I f / d s n ' / ,5 5 / C?6 _ (5) 
Laboratory Generation of Rayleigh Fading 
L. N. RATHNAYAKE 
Thesis submitted 
to 
the University of Moratuwa, Sri Lanka 
UBFtARY 
in partial fulfillment of the requirement for the degree of 
Master of Engineering 
m 
Electronics & Telecommunications 
September 2006 
l iiivtrsin of \ l o i a l u « a 
8 7 1 3 5 
87135 
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The work presented in this dissertation has not been 
submitted for the fulfillment of any other degree 
L N Rathn^ 
C a n d i d a t e 
rake 
71 
Prof (Mrs.) D i l e e k a D i a s 
S u p e r v i s o r 
u 
A c k n o w l e d g e m e n t s 
I a m v e r y t h a n k f u l to m y s u p e r v i s o r Prof (Mrs. ) D i l e e k a D i a s for t h e g u i d a n c e 
a n d s u p p o r t g iven to m e by h e r d u r i n g t h e p u r s u i t of m y M a s t e r ' s d e g r e e . S h e 
h a s b e e n v e r y he lp fu l a n d I a m g r a t e f u l for h e r w i l l i n g n e s s a n d r e a d i n e s s in 
g iv ing d i r e c t i o n to m y t h e s i s work . 
I w o u l d l ike to t h a n k M r . C h a n d a n a P e i r i s for h i s i n v a l u a b l e i d e a s a n d 
s u g g e s t i o n s d u r i n g t h e c o u r s e of m y t h e s i s work . 
L a s t , b u t n o t l e a s t , I w o u l d l ike to t h a n k m y fami ly w h o w e r e a s o u r c e of 
c o n s t a n t s u p p o r t a n d e n c o u r a g e m e n t . 
iii 
Abstract 
Mobile radio channel simulators are essential for repeatable system tests in a 
development , design, or test laboratory. Due to the random, uncontrollable nature o f the 
mobi le propagation path, it is difficult to generate repeatable field test results. Also doing 
field tests in a mobi le environment is considerably more expens ive . 
An approach for hardware simulation o f Rayleigh fading is presented in this thesis. The 
heart o f the simulator is a Digital Signal Processor (DSP) , which implements the random 
noise and the digital filtering necessary for the generation o f a Rayle igh faded signal. 
The results indicate that the proposed hardware simulator can simulate Rayleigh fading 
with a high degree o f accuracy. The envelope o f the generated Rayleigh fading had been 
observed by an Osc i l loscope . The observations have been done also for carrier frequency 
o f 9 0 0 M H z . 
i v 
Contents 
A c k n o w l e d g e m e n t s iii 
A b s t r a c t iv 
L i s t of F i g u r e s vi 
C h a p t e r 
1. I n t r o d u c t i o n 
1.1. Motivation 1 
1.2. Previous Related Research 2 
1.3. Outl ine of th is Thesis 2 
2. R a y l e i g h F a d i n g S i m u l a t o r 
2.1. Rayleigh Fading Channel 3 
2.2. Channe l Simulat ion Model 9 
3. I m p l e m e n t a t i o n of R a y l e i g h F a d i n g S i m u l a t o r 
3.1. H a r d w a r e 11 
3.2. FIR Low Pass Fil ter (LPF) 14 
3.3. L i n e a r - F e e d b a c k Shif t R e g i s t e r (LFSR) 15 
3.4. Pseudo-Random Binary Sequence (PRBS) by a LFSR 17 
3.5. Genera t ing AWGN source 18 
4. P r o g r a m s a n d R e s u l t s 
4.1. P rograms 20 
4.2. Resul ts 27 
5. D i s c u s s i o n of R e s u l t s & C o n c l u s i o n 
5.1. Discussion of Resul ts 32 
5.2. Conclusion 37 
5.3. Directions for F u t u r e Work 37 
R e f e r e n c e s 38 
r V 
List of Figures 
2.1 A typical mobile s i tuat ion 3 
2.2 A typical Rayleigh fading envelope at 900 MHz Abstract 4 
2.3 Rayleigh probabili ty density function 5 
2.4 Cumula t ive Distr ibut ion Function of a Rayleigh faded envelope 6 
2.5 Effect of Motion 7 
2.6 Faded Power Spect rum 8 
2.7 Theoretical Fade Simulator 9 
2.8 Implemented Rayleigh Fade Simulator 10 
3.1 System Archi tecture 12 
3.2 ADSP-BF535 EZ-KIT Lite demonstra t ion board 13 
3.3 Digital Low Pass Fil ter 14 
3.4 4-Bit LFSR, Tap Sequence; [4,1] 15 
4.1 Main Flow Char t 20 
4.2 Flow cha r t to obtain the PRBS generated Gauss ian Noise 21 
4.3 Setup to display the faded signal on an Oscilloscope 25 
4.4 Fil ter Response 27 
4.5 Rayleigh Envelope [MATLAB generated noise] 28 
4.6 CPDF of Rayleigh envelope [MATLAB genera ted noise] 28 
4.7 Rayleigh Envelope [PRBS generated noise] 29 
4.8 CPDF of Rayleigh envelope [PRBS generated noise] 29 
4.9 Rayleigh fading envelope a t 900 MHz [MATLAB genera ted noise]. . . 30 
4.10 Rayleigh fading envelope a t 900 MHz [PRBS genera ted noise] 31 
5.1 Resul ts obtained from Visual DSP++ 35 
5.2 Rayleigh Fading envelopes 36 
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