delay spread rayleigh channel for OFDM

Hello, To simulate an OFDM transmission I'm supposing that the delay spread is less than the cyclic prefix , so I define a signal matrix S where the columns represents the OFDM symbols and the rows represent the subcarriers (16 subcarriers) . so that the received signal in frequency domain will be Y=S.*H +N where H is the channel matrix (in frequency domain) and N the gaussian noise matrix, My problem is that I have to use a Rayleigh channel with a delay spread=0.01*T where T is the OFDM symbl duration so how can I create this channel ?

[Ala Gouissem]

to make things more simple , you can suppose that I'm transmitting only one OFDM symbol ,

so I have a modulated signal composed from 16 symbols and I want to multiply it by a certain rayleigh channel h with a dely spread =0.01*T

so how to create this h

Answer 1

[Rahul Gulia]

Hi Ala.

I just came across your question. Just answering, so that people in the future can get help from.

Here is a MATLAB code to model a Rayleigh channel.

% Final code

% Simulation of Rayleigh channel

clc;

clear all;

close all;

warning off;

% Parameters

nobpc = 10^6;

Es = 1;

SNRdb = 0:20;

M = 4;

Rm = log2(M);

% Transmitting data generation

Tx_bits = round(rand(1,nobpc));

oddData = Tx_bits(1:2:end);

evenData = Tx_bits(2:2:end);

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

figure, polar(angle(Tx_symb),abs(Tx_symb),'*');

BER = zeros(1,length(SNRdb));

index = 1;

for i =SNRdb

SNR = 10.^(i/10);

noiseSigma = sqrt(1./(2*Rm*SNR));

errors = 0;

%Creating a complex noise for adding with QPSK modulated signal

noise = noiseSigma*(randn(1,length(Tx_symb))+1i*randn(1,length(Tx_symb)));

% Creating a Rayleigh channel with variance 0.5

h = sqrt(0.5*((randn(1,length(Tx_symb))).^2+(randn(1,length(Tx_symb))).^2));

% Transmitted signal

Rx_symb = Tx_symb.*h + noise;

% Equalizer

Rx_symb = Rx_symb./h;

%ML Detector

detected_real = real(Rx_symb)>=0;

detected_img = imag(Rx_symb)>=0;

Rx_bits=reshape([detected_img;detected_real],1,nobpc);

%Bit Error rate Calculation

BER(index) = sum(xor(Tx_bits,Rx_bits))/nobpc;

index=index+1;

end

% Theoretical BER for Rayleigh channel

SNR1 = 10.^(SNRdb/10);

theoreticalBER =0.5*(1 - sqrt(SNR1./(SNR1+1)));

figure,semilogy(SNRdb,BER,'r--'),title('SNR vs BER for Rayleigh channel');

grid on;

hold on;

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

xlabel("SNRdb");

ylabel("BER");

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

grid on;

figure, semilogy(SNRdb,theoreticalBER,'b'), title("Theoretical curve of SNR Vs BER for Rayleigh Channel"), xlabel("SNRdb"),ylabel("BER");