MATLAB: : Mean square error vs SNR plot

Question

I am having difficulty in understanding the logic behind generating a plot of SNR (db) vs MSE. Different Signal to Noise Ratio (SNR) is created by varying the noise power . The formula of MSE is averaged over T independent runs.

For each SNR, I generate NEval = 10 time series. How do I correctly plot a graph of SNR vs MSE when SNR is in the range = [0:5:50]? Below is the pseudo code.

 N = 100; %Number_data_points
NEval = 10; %Number_of_different_Signals
Snr = [0:5:50];
T = 1000; %Number of independent runs

MSE = [1];
for I = 1:T
 for snr = 1: length(Snr)
   for expt = 1:NEval
    %generate signal
      w0=0.001;  phi=rand(1);
    signal = sin(2*pi*[1:N]*w0+phi); 
    % add zero mean Gaussian noise
    noisy_signal = awgn(signal,Snr(snr),'measured');
    % Call Estimation algorithm
    %Calculate error
    end
  end
end

plot(Snr,MSE); %Where and how do I calculate this MSE

I would guess it is because there is a practical limitation of how much SNR can be improved. In general a filter of too high order is not necessary. Therefore it is usually good to stop when signal quality improves slow enough (per pole). Normally you also introduce a penalty function which magnitude increases per filter order. That one adds to the MSE. — patrik

Kostya Kostya · Accepted Answer · 2014-10-28T23:26:37

As explained here (http://www.mathworks.nl/help/vision/ref/psnr.html) or other similar sources, MSE is simply the mean squared error between the original and corrupted signals. In your notations,

w0=0.001;
signal = sin(2*pi*[1:N]*w0);
MSE = zeros(T*Neval,length(Snr));
for snr = 1:length(Snr)
    for I = 1:T*Neval     %%note, T and Neval play the same role in your pseudo code
        noisy_signal = awgn(sin(2*pi*[1:N]*w0+rand(1)),Snr(snr),'measured');
        MSE(I,snr) = mean((noisy_signal - signal).^2);
    end
end
semilogy(Snr, mean(MSE))  %%to express MSE in the log (dB-like) units

For the case of signals of different lengths:

w0=0.001;
Npoints = [250,500,1000];    
MSE = zeros(T,length(Npoints),length(Snr));
for snr = 1:length(Snr)
  for ip = 1:length(Npoints) 
    signal = sin(2*pi*[1:Npoints(ip)]*w0);
    for I = 1:T
        noisy_signal = awgn(sin(2*pi*[1:Npoints(ip)]*w0+rand(1)),Snr(snr),'measured');
        MSE(I,ip,snr) = mean((noisy_signal - signal).^2);
    end
  end
end
semilogy(Snr, squeeze(mean(mean(MSE,1),2)) )

MATLAB: : Mean square error vs SNR plot

1 Answers