The Capacity of Fading Vector Gaussian Channels Under Amplitude Constraints on Antenna Subsets

TL;DR

This paper derives upper bounds on the capacity of fading vector Gaussian channels with amplitude constraints, considering transmitter configurations with antenna subsets and power amplifiers, providing tight bounds for high and low SNR regimes.

Contribution

It introduces new upper bounds on channel capacity under amplitude constraints for antenna subset configurations, applicable across different SNR levels.

Findings

High SNR upper bound is tight in that regime.

Low SNR upper bound provides accurate capacity estimates.

Bounds are specifically applied to systems with per-antenna power amplifiers.

Abstract

Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-noise ratio (SNR) values and, as we prove, it is tight in this regime; The second upper bound is accurate at low SNR. Furthermore, the derived upper bounds are applied to the relevant case of amplitude constraints induced by employing a distinct power amplifier for each transmitting antenna.