M-ary Poisson Detection and Optical Communications

This paper presents an investigation of the problem of maximum likelihood detection of one of
M
Poisson processes in a background of additive Poisson noise. When the observables correspond to counts of emitted photoelectrons, the problem models a discrete version of a coherent
M
-ary optical communication system using photon counters in the presence of background radiation. Consideration is given to an average distance and a detection probability criterion. The advantages of an
M
-ary pulsed intensity set (Poisson intensities wholly concentrated in a single counting interval) are demonstrated. The performance of such intensity sets is exhibited in terms of error probabilities, pulse widths, signal-tonoise ratio, and channel capacity. Behavior as a function of number
M
of intensities is also discussed. By appropriate conversion these results may be used for determining power requirements in an optical pulse position modulation system.