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

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)].

A neural-counting model incorporating refractoriness and spread of excitation. I. Application to intensity discrimination

“…• however,Teich, Prucnal, and Vannucci, 1977;Prucnal and Teich, 1978; Teich el al., 1979). We are rewarded, nevertheless, by the success that a closely related model affords us in dealing with the estimation of loudness and with masking, and we shall address these problems in the future.…”

Wideband FSK Optical Fiber Communication Experiment

“…By now the merits of frequency modulation (FM) in radio communication are widely recognized [1][2][3][4][5][6]. However, all attempts to utilize FM in optical communications have been thwarted by the lack of tunable sources [7], so that various subcarrier FM intensity modulation schemes have been resorted to [8][9][10].…”

On the Performance of Single-Threshold Detectors for Binary Communications in the Presence of Gaussian Mixture Noise

“…Although the sign detector and other single-threshold detectors have been studied extensively in the literature [1], [12], [13], no comparative study has been performed between the sign detector and the other single-threshold detectors in the presence of Gaussian mixture noise. The main contributions of this paper can be summarized as follows.…”