Detectability of signals in Laplace noise

Author

Helstrom, C.W.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., La Jolla, CA

Volume

25

Issue

2

fYear

1989

fDate

3/1/1989 12:00:00 AM

Firstpage

190

Lastpage

196

Abstract

Closed-form expressions for the false-alarm and detection probabilities attained by the optimum and the linear detectors of a positive signal in n independent samples of noise having a bilateral exponential or Laplace distribution require lengthy computation when n is large, and those for the optimum detector suffer from round-off error because their terms alternate in sign. It is shown how the method of saddlepoint integration can be conveniently applied to compute these probabilities, and numerical comparisons of the accuracies of the methods are presented. The relative efficiency of the two detectors is calculated as a function of n and found to approach the asymptotic value of 2 very slowly

Keywords

Laplace transforms; integration; probability; signal detection; Laplace distribution; Laplace noise; bilateral exponential; detection probabilities; linear detectors; optimum detector; positive signal; relative efficiency; round-off error; saddlepoint integration; Closed-form solution; Density functional theory; Detectors; Distributed computing; Probability density function; Probability distribution; Roundoff errors; Signal analysis; Signal detection; Statistical distributions; Statistics;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/7.18680

Filename

18680