Free-Space Optical MIMO Transmission with APD Receivers in Atmospheric Turbulence

In this paper we analyze multiple-input multiple-output (MIMO) free-space optical (FSO) communication systems with Q-ary pulse position modulation (PPM) and avalanche photodiodes (APDs) in the receiver array in the presence of atmospheric turbulence, and derive the general maximum-likelihood (ML) detection rule and the Chernoff bound on error probability (Pe) for the MIMO setup. The obtained analytical results are evaluated under both the Webb-Gaussian and jointly-Gaussian models for receiver outputs. It is shown that accuracy of jointlyGaussian modelling increases with receiver-array size. Moreover, MIMO systems with APD receivers are shown to be markedly superior to analogous non-diverse systems, particularly in strong turbulence, with full spatial diversity achieved in a Rayleigh channel. Finally, it is show that for a given thermal noise level, selection of APD gain based on a non-fading SNR criterion for a single APD receiver results in nearly-optimal Pe in MIMO systems at arbitrary levels of atmospheric turbulence.