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 distribution 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 correlation of the form E[hpj h̄qk] = ∑t s=1 Ψ (s) jk Ψ̂ (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.