Equalizing Using a Training Sequence :: Equalizers (Communications Toolbox)

Communications Toolbox

Equalizing Using a Training Sequence

In typical applications, an equalizer begins by using a known sequence of transmitted symbols when adapting the equalizer weights. The known sequence, called a training sequence, enables the equalizer to gather information about the channel characteristics. After the equalizer finishes processing the training sequence, it adapts the equalizer weights in decision-directed mode using a detected version of the output signal. To use a training sequence when invoking the equalize function, include the symbols of the training sequence as an input vector.

Note As an exception, CMA equalizers do not use a training sequence. If an equalizer object is based on CMA, then you should not include a training sequence as an input vector.

The code below illustrates how to use equalize with a training sequence. The training sequence in this case is just the beginning of the transmitted message.

% Set up parameters and signals.
M = 4; % Alphabet size for modulation
msg = randint(1500,1,M); % Random message
modmsg = pskmod(msg,M); % Modulate using QPSK.
trainlen = 500; % Length of training sequence
chan = [.986; .845; .237; .123+.31i]; % Channel coefficients
filtmsg = filter(chan,1,modmsg); % Introduce channel distortion.

% Equalize the received signal.
eq1 = lineareq(8, lms(0.01)); % Create an equalizer object.
eq1.SigConst = pskmod([0:M-1],M); % Set signal constellation.
[symbolest,yd] = equalize(eq1,filtmsg,modmsg(1:trainlen)); % Equalize.

% Plot signals.
h = scatterplot(filtmsg,1,trainlen,'bx'); hold on;
scatterplot(symbolest,1,trainlen,'g.',h);
scatterplot(eq1.SigConst,1,0,'k*',h);
legend('Filtered signal','Equalized signal',...
   'Ideal signal constellation');
hold off;

% Compute error rates with and without equalization.
demodmsg_noeq = pskdemod(filtmsg,M); % Demodulate unequalized signal.
demodmsg = pskdemod(yd,M); % Demodulate detected signal from equalizer.
[nnoeq,rnoeq] = symerr(demodmsg_noeq(trainlen+1:end),...
   msg(trainlen+1:end));
[neq,req] = symerr(demodmsg(trainlen+1:end),...
   msg(trainlen+1:end));
disp('Symbol error rates with and without equalizer:')
disp([req rnoeq])

The example goes on to determine how many errors occur in trying to recover the modulated message with and without the equalizer. The symbol error rates, below, show that the equalizer improves the performance significantly.

Symbol error rates with and without equalizer:
         0    0.3410

The example also creates a scatter plot that shows the signal before and after equalization, as well as the signal constellation for QPSK modulation. Notice from the plot that the points of the equalized signal are clustered more closely around the points of the signal constellation.

Using Adaptive Equalizers

Equalizing in Decision-Directed Mode