Capacity of the MIMO optical fading channel

We determine the capacity of a shot-noise limited direct detection multiple-input multiple-output (MIMO) optical channel subject to block fading. Information is sent over this channel by modulating the intensity of a number of optical signals, one corresponding to each transmit aperture, and individual photon arrivals are observed at each receive aperture for the purpose of detection. The transmitted signals are subject to peak and average power constraints. The fading occurs in blocks of fixed duration during each of which the path gain matrix remains constant, and changes across successive blocks in an independent and identically distributed fashion. We obtain a single-letter characterization of the capacity of this channel when the receiver is provided with perfect channel state information (CSI) while the transmitter CSI can be imperfect. We demonstrate that a binary signaling scheme with arbitrarily fast intertransition times through each of the transmit apertures achieves channel capacity. Some interesting properties of the optimum transmission strategies are discussed