Receiver Optimization in Turbulent Free-Space Optical MIMO Channels With APDs and $Q$-ary PPM

We propose an accurate, robust avalanche photodiode (APD) receiver optimization scheme for multiple-input/multiple-output (MIMO) free-space optical links with $Q$-ary pulse position modulation in the presence of atmospheric turbulence. Through extensive error probability $(P_{e})$ analysis, we show that selecting the APD gain such that the nonfading receiver-array signal-to-noise ratio is maximized essentially minimizes $P_{e}$ in turbulent MIMO channels with $M = 2$ transmitters and $N = 2$ receivers, for several turbulence and background-radiation levels of interest.