function RRC_PSK_BER_SNR(rolloff, M, numSymbs) %% Set defaults for inputs if nargin < 3 numSymbs = 1000; end if nargin < 2 M = 2; end if nargin < 1 rolloff = 0.5; end if isOctave() pkg load communications end %% https://www.mathworks.com/help/signal/ref/rcosdesign.html %% https://www.mathworks.com/help/comm/ug/pulse-shaping-using-a-raised-cosine-filter.html span = 6; % filter span sps = 4; rrcFilter = rcosdesign(rolloff, span, sps, 'sqrt'); EbN0_db = 0:0.2:10; EbN0 = 10 .^ (EbN0_db ./ 10); Es = 1; Eb = Es / log2(M); N0 = Eb ./ EbN0; EsN0 = EbN0 .* log2(M); EsN0_db = 10 .* log10(EsN0); plotlen = length(EbN0); ber = zeros(1, plotlen); data = randi([0 M - 1], numSymbs, 1); modData = pskmod(data, M, 0, 'gray'); txSig = upfirdn(modData, rrcFilter, sps); for i = 1:plotlen snr = EbN0_db(i) + 10 * log10(log2(M));% - 10 * log10(sps); % why sps? rxSig = awgn(txSig, snr); rxFilt = upfirdn(rxSig, rrcFilter, 1, sps); rxFilt = rxFilt(span + 1 : end - span); % remove filter delay demodData = pskdemod(rxFilt, M, 0, 'gray'); [bitErrors, ber(i)] = biterr(data, demodData); end fig1 = figure(1); clf; %% Plot simulated results semilogy(EbN0_db, ber, 'r', 'LineWidth', 2); hold on; %% Plot theoretical curve %% BPSK: bit error when noise Nr > sqrt(Eb) %% Pr(Nr > sqrt(Eb)) %% = Pr(Z > sqrt(Eb) / sqrt(N0/2)) %% %% QPSK = 2 BPSKs, one real and one imaginary, each with one bit %% so BER is the same as BPSK (assuming Gray code) if M == 2 || M == 4 ber_th = qfunc(sqrt(2 * EbN0)); semilogy(EbN0_db, ber_th, 'b', 'LineWidth', 1); legend('Simulated RRC', 'Discrete'); else %% Approximation: J.G. Proakis and M. Salehi, 2000, Contemporary %% Communication Systems using MATLAB (Equations %% 7.3.18 and 7.3.19), Brooks/Cole. ber_ap = 2 * qfunc(sqrt(EbN0 * log2(M) * 2) * sin(pi / M)) / log2(M); semilogy(EbN0_db, ber_ap, 'b', 'LineWidth', 1); legend('Simulated RRC', 'Discrete'); end title(strcat(num2str(M), '-PSK RRC with Gray code')); grid on; xlabel('$E_b/N_0$ (dB)'); ylabel('BER'); formatFigure; %saveas(gcf, strcat('BER_SNR_', num2str(M), 'PSK_', num2str(numSymbs), ... % '.svg')); %scatterplot(rxFilt); %eyediagram(rxFilt, sps); end