alamoutiofdm2x2.m

some code in mimo ofdm

%************************************************************************
%Alamouti Coding for OFDM with 2x2 antenna configuration
%
%Num_RxAnt: the number of receive antenna
%M: M-ary digital modulation
%
%
%************************************************************************

clc;
clear all;
%repeat for different receive antennas
M = 4; %M-ary QAM Modulation Scheme
SNR_max = 10;
Bn = 200; %the number of OFDM symbol will being transmitted
randn('state',0); %Remove it if you want a random start of the randn generator
randn('state',0); %Remove it if you want a random start of the randn generator
z = 1;
%Creating Fl matrix for decoding Alamouti code
for n = 1:64
    for l = 1:16
        F(n,l) = exp(-(j*2*pi*(l-1)*(n-1))/64);
    end
end
l = 0;
n = 0;
Fl = [F zeros(size(F));zeros(size(F)) F];

for k = 1:0.5:SNR_max
    snr = 10.^(k/10);
    sig = 0.5/snr;
    Smv = floor(M*rand(2,64*Bn)); %transmitted alphabet
    Sm = exp(j*2*pi/M*Smv)/sqrt(2); %transmitted symbols
    %Sm = 2x(64*Bn) matrix, the block of input is going to be transmitted with constant SNR
    
    %calculating y in time domain and change it to frequency domain then apply detection part
    for p = 1:Bn
        Sof = Sm(:,(1+(p-1)*64:p*64)); %transmitted OFDM block with constant SNR
        Sofc = conj(Sof);
        %Taking IFFT of the block
        Sot = [ifft(Sof(1,:));ifft(Sof(2,:))];
        Sotc = [ifft(Sofc(1,:));ifft(Sofc(2,:))];
        %Creating channel matrix with l = 16 multipaths
        for l = 0:15
            sig2 = 0.395*exp(-0.5*l);
            h(:,l+1) = (randn(4,1)+j*rand(4,1))/sqrt(2)*sqrt(sig2);
        end
        %Creating Toeplitz matrix for each of impulse response separately and calculation corresponding received signal y
        ns = sqrt(sig).*(randn(80,4)+j*randn(80,4));
        
        y011 = [toeplitz([h(1,:) zeros(1,64)],[h(1,1) zeros(1,79)])]*[Sot(1,:) Sot(1,1:16)].';
        y012 = [toeplitz([h(2,:) zeros(1,64)],[h(2,1) zeros(1,79)])]*[Sot(2,:) Sot(2,1:16)].';
        y0 = y011 + y012 + ns(:,1); %at time t1 for received antenna 1
        
        y111 = [toeplitz([h(1,:) zeros(1,64)],[h(1,1) zeros(1,79)])]*-[Sotc(2,:) Sotc(2,1:16)].';
        y112 = [toeplitz([h(2,:) zeros(1,64)],[h(2,1) zeros(1,79)])]*[Sotc(1,:) Sotc(1,1:16)].';
        y1 = y111 + y112 + ns(:,2); %at time t2 for received antenna 1
        
        y021 = [toeplitz([h(3,:) zeros(1,64)],[h(3,1) zeros(1,79)])]*[Sot(1,:) Sot(1,1:16)].';
        y022 = [toeplitz([h(4,:) zeros(1,64)],[h(4,1) zeros(1,79)])]*[Sot(2,:) Sot(2,1:16)].';
        y2 = y021 + y022 + ns(:,3); %at time t1 for received antenna 2
        
        y121 = [toeplitz([h(3,:) zeros(1,64)],[h(3,1) zeros(1,79)])]*-[Sotc(2,:) Sotc(2,1:16)].';
        y122 = [toeplitz([h(4,:) zeros(1,64)],[h(4,1) zeros(1,79)])]*[Sotc(1,:) Sotc(1,1:16)].';
        y3 = y121 + y122 + ns(:,4); %at time t2 for received antenna 2
        
        %Removing CP and transform the signals to frequency domain
        ya0 = [y0(65:79,1);y0(16:64,1)];
        YA0 = fft(ya0);
        
        ya1 = [y1(65:79,1);y1(16:64,1)];
        YA1 = fft(ya1);
        
        ya2 = [y2(65:79,1);y2(16:64,1)];
        YA2 = fft(ya2);
        
        ya3 = [y3(65:79,1);y3(16:64,1)];
        YA3 = fft(ya3);
        
        Y = [YA0 conj(YA1) YA2 conj(YA3)];
        
        %Creating subcarrier matrix in frequency domain
        ht=[(h(1,:)).' (h(2,:)).';(h(3,:)).' (h(4,:)).'];
        H = Fl*ht;
        
        %Alamouti Decoding
        for Kc = 1:64
            YC = Y(Kc,:);
            Yc = YC.';
            Hc = [H(Kc,1) H(Kc,2);H(Kc,2)' -H(Kc,1)';H(Kc+64,1) H(Kc+64,2);H(Kc+64,2)' -H(Kc+64,1)'];
            X_ = (Hc)'*Yc;
            %Selecting 2 symbols from OFDM block, send it and retrive it until the end of the OFDM block as well as for Bn OFDM block
            ang = angle(X_); %receive angles
            S_ = mod(round(ang/(2*pi/M)),M); %received alphabet, its another
            S_det_mat(:,(64*(p-1)+Kc)) = S_; %Output one OFDM transmission block
        end
    end
        
        %Calculating bit error rate
        BER = 0;
        ERROR = 0;
        for p = 1:2
            for u = 1:64*Bn
                if Smv(p,u) ~= S_det_mat(p,u)
                    ERROR = ERROR + 1;
                end
            end
        end
        ber(z) = ERROR/(2*64*Bn);
        z = z + 1;
end
Snr = 1:0.5:SNR_max;
ber2 = ber;

%plot the bit error rate
semilogy(Snr,ber2,'bh-','LineWidth',2.0);
xlabel('SNR [dB]');
ylabel('BER');
title('Bit Error Rate Evaluation for OFDM system with Alamouti coding and perfect CSI, M-ary QAM Modulation');
grid on;