Performance Bounds for Free-Space Optical MIMO Systems with APD Receivers in Atmospheric Turbulence

Performance bounds of free space optical (FSO) systems with multiple laser transmitters and multiple avalanche photodetectors (APDs) are evaluated for terrestrial, line-of- sight communication. Specifically, analytical upper bounds on average uncoded error rate in turbulent multiple-input multiple- output (MIMO) channels with Q-ary pulse position modulation (PPM) are derived for arbitrary observable densities, and are used to quantify APD-based performance improvements over pin detector arrays in non-fading, lognormal, and negative exponential channels. Moreover, it is shown that despite the high complexity of APD array statistics, these performance gains can be accurately predicted using a jointly-Gaussian model for APD array outputs. Both maximum likelihood (ML) and sub-optimal combining rules are derived, and a simple equal gain combiner (EGC) that performs close to optimum is demonstrated. Finally, APD gain selection is discussed.