On Slow-Fading MIMO Systems With Nonseparable Correlation

In a frequency-selective slow-fading channel in a multiple-input multiple-output (MIMO) system, the channel matrix is of the form of a block matrix. A method is proposed to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. Asymptotic eigenvalue distribution of $HH^*$ is also calculated, where the entries of $H$ are jointly Gaussian, with a correlation of the form $E[h_{pj}\bar h_{qk}]= \sum_{s=1}^t \Psi^{(s)}_{jk}\mathhat\Psi^{(s)}_{pq}$ (where $t$ is fixed and does not increase with the size of the matrix). An operator-valued free probability approach is used to achieve this goal. Using this method, a system of equations is derived, which can be solved numerically to compute the desired eigenvalue distribution.