MATLAB: Generate noise using Box muller meathod

box mullerguassian noisenoisenoise generation

What are the other meathod for generating Guassian Noise?
I wrote code for Box muller like:
noise = rand(2,length(data));
AWGN_noise = zeros(1,length(data));
for i1=1:length(data)
AWGN_noise(i1) = sigma_noise * sqrt(-2*log(noise(1,i1)))*cos(2*pi*noise(2,i1));
end
The thing is that I'm not getting much variance in values after Box Muller Transformation. Suggest me some good code to generate guassian noise.

Best Answer

If I set sigma_noise to 1, then the variance of your noise is also 1, exactly as I would expect. (See for example http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform.) If you increase the value of sigma_noise, then you'll get more variance.
Also, your code can be vectorized to have a significant speedup. Replace your for loop with:
AWGN_noise = sigma_noise * sqrt(-2*log(noise(1,:))).*cos(2*pi*noise(2,:));
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