New bounds for the generalized marcum Q-function

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31 Citations (Scopus)

Abstract

In this paper, we study the generalized Marcum Q-function Qν where a ν > 0 and b ≥ 0. Our aim is to extend the results of Corazza and Ferrari IEEE Trans. Inf. Theory, vol. 48, pp. 3003-3008, 2002) to the generalized Marcum Q-function in order to deduce some new tight lower and upper bounds. The key tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind and some classical inequalities, i.e., the Cauchy-Buniakowski-Schwarz and Chebyshev integral inequalities. These bounds are shown to be very tight for large b, i.e., the relative errors of our bounds converge to zero as b increases. Both theoretical analysis and numerical results are provided to show the tightness of our bounds.

Original languageEnglish
Pages (from-to)3091-3100
Number of pages10
JournalIEEE Transactions on Information Theory
Volume55
Issue number7
DOIs
Publication statusPublished - Jul 15 2009

Keywords

  • Cauchy-Buniakowski-Schwarz and Chebyshev integral inequalities
  • Generalized Marcum Q-function
  • Lower and upper bounds
  • Modified Bessel functions of the first kind

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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