On slow-fading non-separable correlation MIMO systems

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. We propose a method to calculate the limit of the eigenvalue distri- bution of block matrices if the size of the blocks tends to infinity. We will also calculate the asymptotic eigenvalue distribution of HH�, where the entries of H are jointly Gaussian, with a corre- lation of the form E(hpjhqk) = P t s=1 � (s) jk ˆ �(s) pq (where t is fixed and does not increase with the size of the matrix). We will use an operator-valued free probability approach to achieve this goal. Using this method, we derive a system of equations, which can be solved numerically to compute the desired eigenvalue distribution.