Equalize BSPK Signal

Equalize a BPSK signal using a linear equalizer with an least mean square (LMS) algorithm.

Generate random binary data and apply BPSK modulation.

data = randi([0 1],1000,1);
modData = pskmod(data,2);

Apply two-tap static fading to the modulated signal.

rxSig = conv(modData,[0.5 0.05]);

Create an LMS adaptive algorithm object with a step size of 0.06.

alg = lms(0.06);

Create a linear equalizer object having 8 taps using the previously created algorithm object. Set the reference tap index to 4.

eqlms = lineareq(8,alg);
eqlms.RefTap = 4;

Equalize the received signal, rxSig, while using the first 200 data bits as a training sequence.

trSeq = data(1:200);
[eqSig,~,e] = equalize(eqlms,rxSig,trSeq);

Filter and plot the power of the received (nonequalized) signal. The magnitude of the signal has been attenuated by the channel.

rxSigPwr = filter(0.1*ones(10,1),1,abs(rxSig)).^2;
plot(rxSigPwr)
title('Received Signal')
xlabel('Bits')
ylabel('Power (W)')

Plot the equalized signal. The signal reaches the intended power level of 1 W.

eqSigPwr = filter(0.1*ones(10,1),1,abs(eqSig)).^2;
plot(eqSigPwr)
title('Equalized Signal')
xlabel('Bits')
ylabel('Power (W)')

Plot the magnitude of the error estimate, e. The error decreases until it is nearly zero after 400 bits.

plot(abs(e))
title('Error Estimate')
xlabel('Bits')
ylabel('Amplitude (V)')