# How to Combine white gaussian random noises from different Seeds?

I have generated two different white gaussian random noises in MATLAB using two different seeds. For example:

Asn1 = sqrt(noisepow1/2)* (randn(size(As))+1i*(randn(size(As))));
Asn2 = sqrt(noisepow2/2)* (randn(size(As))+1i*(randn(size(As))));


Here, noisepow1 and noisepow2 are amplitudes of noise powers, As is signal array.

I will need to add these two noises to calculate the SNR. As the two noises are from different sources, I am confused about how to add these two noise signals. I can't simply just add Asn1 and Asn2 to calculate the total noise, because some signal samples will have opposite phases. Should I add like below:

AA =  sqrt(noisepow1/2).*(randn(size(As)));

BB =  sqrt(noisepow2/2).*(randn(size(As)));

Asn = AA+BB + 1i*(AA+BB);


I am confused about the addition operation of these two white Gaussian random noise signals. Any suggestion would be helpful.

## 1 Answer

I can't simply just add Asn1 and Asn2 to calculate the total noise, because some signal samples will have opposite phases.

On the contrary! Uncorrelated noise is the only thing where adding the noise simply leads to noise with twice the power.

So, yes, you simply add the noises, and if you're doing it right, then the resulting noise will have variance noisepow1+noisepow2.

• Thanks for your response. I have checked that var(Asn1)+var(Asn2) = var(Asn1+Asn2). So variance matched. But the problem is that, when I add the resulting noise signals with the transmitted signal in the system and check the bit error rate (BER) at the receiver, I find that the BER fluctuates randomly with increasing the SNR of the system. So, I thought if there's any problem with the addition of noise phases in the signal. – Arin Dutta Jun 10 at 15:46
• well, that's a property of your receiver then - or your simply not simulating enough bits to come to a sufficient statistic. But if you sit down and simply write down the probability density of a sum of two normally distributed random variables, you'll notice it's still a normally distributed random variable. It literally makes no difference whether you generate one gaussian noise process with the sum variance, or sum two gaussian noise processes. – Marcus Müller Jun 10 at 15:48