JPL's Wireless Communication Reference Website

Chapter: Wireless Channels
Section: Multipath fading, Rayleigh fading, Probability.

Plot of probability distribution of received signal amplitude

Exercise

write a computer program that plots the probability that a Rayleigh fading signal drops below a certain threshold. Show that the curve can be plotted as a function of a fade margin, i.e., the ratio between the local mean power and the threshold.

If the receiver can choose between L (L= 1,2, ..) different antennas and each antenna sees an independently fading signal, how does this improve the probability?

Solution 1.


Probability of fade versus fade margin.

Matlab Code

The above curve was plotted using the following code: 

%-------------------------------------------

xaxis   =  [];
y1  =  [];
y2  =  [];
y3  =  [];
y4 =  [];
y5 =  [];
y97 =  [];
y6 =  [];
y95 =  [];


for k = 0:200
 
    x = k/100;
    prob = 1 - exp(-1* x);
  
  
 
   
    xaxis =  [xaxis, x];
    y1 = [y1, prob];   
    y2 = [y2, prob2];   
     y3 = [y3, prob^3];   
     y4 = [y4, prob^4];   
 

end;
%------------for k = -200:300 -----------------------


%semilogy(xaxis,y1, 'y-',xaxis, y2, 'y-.',xaxis,y3,'c+',xaxis,y4,'cx',xaxis,y5,'c*')
 plot(xaxis,y1, 'y-',xaxis,y2, 'y-',xaxis,y3, 'y-',xaxis,y4, 'y-')

axis([0 2 0 1])
xlabel('Threshold / Local-Mean Power')

text( 1.5 ,0.85,'L=1')
text( 1.6 ,0.7,'2')
text( 1.6 ,0.55,'3')
text( 1.6 ,0.36,'4')

ylabel('Signal Outage Probability')
%program end

Solution 2.
Probability of fade versus fade margin in dB. Various degrees of selection diversity

Matlab Code

The above curve was plotted using the following code: 
%-------------------------------------------

%-------------------------------------------
%----------initialize counter--------------

xaxis   =  [];
y1  =  [];
y2  =  [];
y3  =  [];
y4 =  [];
y5 =  [];
y97 =  [];
y6 =  [];
y95 =  [];


for k = 0:200
 
    x = k/100;
    prob = 1 - exp(-1* x);
    xaxis =  [xaxis, x];
    y1 = [y1, prob];   
    y2 = [y2, prob2];   
     y3 = [y3, prob^3];   
     y4 = [y4, prob^4];   
 

end;
%------------for k = -200:300 -----------------------

%semilogy(xaxis,y1, 'y-',xaxis, y2, 'y-.',xaxis,y3,'c+',xaxis,y4,'cx',xaxis,y5,'c*')
 plot(xaxis,y1, 'y-',xaxis,y2, 'y-',xaxis,y3, 'y-',xaxis,y4, 'y-')

axis([0 2 0 1])
xlabel('Threshold / Local-Mean Power')

text( 1.5 ,0.85,'L=1')
text( 1.6 ,0.7,'2')
text( 1.6 ,0.55,'3')
text( 1.6 ,0.36,'4')

ylabel('Signal Outage Probability')
%program end



JPL's Wireless Communication Reference Website © Jean-Paul M.G. Linnartz, 1999.