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Free probability based capacity calculation for MIMO channels with transmit or receive correlation

We apply tools from free probability theory to the asymptotic analysis of MIMO systems with spatial correlation at the transmitter or receiver side. The MIMO channel is modeled by a one-sided Kronecker model with exponential transmitter or receiver correlation matrix. We compute the asymptotic channel capacity based on a calculation of the asymptotic eigenvalue pdf. The dependence of the asymptotic channel capacity on the SNK, dimension ratio, and correlation parameter is studied. Finally, it is demonstrated that the asymptotic capacity closely approximates the simulated capacity of finite-dimensional MIMO channels already for moderate system dimensions.