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

Paul R. Prucnal, Malvin Carl Teich

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

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)].

Original languageEnglish (US)
Pages (from-to)3576-3583
Number of pages8
JournalApplied Optics
Volume17
Issue number22
DOIs
StatePublished - Nov 15 1978
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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