BER/SNR plots for discrete BPSK over AWGN
authorAdrian Iain Lam <adrianiainlam@users.noreply.github.com>
Sun, 21 Oct 2018 16:02:20 +0000 (17:02 +0100)
committerAdrian Iain Lam <adrianiainlam@users.noreply.github.com>
Sun, 21 Oct 2018 16:02:20 +0000 (17:02 +0100)
BPSK_BER_SNR_1000.svg [new file with mode: 0644]
BPSK_BER_SNR_1000000.svg [new file with mode: 0644]
SNRvsBER_BPSKdiscrete.m [new file with mode: 0644]
decodeNoisyBPSK.m [new file with mode: 0644]
discreteAWGN.m [new file with mode: 0644]
formatFigure.m [new file with mode: 0644]
isOctave.m [new file with mode: 0644]
randomPSK.m [new file with mode: 0644]

diff --git a/BPSK_BER_SNR_1000.svg b/BPSK_BER_SNR_1000.svg
new file mode 100644 (file)
index 0000000..1f4ce97
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diff --git a/SNRvsBER_BPSKdiscrete.m b/SNRvsBER_BPSKdiscrete.m
new file mode 100644 (file)
index 0000000..4a6c30d
--- /dev/null
@@ -0,0 +1,53 @@
+function SNRvsBER_BPSKdiscrete(numBits)
+  if nargin < 1
+    numBits = 1000;
+  end
+
+  if isOctave()
+    pkg load communications
+  end
+
+  %% SNR: Eb/N0
+  snr_db = 0:0.2:10;
+  snr = 10 .^ (snr_db ./ 10);
+
+  %% Eb is assumed to be 1
+  %% noise N ~ Gaussian(mean=0, variance=N0/2)
+  N0 = 1 ./ snr;
+
+  ber = zeros(1, length(snr));
+
+  data = randomPSK(2, numBits);
+
+  for i = 1:length(snr)
+    noisyData = discreteAWGN(data, N0(i));
+    decodedData = decodeNoisyBPSK(noisyData);
+
+    bitErrors = sum(data ~= decodedData);
+    ber(i) = bitErrors / numBits;
+  end
+
+  fig1 = figure(1);
+  clf;
+
+  %% Plot simulated results
+  semilogy(snr_db, ber, 'r', 'LineWidth', 2);
+  hold on;
+
+  %% Plot theoretical curve
+  %% BPSK: bit error when noise N > sqrt(Eb)
+  %%   Pr(N > sqrt(Eb))
+  %% = Pr(Z > sqrt(Eb) / sqrt(N0/2))
+  %% = Q(sqrt(2 * SNR))
+  ber_th = qfunc(sqrt(2 * snr));
+  semilogy(snr_db, ber_th, 'b', 'LineWidth', 1);
+
+  grid on;
+  xlabel('$E_b/N_0$ (dB)');
+  ylabel('BER');
+  legend('Simulated', '$Q\left(\sqrt{2 E_b / N_0}\right)$');
+
+  formatFigure;
+  saveas(gcf, strcat('BPSK_BER_SNR_', num2str(numBits), '.svg'));
+
+end
diff --git a/decodeNoisyBPSK.m b/decodeNoisyBPSK.m
new file mode 100644 (file)
index 0000000..70ef8f8
--- /dev/null
@@ -0,0 +1,3 @@
+function x = decodeNoisyBPSK(noisyData)
+  x = (noisyData > 0) - (noisyData <= 0);
+end
diff --git a/discreteAWGN.m b/discreteAWGN.m
new file mode 100644 (file)
index 0000000..1aab2b9
--- /dev/null
@@ -0,0 +1,3 @@
+function x = discreteAWGN(data, N0)
+  x = data + normrnd(0, sqrt(N0 / 2), 1, length(data));
+end
diff --git a/formatFigure.m b/formatFigure.m
new file mode 100644 (file)
index 0000000..7d5796a
--- /dev/null
@@ -0,0 +1,8 @@
+if ~isOctave()
+  set(gcf, 'defaultTextInterpreter', 'Latex');
+  set(gcf, 'defaultLegendInterpreter', 'Latex');
+  set(gca, 'TickLabelInterpreter', 'Latex');
+end
+set(gca, 'FontSize', 14);
+leg = findobj(gcf, 'Type', 'Legend');
+set(leg, 'FontSize', 14);
diff --git a/isOctave.m b/isOctave.m
new file mode 100644 (file)
index 0000000..1c9c190
--- /dev/null
@@ -0,0 +1,15 @@
+%% Taken from the GNU Octave Manual, (c) 1996-2016 John W. Eaton
+%% https://octave.org/doc/v4.0.3/How-to-distinguish-between-Octave-and-Matlab_003f.html
+
+%%
+%% Return: true if the environment is Octave.
+%%
+function retval = isOctave
+  persistent cacheval;  % speeds up repeated calls
+
+  if isempty (cacheval)
+    cacheval = (exist ("OCTAVE_VERSION", "builtin") > 0);
+  end
+
+  retval = cacheval;
+end
diff --git a/randomPSK.m b/randomPSK.m
new file mode 100644 (file)
index 0000000..7521bef
--- /dev/null
@@ -0,0 +1,15 @@
+function x = randomPSK(n, len)
+  % symbols: nth roots of unity
+  % i.e. solutions to polynomial x^n - 1 = 0
+  symbols = roots([1 zeros(1, n-1) -1]);
+
+  x = zeros(1, len);
+  for i = 1:len
+    x(i) = randomChoice(symbols);
+  end
+end
+
+function x = randomChoice(arr)
+  i = randi(length(arr));
+  x = arr(i);
+end