On slow-fading non-separable correlation MIMO systems

Abstract

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 $H{H}^{\ast }$, where the entries of $H$ are jointly Gaussian, with a correlation of the form $E[h_{pj}{\bar{h}}_{qk}]={\sum }_{s=1}^t{\Psi }_{jk}^{(s)}{\hat{\Psi }}_{pq}^{(s)}$ (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.

24 pages and 3 figures