Complex singular wishart matrices and multiple-atenna systems

In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m times m Hermitian matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m times n complex matrices is derived. Then the density functions are formulated for all rank n complex singular Wishart distributions. From this, the joint eigenvalue densities of low rank complex Wishart matrices are derived. Finally, using these densities spatially correlated multiple-antenna Rayleigh channel capacities are evaluated