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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;
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