# Complex normal Gaussian noise

I would like to create complex normal Gaussian noise with dimensions $(M,N)$. The noise should be zero mean and the variance should be equal to one.

How can I do so?

You should use the the standard formula:

s = randn(m, n) + 1i*randn(m, n);


And as pointed out by MBaz, the output should be scaled accordingly by $\frac{1}{\sqrt{2}}$

s = s/sqrt(2);


More on that topic you can find for example in a book Digital Media Processing by Hazarathaiah Malepati:

It should generate exactly what you want.

• You'll have to scale by $\frac{1}{\sqrt2}$ to get unit variance in the complex case. – David Jul 23 '15 at 11:45
• @David can you please explain why that is?? – Wanderer Jul 23 '15 at 12:46
• @DimitriC The variance of a complex RV is equal to the variance of its real part plus the variance of its imaginary part. – MBaz Jul 23 '15 at 13:36