NDLI: On the PDF of the sum of random vectors

Content Provider	IEEE Xplore Digital Library
Author	Abdi, A. Hashemi, H. Nader-Esfahani, S.
Copyright Year	1972
Abstract	There are various cases in physics and engineering sciences (especially communications) where one requires the envelope probability density function (PDF) of the sum of several random sinusoidal signals. According to the correspondence between a random sinusoidal signal and a random vector, the sum of random vectors can be considered as an abstract mathematical model for the above sum. Now it is desired to obtain the PDF of the length of the resulting vector. Considering the common and reasonable assumption of uniform distributions for the angles of the vectors, many researchers have obtained the PDF of the length of the resulting vector only for special cases. However in this paper, the PDF is obtained for the most general case in which the lengths of vectors are arbitrary dependent random variables. This PDF is in the form of a definite integral, which may be inappropriate for analytic manipulations and numerical computations. So an appropriate infinite Laguerre expansion is also derived. Finally, the results are applied to solve a typical example in computing the scattering cross section of random scatterers.
Starting Page	7
Ending Page	12
Page Count	6
File Size	131531
File Format	PDF
ISSN	00906778
Volume Number	48
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Random variables Radar scattering Light scattering Electromagnetic scattering Random media Fading Clutter Laser radar Physics Probability density function
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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