Ergodic Mutual Information Analysis for Multi-Keyhole MIMO Channels

We use non-asymptotic random matrix theory to obtain new expressions for certain statistical properties of spatially uncorrelated multi-keyhole multiple-input multiple-output (MIMO) channels. These include closed-form expressions for the distribution and moments of an unordered eigenvalue, as well as solutions for the expected log-determinant and expected characteristic polynomial. Our results are general for arbitrary numbers of transmit and receive antennas, and arbitrary number of keyholes with possibly differing powers. Based on these, we derive exact closed-form expressions and simplified upper and lower bounds for the ergodic mutual information, assuming that channel state information (CSI) is only known at the receiver. Results show that the capacity of multi-keyhole channels is typically worse than that for rich-scattering MIMO Rayleigh channels.