Added root raised cosine pulse shaping.

Not very sure about the SNR calculation.

diff --git a/RRC_PSK_BER_SNR.m b/RRC_PSK_BER_SNR.m
new file mode 100644 (file)
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