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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;
-