NDLI: Simple Tight Exponential Bounds on the First-Order Marcum Q-Function via the Geometric Approach

Content Provider	IEEE Xplore Digital Library
Author	Pool Yuen Kam Rong Li
Copyright Year	2006
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore (Pool Yuen Kam; Rong Li)
Abstract	The geometric interpretation of the first-order Marcum Q-function, Q(a, b), has been shown as the probability that a complex, Gaussian random variable Z with real, nonzero mean a takes on values outside of a circular region $C_{O,b}$ of radius b centered at the origin O. Based on this interpretation, many new, simple, tight, upper/lower exponential bounds on Q(a, b) are easily obtained by computing the probability of Z lying outside of some simple geometrical shapes, such as circular regions, semicircular regions, sectors, and angular sectors of annuli, whose boundaries tightly enclose, or are tightly enclosed by the boundary of $C_{O,b}.$ The new bounds presented here only involve two exponential functions, and the best of them are in most cases much tighter than the best existing exponential bounds. In addition to these bounds, more new bounds can be obtained by using similar methods. Even some bounds in the literature can also be obtained via this geometric approach
Starting Page	1085
Ending Page	1089
File Size	204229
Page Count	5
File Format	PDF
ISBN	142440505X
DOI	10.1109/ISIT.2006.261951
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Random variables Fading Error probability Shape Digital communication Probability density function Performance analysis
Content Type	Text
Resource Type	Article

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