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Multiple-input multiple-output (MIMO) and multiple-input single-output (MISO) schemes have yielded promising results in free space optical (FSO) communications by providing diversity against fading of the received signal intensity. In this paper, we have analyzed the probability of error performance of a muliple-input single-output (MISO) free-space optical channel that employs array(s) of detectors at the receiver. In this regard, we have considered the maximal ratio combiner (MRC) and equal gain combiner (EGC) fusion algorithms for the array of detectors, and we have examined the performance of these algorithms subject to phase and pointing errors for strong atmospheric turbulence conditions. It is concluded that when the variance of the phase and pointing errors are below certain thresholds, signal combining with a single array of detectors yields significantly better performance than a multiple arrays receiver. In the final part of the paper, we examine the probability of error of the single detector array receiver as a function of the beam radius, and the probability of error is minimized by (numerically) optimizing the beam radius of the received signal beams.

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Random jitter or offset between the transmitter/receiver clocks is an important parameter that has to be accurately estimated for optimal detection of Pulse Position Modulation (PPM) symbols for high data-rate optical communications. This parameter in general is modeled as an unknown random quantity that depends on the clock drift between the transmitter/receiver clocks, and the random motion between the transmitter and receiver stations. In this paper, we have modeled the time jitter for two scenarios-phase modulation jitter and frequency modulation jitter. The phase modulation jitter is modeled as a Gaussian random variable which is estimated with the help of a maximum a posteriori probability (MAP) estimator. The frequency modulation jitter is characterized as a random walk, and this leads to the jitter modeling as a state space variable in the context of a dynamical system. Since the observations are the photon counts in each slot of a PPM symbol (for both MAP estimation and tracking), the resulting dynamical model is highly nonlinear, and therefore, particle filters are employed for tracking the frequency modulation jitter. We evaluate the performance of the maximum a posteriori estimators and particle filters both in terms of the relative mean-square error and probability of error, and for various signal-to-noise ratios. Furthermore, this evaluation is also carried out for low photon rates that are typical for deep space communications. We conclude that with MAP estimation and particle filters that estimate/track the time offset, we achieve a significant performance gain in terms of probability of error as compared to systems that do not have a time synchronization system in place.