DIGITAL COMMUNICATIONS
Project
BPSK BER Performance Analysis
Submitted By: Shakeel ur REHMAN
Case Roll No.
Dated: 14-01-2008
Introduction
The general Binary phase shift keying (BPSK) can be represented as
S(t)=exp(2*j*pi*(M/2))
Implementation in Matlab
The implementation of the project is as follows.
The steps involved are:
Step 1: Defining Parameters like used Dbs range ,defining reference
signal ,calculate loop counter.
Step 2: Generation of a random binary data stream
The matlab command used generate this sequence is
data=randint(1,1,[0 M-1]); %random data generated
Step 3: Generate transmitted signal and add channel noise.
s=exp(2*j*pi*data/M); %signal tobe transmitted
n=sqrt(varn)*(randn(1,1)+j*randn(1,1)); %Complex gaussian
distributed random data ???????
x=s+n; % signal tobe transmitted
for rayleigh channel we use
n=sqrt(varn)*(randn(1,1)+j*randn(1,1)); %Complex gaussian distributed
random data
h=sqrt(0.5)*(randn(1,1)+j*randn(1,1)); %rayleigh random
variable
x=h*s+n; % signal tobe transmitted
Step 4: Receive signal and use ML decoding.
f=(abs(x*ones(2,1)-srf)).^2; % abs(( received signal - reference
symbols )) ^2
[fmn,argd]=min(f); % for complex f=min(abs(f)),so [number
index]=min(f)
dr=argd-1; %get the index
bit_err=bit_err+(dr~=data);%if the received is not equal to
data then increment error count
Step 5:check for error and compute BER
poe_n(k)=bit_err/LEN(k); %no of errors/100,0000
poe_n_exact(k)=qfunc(1/sqrt(varn));
Error Probability of BPSK
The probability of bit-error for BPSK is:
.
The probability of bit-error for BPSK for rayleigh channel is:
Where a is rayleigh distributed random variable.on simplification
we can get the following Pe.
.
Pe decreases linearly for rayleigh channel while it is decreasing
exponentially in AWGN channel.
In order to improve the Pe we can use multiple receivers which
is called diversity.
Diversity is the primary technique used to improve performance on
a fading channel.The main idea behind the diversity is to provide
the receiver with multiple versions of the same tx signal over
