Calculation of moments of complex Wishart and complex inverse Wishart distributed matrices

The calculation of moments of complex Wishart and complex inverse Wishart distributed random matrices is addressed. In applications such as radar, sonar or seismics, complex Wishart and complex inverse Wishart distributed random matrices are used to model the statistical properties of complex sample covariance matrices and complex inverse sample covariance matrices, respectively. Moments of these random matrices are often needed, for example, in studies of the asymptotic properties of parameter estimates. A derivation of the probability density function of complex inverse Wishart distributed random matrices is given. Furthermore, strategies are outlined for the calculation of the moments of both complex Wishart and complex inverse Wishart distributed matrices.