Capacity Results for MIMO Optical Intensity Channels With Individual Intensity Constraints

Abstract

In this paper, we investigate the capacity of a multiple-input multiple-output (MIMO) optical intensity channel (OIC) with peak- and average-intensity constraints individually imposed on each transmitter. We first consider the case where the average input intensities are required to be equal to preassigned constants due to the requirement of illumination quality and color temperature. For the MIMO OIC with a strongly connected channel graph, we prove that its strongest eigen-subchannel must have positive channel gains, which reveals the underlying relationship between the MIMO OIC and the multiple-input single-output OIC. In the general case, we derive various capacity bounds by standard information theoretic tools and investigate several transceivers with certain architectures. In the special case where the channel rank is one less than the number of transmitters, we derive an equivalent capacity expression from the perspective of convex geometry, and new capacity lower bounds are derived based on this equivalent expression. Finally, the developed results are extended to another type of channels, where the average input intensities are required to be no larger than preassigned constants. These derived bounds are numerically verified to approach the capacity in the low or high signal-to-noise ratio regime.