 As such, the magnitude formula_88 of a standard complex normal random variable will have the Rayleigh distribution and the squared magnitude formula_89 will have the exponential distribution, whereas the argument will be distributed uniformly on formula_90.If formula_91 are independent and identically distributed "n"-dimensional circular complex normal random vectors with formula_3, then the random squared norm
has the generalized chi-squared distribution and the random matrix
has the complex Wishart distribution with formula_95 degrees of freedom.This distribution can be described by density function
where formula_97, and formula_50 is a formula_99 nonnegative-definite matrix.