Hi
It is just to keep variance of each sample to be one. randn() function in MATLAB results in a Gaussian noise with zero mean and unit variance. So, variance of randn() + j randn() would be 2 and to keep its variance to be 1 a scaling factor of 1/sqrt(2) is multiplied.
I mean the variance of sum of two independent normal Gaussian Random variable is 2. (Agree)
but when scalar factor (1/sqrt(2)) is multiplied the results is 1/sqrt(2) not 1.
plz explain, I am confused.
Hi
Kindly note that \[var(aX) = a^2 var(X) \]. So, multiplying by \[\frac{1}{\sqrt{2}}\] scales variance by \[\frac{1}{2}\]. Thus total variance is (1+1)/2=1.