The Capacity of MIMO Channels with Per-Antenna Power Constraint

TL;DR

This paper determines the capacity of MIMO channels under per-antenna power constraints, revealing optimal signaling structures, formulating the problem as an SDP, and providing an efficient algorithm for practical implementation.

Contribution

It introduces a novel capacity characterization under per-antenna power constraints, including a closed-form solution and an efficient algorithm for optimal input signaling.

Findings

Capacity with equal per-antenna constraints approaches sum power capacity

Skewed constraints cause divergence between per-antenna and sum power capacities

Eigenbeam matching does not improve capacity and can be detrimental

Abstract

We establish the optimal input signaling and the capacity of MIMO channels under per-antenna power constraint. While admitting a linear eigenbeam structure, the optimal input is no longer diagonalizable by the channel right singular vectors as with sum power constraint. We formulate the capacity optimization as an SDP problem and solve in closed-form the optimal input covariance as a function of the dual variable. We then design an efficient algorithm to find this optimal input signaling for all channel sizes. The proposed algorithm allows for straightforward implementation in practical systems in real time. Simulation results show that with equal constraint per antenna, capacity with per-antenna power can be close to capacity with sum power, but as the constraint becomes more skew, the two capacities diverge. Forcing input eigenbeams to match the channel right singular vectors achieves no improvement over independent signaling and can even be detrimental to capacity.