Distribution of the envelope of a sum of random sine waves and Gaussian noise

Author

Helstrom, Carl W.

Author_Institution

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

Volume

35

Issue

2

fYear

1999

fDate

4/1/1999 12:00:00 AM

Firstpage

594

Lastpage

601

Abstract

The cumulative distribution of the envelope of the sum of a sinusoidal signal, a number M of randomly phased interfering sine waves, and, possibly, Gaussian noise is expressed as the sum of Marcum´s Q-function and an asymptotic series of Laguerre polynomials, much like the ordinary Edgeworth series for the distribution of the sum of a number of independent random variables. A test of the method with M=20 showed that its computation requires about 2% of the time needed for numerical inversion of the characteristic function of the distribution

Keywords

Bessel functions; Gaussian distribution; Gaussian noise; higher order statistics; information theory; polynomials; random processes; series (mathematics); signal detection; Bessel function; Gaussian noise; Laguerre polynomials; Marcum´s Q-function; Rayleigh-Rice distribution; asymptotic series; cumulative PDF; cumulative distribution; numerical inversion; quasi-Edgeworth series; random sine waves; randomly phased interfering sine waves; sinusoidal signal; sum envelope distribution; Distributed computing; Frequency; Gaussian noise; Interference; Narrowband; Polynomials; Random variables; Reflection; Sampling methods; Testing;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/7.766940

Filename

766940