Calculation of Cumulative Distributions and Detection Probabilities in Communications and Optics.
Abstract
This report treats the numerical computation of cumulative distributions of random variables occurring primarily in communications, radar, and optics when their moment-generating or probability-generating functions are known. The cumulative distribution of a continuous random variable is expressed as a Laplace inversion integral of its moment-generating function, that of an integer-valued random variable as a contour integral that arises from Cauchy's theorem and whose integrand involves the probability-generating function. These integrals are evaluated by numerical quadrature along contours in the complex plane chosen for efficiency and convenience. Applications include radar detection probabilities with fading and unfading signals and fixed-threshold and constant-false-alarm-rate receivers; the distributions of the integrated output of a linear rectifier and of the filtered output of a qadratic rectifier; the error probability in a binary symmetric communication channel with intersymbol and cochannel interference; the distribution of shot noise; the distributions of the numbers of electrons emerging from photoelectric detectors, photomultipliers, and avalanche diodes; and significance probabilities in statistical rank tests.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 31, 1986
- Accession Number
- ADA175082
Entities
People
- Carl W. Helstrom
Organizations
- University of California, San Diego