QPSK Modulation and Demodulation In Rayleigh Fading

MATLAB PROGRAM

clear; clc;

%---------Input Fields------------------------

N=1000000;%Number of input bits

EbN0dB = 0:1:35; % Eb/N0 range in dB for simulation

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

data=randn(1,N)>=0; %Generating a uniformly distributed random 1s and 0s

oddData = data(1:2:end);

evenData = data(2:2:end);

qpskModulated = sqrt(1/2)*(1i*(2*oddData-1)+(2*evenData-1)); %QPSK Mapping

M=4; %Number of Constellation points M=2^k for QPSK k=2

Rm=log2(M); %Rm=log2(M) for QPSK M=4

BER = zeros(1,length(EbN0dB)); %Place holder for BER values for each Eb/N0

index=1;

for i=EbN0dB,

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

%Channel Noise for various Eb/N0

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

%Adding noise with variance according to the required Eb/N0

EbN0 = 10.^(i/10); %Converting Eb/N0 dB value to linear scale

%Creating a complex noise for adding with QPSK modulated signal

noise = 1/sqrt(2*Rm)*(randn(1,length(qpskModulated))+1i*randn(1,length(qpskModulated)));

n = noise*10^(-EbN0dB(index)/20); %Scaling the noise for required Eb/N0

%Rayleigh Flat Fading factor- single tap

h=1/sqrt(2)*(randn(1,length(qpskModulated))+1i*randn(1,length(qpskModulated)));

received = h.*qpskModulated + n;

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

%Coherent Receiver for Rayleigh Channel

received_cap=received./h; %Assuming that h is known at the signal accurately

%Threshold Detector

detected_real = real(received_cap)>=0;

detected_img = imag(received_cap)>=0;

estimatedBits=reshape([detected_img;detected_real],1,[]);

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

%Bit Error rate Calculation

BER(index) = sum(xor(data,estimatedBits))/length(data);

index=index+1;

end

%Plot

figure;

semilogy(EbN0dB,BER,'r--');

hold on;

EbN0=10.^(EbN0dB/10); %Eb/N0 in Linear Scale

theoreticalBER = 0.5*(1-sqrt(EbN0./(1+EbN0)));

semilogy(EbN0dB,theoreticalBER,'b*');

title('SNR per bit (Eb/N0) Vs BER Curve for QPSK Modulation Scheme');

xlabel('SNR per bit (Eb/N0) in dB');

ylabel('Bit Error Rate (BER)');

legend('Simulated','Theoretical-QPSK','Theoretical-QPSK');

grid on;

SIMULATED OUTPUT