Arbitrary beamforming based FSO MIMO system in atmospheric turbulence and misalignment errors

An arbitrary beamforming scheme is analyzed in a 2 × 2 multiple-input multiple-output (MIMO) free-space optical (FSO) communication system. The probability density function (PDF) and moment generating function (MGF) of the instantaneous received signal-to-noise ratio (SNR) in the receiver are derived for Gamma-Gamma distributed non-identical FSO links. We also consider the effect of zero-boresight misalignment errors where the radial misalignment is assumed to be Rayleigh distributed. Using the MGF of the SNR, the error performance of the considered FSO system is investigated. Specifically, we derive the expression for average symbol error rate (SER) for subcarrier intensity modulated (SIM) M-ary phase shift keying (MPSK). Contrary to the fact that repetition scheme (equal-weight beamforming) is optimal in identical channel conditions, it is observed in this paper that for non-identical turbulence channels, arbitrary beamforming with proper selection of weights can outperform the repetition beamforming.