Generalizing the real multivariate Gaussian distribution to the complex
case is not straightforward but one common approach is to replace the
real symmetric variance matrix with a Hermitian positive-definite
matrix. The cmvnorm package provides some functionality for
the resulting density function.
References
N. R. Goodman 1963. “Statistical analysis based on a certain
multivariate complex Gaussian distribution”. The Annals of
Mathematical Statistics. 34(1): 152--177
R. K. S. Hankin 2015. “The complex multivariate
Gaussian distribution”. R News, volume 7, number 1.