Alamouti-STBC.rar_Alamouti_STBC Alamouti _STBC codes_alamouti ma

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % All rights reserved by Krishna Pillai, http://www.dsplog.com % The file may not be re-distributed without explicit authorization % from Krishna Pillai. % Checked for proper operation with Octave Version 3.0.0 % Author : Krishna Pillai % Email : krishna@dsplog.com % Version : 1.0 % Date : 16th October 2008 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Script for computing the BER for BPSK modulation in a % Rayleigh fading channel with Alamouti Space Time Block Coding % Two transmit antenna, 1 Receive antenna clear N = 10^6; % number of bits or symbols Eb_N0_dB = [0:25]; % multiple Eb/N0 values for ii = 1:length(Eb_N0_dB) % Transmitter ip = rand(1,N)>0.5; % generating 0,1 with equal probability s = (1/sqrt(2))*ip; % BPSK modulation 0 -> -1; 1 -> 0 % Alamouti STBC sCode = zeros(2,N); sCode(:,1:2:end) = (1/sqrt(2))*reshape(s,2,N/2); % [x1 x2 ...] sCode(:,2:2:end) = (1/sqrt(2))*(kron(ones(1,N/2),[-1;1]).*flipud(reshape(conj(s),2,N/2))); % [-x2* x1* ....] h = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % Rayleigh channel hMod = kron(reshape(h,2,N/2),ones(1,2)); % repeating the same channel for two symbols n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % white gaussian noise, 0dB variance % Channel and noise Noise addition y = sum(hMod.*sCode,1) + 10^(-Eb_N0_dB(ii)/20)*n; % Receiver yMod = kron(reshape(y,2,N/2),ones(1,2)); % [y1 y1 ... ; y2 y2 ...] yMod(2,:) = conj(yMod(2,:)); % [y1 y1 ... ; y2* y2*...] % forming the equalization matrix hEq = zeros(2,N); hEq(:,[1:2:end]) = reshape(h,2,N/2); % [h1 0 ... ; h2 0...] hEq(:,[2:2:end]) = kron(ones(1,N/2),[1;-1]).*flipud(reshape(h,2,N/2)); % [h1 h2 ... ; h2 -h1 ...] hEq(1,:) = conj(hEq(1,:)); % [h1* h2* ... ; h2 -h1 .... ] hEqPower = sum(hEq.*conj(hEq),1); yHat = sum(hEq.*yMod,1)./hEqPower; % [h1*y1 + h2y2*, h2*y1 -h1y2*, ... ] yHat(2:2:end) = conj(yHat(2:2:end)); % receiver - hard decision decoding ipHat = real(yHat)>0; % counting the errors nErr(ii) = size(find([ip- ipHat]),2); end simBer = nErr/N; % simulated ber EbN0Lin = 10.^(Eb_N0_dB/10); theoryBer_nRx1 = 0.5.*(1-1*(1+1./EbN0Lin).^(-0.5)); p = 1/2 - 1/2*(1+1./EbN0Lin).^(-1/2); theoryBerMRC_nRx2 = p.^2.*(1+2*(1-p)); pAlamouti = 1/2 - 1/2*(1+2./EbN0Lin).^(-1/2); theoryBerAlamouti_nTx2_nRx1 = pAlamouti.^2.*(1+2*(1-pAlamouti)); close all figure semilogy(Eb_N0_dB,theoryBer_nRx1,'bp-','LineWidth',2); hold on semilogy(Eb_N0_dB,theoryBerMRC_nRx2,'kd-','LineWidth',2); semilogy(Eb_N0_dB,theoryBerAlamouti_nTx2_nRx1,'c+-','LineWidth',2); semilogy(Eb_N0_dB,simBer,'mo-','LineWidth',2); axis([0 25 10^-5 0.5]) grid on legend('theory (nTx=1,nRx=1)', 'theory (nTx=1,nRx=2, MRC)', 'theory (nTx=2, nRx=1, Alamouti)', 'sim (nTx=2, nRx=1, Alamouti)'); xlabel('Eb/No, dB'); ylabel('Bit Error Rate'); title('BER for BPSK modulation with Alamouti STBC (Rayleigh channel)');