Capacity Results for Multiple-Input Multiple-Output Optical Wireless Communication With Per-Antenna Intensity Constraints

TL;DR

This paper analyzes the capacity of MIMO optical intensity channels under per-antenna constraints, deriving bounds and exact expressions, especially for specific channel conditions, to improve understanding of optical wireless communication limits.

Contribution

It provides new capacity bounds and exact expressions for MIMO optical intensity channels with per-antenna constraints, including cases with equal and no larger average intensities.

Findings

Capacity bounds approach true capacity at low/high SNR

Eigen-subchannel with positive gains in strongly connected channels

New capacity expressions for rank-deficient channels

Abstract

In this paper, we investigate the capacity of a multiple-input multiple-output (MIMO) optical intensity channel (OIC) under per-antenna peak- and average-intensity constraints. We first consider the case where the average intensities of input are required to be equal to preassigned constants due to the requirement of illumination quality and color temperature. When the channel graph of the MIMO OIC is strongly connected, we prove that the strongest eigen-subchannel must have positive channel gains, which simplifies the capacity analysis. Then we derive various capacity bounds by utilizing linear precoding, generalized entropy power inequality, and QR decomposition, etc. These bounds are numerically verified to approach the capacity in the low or high signal-to-noise ratio regime. Specifically, when the channel rank is one less than the number of transmit antennas, we derive an equivalent capacity expression from the perspective of convex geometry, and new lower bounds are derived based on this equivalent expression. Finally, the developed results are extended to the more general case where the average intensities of input are required to be no larger than preassigned constants.