Generate noise using Box muller meathod

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.

Answer 1

[the cyclist]

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,:));

[Ronak Sakaria]

Thanks man... How can I increase my variance. Also I need to check the energy of noise signal. I'm implementing QPSK Modulation and Demodulation and I need to match energy so that i can have nearly eqal BER plot. Help me with this.

[the cyclist]

As I mentioned already in my answer, if you increase the value of "sigma_noise", you'll increase the variance of AWGN_noise.

I don't know anything more about the techniques you mention, so I'm afraid I can't help with that.

[Ronak Sakaria]

Are you aware of Sigma for QPSK modulation? My theory and simulation BER result doesnt match very much. I know that it depends on sigma of noise but i have tried various values of sigma and i am not getting good simultation BER curve, And thanks for suggesting alternate for for loop. I'm making less error than theoritical case at higher SNR.

[Ali Sabra]

Hello everyone,

Can anybody body tell me how to change mean of the generated Gaussian RV using this method ?

Answer 2

[Peter Perkins]

Is there some reason why you are not using the randn function?

[Ronak Sakaria]

Well no need to use randn function. I'm trying not to use any predefined function in matlab like randn, and other related to QPSK modulation.