Howtosignalprocessing
- What is circularly symmetric complex Gaussian?
- How do you generate a complex Gaussian random variable in Matlab?
What is circularly symmetric complex Gaussian?
A complex circularly-symmetric gaussian random variable has the property that eiθz has the same probability density function for all θ. Generalizing, a complex, jointly gaussian random vector z = x + iy is circularly symmetric when the vector eiθz has the same multivariate probability density function for all θ.
How do you generate a complex Gaussian random variable in Matlab?
We have as matlab function randn generates Gaussion randome variables . x = 1/sqrt(2)*(randn(N, 1) + 1i*randn(N,1)); It can be shown that: Therefore the factor of 1/sqrt(2) is correct if one wants to generate 0-mean complex Gaussian variable with variance of 1 (std is also 1 for 0-mean randome variable).
