Monotonicity Results for Coherent MIMO Rician Channels

TL;DR

This paper proves that the mutual information and outage probability in coherent MIMO Rician channels are monotonic functions of the LOS matrix, with implications for channel capacity and multiple-access channels.

Contribution

It establishes the monotonic relationship between the LOS matrix and information-theoretic measures in Rician MIMO channels, including necessary conditions and extensions.

Findings

Mutual information is monotonic in the LOS matrix D.

Outage probability decreases monotonically with D.

Channel capacity increases with the singular values of D.

Abstract

The dependence of the Gaussian input information rate on the line-of-sight (LOS) matrix in multiple-input multiple-output coherent Rician fading channels is explored. It is proved that the outage probability and the mutual information induced by a multivariate circularly symmetric Gaussian input with any covariance matrix are monotonic in the LOS matrix D, or more precisely, monotonic in D'D in the sense of the Loewner partial order. Conversely, it is also demonstrated that this ordering on the LOS matrices is a necessary condition for the uniform monotonicity over all input covariance matrices. This result is subsequently applied to prove the monotonicity of the isotropic Gaussian input information rate and channel capacity in the singular values of the LOS matrix. Extensions to multiple-access channels are also discussed.