A model that is sufficiently general to describe the predominant statistical characteristics of the output of many real optical detectors is formulated. This model is used to study the optimum receiver processing for direct-detection optical communication systems. In particular, the structures of detectors and estimators for randomly filtered doubly stochastic Poisson processes observed in additive white Gaussian noise are considered. Representations for the posterior statistics of a vector-valued Markov process that modulates the intensity of the doubly stochastic Poisson process are obtained. Quasi-optimum estimators and detectors are specified in general terms and specialized for several important applications. These include a demodulator for subcarrier angle modulation, a detector structure for binary signaling with known intensities, and a detector structure for binary signaling in the turbulent atmosphere.

A reasonable model for the atmosphere as an optical communication channel is presented and then reduced, with some approximation, to an equal-strength diversity system. By using the realistic assumption of a very large variance for the channel's random phase, the operations that the maximum-likelihood receiver must perform are determined. This resulting receiver is also a min-max receiver. Functional bounds to the error probability that results with orthogonal waveforms are determined. The variation of these bounds with the energy-to-noise ratio per diversity path and with the amount of atmospheric turbulence is discussed, and numerical results are presented for the low-rate (union-bound) performance. These results demonstrate that the error probability depends strongly on the amount of turbulence. However, if the amount of diversity can be controlled, the minimum energy-to-noise ratio per information bit for which the error probability can be made to vanish is independent of the turbulence. This minimum is just that which would exist in the absence of turbulence.