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Rayleigh Multipath Fading Channel Emulator
Prepared by:

Wesley Scott New
Prepared for:

Dr Emmanuel Bejide University of Cape Town Department of Electrical Engineering

This thesis is submitted to the University of Cape Town in partial fulfillment of the academic requirements for the Degree of Bachelor of Science in Engineering

October 29, 2007

i

Declaration
I declare that thework submitted in this report is my own, references to other works have been given as appropriate. I am submitting it for examination for the Degree of BSc in Electrical Engineering at the University of Cape Town.

Name: Wesley New Signature:

___________________

Date: October 2007

Wesley New

Multipath Fading Channel Emulator

ii

Abstract
Multipath fading is a common phenomenonin wireless communications. It causes attenuation and signal distortion. Multipath channels are caused by effects such as reflection, refraction and diffraction. The theory behind the multipath fading is discussed. Rayleigh and Ricean channel models are examined and compared. An emulator is designed to aid signal testing over multipath channels. In particular, an uncorrelated Rayleigh multipathchannel is simulated, using Matlab and then implemented into hardware using VHDL. Correlated fading is examined and also modelled in Matlab.

Wesley New

Multipath Fading Channel Emulator

iii

Acknowledgments
I would like to express my gratitude to my supervisor Dr Emmanuel Bejide for the hours of discussions and support he has invested in helping with this thesis. Thank you for your timeand intellectual conversations. Many thanks go to my parents for their support and for encouraging me to work. Thank you for the financial, emotional and physical support. I wish to thank friends and engineering colleagues that have been with me throughout the duration of my degree. I have made some amazing friendships that I’m sure will last an eternity. Thanks guys. And I would like to thank mySaviour, the Lord Jesus Christ, for without him, I would never be where I am today. Lord I thank you for dying on the cross to cleans our sins and provide way to your Father and eternal salvation. And thank you for showing me your plan for my life for this coming year.

Wesley New

Multipath Fading Channel Emulator

Contents

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Contents
List Of Figures 1 Introduction 1.1 1.2 1.3 1.41.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scope and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 2 2 3 3 4 6 6 88 11 17 19 20 23 23 23 26 27 30 30 32 35 40

2 Background 2.1 2.2 The Wireless Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . Multipath Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 2.2.2 2.2.3 2.2.4 2.3 Causes of Multipath Fading . . . . . . . . . . . . . . . . . . . Characterisation of Multipath Fading Channels . . . . . . . . . Rayleigh Fading Model . .. . . . . . . . . . . . . . . . . . . . Rician Fading Model . . . . . . . . . . . . . . . . . . . . . . .

Doppler Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Modeling the Channel with Matlab 3.1 Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 3.1.2 3.1.3 3.2 Multipath Channel Model . . . . . . . . . . . . . . . . . . . . The MatlabModel . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Correlated Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . 3.2.1 3.2.2 3.2.3 Doppler Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . Correlated Channel . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . ....
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