Free-Space Optical Communications with Detector Arrays: A Mathematical Analysis

Photon counting detector arrays are commonly used for free-space optical communications in deep space. Such detector arrays - by virtue of their size - help in the collection of the optical signal even when there is some misalignment between the transmitter and receiver systems. In this paper, we argue that, for the common Gaussian beam profile, a detector array receiver is more useful for minimizing the probability of error than a single detector receiver of the same dimensions. Furthermore, the improvement in the error probability is more pronounced for low signal-to-noise ratio conditions, and the probability of error decreases monotonically as a function of the number of detectors in the array. However, communication with detector arrays results in a larger computational and hardware complexity at the receiver.