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)].

© 1978 Optical Society of America

Signal-to-noise ratio in optical heterodyne detection for Gaussian fields

Takashi Takenaka, Kazumasa Tanaka, and Otozo Fukumitsu
Appl. Opt. 17(21) 3466-3471 (1978)

Generalized performance parameter for single-threshold detection systems

Paul R. Prucnal
Appl. Opt. 19(21) 3606-3610 (1980)

Detection of 1-of-M orthogonal signals: asymptotic equivalence of likelihood ratio and multiband models

Theodore E. Cohn
Opt. Lett. 3(1) 22-23 (1978)

Signal current probability distribution for optical heterodyne receivers in the turbulent atmosphere. 1: Theory

James H. Churnside and Charles M. McIntyre
Appl. Opt. 17(14) 2141-2147 (1978)

Multiple pulse detection in atmospheric turbulence

Russell E. Warren
Appl. Opt. 17(17) 2721-2723 (1978)