Communication under the Poisson regime

By "Poisson regime" we mean a model in which intelligence is communicated by random discrete occurrences in time that obey Poisson statistics of arbitrarily time-varying mean, as for example when modulated electromagnetic radiation and background radiation at optical frequencies is incoherently detected by photon-sensitive surfaces. The problems of optimal detection of signals of arbitrary shape and of the estimation of signal amplitude and delay are treated under a maximum-likelihood criterion. Detection probabilities, delay estimation errors, and the probability of "noise threshold" in delay estimation, are derived. Some results are basically different from those of parallel problems treating known signals in Gaussian noise. The treatment is based on a representation of nonstationary Poisson processes in which the observables are the instants of the occurrences rather than their numbers in given intervals of time.