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Applied Optics

Applied Optics


  • Vol. 17, Iss. 22 — Nov. 15, 1978
  • pp: 3576–3583

Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications

Paul R. Prucnal and Malvin Carl Teich  »View Author Affiliations

Applied Optics, Vol. 17, Issue 22, pp. 3576-3583 (1978)

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A single-threshold processor is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems we consider encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (nonpositive) signal, embedded in additive, independent, and noninterfering noise, where the range of the signal and noise is discrete. We show that a comparison of the sum of the observations with a unique threshold comprises optimum processing, if a weak condition on the noise is satisfied, independent of the signal. Examples of noise densities that satisfy and violate our condition are presented. The results are applied to a generalized photocounting optical communication system, and it is shown that most components of the system can be incorporated into our model. The continuous case is treated elsewhere [ IEEE Trans. Inf. Theory IT-25, (March, 1979)].

© 1978 Optical Society of America

Original Manuscript: May 30, 1978
Published: November 15, 1978

Paul R. Prucnal and Malvin Carl Teich, "Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications," Appl. Opt. 17, 3576-3583 (1978)

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