From de9186c17fb4fae6639be71c01721f6edd5ea720 Mon Sep 17 00:00:00 2001 From: Adrian Iain Lam Date: Wed, 24 Oct 2018 01:16:06 +0100 Subject: [PATCH] Added root raised cosine pulse shaping. Not very sure about the SNR calculation. --- RRC_PSK_BER_SNR.m | 94 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 94 insertions(+) create mode 100644 RRC_PSK_BER_SNR.m diff --git a/RRC_PSK_BER_SNR.m b/RRC_PSK_BER_SNR.m new file mode 100644 index 0000000..73d67f3 --- /dev/null +++ b/RRC_PSK_BER_SNR.m @@ -0,0 +1,94 @@ +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 -- 2.7.4