Reliable Communication over an Optical Fading Channel

We consider a single-user multiple input multiple output (MIMO) shot-noise limited Poisson fading channel over which information signals are transmitted by modulating the intensities of multiple optical beams, one from each transmit aperture; and individual photon arrivals are counted at multiple receive photodetector apertures. The transmitted signals undergo multiplicative fading, and the fading occurs in coherence intervals of fixed duration in each of which the fade (channel state) matrix remains constant, and changes across successive such intervals in an i.i.d. 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. Properties of the optimal transmission strategies are also described.