In this article, we introduce iterative deterministic equivalents as a novel
technique for the performance analysis of communication systems whose channels
are modeled by complex combinations of independent random matrices. This
technique extends the deterministic equivalent approach for the study of
functionals of large random matrices to a broader class of random matrix models
which naturally arise as channel models in wireless communications. We present
two specific applications: First, we consider a multi-hop amplify-and-forward
(AF) MIMO relay channel with noise at each stage and derive deterministic
approximations of the mutual information after the Kth hop. Second, we study a
MIMO multiple access channel (MAC) where the channel between each transmitter
and the receiver is represented by the double-scattering channel model. We
provide deterministic approximations of the mutual information, the
signal-to-interference-plus-noise ratio (SINR) and sum-rate with
minimum-mean-square-error (MMSE) detection and derive the asymptotically
optimal precoding matrices. In both scenarios, the approximations can be
computed by simple and provably converging fixed-point algorithms and are shown
to be almost surely tight in the limit when the number of antennas at each node
grows infinitely large. Simulations suggest that the approximations are
accurate for realistic system dimensions. The technique of iterative
deterministic equivalents can be easily extended to other channel models of
interest and is, therefore, also a new contribution to the field of random
matrix theory.Comment: submitted to the IEEE Transactions on Information Theory, 43 pages, 4
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