MATLAB: : Mean square error vs SNR plot - matlab

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

Answer 1

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)) )