On The Capacity of Gaussian MIMO Channels Under The Joint Power Constraints

TL;DR

This paper derives a closed-form solution for the capacity and optimal signaling of Gaussian MIMO channels under combined total and per-antenna power constraints, analyzing different SNR regimes.

Contribution

It provides the first full-rank closed-form solution with necessary and sufficient conditions for Gaussian MIMO channel capacity under joint power constraints.

Findings

Isotropic signaling is optimal at high SNR.

Rank-1 signaling is not always optimal at low SNR.

Unique properties of optimal covariance matrices are identified.

Abstract

The capacity and optimal signaling over a fixed Gaussian MIMO channel are considered under the joint total and per-antenna power constraints (TPC and PAC). While the general case remains an open problem, a closed-form full-rank solution is obtained along with its sufficient and necessary conditions. The conditions for each constraint to be inactive are established. The high and low-SNR regimes are studied. Isotropic signaling is shown to be optimal in the former case while rank-1 signaling (beamforming) is not necessarily optimal in the latter case. Unusual properties of optimal covariance under the joint constraints are pointed out.