKE receiver

however, works only on the basis that these multipath components are practically

uncorrelated from one another when their relative propagation delays exceed a chip period.

Figure 2.6 shows the model of a RAKE receiver with three correlators. This RAKE

receiver design is used in the IS-95 system, where each of the three strongest time-shifted

multipath signals is demodulated and weighted independently. The spreading code in the

despreading process needs to be synchronized to the delay spread of the multipath signal, so

that the outputs of each correlator can be summed to produce a stronger and more accurate

signal. Note that in a RAKE receiver, if the outputs from one correlator are corrupted by

fading, the corrupted signal may be discounted through the weighting process. Decisions

based on the combination of the three separate correlator outputs are able to provide a form

of diversity, which can overcome fading and thereby improve the CDMA reception. The

outputs of these three correlators are denoted as Z1, Z2 and Z3. The overall signal Z’ is given

by:

mm

m ZZ ∑=

=3

1' α (2.4)

where m represents each of the three correlators.

Each correlator of the RAKE receiver is represented by three coefficients: (1) Time

delay; (2) Phase shift; (3) Amplitude gain/attenuation, as shown in figure 2.6. In this thesis,

these coefficients are estimated via the LMS algorithm (see Chapter 4).


In summary, this chapter briefly explains the CDMA concept from the transmitter front

to the receiver end. In the next chapter, we will look at how signal is propagated in a wireless

channel and how it may affect the CDMA system.

Figure 2.6 An implementation of a RAKE receiver with 3 correlators

Distorted Signal

Delay

Spreading Code

1sτ

Phase & Gain Adjustors

11 , ss φα

Correlator 1

Delay

Spreading Code

2sτ


22 , ss φα

Correlator 2

Delay

Spreading Code

3sτ


33 , ss φα

Correlator 3

∑

∫ dt(.)Decision Device

s’(t)

Z’ Z m’(t)

Output data

Z3 Z2 Z1

13

C h a p t e r 3

3. SIGNAL PROPAGATION CHARACTERISTICS FOR WIRELESS COMMUNICATION

Wireless communication has proved to be vital in our daily lives. However, the

performance of the wireless communications systems is often limited or corrupted due to the

nature of the mobile radio channel. In an urban environment, the transmission path between

the transmitter and the receiver is severely obstructed by buildings and trees. Hence, a

transmitted signal may travel through a direct line-of-sight (LOS) path and many multiple

paths depending on the characteristics of the radio channel. Unlike wired channels that are

stationary and predictable, radio channels are extremely random and difficult to model.

In general, a signal transmitting in a channel experiences two types of fading: (1) Large-

scale fading; and (2) Small-scale fading. The mechanisms behind these two fading types are

diverse, but can generally be attributed to reflection, diffraction and scattering [1]. These

three propagation mechanisms are illustrated in figure 3.1. Other transmission impairments

in the wireless channel include free space loss, thermal noise and atmospheric absorption [9].

In this chapter, we focus mainly on the three propagation mechanisms that cause the

occurrence of small-scale multipath fading. The concept of how a RAKE receiver can be

implemented to recover the time-dispersed signals in a multipath channel is explained in

section 2.6.

Chapter 3 • Signal Propagation Characteristics For Wireless Communication 14

Figure 3.1 The three mechanisms in signal propagation in a multipath channel

3.1 Reflection

Reflection occurs when a propagating electromagnetic wave encounters a surface that is

large relative to the wavelength of the propagating wave [1]. This reflected wave as illustrated

in figure 3.2 may interfere constructively or destructively at the receiver due to the change in

phase shift after reflection. Sources for reflections include the surface of the earth, buildings

and walls.

Figure 3.2 Reflection of a wave

incident wave

reflected wave


3.2 Diffraction

Figure 3.3 shows that diffraction can occur at the edge of an impenetrable body or at a

surface with sharp irregularities that is large compared to the wavelength of the radio wave

[7]. The secondary waves resulting from such edges or surfaces are partially reflected and

retransmitted with a bend of waves around the obstacle. This allows the signal to be

transmitted even when there is no LOS path between the transmitter and the receiver.

Figure 3.3 Diffraction of a wave

3.3 Scattering

Scattering occurs when the radio path between the transmitter and receiver consists of

large amount of objects with dimensions that are small compared to the wavelength of the

signal [1]. Figure 3.4 shows that the scattered waves can be produced by rough surfaces or by

other irregularities in the channel such as foliage and traffic signs.

Figure 3.4 Scattering of waves

primary wave

secondary wave

propagating wave

scattered waves

scattered waves


3.4 Large-scale Fading

Large-scale fading is primarily attributed to path loss [1] when the received signal

strength decays over relatively large distances (several hundreds or thousands of meters)

between the transmitter and the receiver as shown in figure 3.5. It is otherwise known as

slow fading or shadowing, and is characterised by a long delay spread in figure 3.6.

Figure 3.5 Signal strength decays as the path distance increases

Figure 3.6 Large-scale and small-scale fading

Small-scale fading: Signal fades rapidly

Large-scale fading: Signal fades gradually

with distance


3.5 Small-scale Fading

Small-scale fading as shown in figure 3.6, manifests itself as rapid fluctuations in the

voltage envelope of the received signal over a short period of time or travel distance (a few

wavelengths) [1]. It is caused by the interference between two or more versions of the

transmitted signal arriving at the receiver with a spread of different times. These time-shifted

signals are called multipath signals, which can be represented as ‘taps’ in an impulse-response

model of a channel.

Effects of multipath fading can be classified as flat or frequency selective. For flat fading,

only the amplitude of the received signal can vary due to the constructive and destructive

interference from the time-shifted signals. Frequency selective fading is due to the time

dispersion of the received signal and is the cause of inter-symbol interference (ISI).

A tapped-delay line model shown in figure 3.7 demonstrates both the properties of flat

and frequency selective fading. Each multipath signal has a different time delay (τ), amplitude

level (α) and phase shift (Ǿ), which will interfere with one another at the receiver, producing

a totally distorted version of the original transmitted signal with the additive of noise.

Figure 3.7 Tapped delay line model of a multipath fading channel

Direct Path LOS

000 ,, φατ

Multipath 2 AWGN (Noise)

Faded Signal

Transmitted signal

Delay

Delay

Delay

Σ Σ u(k)

111 ,, φατ φατ

222 ,, φατ

NNN φατ ,,

Multipath 1

Multipath N

18

C h a p t e r 4

4. ADAPTIVE FILTERS – THE LMS ALGORITHM

Adaptive filtering is a key ingredient for fighting echoes in the communication

architecture [10], [11]. An echo, in any context, is a delayed and perhaps a distorted version

from the original transmitted signal [12]. The occurrence of echoes in a communication

system relates to the multipath signals that are present in the communication channel. In

voice transmission, the magnitude and spectral distortions caused by echoes deteriorate the

transmission quality due to the overlapping of different time-shifted signals over a spread of

arrival times at the receiver. Echo cancellation [12] is possible with the implementation of the

adaptive filter.

Adaptive filters can be categorized according to their type, structure and algorithm

implementation [11]. The adaptive filter considered in this thesis is a non-linear type;

maximum likelihood sequence estimation (MLSE) filter structure implemented using the least

mean square (LMS) algorithm. The following sections in this chapter explain the concept of

the LMS adaptive finite impulse response (FIR) filter and the implementation of the activity

detection algorithm.

4.1 Overview of the LMS Adaptive Filter

The system we consider throughout this thesis is shown in figure 4.1. This system

describes the estimation of an unknown channel through the implementation of the LMS

adaptive filtering via parallel configuration [13]. Both the unknown channel and the adaptive

FIR filter model are excited by a training sequence, u(k). The adaptive FIR filter output, yy(k)

is compared with the unknown channel output, y(k) to produce the error signal, e(k). This

error represents the difference between the unknown channel and the model output, which is

also equivalent to the noise, nn(k) added into the system. The error signal is then inputted to

the LMS adaptive algorithm, which corrects the individual tap weights of the filter. This

process is repeated through several iterations until the error signal becomes sufficiently small.

Chapter 4 • Adaptive Filters - The LMS Algorithm 19

Through this implementation, the noise in the channel is effectively cancelled and the

resultant FIR filter response now closely represents that of the previously unknown channel.

Figure 4.1 LMS adaptive FIR filter in parallel with the time invariant unknown channel

4.2 Fundamentals of the LMS Algorithm

The LMS algorithm was first proposed by Widrow and Hoff at the Stanford University

in 1960 [10]. Until now, the algorithm is still widely used due to its simplicity and cheap

implementation [11]. The LMS algorithm is seen as having low computational complexity,

good stability properties, relatively good robustness against implementation errors and

simplicity of its behaviour. The following subsections describe the LMS algorithm equation.

4.2.1 Derivation of the Standard LMS Algorithm [12], [13], [15], [16]

From figure 4.1, we assume that the unknown channel is linear and time invariant

modelled by a FIR filter, h(z-1) given by:

11

110

1)( +−−

−− +⋅⋅⋅++= nn zhzhhzh (4.1)

where z-1 is the unit delay operator and n is the tap length. The LMS adaptive FIR filter, hh

has a tap delay line structure given by:

11

110

1)( +−−

−− +⋅⋅⋅++= mm zhhzhhhhzhh (4.2)

Channel Impulse Response

(h)

Channel Estimate (hh)

Σ Σ

Noise

Pilot Signal / Training Sequence

u(k) z(k) = u(k) * h y(k) = z(k) + nn(k) e(k) = y(k) – yy(k)

Unknown channel

Adaptive FIR filter

yy(k) = u(k) * hh

nn(k)

+ -

Error signal

LMS Algorithm


where m is the tap length for the adaptive filter. All tap coefficients of hh(k) are initially set to

zero. The training sequence, u(k) and noise, nn(k) is assumed to be a zero mean wide sense

stationary process and that these two signals are uncorrelated with each other. The observed

output from the unknown channel is given by:

hkukz ⊗= )()( (4.3a)

or hkUkz T ⋅= )()( (4.3b)

where means the convolution function and

T

nkukukukU

+−⋅⋅⋅−= )1()1()()( (4.4)

T

nhhhh

= −110 L (4.5)

The channel output obtain from equation (4.3b) is additive to the noise, nn(k) and the output

signal y(k) is given by:

)()()( knnhkUky T +⋅= (4.6)

The output from the adaptive filter is given by:

hhkUkyy T ⋅= )()( (4.7)

where

T

nhhhhhhhh

= −110 L (4.8)

The output of the adaptive filter is subtracted from the output of the unknown channel to

obtain the error signal, e(k):

)()()()()()( knnhhhkUkyykyke T +−⋅=−= (4.9)


The error signal, e(k) obtained in equation (4.9) shall ideally be equal to the noise, nn(k). This

will mean that the LMS algorithm has successfully estimated the unknown channel, h. The

LMS algorithm updates as the tap coefficients by weighting them using the equation:

)()(*)(*)1( kUkekhhkhh ⋅⋅+=+ µ (4.10)

where * is the complex conjugate, U(k) is the training sequence vector obtain from equation

(4.4) and μ is known as the adaptation parameter or the step size factor (see section 4.2.2).

4.2.2 Convergence and Stability of the Standard LMS Algorithm

The step size, μ is a major parameter in the LMS algorithm derived in equation (4.10).

This parameter is considered important as it influences the convergence and stability rate of

the LMS adaptive filter [11]. A smaller μ results in a slower convergence rate but have a more

accurate and stable result, while a larger μ have a faster convergence rate but leads to an

unstable system. The selection of the step size, μ is therefore crucial for its performance to

provide a good convergence rate and stability in the system. The LMS algorithm will

converge and remain stable as long as the step size fulfils the range given by:

∑

+−=

<< k

nkiiu

1

2 )(

20 µ (4.11)

where k is the current time interval and n is the tap length.

4.3 Activity Detection Algorithm

The focal point of this thesis is the detection of ‘important’ taps in the channel impulse

response. The impulse response of a wireless channel may be represented by sparsely

separated active taps interspersed with zero or inactive taps [14]. The LMS adaptive filter as

shown in figure 4.1 generally estimates the impulse response with accurate tap positions and

coefficients. However, this adaptation process includes the estimation of the zero taps as

weak and negligible responses that may lead to a high computational cost as well as poor

asymptotic performance and convergence rate.

Dr. John Homer proposed an active tap detection algorithm [12], [13], [14], [15] that

involves estimating only the active taps. This detection algorithm requires an activity measure


and an activity threshold, which are structurally consistent for white input signals particularly

examine in this thesis. The algorithm uses an approximate least squares (LS) based cost

function to locate the active taps within the impulse response and subsequently estimates

these detected taps [18]. With the implementation of this detection algorithm, we are able to

modify the activity threshold for selecting the more significant multipath signals for

demodulation. This would allow a lower computational cost for reducing the number of

correlators in use and even lead to better asymptotic performance. The formula for the

activity measure and activity threshold is shown in the next sections.

4.3.1 Activity Measure

Under the assumption of a white input signal as mentioned in section 4.2.1, the activity

measure, XN is given by:

∑

∑

+=

+=

−

−⋅∗

=N

jk

N

jk

N

jku

jkuky

jX

1

2

2

1

)(

)()(

)( (4.12)

where y*(k) is the complex conjugate of y(k), j is the active tap index and N is the current

sample interval. To discriminate the active taps from inactive taps, we need the activity

threshold such that if XN (j) is more than the threshold value, the tap will only be detected as

an active tap. The formula for the activity threshold is discussed in the next subsection.

4.3.2 Activity Threshold

The activity threshold has a theoretical basis [13] and is determined by the threshold

factor given by:

NfactorthresholdT yN log.)._( 2σ= (4.13)

where σy2 is the variance of y(k).

( )∑=

=N

ky ky

N 1

22 1σ (4.14)


In this thesis, we investigate the effect of varying the threshold factor in the activity

threshold as in equation (4.13). It is expected that an increase in the threshold factor will

reduce the number of detected active taps in the impulse response of the adaptive filter. The

active tap criterion is given by:

NN TX > (4.15)

where XN is the activity measure in equation (4.12) and TN is the activity threshold in

equation (4.13).

The active tap criterion is implemented to the RAKE receiver in the CDMA system

where the algorithm is used to select the significant multipath signals for demodulation. In

the next chapter, we look into how the LMS algorithm and the activity detection algorithm is

implemented into the CDMA system using the MATLAB® model.

24

C h a p t e r 5

5. MATLAB® MODEL

MATLAB® (short for MATrix LABoratory) is a special-purpose computer program

optimised to perform engineering and scientific calculations. The use of MATLAB® version

6.5 for this thesis enables the development of simulations, which compute the complicated

mathematical formulas and display the simulation results in a graphical form for analysis [17]. The mathematical formulas include calculation of the LMS algorithm, activity measure and

the processing of the information signal in a simulated CDMA communications

environment, with the presence of thermal noise and multipath effects. Results such as the

SNR performance, bit errors, activity detection and asymptotic multipath estimation error are

examined for analytical discussion in chapter 6.

A Graphics User Interface (GUI) is created to aid users in developing an easy-to-use and

friendly environment. Users are able to enter various design parameters and select different

multipath channels to observe and compare the output results. The following sections will

discuss about the functionality of the simulation models and the operation of the GUI.

5.1 Overview

From the theoretical knowledge provided in the earlier chapters on CDMA systems and

the concept of the LMS algorithm with activity detection, we have come up with an

innovative idea of integrating these two technologies together to increase the SNR

performance of the received signal. The implementation of this new signal detection

technique within the RAKE receiver is named ‘CDMA Detection Guided RAKE Receiver’

and is designed to demodulate all ‘important’ multipath signals in the unknown channel. The

estimation of the unknown channel is based on the use of an adaptive filter via the LMS

algorithm and the ‘important’ multipath signals are identified with the activity detection

algorithm. This subsequently determines the number of correlators for the RAKE receiver

where each correlator demodulates each ‘important’ multipath signal individually. With the

Chapter 5 • MATLAB® Model 25

number of correlators increased in the RAKE receiver, the received signal power will

correspondingly improve leading to a better signal reception. However, the addition of the

correlators results in a higher computational cost to the system. The activity threshold is

implemented so that only the ‘important’ multipath signals above this threshold will be

demodulated, ignoring the small and negligible signals. The value of the activity threshold

factor may be increased to detect fewer multipath signals leading to fewer correlators in the

RAKE receiver and hence a lower overall cost of the system.

5.1.1 Three-Model Simulation

In this thesis, we have developed three CDMA models to show the performance of the

CDMA Detection Guided RAKE Receiver using the MATLAB® simulation software.

Figure 5.1 shows the flowchart for the simulation of the three models and the respective

source codes can be found in Appendix A.1 – A.3. The design parameters used in the

computation of a particular simulation are kept similar for the three models in order to

obtain a fair comparison. The functionality of each component in the flowchart is explained

in sections 5.2 – 5.9.

The first model represents the current CDMA RAKE receiver that utilises three

correlators. The LMS algorithm is used to estimate the unknown channel and if the channel

estimate has more than three active taps, this current system will only allow the three

strongest time-shifted multipath signals to be demodulated. In this way, other multipath

signals that are as important will not be demodulated and this may result in bit errors within

the recovered information signal. Results showing this phenomenon can be found in section

6.1.2.

The second CDMA RAKE receiver model that we develop is based on the standard

LMS algorithm. This model detects all the multipath signals and each signal is demodulated

by a correlator. Although this may be seen as the ‘ideal’ case in which all multipath signals are

demodulated to enable an increase in the SNR performance, this model is not possible in the

real world as it is hugely expensive and impractical to implement.

The third model is the CDMA Detection Guided RAKE Receiver of which this thesis is

based on. This model determines the number of correlators to be utilised, depending on the

number of active multipath signals detected. However, if more than seven multipath signals


are detected, only the seven strongest signals will be demodulated. The characteristics of this

model proved to be more advantageous than the prior two models for its ability to minimise

the number of correlators in the RAKE receiver and yet maintain an improved SNR

performance.

5.1.2 GUI Implementation

The GUI can be represented in a flowchart as shown in figure 5.2. It has five user-input

variables to allow for different combinations. These five design parameters namely: (1) Walsh

code; (2) Noise factor; (3) Step size; (4) Threshold factor; and (5) Multipath channel selection

must be input before any simulation process can take place. The multipath channel selection

option is interactive as it helps the user to visualize the impulse response of the selected

channel.

The simulated output shows the SNR performance and the number of correlators in use

for each of the three models. Graphs that correspond to the channel estimate, Walsh code

plot, input verus output bit plot and asymptotic error can be displayed by clicking on the

respective push buttons of each model.

For easy referencing and identification, each model is associated with a unique

background colour. Figure 5.3 features the screenshot of the GUI. The current RAKE

receiver model is yellow in colour, the standard LMS based RAKE receiver is green in colour

and the detection guided RAKE receiver is cyan in colour. The complete GUI coding can be

found in Appendix B.


Figure 5.1 Flowchart of the simulation

START

Generate PN Sequence PN_seq_I/Q

Generate Walsh Code Wodd, Weven

Generate Bit Stream training_signal/input_bit

Generate Multipath Ch. h

Spreading Code Generated (Bits in antipodal form)

Wcode_PN_seq_I/Q

QPSK Modulated Signal Real, Imag

Complex Baseband Signal (Real + Imag*j)

complex_baseband_signal

conv

Thermal Noise Added (channel_output + thermal_noise)

y

Current RAKE Receiver with three Correlators

(Selects the 3 strongest taps from the channel estimate)

rake1_output_total

Standard LMS Based RAKE Receiver

(Selects all taps from the channel estimate)

rake2_output_total

Detection Guided RAKE Receiver

(Selects taps above activity threshold / a max of 7 strongest taps from the channel estimate)

rake3_output_total

xor

multiplication

Standard LMS Algorithm /

Activity Detection Algorithm

Display Recovered Bit Stream



END


Figure 5.2 Flowchart of the GUI

START

User to enter the design parameters: 1. Walsh code (1-64) 2. Noise factor (1-15) 3. Step size (0-0.075) 4. Threshold factor (1-10) 5. Select a multipath channel

Click on Simulate?

Display SNR for each of the three models

Display number of RAKE receiver utilised for each

of the three models

Click on Channel

Estimate? Click on Walsh Code

Plot?

Click on I/P vs O/P

Plot? Click on Asymptotic

Error?

Click on Algorithm Compare?

Plot figure for selected function

Exit?

END

Yes

Yes

Yes Yes Yes

Yes Yes

No

No

To try another simulation


Figure 5.3 Screenshot of the GUI

5.2 Bit Streams

Two types of bit streams have been employed in all the three models we considered.

The first type is the training sequence that comprises of 150 pseudo-randomised bits while

the second type is the input data bit stream that contains 10 pseudo-randomised bits.

5.2.1 Training Sequence

A training sequence is used in the simulations for estimating the channel impulse

response. The ‘rand’ function generates arrays of random numbers whose elements are

uniformly distributed in the interval (0,1). This training sequence is then converted an

antipodal set containing only amplitudes values of ±1. The training sequence is generated as

follows:

training_signal = fix(2*rand(1,150)); training_signal_polar = (2*training_signal - 1); % training sequence in antipodal form


5.2.2 Input Bit Sequence

The input bit stream is also generated using the ‘rand’ function. This input sequence

simulates the information signal to be sent to the channel for retrieving by the RAKE

receiver. Any errors resulting from the transmission can be shown in the input verus output

bit plot in figure 5.4. The coding for generating the random information signal is highlighted

below:

input_bit = fix(2*rand(1,10)); input_bit_polar = (2*input_bit - 1); % input signal in antipodal form

Figure 5.4 An example of the input verus output bit plot where bits 7 and 8 have errors

5.3 Walsh Code

A 64 by 64 Walsh function matrix (see section 2.4) is used to generate the Walsh codes

for the simulations. A user is able to choose from any of the 64 Walsh codes by entering a

number (1-64) in the ‘Step 1’ edit box on the GUI. An example of the 10th row on the Walsh

code matrix is plotted in figure 5.5. The following code describes the generation of the Walsh

matrix:


W1 = [0]; W2 = [W1 W1; W1 ~W1]; W4 = [W2 W2; W2 ~W2]; W8 = [W4 W4; W4 ~W4]; W16 = [W8 W8; W8 ~W8]; W32 = [W16 W16; W16 ~W16]; W64 = [W32 W32; W32 ~W32]; % 64 x 64 Walsh code matrix

Figure 5.5 The Walsh code for the 10th row of the matrix function

The first row of the Walsh matrix contains the all zero bits, which corresponds to the

pilot signal used for training the channel estimate:

Wcode = W64(1, :); % training sequence

The Walsh code sequence needs to be separated into the I and Q-channel for QPSK

modulation. The odd bits for the Walsh code, Wodd are used in the I-channel whereas the

even bits, Weven are used in the Q-channel:

Wodd = Wcode(1:2:length(Wcode)); % Walsh code for I-channel Weven = Wcode(2:2:length(Wcode)); % Walsh code for Q-channel


Both Wodd and Weven are then XOR with the corresponding PN sequences to obtain the

randomness property. With the aim of achieving a zero DC signal value, the bits are

converted to the antipodal form.

5.4 PN Sequence

The advantages of using a PN sequence are mentioned in section 2.3. The PN sequences

are typically periodically generated using linear feedback shift registers. However, we use the

‘rand’ function in the simulation to approximate the generation of the PN sequences and we

assume that the length of the PN sequence corresponds to the length of the bit streams. The

bits for the PN sequence are randomly generated as shown in the coding:

PNseq_I = fix(2*rand(1,length(bit_stream)*32)); % PN sequence for the I-channel PNseq_Q = fix(2*rand(1,length(bit_stream)*32)); % PN sequence for the Q-channel

The PN sequence is then XOR with the selected Walsh code in the I and Q-channel as

illustrated in figure 5.6. This forms the spreading code for the CDMA spread spectrum

system. An identical spreading code is made available at the receiving end for the recovering

of input signals. The system model for QPSK modulation in a CDMA transmitter is shown

in figure 5.6. The XOR operation is as follows:

for n = (1:length(bit_stream)) WcodePN_I = xor(Wodd,PNseq_I((32*(n-1)+1):32*n)); % spreading code for I-channel WcodePN_Q = xor(Weven,PNseq_Q((32*(n-1)+1):32*n)); % spreading code for the Q-channel WcodePN_I_polar(32*(n-1)+1:32*n) = (2*WcodePN_I - 1); % Q-spreading code in antipodal WcodePN_Q_polar(32*(n-1)+1:32*n) = (2*WcodePN_Q - 1); % I-spreading code in antipodal end

5.5 Complex Baseband Signal

The odd bits of the input stream are spread by WcodePN_I_polar while the even bits of

the input stream is spread by WcodePN_Q_polar. In this simulation, the transmitted signal is

not modulated by a carrier frequency and is represented as the complex baseband signal. The

transformation of the input signal to the complex baseband signal is shown in figure 5.6. The

following code extracts explains how the complex baseband signal is obtained:


for n = (1:length(bit_stream)) Real = [training_signal_polar(n)*WcodePN_I_polar((32*(n-1)+1):32*n)]; Imag = [training_signal_polar(n)*WcodePN_Q_polar((32*(n-1)+1):32*n)]; complex_baseband_signal(32*(n-1)+1:32*n)=Real + Imag*j; % complex baseband signal end

Figure 5.6 System model showing the transformation of the input bit steam to the complex

baseband signal

5.6 Channel Impulse Response

A total of four channel impulse responses have been created to represent the different

multipath channels. Channels 1-3 have a prefixed number of ‘important’ multipath signals to

illustrate the findings in chapter 6 whereas channel 4 is used to simulate a randomised

impulse response. The GUI allows the user to choose from any one of the multipath

channels for simulation by selecting from the option buttons. The selected channel can be

viewed instantly from the GUI, thus enabling the user to visually select the desired channel.

The coding listed below has twenty taps with three prominent multipath signals having

the amplitude values of 2.1, 3.1 and –2.5 respectively as shown in figure 5.7:

xor

input_bit

Wodd WcodePN_I

Weven WcodePN_Q

I-channel

xor

PNseq_I

PNseq_Q

j Q-channel

complex_baseband_signal Σ


% channel impulse response, h h = [0,0,(0.1*randn(1,2)),2.1,(0.1*randn(1,5)),3.1,(0.1*randn(1,5)),-2.5,(0.1*randn(1,3))];

Figure 5.7 Channel impulse response of a multipath channel

5.7 Thermal Noise

Thermal noise is added into the system for simulating the real mobile radio channel.

This noise component is complex and random in nature whose elements are normally

distributed with zero mean. The length of the thermal noise corresponds to the length of the

bit streams, which indicates that every bit is affected by the noise in the system. In this thesis,

noise is induced into the signal in the multipath channel.

The GUI allows the user to enter a noise factor for the simulation in the ‘Step2’ edit

box, which represents the root-mean-square (r.m.s) value of the noise signal. The square of

the r.m.s value gives the noise power. The effect of varying the noise power will be examined

and used for performance comparison of the three models. The noise is generated as follows:

thermal_noise = randn(1,length(bit_stream)*32)*noise_factor + randn(1,length(bit_stream)*32)*noise_factor*j; % thermal noise in a channel


5.8 Channel Estimate

As mentioned in section 5.2.1, a training sequence is used to train up the finite impulse

estimator response of a simulated channel. This channel estimator uses the LMS adaptive

algorithm. An example of this is shown in figure 5.8. With the implementation of the activity

detection algorithm, the channel estimate is able to identify the ‘important’ multipath signals

for demodulation in each correlator of the RAKE receiver.

The LMS algorithm discussed in chapter 4 is implemented in the simulation, where h

represents the channel response and hh represents the channel estimate. The LMS algorithm

coding is shown below where y(k) is the output of the channel, yy(k) is the output of the

estimator and e(k) is the error signal. The channel estimation error, he(k) is plotted to show

the effect of the step size, mu on the convergence rate and stability of the estimation. The

LMS adaptive FIR filter system model can be found in figure 4.1. The LMS algorithm

formula from equation (4.10) requires the ‘conj’ function to transform hh and e(k) to its

complex conjugate form.

The GUI allows a user to choose a step size value from equation (4.11) in the ‘Step 3’

edit box to observe the effects of varying this constant in the CDMA system.

hh = zeros(1,length(h)); uu = zeros(length(h),1); shift = diag(ones(1,(length(h) - 1)), -1); for k = 1:length(complex_baseband_signal) uu = shift * uu; uu(1) = complex_baseband_signal(k); yy(k) = hh * uu; e(k) = y(k) - yy(k); hh = conj(hh) + mu * (uu.') * conj(e(k)); % LMS algorithm formula (refer to equation (4.10)) he(k) = (h-hh) * (h-hh)'; % asymptotic error =>same operation as (abs(h-hh))^2 end

The algorithm for activity detection discussed in section 4.3 allows the active taps, which

are above the activity threshold to be detected as ‘important’ taps. The coding below suggests

that if the activity measure for a particular tap is below the activity threshold, the tap will be

assigned a zero value in the channel estimate. A user will be able see the effects of varying the


threshold factor in the ‘Step 4’ edit box. An increase in the threshold factor leads to a fewer

number of active taps being detected.

if activity_eqn(tap) > (threshold_factor * var_y * log10(k)) % refer ‘activity_eqn’ to equation (4.12) active(tap)=1; else active(tap)=0; end % LMS algorithm formula hh(tap) = active(tap) * (conj(hh(tap)) + mu * complex_baseband_signal(k+1-tap) * conj(e(k)));

Figure 5.8 Taps below the activity threshold are detected as zero taps in the channel

estimate


5.9 RAKE Receiver

The respective channel estimate obtained for the three models are used in the

demodulation of the transmitted signal. The current RAKE receiver model sorts the channel

estimate for selecting the three ‘strongest’ multipath signals while the detection guided

RAKE receiver model is designed to allocate each ‘important’ multipath signal to a correlator

with a maximum of seven correlators. The ‘abs’ function computes the absolute value on

each tap of the channel estimate so that signals that are 180° out of phase can be ranked in

terms of signal amplitude with the ‘sort’ function shown below.

sort(abs(hh)); % sort all taps of the channel-estimate impulse response in the descending order

The standard LMS based RAKE receiver does not require any sorting function as it

simply assigns a correlator to each of the multipath signal. Each correlator in the RAKE

receiver is only able to demodulate effectively when the spreading code is synchronized in

accordance to the delay spread of the respective multipath signal. This simulation is based on

the assumption that the delay between adjacent taps on the impulse response model

corresponds to a value more than the chip interval. The following codes execute the

synchronization of the spreading code for each correlator, where m is the tap position of each

multipath signal, WcodePN_I/Q_polar is the spreading code, WcodePN_I/Q_polar0 is the

synchronized spreading code and hh(m) is the phase/gain adjustor.

for m = 1:length(hh) % synchronization of spreading code for I/Q-channel WcodePN_I_polar0 = [(ones(1,(m-1))*-1), WcodePN_I_polar]; WcodePN_Q_polar0 = [(ones(1,(m-1))*-1), WcodePN_Q_polar]; for n = (1:length(input_bit_polar)) correlator_I = real(y(32*(n-1)+1 : 32*n)); % received signal in I-channel rake_I(n) = hh(m) * sum(correlator_I .* WcodePN_I_polar0((32*(n-1)+1):32*n)); % despread correlator_Q = imag(y(32*(n-1)+1 : 32*n)); % received signal in Q-channel rake_Q(n) = hh(m) * sum(correlator_Q .* WcodePN_Q_polar0((32*(n-1)+1):32*n)); % despread rake_output(n) = rake_I(n) + rake_Q(n); % output signal from individual correlator end rake_output_total = rake_output + rake_output_total; % output signal from RAKE receiver end;


5.10 Decision Device

The analogue output antipodal signal obtained from the RAKE receiver is inputted into

a decision device to transform it into a unipolar signal. The ‘sign’ function assigns a logic ‘1’ if

the amplitude level of the corresponding bit is greater than zero and a logic ‘0’ if the

amplitude level of the corresponding bit is less than zero. The received output_bit is checked

with the input signal for any transmission errors.

output_bit = (sign(rake_output_total) + 1) / 2;

The SNR values for the three models are individually calculated based on the output

signal strength obtained at the decision device. The results from the simulation showing the

transmission errors and SNR performance are used for comparison among the three models

and discussed in the next chapter.

39

C h a p t e r 6

6. RESULTS AND DISCUSSION

The detection guided RAKE receiver model is thoroughly tested and simulation results

are compared with the current RAKE receiver model and the standard LMS based RAKE

receiver model. Several combinations of the design parameters are examined and discussed in

the following sections of this chapter. We look at how the detection guided RAKE receiver is

able to detect and select the important multipath signals for demodulation, resulting in a

better SNR and an overall lower computational cost.

In this chapter, we examine and analyse the findings from the simulated results using

MATLAB®. They are categorized into the following sections:

• Section 6.1: Effects on increasing the noise factor

• Section 6.2: Effects on increasing the threshold factor

• Section 6.3: SNR performance for the three models

• Section 6.4: Comparison on the asymptotic multipath estimation error

Chapter 6 • Results and Discussion 40

6.1 Effects on Increasing the Noise Factor

In this section, we investigate the effects of increasing the noise factor. A noise factor of

value two, eight and nine are inputted to the system. All other design parameters remain

unchanged for this section of the finding. It is expected that an increase in the noise factor

will lead to a lower SNR performance. This phenomenon is shown in tables 6.1, 6.2 and 6.3,

where the SNR performance decreases about 13dB on average between the lowest and

highest noise factor values simulated.

Furthermore, with the increase in the noise factor, the simulation results show that the

current RAKE receiver has a bit error in the signal output (see Figure 6.4) as compared to the

other two models (see Figures 6.5 and 6.6). The channel estimates of figures 6.1 and 6.4 show

different impulse response due to the effect of noise. The standard LMS based RAKE

receiver and the detection guided RAKE receiver utilise more correlators, and consequently

both of these models are able to effectively demodulate the transmitted signal without errors.

When the noise factor is increased to a value of nine, the standard LMS based RAKE

receiver model surface an error bit. The increase noise power to the system has allowed the

introduction of smaller multipath signals to interfere with the prominent ones. On the other

hand, the detection guided RAKE receiver is able to filter out these unwanted multipath

signals through the implementation of the activity detection algorithm. The simulation results

show that it is probably not effective and efficient to provide a correlator for each multipath

signal.

From table 6.1, the detection guided RAKE receiver shows a SNR value of 77.8748dB,

which is approximately 4.6dB higher than the SNR for the current RAKE receiver (see

Section 6.3). A 3dB improvement in the SNR means that the SNR has doubled. The SNR

value for the detection guided RAKE receiver is very similar to the standard LMS based

RAKE receiver although it is able to achieve this SNR value with a much smaller number of

correlators. In this simulation, the detection guided RAKE receiver’s performance is (20/5)

= 4 times better than the standard LMS based RAKE receiver.

The earlier discussions are based on the results achieved from the MATLAB®

simulation. Graphs and tables are plotted to support the findings for this simulation.


6.1.1 Noise Factor = 2.0

DESIGN PARAMETERS

Walsh code row Noise factor Step size Threshold factor

35 2.0 0.0025 3

Number of multipath

signals detected Number of

correlators utilised Number of bit

errors Signal-to-noise ratio

(dB)

Current RAKE receiver

3 3 0 73.2889

Standard LMS based RAKE receiver

20 20 0 77.8604

Detection Guided RAKE receiver

5 5 0 77.8548

Table 6.1 Effects on varying the noise factor to 2.0

Figure 6.1 Simulated results for the current RAKE receiver on the channel estimate and the

input verus output bit plot for noise factor = 2.0


Figure 6.2 Simulated results for the standard LMS based RAKE receiver on the channel

estimate and the input verus output bit plot for noise factor = 2.0

Figure 6.3 Simulated results for the detection guided RAKE receiver on the channel




DESIGN PARAMETERS


35 8.0 0.0025 3

Number of multipath




(dB)


3 3 1 61.9979


20 20 0 65.8324


5 5 0 65.7795











DESIGN PARAMETERS


35 9.0 0.0025 3

Number of multipath




(dB)


3 3 2 61.1086


20 20 1 64.8677


5 5 0 64.7526










6.2 Effects on Increasing the Threshold Factor

In this section, we investigate the effects of increasing the threshold factor for the

simulations. All other design parameters remain unchanged for this section of the finding.

From the activity threshold in equation (4.13), we understand that an increase in the

threshold factor leads to the detection of higher activity measures. The simulated results

tabulate in tables 6.4 and 6.5 show this phenomenon.

The detection guided RAKE receiver with a threshold factor of three detects eight

multipath signals as compared the same system using a threshold factor of six and detecting

only six multipath signals. Through this experiment, we have found success as the latter

simulation has a relatively close SNR value with the former. This shows that the activity

detection algorithm has effectively filter out two ‘negligible’ multipath signals and efficiently

lowered the computational cost of the system with the implementation of fewer correlators.

The detection guided RAKE receiver in this model has been designed to maximize up to

seven correlators in which more correlators would be a waste of resource. This is shown in

tables 6.4 and 6.5 that the average SNR difference between the standard LMS based RAKE

receiver and the detection guided RAKE receiver is only about 0.3dB, with a maximal use of

correlators.

The varying of the threshold factor does not have any impact on the current RAKE

receiver and the standard LMS based RAKE receiver. However, it is noted that the detection

guided RAKE receiver is again able to successfully recovery the original signal whereas the

current RAKE has a bit error as shown in figure 6.10.

The result of this simulation clearly shows that the threshold factor for the activity

detection algorithm plays an important part in the selection of the multipath signals for

demodulation. A lower threshold factor may mean the detection of more negligible multipath

signals whereas a higher threshold factor may suggest not being able to detect enough

multipath signals for proper demodulation.


6.2.1 Threshold Factor = 3.0

DESIGN PARAMETERS


50 8.0 0.0025 3.0

Number of multipath




(dB)


3 3 1 70.1999


20 20 0 74.0431


8 7 0 73.8512

Table 6.4 Effects on varying the threshold factor to 3.0

Figure 6.10 Simulated results for the current RAKE receiver on the channel estimate and

the input verus output bit plot for threshold factor = 3.0


Figure 6.11 Simulated results for the standard LMS RAKE receiver on the channel

estimate and the input verus output bit plot for threshold factor = 3.0


estimate and the input verus output bit plot for threshold factor = 3.0


6.2.2 Threshold Factor = 6.0

DESIGN PARAMETERS


50 8.0 0.0025 6.0

Number of multipath


correlators utilised Number of bit errors

Signal-to-noise ratio (dB)


3 3 1 70.1999


20 20 0 74.0431


6 6 0 73.7033

Table 6.5 Effects on varying the threshold factor to 6.0

Figure 6.13 Simulated results for the

detection guided RAKE receiver on the

channel estimate for threshold factor = 6.0

Figure 6.14 Simulated results for the

detection guided RAKE receiver on the

asymptotic error and active taps detection

for threshold factor = 6.0


6.3 SNR performance for the Three Models

The SNR performance for the three models is plotted and shown in figure 6.15. Each

model is simulated for twenty times over an increasing noise factor. The SNR performance

for the current RAKE receiver is found to have an average of 4dB lower than the standard

LMS based RAKE receiver and the detection guided RAKE receiver. However, the standard

LMS based RAKE receiver utilises twenty correlators as compared to detection guided

RAKE receiver, which only limits to seven correlators and yet achieving a comparable SNR

value.

6.4 Comparison on the Asymptotic Multipath Estimation Error

From the theory as discuss in section 4.3, the asymptotic multipath estimation error plot

in figure 6.16 shows that the detection guided RAKE receiver has a better asymptotic

performance as compared to the standard LMS based RAKE receiver. The plot in figure 6.16

is simulated with a noise factor of 9.0, a threshold factor of 2.0 and a step size factor of

0.0025. As the input noise factor is reasonably high, the asymptotic error for both the

receivers are generally higher as well.

~70dB

~66dB

Figure 6.15 SNR comparison

among the three models derived

Figure 6.16 Asymptotic multipath

estimation error comparison between

the LMS algorithm and the activity

detection algorithm

52

C h a p t e r 7

7. CONCLUSION

The aim of this thesis as mentioned in chapter 1 is to incorporate a new signal detection

technique within the RAKE receiver to identify the ‘important’ multipath signals in the

wireless channel. In the course of this thesis, we have developed a simulation using

MATLAB®. This simulation implements the standard LMS algorithm and the activity

detection algorithm in the adaptive process of estimating the channel impulse response. It

has found that the detection guided RAKE receiver outperforms the current RAKE receiver

and the standard LMS based RAKE receiver. Section 7.1 will summarize this thesis and

Section 7.2 will provide some suggestions to any future work in this topic.

7.1 Summary of Findings

This thesis presents a simulated CDMA system with the RAKE receiver that is able to

function more efficiently and effectively as compared to the current technology. This RAKE

receiver incorporates the activity detection algorithm where it involves an activity measure

and an activity threshold. A multipath signal whose activity measure is below the threshold is

detected as a negligible multipath signal and will not be consider for demodulation. Hence,

this algorithm only allows the detection of the ‘important’ multipath signals depending on a

decisive threshold factor.

The implementation of the detection guided RAKE receiver has found to perform

much better than the current RAKE receiver and the standard LMS based RAKE receiver.

The proposed RAKE receiver is able to obtain a better SNR performance than the current

RAKE receiver using a minimum number of correlators. The effect of noise in the channel is

found to have the least affect to the detection guided RAKE receiver, which makes it less

prone to errors.

Chapter 7 • Conclusion 53

Overall, the detection guided RAKE receiver has shown to achieve a superior

performance and more research work should be continued to explore the many more

capabilities of this algorithm.

7.2 Suggestions to Possible Future Work

The activity detection algorithm has proven its intended function and has shown to be

cost effective as well. However, the value of the threshold factor does not have any

significant meanings on the amplitude of the multipath signals. This thesis has proposed that

multipath signals above the amplitude value given by:

( )factorthreshold _log1 (7.1)

should be considered as an active multipath signal. This equation (7.1) works well for small

threshold factor but fails when the threshold factor is increased to a larger value.

Future work should include the computation of this threshold amplitude for the activity

detection algorithm to allow a better representation on the selections of the taps.

54

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[3] CDMA Development Group. 2002. RAKE Receiver: Another Advantage of CDMA over Other Systems. http://www.cdg.org/tech/abcs/lec1/text/abc_1_3_36.txt [Accessed Oct 14 2002].

[4] Buckley, S. 2000. 3G Wireless: Mobility Scales New Heights. Telecommunications Magazine.

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[13] Homer, J., Mareels, I., Bitmead, R.R., Wahlberg, B., & Gustafsson, F. 1998. LMS estimation via structural detection. IEEE Transactions on Signal Processing, 46(10): 2651-2663.

[14] Homer, J. 1998. Detection guided LMS estimation of sparse channels. Global Telecommunications Conference, 6:3704-3709.

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[15] Homer, J., Bitmead, R.R., & Mareels, I. 1998. Quantifying the effects of dimension on the convergence rate of LMS adaptive FIR estimator. IEEE Transactions on Signal Processing, 46 (10): 2611-2615.

[16] Homer, J. 2000. Detection guided NLMS estimation of sparsely parametrized channels. IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, 47(12): 1437-1442.

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RAKE Thesis