📄 ofdms.m
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% By Alger 2007
% Basic BPSK+OFDM system 1Tx+1Rx in rayleigh fading channel using Jakes' model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Initialing %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function BER = OFDMs(SNRindB, fm, d, M)
%clear;SNRindB = 10;fm = 0;d = 1;M = 12;
% OFDM parameters
fs = 800000; % sampling rate/Bandwidth
Ncarr = 128; % number of subcarriers
GIlen = 160; % length of OFDM symbol plus cyclic prefix
CPlen = GIlen - Ncarr; % length of cyclic prefix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Channel source %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% generate infomation bits
X_info = randint(Ncarr,1); % binary bits
X_send = 2*X_info - 1; % BPSK modulation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% IFFT %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ifft with length Ncarr
z_ifft = (sqrt(Ncarr)*ifft(X_send,Ncarr)).'; % sqrt(Ncarr) should be mutiplied to maintain the Power
% adding cyclic prefix
Z_ofdm = [z_ifft(Ncarr-CPlen+1:Ncarr) z_ifft]; % final OFDM sampled signals with CP
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% channel %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% generate random channel matrix "h" with rayleigh distribution and Doppler shift by Jakes' model
h = zeros(M , Ncarr); % channel matrix
r = zeros(1 , Ncarr); % received signal
% multi-paths channel following exponential delay model
TapGain = sqrt( (1-exp(-1/d)) / (1-exp(-M/d)) );
for i = 1:M
h(i,:) = TapGain * jakes(Ncarr,fm,fs);
r = r + h(i,:) .* Z_ofdm( (CPlen-i+2):(GIlen-i+1) );
TapGain = TapGain * exp(-1/d/2);
end
R = awgn(r,SNRindB); % AWGN
%R = r;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% IFFT %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fft
z_fft = fft(R,Ncarr)/sqrt(Ncarr); % 1/sqrt(Ncarr) should be multiplied
% Calculate the frequecy domain response
h_est = sum(h,2)/Ncarr;
H = fft([h_est; zeros(Ncarr-M,1)]);
% equlization in frequence domain
X_receive = z_fft.'./H; % the received symbols
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Demodulate %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% demodulate the receive symbols
X_sink = (1 + sign(real(X_receive)))/2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Error counts %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% bit error ratio
[bit,ratio] = biterr(X_info,X_sink);
BER = ratio;
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