Upper and Lower Bounds on the Capacity of Amplitude-Constrained MIMO Channels

TL;DR

This paper derives new upper and lower bounds on the capacity of MIMO channels with amplitude constraints, showing they are tight in high amplitude regimes and scale linearly with antenna numbers.

Contribution

It introduces novel bounds for amplitude-constrained MIMO channel capacity, providing tight estimates and scaling behavior insights.

Findings

Bounds are within a constant gap for invertible channel matrices.

Bounds are tight in high amplitude regimes.

Capacity scales linearly with the minimum of transmit and receive antennas.

Abstract

In this work, novel upper and lower bounds for the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the high amplitude regime, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similarly to the case of average power-constrained inputs.