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

By D. Maiwald, D. Kraus. 2000

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All Invariant Moments of the Wishart Distribution (2004, background): “This is considered in the literature as a difficult problem (see Haff, 1982; von Rosen, 1988; Lauritzen, 1996, p. 259; Maiwald & Kraus, 2000).”
Expectations of Functions of Complex Wishart Matrix (2011, methodology): “Complex Wishart and complex inverse Wishart distributed random matrices are used in applications like radar, sonar, or seismic in order to model the statistical properties of complex sample covariance matrices and complex inverse sample covariance matrices, respectively (Maiwald and Kraus [19]).”
Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer? (2014, unknown): “By using [39, Eq.”
The complex Wishart distribution and the symmetric group (2003, methodology): “…f ( 1)( 0)r 0( 1)(h1; : : : ; hk):(2.19)Note that we can use (2.19) in Theorem 4 to compute moments of S 1 of the formIE(Q1 j;l r S ajljk S bjljl ) , just as we used Theorem 1 to compute similar moments of S.For k 4; Theorem 4 gives as a particular case formulas 50-54 of Maiwald and Kraus(2000).”