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Open AccessArticle

Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime

1
Department of Electrical and Computer Engineering, University of Michigan, Dearborn, MI 48128, USA
2
Department of Electrical and Computer Engineering, Mississippi State University, Starkville, MS 39762, USA
3
Center for Intelligent Networking and Communications, University of Electronic Science and Technology of China, Chengdu 611731, China
4
MOEKLAS and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
*
Author to whom correspondence should be addressed.
Partial results of this work related to the Jacobi MIMO channels have been presented in the IEEE Global Communications Conference, Abu Dhabi, UAE, 2018.
Entropy 2019, 21(11), 1071; https://doi.org/10.3390/e21111071
Received: 24 September 2019 / Revised: 25 October 2019 / Accepted: 31 October 2019 / Published: 1 November 2019
(This article belongs to the Special Issue Random Matrix Approaches in Classical and Quantum Information Theory)
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. View Full-Text
Keywords: matrix integrals; MIMO mutual information; non-asymptotic analysis; random matrix theory matrix integrals; MIMO mutual information; non-asymptotic analysis; random matrix theory
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Wei, L.; Liu, C.-H.; Liang, Y.-C.; Bai, Z. Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime. Entropy 2019, 21, 1071.

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