Calculate Mean Square Error Performance Using LMS Filter

R2026b

This example shows how to use the LMS Filter block to calculate the mean square error while performing system identification in additive white Gaussian noise (AWGN). You can generate the HDL code from the LMSFilter subsystem in this Simulink® model.

Set Up Input Variables

Set up these workspace variables for the model. These variables configure the LMS Filter block.

filterLength = 64;
stepSize = 0.2/(1*filterLength); % recommended step size is less than
                                 % 1/(2 x power of input signal x filter
                                 % length)
frameSize = 2;
inptType = 1;                    % 0 means real; 1 means complex
niter = 20;                      % number of iterations to run for calculating mean square error
dataLength = 2800;
simtime = dataLength/frameSize + 100;
errSumAbsSq = zeros(1,dataLength);
errRefSumAbsSq = zeros(1,dataLength);

Generate Input Data and Run Model

Generate input data for the LMS Filter block and the reference System object™ dsp.LMSFilter for niter number of iterations.

for k = 1:niter
    % Create filter object
    filterObj = dsp.FIRFilter;
    num = normalize(randn(1,filterLength) + inptType*1i*randn(1,filterLength))/sqrt(filterLength);
    filterObj.Numerator = num;

    % Use dsp.LMSFilter object for reference
    lmsfilt = dsp.LMSFilter(filterLength, 'StepSize', stepSize);

    % Generate input data
    observedSignal = fi(randn(dataLength,1,'like',num),1,18,15);
    noise = 0.012*randn(dataLength,1);
    validIn = true(dataLength,1);

    % Generate desired signal by adding noise to filtered data
    desiredSignal = fi(filterObj(double(observedSignal)) + noise,1,18,15);

    % Capture reference output values and calculate average of absolute
    % square error
    [filtOutRef,errRef,wtsRef] = lmsfilt(double(observedSignal),double(desiredSignal));
    errRefSumAbsSq = errRefSumAbsSq + abs(errRef(1:dataLength)).^2.';

    % Simulate model
    LMSModel = 'HDLLMSBlock';
    load_system(LMSModel);% run this command to open the model
    lms = sim(LMSModel);

    % Capture model output and calculate average of absolute square error
    validOut = squeeze(lms.validOut);
    errOutLMS = squeeze(double(lms.errOut)).';
    if frameSize ==1
        errOutAbsSq = abs(errOutLMS(:,validOut)).^2.';
    else
       errOutAbsSq = abs(errOutLMS(validOut,:)).^2.';
    end
    errOutAbsSq = errOutAbsSq(:).';
    errSumAbsSq = errSumAbsSq + errOutAbsSq(1:dataLength);

    % To reset the internal states of the object
    reset(filterObj)
    reset(lmsfilt)
end

Plot Mean Square Error

Plot the mean square error in dB against the LMS Filter block output and the LMS filter reference output.

meanSqErrRefLMS_dB = 10*log10(errRefSumAbsSq/niter);
meanSqErrLMS_dB = 10*log10(errSumAbsSq/niter);
figure
plot(meanSqErrRefLMS_dB)
hold on
plot(meanSqErrLMS_dB)
title('Mean Squared Error Performance')
xlabel('Sample Index')
ylabel('Squared Error Value (in dB)')
legend('LMS filter reference','LMS filter block')