On the Eigenvalue Distribution of Correlated MIMO Channels by Character Expansion of Groups

Multiple-input multiple-output (MIMO) channels have been studied from various aspects including the average of the mutual information between the transmitter and receiver (ergodic capacity) when the channel gains are known to the receiver only. A common approach for capacity analysis is to find the moment generating function (MGF) of the mutual information and by direct differentiation, the mean of the mutual information (capacity) is calculated. Recently, character expansions of groups have been used for integration over unitary matrices to obtain the joint eigenvalue distribution of the correlated Wishart matrix i.e. HH* where H is the zero mean full correlated complex Gaussian random MIMO channel matrix. In this paper, we show that the previous attempt for capacity analysis of full correlated MIMO channels is correct for square channel matrices only. We modify the approach from square matrices to rectangular matrices to obtain the correct joint eigenvalue distribution of the correlated Wishart matrix. The result can be used to obtain the MGF and the capacity of full correlated MIMO channels.