Capacity Bounds for Peak-Constrained Multiantenna Wideband Channels

TL;DR

This paper derives bounds on the capacity of peak-constrained MIMO wideband channels with spatial and temporal selectivity, providing insights into optimal antenna use and the impact of spatial correlation.

Contribution

It introduces explicit capacity bounds for general MIMO channels with peak constraints and derives a closed-form expression for capacity in the infinite bandwidth limit.

Findings

Using one transmit antenna is optimal in uncorrelated channels.

Rank-one beamforming is optimal in correlated channels.

Spatial correlation enhances capacity.

Abstract

We derive bounds on the noncoherent capacity of a very general class of multiple-input multiple-output channels that allow for selectivity in time and frequency as well as for spatial correlation. The bounds apply to peak-constrained inputs; they are explicit in the channel's scattering function, are useful for a large range of bandwidth, and allow to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. Furthermore, we obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this expression, we conclude that in the wideband regime: (i) it is optimal to use only one transmit antenna when the channel is spatially uncorrelated; (ii) rank-one statistical beamforming is optimal if the channel is spatially correlated; and (iii) spatial correlation, be it at the transmitter, the receiver, or both, is beneficial.