| 1 | function RRC_PSK_BER_SNR(rolloff, M, numSymbs) |
| 2 | %% Set defaults for inputs |
| 3 | if nargin < 3 |
| 4 | numSymbs = 1000; |
| 5 | end |
| 6 | if nargin < 2 |
| 7 | M = 2; |
| 8 | end |
| 9 | if nargin < 1 |
| 10 | rolloff = 0.5; |
| 11 | end |
| 12 | |
| 13 | if isOctave() |
| 14 | pkg load communications |
| 15 | end |
| 16 | |
| 17 | %% https://www.mathworks.com/help/signal/ref/rcosdesign.html |
| 18 | %% https://www.mathworks.com/help/comm/ug/pulse-shaping-using-a-raised-cosine-filter.html |
| 19 | span = 6; % filter span |
| 20 | sps = 4; |
| 21 | |
| 22 | rrcFilter = rcosdesign(rolloff, span, sps, 'sqrt'); |
| 23 | |
| 24 | EbN0_db = 0:0.2:10; |
| 25 | EbN0 = 10 .^ (EbN0_db ./ 10); |
| 26 | |
| 27 | Es = 1; |
| 28 | Eb = Es / log2(M); |
| 29 | N0 = Eb ./ EbN0; |
| 30 | |
| 31 | EsN0 = EbN0 .* log2(M); |
| 32 | EsN0_db = 10 .* log10(EsN0); |
| 33 | |
| 34 | plotlen = length(EbN0); |
| 35 | |
| 36 | ber = zeros(1, plotlen); |
| 37 | |
| 38 | data = randi([0 M - 1], numSymbs, 1); |
| 39 | modData = pskmod(data, M, 0, 'gray'); |
| 40 | |
| 41 | txSig = upfirdn(modData, rrcFilter, sps); |
| 42 | |
| 43 | for i = 1:plotlen |
| 44 | snr = EbN0_db(i) + 10 * log10(log2(M));% - 10 * log10(sps); % why sps? |
| 45 | rxSig = awgn(txSig, snr); |
| 46 | |
| 47 | rxFilt = upfirdn(rxSig, rrcFilter, 1, sps); |
| 48 | rxFilt = rxFilt(span + 1 : end - span); % remove filter delay |
| 49 | |
| 50 | demodData = pskdemod(rxFilt, M, 0, 'gray'); |
| 51 | |
| 52 | [bitErrors, ber(i)] = biterr(data, demodData); |
| 53 | end |
| 54 | |
| 55 | fig1 = figure(1); |
| 56 | clf; |
| 57 | |
| 58 | %% Plot simulated results |
| 59 | semilogy(EbN0_db, ber, 'r', 'LineWidth', 2); |
| 60 | hold on; |
| 61 | |
| 62 | %% Plot theoretical curve |
| 63 | %% BPSK: bit error when noise Nr > sqrt(Eb) |
| 64 | %% Pr(Nr > sqrt(Eb)) |
| 65 | %% = Pr(Z > sqrt(Eb) / sqrt(N0/2)) |
| 66 | %% |
| 67 | %% QPSK = 2 BPSKs, one real and one imaginary, each with one bit |
| 68 | %% so BER is the same as BPSK (assuming Gray code) |
| 69 | if M == 2 || M == 4 |
| 70 | ber_th = qfunc(sqrt(2 * EbN0)); |
| 71 | semilogy(EbN0_db, ber_th, 'b', 'LineWidth', 1); |
| 72 | legend('Simulated RRC', 'Discrete'); |
| 73 | else |
| 74 | %% Approximation: J.G. Proakis and M. Salehi, 2000, Contemporary |
| 75 | %% Communication Systems using MATLAB (Equations |
| 76 | %% 7.3.18 and 7.3.19), Brooks/Cole. |
| 77 | ber_ap = 2 * qfunc(sqrt(EbN0 * log2(M) * 2) * sin(pi / M)) / log2(M); |
| 78 | semilogy(EbN0_db, ber_ap, 'b', 'LineWidth', 1); |
| 79 | legend('Simulated RRC', 'Discrete'); |
| 80 | end |
| 81 | |
| 82 | title(strcat(num2str(M), '-PSK RRC with Gray code')); |
| 83 | grid on; |
| 84 | xlabel('$E_b/N_0$ (dB)'); |
| 85 | ylabel('BER'); |
| 86 | |
| 87 | formatFigure; |
| 88 | %saveas(gcf, strcat('BER_SNR_', num2str(M), 'PSK_', num2str(numSymbs), ... |
| 89 | % '.svg')); |
| 90 | |
| 91 | %scatterplot(rxFilt); |
| 92 | %eyediagram(rxFilt, sps); |
| 93 | |
| 94 | end |