Variable step-size LMS in comm.LinearEqualizer (varlms replacement)

Hi,

In https://www.mathworks.com/help/comm/release-notes.html?searchHighlight=varlms&s_tid=srchtitle_varlms_2 I found that varlms (as well as normlms and signlms) should be replaced by comm.LinearEqualizer with LMS algorithm. However, I am unable to find equivalent of a variable-step size LMS (StepSize property of comm.LinearEqualizer seems fixed).

Is variable-step LMS not available in comm.LinearEqualizer?

Thanks!

Answer 1

[Sachin Lodhi]

Based on my understanding, it seems that you are seeking an alternative solution to the varlms function, which has been removed in MATLAB R2022a. However, you can achieve the equivalent functionality by utilizing either the comm.LinearEqualizer or comm.DecisionFeedback objects with the LMS Adaptive Algorithm. By adjusting the step size with each iteration, you can achieve the desired behavior. I have provided a sample code snippet below that demonstrates the usage of comm.LinearEqualizer with a variable step:

% Define the channel and transmit signal
channel = [0.9 0.2 0.1] % Example channel coefficients

channel = 1×3

0.9000 0.2000 0.1000

txSignal = randi([0 1], 1000, 1); % Random binary transmit signal.
% Apply the channel to the transmit signal
rxSignal = filter(channel, 1, txSignal);
%Create a linear equalizer object
equalizer = comm.LinearEqualizer('Algorithm', 'LMS', 'StepSize', 0.01, 'Constellation', [0 1]);

for i = 1:3
    % Update the step size for each iteration
    stepSize = 0.01 + 0.001 * i; % Example of a variable step size
    
    % Set the step size in the equalizer object
    equalizer.StepSize = stepSize;
    
    % Perform equalization for the current symbol
    [eqSignal, error] = equalizer(rxSignal, txSignal);

    % Plot the original and equalized signals
    figure;
    subplot(2, 1, 1);
    stem(txSignal, 'filled');
    title('Original Transmit Signal');
    subplot(2, 1, 2);
    stem(eqSignal, 'filled');
    title('Equalized Signal');

end

% Display the equalizer object properties
equalizer

equalizer = 
  comm.LinearEqualizer with properties:

                Algorithm: 'LMS'
                  NumTaps: 5
                 StepSize: 0.0130
            Constellation: [0 1]
             ReferenceTap: 3
               InputDelay: 0
    InputSamplesPerSymbol: 1
    TrainingFlagInputPort: false
       AdaptAfterTraining: true
     InitialWeightsSource: 'Auto'
       WeightUpdatePeriod: 1

Also please refer to these links for further information -

Equalize modulated signals using linear filtering - MATLAB - MathWorks India

Equalize modulated signals using decision feedback filtering - MATLAB - MathWorks India

I hope the suggestions help you address your requirements.