MIMO Optical Intensity Channels with Peak Intensity Constraints: Low-SNR Capacity

The capacity of the intensity-modulation direct-detection (IM-DD) multiple-input multiple-output channel is studied under average and peak intensity constraints. We focus on the low signal-to-noise ratio (SNR) regime where the constraints proportionally vanish, or alternatively, where the noise power is large. A general upper bound on the capacity of this channel is derived. Then, this bound is shown to be tight at low SNR, where it coincides with the achievable rate of (i) on-off keying (OOK), spatial repetition coding, and maximum-ratio combining under individual average constraint and (ii) OOK with maximally-correlated inputs under a sum average constraint. This leads to a low-SNR capacity characterization of the channel.