Asymptotic ML Detection for the Photon Counting Channel

Recent technological advances in single photon detectors have paved the way for laser-based interplanetary communications, targeting data rates higher than those achievable in the radio part of the spectrum. The development of photon counting receiver algorithms specific to this channel is required. In particular, maximum likelihood (ML) detection must incorporate the typical Bose-Einstein distribution of background noise photons. We overcome the unwieldy expression of the ML detection metric by deriving an asymptotically tight approximation, converging in variance, which is linear in the data and whose coefficients can be explicitly calculated.