TL;DR: The complex multivariate Gaussian and Wishart densities are often encountered in the analysis of statistical signal processing algorithms in frequency domain array processing as discussed by the authors, and the derivation of the probability density function of forms involving complex Gaussian random vectors and complex Wishart matrices may be simplified by the use of standard theorems found in multivariate statistics for real Gaussian matrix and real Wishart matrix.
Abstract: : The complex multivariate Gaussian and Wishart densities are often encountered in the analysis of statistical signal processing algorithms in frequency domain array processing. The derivation of the probability density function of forms involving complex Gaussian random vectors and complex Wishart matrices may be simplified by the use of standard theorems found in multivariate statistics for real Gaussian random vectors and real Wishart matrices. This memorandum contains the extensions to the complex case of a selection of these theorems.