Abstract
In this work, an analytical framework for deriving the exact moments of multiple-input- multiple-output (MIMO) mutual information in the high-signal-to-noise ratio (SNR) regime is proposed. The idea is to make efficient use of the matrix-variate densities of channel matrices instead of the eigenvalue densities as in the literature. The framework is applied to the study of the emerging models of MIMO Rayleigh product channels and Jacobi MIMO channels, which include several well-known channels models as special cases. The corresponding exact moments of any order for the high-SNR mutual information are derived. The explicit moment expressions are utilized to construct simple yet accurate approximations to the outage probability. Despite the high-SNR nature, simulation shows usefulness of the approximations with finite SNR values in the scenario of low outage probability relevant to MIMO communications.
Highlights
IntroductionMutual information is one of the most important quantities in information theory. It is crucial in the analysis and design of various communications and signal processing systems
Mutual information is one of the most important quantities in information theory.It is crucial in the analysis and design of various communications and signal processing systems.In multiple-input-multiple-output (MIMO) communications, the supremum of the mutual information provides the fundamental performance measure of the channel capacity
We study the impact of finite signal-to-noise ratio (SNR) on the accuracy of the outage probability
Summary
Mutual information is one of the most important quantities in information theory. It is crucial in the analysis and design of various communications and signal processing systems. The idea of the proposed approach stems from our observations that moment expressions of high-SNR mutual information can be efficiently obtained by means of integrals over matrix-valued channel densities This is contrary to the existing approach [1,2,3,4,5,6,8,9,10,11], where the starting point is the seemingly simpler integrals over the eigenvalue densities of channel matrices. As an application of our results, we may study as a possible future work the distribution of the power offset pertaining to the nonergodic channels, an open problem discussed in [13] This open problem has been partially addressed in [14] for the case of a product of two MIMO Rayleigh channels
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