CMA FSK equaliser simulation

git-svn-id: https://svn.code.sf.net/p/freetel/code@3014 01035d8c-6547-0410-b346-abe4f91aad63

diff --git a/codec2-dev/octave/cma.m b/codec2-dev/octave/cma.m
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+% cma.m
+%
+% Constant modulus equaliser example from:
+%
+% http://dsp.stackexchange.com/questions/23540/matlab-proper-estimation-of-weights-and-how-to-calculate-mse-for-qpsk-signal-f
+%
+% Adapted to run bpsk and fsk signals
+
+    rand('seed',1);
+    randn('seed',1);
+
+    N = 5000;           % # symbols
+    h = [1 0 0 0 0 0 0.0 0.5];  % simulation of HF multipath channel impulse response
+    h = h/norm(h);
+    Le = 20;            % equalizer length
+    mu = 1E-3;          % step size
+    snr = 30;           % snr in dB
+    M = 10;             % oversample rate, e.g. Rs=400Hz at Fs=8000Hz
+
+    tx_type = "fsk";   % select modulation type here "bpsk" or "fsk"
+
+    if strcmp(tx_type, "bpsk")
+      s0 = round( rand(N,1) )*2 - 1;     % BPSK signal
+      s0M = zeros(N*M,1);                % oversampled BPSK signal
+      k = 1;
+      for i=1:M:N*M
+       s0M(i:i+M-1) = s0(k);
+        k ++;
+      end
+    end
+
+    if strcmp(tx_type, "fsk")
+      tx_bits = round(rand(1,N));
+
+      % continuous phase FSK modulator
+
+      w1 = pi/4;
+      w2 = pi/2;
+      tx_phase = 0;
+      tx = zeros(M*N,1);
+
+      for i=1:N
+        for k=1:M
+          if tx_bits(i)
+            tx_phase += w2;
+          else
+            tx_phase += w1;
+          end
+          tx((i-1)*M+k) = exp(j*tx_phase);
+        end
+      end
+
+      s0M = tx;
+    end
+
+    s = filter(h,1,s0M);                % filtered signal
+
+    % add Gaussian noise at desired snr
+
+    n = randn(N*M,1);
+    vs = var(s);
+    vn = vs*10^(-snr/10);
+    n = sqrt(vn)*n;
+    r = s + n;          % received signal
+
+    e = zeros(N*M,1);   % error
+    w = zeros(Le,1);    % equalizer coefficients
+    w(Le)=1;            % actual filter taps are flipud(w)!
+
+    yd = zeros(N*M,1);
+
+    for i = 1:N*M-Le,
+        x = r(i:Le+i-1);
+        y = w'*x;
+        yd(i)=y;
+        e(i) = abs(y).^2 - 1;
+        w = w - mu * e(i) * real(conj(y) * x);
+    end
+
+    np = 100;           % # sybmols to plot (last np will be plotted); np < N!
+
+    figure(1); clf;
+    %subplot(211), plot( 1:np, e(N-np+1-Le+1:N-Le+1).*e(N-np+1-Le+1:N-Le+1)), title('error')
+    subplot(211), plot(e.*e), title('error');
+    subplot(212), stem(conv(flipud(w),h)), title('equalized channel impulse response')
+
+    figure(2); clf;
+    subplot(311)
+    plot(1:np, s0M(N-np+1:N))
+    title('transmitted, received, and equalized signal')
+    subplot(312)
+    plot(1:np, r(N-np+1:N))
+    subplot(313)
+    plot(1:np, yd(N-np+1-Le+1:N-Le+1))
+
+    figure(3); clf;
+    h1 = freqz(h);
+    h2 = freqz(flipud(w));
+    h3 = freqz(conv(flipud(w),h));
+    subplot(311); plot(20*log10(abs(h1)));
+    title('channel, equaliser, combined freq resp')
+    subplot(312); plot(20*log10(abs(h2)));
+    subplot(313); plot(20*log10(abs(h3)));
+
+    figure(4);
+    subplot(211)
+    plot(20*log10(abs(fft(s0M))))
+    axis([1 length(s0M) 0 80]);
+    grid;
+    subplot(212)
+    plot(20*log10(abs(fft(s))))
+    axis([1 length(s0M) 0 80]);
+    grid;
+