Title :
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
fDate :
4/1/1999 12:00:00 AM
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;
Journal_Title :
Aerospace and Electronic Systems, IEEE Transactions on
