QPSK.rar_Digital communicatio_QPSK

clc clear all; close all; N = 10^6; % number of bits or symbols Eb_N0_dB = [0:25]; % multiple Eb/N0 values nRx = 2; tRx = 1; for ii = 1:length(Eb_N0_dB) % Transmitter ip = (2*(rand(1,N)>0.5)-1) + j*(2*(rand(1,N)>0.5)-1); % generating 0,1 with equal probability s = (1/sqrt(2))*ip; % QPSK modulation 0 -> -1; 1 -> 0 % Alamouti STBC sCode = 1/sqrt(2)*kron(reshape(s,2,N/2),ones(1,2)) ; % channel h = 1/sqrt(2)*[randn(nRx,N) + j*randn(nRx,N)]; % Rayleigh channel n = 1/sqrt(2)*[randn(nRx,N) + j*randn(nRx,N)]; % white gaussian noise, 0dB variance y = zeros(nRx,N); yMod = zeros(nRx*2,N); hMod = zeros(nRx*2,N); for kk = 1:nRx hMod = kron(reshape(h(kk,:),2,N/2),ones(1,2)); % repeating the same channel for two symbols hMod = kron(reshape(h(kk,:),2,N/2),ones(1,2)); temp = hMod; hMod(1,[2:2:end]) = conj(temp(2,[2:2:end])); hMod(2,[2:2:end]) = -conj(temp(1,[2:2:end])); % Channel and noise Noise addition y(kk,:) = sum(hMod.*sCode,1) + 10^(-Eb_N0_dB(ii)/20)*n(kk,:); % Receiver yMod([2*kk-1:2*kk],:) = kron(reshape(y(kk,:),2,N/2),ones(1,2)); % forming the equalization matrix hEq([2*kk-1:2*kk],:) = hMod; hEq(2*kk-1,[1:2:end]) = conj(hEq(2*kk-1,[1:2:end])); hEq(2*kk, [2:2:end]) = conj(hEq(2*kk, [2:2:end])); end % equalization 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=2, Alamouti)'); xlabel('Eb/No, dB'); ylabel('Bit Error Rate'); title('BER for QPSK modulation with 2Tx, 2Rx Alamouti STBC (Rayleigh channel)');