A novel representation for the nuttall Q-function

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Abstract

The aim of this work is the derivation of a novel explicit representation for the Nuttall Q-function, Qm,n(a, b). The Nuttall Q-function is a relatively new special function. Its usefulness in wireless communications is evident by its utilization in applications related to the field of digital communications over fading channels, [1]- and the references therein. It is denoted as Qm,n(a, b) and it was first proposed by A. H. Nuttall, in [2], as a generalisation of the Marcum Q-function, Qm(a, b), [3]-[5]. Consequently, M. K. Simon derived, in [6], a closed-form expression for Q m,n(a, b) in terms of Qm(a, b) and the modified Bessel function of the first kind, In(x). This representation has a finite series form and is valid only for the case that the sum of its two order indices -m + n- is an odd integer. In the same context, establishment of monotonicity criteria and derivation of tight bounds were given in [7] along with a useful closed-form expression which is valid for the case that m and n are odd multiples of 0.5, i.e m + 0.5 ∈ ℕ, n+ 0.5 ∈ ℕ.

Original languageBritish English
Title of host publication2010 IEEE International Conference on Wireless Information Technology and Systems, ICWITS 2010
DOIs
StatePublished - 2010
Event2010 IEEE International Conference on Wireless Information Technology and Systems, ICWITS 2010 - Honolulu, HI, United States
Duration: 28 Aug 20103 Sep 2010

Publication series

Name2010 IEEE International Conference on Wireless Information Technology and Systems, ICWITS 2010

Conference

Conference2010 IEEE International Conference on Wireless Information Technology and Systems, ICWITS 2010
Country/TerritoryUnited States
CityHonolulu, HI
Period28/08/103/09/10

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