performance of least mean square algorithm against impulsive noise environment.

how will I model an impulsive noise environment in the code given below.

clc;
clear all;
close all; 
%% Desired System (link: http://www.firsuite.net/FIR/AKSOY08_NORCHIP_G40)
sys_desired = [86 -294 -287 -262 -120 140 438 641 613 276 -325 -1009 -1487 -1451 -680 856 2954 5206 7106 8192 8192 7106 5206 2954 856 -680 -1451 -1487 -1009 -325 276 613 641 438 140 -120 -262 -287 -294 86] * 2^(-15);
%% Ergodic Process

for itr=1:100
    %% Defining input and initial Model Coefficients
    %input
    x=randn(1,60000);
    % Model for the LMS Algorithm
    model_coeff = zeros(1,length(sys_desired));
    %% Initial Values of Model Tap
    model_tap = zeros(1,length(sys_desired));
    %% System Output where a 40 dB Noise floor is added
    noise_floor = 40;
    sys_opt = filter(sys_desired,1,x)+awgn(x,noise_floor)-x;
    %% Lower and Upper Bounds of Learning Rate
    %input variance
    input_var = var(x);
    
    % upper bound = 1/(filter_length * input variance)
    mu_max = 1/(input_var*length(sys_desired));
    
    %learning rate for LMS algorithm
    mu_LMS = 0.0004;
    
    % lower bound = learning rate for LMS algorithm
    mu_min = mu_LMS;
     
    for i=1:length(x)
        %% LMS Algorithm
        % model tap values (shifting of tap values by one sample to right)
        model_tap=[x(i) model_tap(1:end-1)];
        % model output
        model_out(i) = model_tap * model_coeff';
        %error
        e_LMS(i)=sys_opt(i)-model_out(i);
        %Updating the coefficients
        model_coeff = model_coeff + mu_LMS * e_LMS(i) * model_tap;
    end
    %% Storing the e_square values after a whole run of LMS 
    
    err_LMS(itr,:) = e_LMS.^2;
     %% Printing the iteration number
    clc
    disp(char(strcat('iteration no : ',{' '}, num2str(itr) )))
end

%% Comparing the Error Curves
figure;
plot(10*log10(mean(err_LMS)),'-b');
grid on;

[Dongyue]

I think the impulsive noise environment is already given, with the following command:

sys_opt = filter(sys_desired,1,x)+awgn(x,noise_floor)-x

where the impulse noise is generated by

awgn(x,noise_floor)-x

You can go through the documentation of awgn() function to view details for generating noise for a signal.

[Dongyue]

https://www.mathworks.com/help/comm/ref/awgn.html

[PARVATHY NAIR]

@Dongyue

thankyou.

so

awgn(x,snr) 

will create awgn noise,

and

 awgn(x,snr) - x

will result in impulsive noise environment.am i correct?If wrong please correct me.

[Image Analyst]

It will be noise. What do you mean by "impulsive" noise? Do you mean like salt and pepper noise where the noise takes on either the max signal value possible, or the min signal value possible but no values in between?

[Mathieu NOE]

hello @PARVATHY NAIR

seems that LMS algorithms and earthquake signals are back ...

what is the difference with this post I already answered ?

Why the same VSSLMS algorithm code not working for the seisimic data? - MATLAB Answers - MATLAB Central (mathworks.com)

Can anyone help me in understanding an algorithm and tell me where am i wrong in simulating the adaptive filter - MATLAB Answers - MATLAB Central (mathworks.com)

and yes , more specifically, LMS algorithms does also exist in variants dedicated to impulsive (non stationnary) signals.

The internet is filled with publications on that topic

Is it again a case wher you consider earthquake signals denoising ?

I see you have posted several questions about the same topic.... also these ones :

understanding the given algorithm - MATLAB Answers - MATLAB Central (mathworks.com)

back to your code :

awgn(x,snr) will create noise on top of signal x (so the result is x + noise here,

and

awgn(x,snr) - x is the noise only ( because x + noise - x = noise)

but awgn does not generate any impulsive noise by itself - but simply a constant amplitude random noise

read the doc : y = awgn(x,snr) adds white Gaussian noise to the vector signal x.

If you want an impulsive noise (that would mimic an earthquake signal ? ) you have to create one by yourself

Still is it not clear what the LMS algorithm is supposed here to do

In the other posts you wanted to clean a recorded signal, but in the litterature about LMS for impulsive noise, the target is usually to reduce the signal itself not only it's uncorrelated noise content.

see for example :

Performance analysis of LMS based algorithms used for impulsive noise cancellation | Request PDF (researchgate.net)

Performance analysis of LMS based algorithms used for impulsive noise cancellation | IEEE Conference Publication | IEEE Xplore

1505.07569.pdf (arxiv.org)

Active noise cancellation algorithms for impulsive noise - PMC (nih.gov)

[PARVATHY NAIR]

earlier we tried to analyse the convergence of LMS algorithm under awgn and i have seen papers where tthey analysed the convergence of certain adaptive algorithms under impulse noise environment.hence the question.