Lower and Upper Bounds for the Generalized Marcum and Nuttall Q-functions

 
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Lower and Upper Bounds for the Generalized Marcum and Nuttall Q-functions

Karagiannidis, Georgios
Mihos, Sotirios
Kapinas, Vasilios

Monotonicity criteria are established for the generalized Marcum Q-function {Q}M(a,b)and the standard Nuttall Q-function Q{M,N}(a,b). Specifically, we present that Q{M}(a,b) is monotonically increasing with regard to its order M, for all ranges of the parameters a,b, whereas Q{M,N}(a,b) possesses analogous monotonicity behavior with respect to M+N, under the assumptions of a _>1 and constant difference M-N _> 1. For the normalized Nuttall {Q}-function {Q}(M,N}(a,b, we also state the same monotonicity criterion without the necessity of restricting the range of the parameter a. By exploiting these results, we propose closed-form upper and lower bounds for the standard and normalized Nuttall {Q}-functions, which for the latter case seem to be very tight. Furthermore, concerning the generalized Marcum {Q}-function, specific tight upper and lower bounds, that have already been proposed in the literature for the case of integer M, are appropriately utilized in order to extend its validity over real values of M. The offered theoretical results can be efficiently applied in the study of digital communications over fading channels, the capacity analysis of multiple-input multiple-output (MIMO) channels and the decoding of turbo or low-density parity-check (LDPC) codes.

Conference / Συνέδριο
info:eu-repo/semantics/conferenceObject

Normalized Nuttall Q-function
Nuttall Q-function
Lower and upper bounds
Generalized Marcum Q-function
Monotonicity

Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (EL)
Aristotle University of Thessaloniki (EN)

Αγγλική γλώσσα

2008
2009-11-04T20:50:02Z


Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης, Πολυτεχνική Σχολή, Τμήμα Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών

3rd International Symposium on Wireless Pervasive Computing, ISWPC 2008, Proceedings, [2008] p.736-739 [Published Version]

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info:eu-repo/semantics/openAccess



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