Quadratic forms on complex random matrices and channel capacity

Quadratic forms on complex random matrices and their joint eigenvalue densities are derived with the goal of studying the ergodic channel capacity of multiple-input multiple-output (MIMO) Rayleigh distributed wireless communication channels. We consider MIMO channels which are correlated at the transmitter and/or the receiver ends and evaluate the corresponding ergodic capacity formulas. These formulas are expressed in terms of complex zonal polynomials. This study shows how channel correlation degrades the capacity of the communication systems.