MATLAB Code M = 4; % QPSK numSymbols = 10000; numTrainingSymbols = 5000; chtaps = [1 0.5*exp(1i*pi/6) 0.1*exp(-1i*pi/8)]; % Generate QPSK symbols data = randi([0 M-1], numSymbols, 1); tx = pskmod(data, M, pi/4); % DFE setup eq = comm.DecisionFeedbackEqualizer; eq.ReferenceTap = 1; eq.NumForwardTaps = 5; eq.NumFeedbackTaps = 3; % SNR sweep snrVec = 0:5:25; % 0,5,10,...25 dB berBefore = zeros(size(snrVec)); berAfter = zeros(size(snrVec)); for k = 1:length(snrVec) % Apply channel and AWGN rx = awgn(filter(chtaps,1,tx), snrVec(k), 'measured' ); % BER before equalization rxDataNoEq = pskdemod(rx, M, pi/4); [~, berBefore(k)] = biterr(data, rxDataNoEq); % Equalize [y,~,~] = eq(rx, tx(1:numTrainingSymbols)); % Phase correction phaseOffset = angle(mean(conj(tx(1:numTrainingSymbols)) .* y(1:numTrainingSymbols))); yCorrected = y * exp(-1i*phaseOffset); % BER after equalization rxDataEq = pskdemod(yCorrected, M, pi/4); [...