[FONT=Times New Roman]Acknowledgements

I would like to thank my supervisor Dr. Conor Brennan for his guidance, assistance and approachability throughout this project. I would also like to thank John Diskin for his work on the ray tracing program. Finally I would like to thank my parents and Laura for their support throughout my project.

Declaration

I hereby declare that, except where otherwise indicated, this document is entirely my own work and has not been submitted in whole or in part to any other university.

Abstract

This project explores the development of a multiple input multiple output (MIMO) simulator using ray tracing techniques. This project gives an overview of ray tracing techniques, beamforming, MIMO channel models and MIMO systems. It explains the ability of MIMO systems to offer significant capacity increases over traditional wireless systems, by exploiting the phenomenon of multipath. By modelling high frequency radio waves as travelling along localized linear trajectory paths, they can be approximated as rays, just as in optics.

The radio environment is then represented using a ray tracing C++ program. I highlight some of the different approaches used to realize a MIMO system, the most important being the Singular Value Decomposition (SVD). I illustrate the development of the MIMO simulator, through explanations of the techniques and algorithms I developed and used. These algorithms model the system under ideal conditions with no noise distortions. I show the use of the MIMO simulator created, and investigate the MIMO channel. The results obtained show the affects of changing the different parameters of the system on the MIMO channel and the radio environment.

Finally, in the conclusion, I discuss the future of MIMO systems and recommend further modifications, which could be made to the MIMO simulator, to create a more accurate and efficient system.

Table Of Contents

CHAPTER 1 - INTRODUCTION...................................... .................................................1

CHAPTER 2 - TECHNICAL BACKGROUND........................................ .........................2

2.1MULTIPATH...................................... .................................................. ...........................3

2.2 RAY TRACING........................................... .................................................. ....................3

2.3 BEAMFORMING....................................... .................................................. ......................4

2.4 LINEAR ARRAYS............................................ .................................................. ................6

2.5 MIMO.............................................. .................................................. ...........................7

2.5.1 MIMO Transmission...................................... .................................................. .......8

2.5.2 The MIMO Channel H................................................. ...........................................9

2.6 GAUSSIAN ELIMINATION....................................... .................................................. ......10

2.7 SINGULAR VALUE DECOMPOSITION (SVD)............................................. .....................12

CHAPTER 3 – IMPLEMENTATION OF RAY TRACING..........................................1 3

3.1 RAY TRACING........................................... .................................................. ..................14

3.1.2 The ray tracing program........................................... ...........................................14

3.2 CONVERGENCE OF ORDER............................................. ................................................26

CHAPTER 4 - IMPLEMENTATION OF MIMO SIMULATOR..................................30

4.1 GAUSSIAN ELIMINATION....................................... .................................................. ......30

4.2 SVD............................................... .................................................. ...........................33

4.2.1 Operation of the SVD algorithm......................................... ..................................33

4.2.2 Matlab SVD............................................... .................................................. .........35

4.3 FURTHER MODIFICATIONS TO THE RAY TRACING PROGRAM..........................................3 9

4.4 PLOTTING THE RESULTS........................................... .................................................. ...40

4.5 THE MIMO SIMLATOR.......................................... .................................................. .....41

4.5.1 MIMO simulator users guide............................................. ...................................43

CHAPTER 5 – RESULTS........................................... .................................................. .....46

5.1 SVD IN FREESPACE......................................... .................................................. ...........46

iv

5.2 NUMBER OF ELEMENTS IN AN ARRAY............................................. ...............................49

Simulation of a MIMO wireless system – John Fitzpatrick

5.3 DIELECTRIC PARAMETERS AND CORRIDOR MODEL............................................. ...........51

CHAPTER 6 - CONCLUSIONS AND FURTHER RESEARCH...................................55

Matlab code for Beamforming....................................... ................................................58

C++ Gaussian Elimination Code.............................................. ....................................60

Matlab Singular Value Decomposition (SVD) Code.............................................. .......64

Matlab ‘mimo’ Code.............................................. .................................................. ......66