Computer Science – Information Theory
Scientific paper
2007-12-26
IEEE Trans. Inf. Theory, vol. 55, no. 8, pp. 3701-3710, Aug. 2009
Computer Science
Information Theory
Published in IEEE Transactions on Information Theory, August 2009. Only slight formatting modifications
Scientific paper
10.1109/TIT.2009.2023710
Monotonicity criteria are established for the generalized Marcum Q-function, $\emph{Q}_{M}$, the standard Nuttall Q-function, $\emph{Q}_{M,N}$, and the normalized Nuttall Q-function, $\mathcal{Q}_{M,N}$, with respect to their real order indices M,N. Besides, closed-form expressions are derived for the computation of the standard and normalized Nuttall Q-functions for the case when M,N are odd multiples of 0.5 and $M\geq N$. By exploiting these results, novel upper and lower bounds for $\emph{Q}_{M,N}$ and $\mathcal{Q}_{M,N}$ are proposed. Furthermore, specific tight upper and lower bounds for $\emph{Q}_{M}$, previously reported in the literature, are extended for real values of M. The offered theoretical results can be efficiently applied in the study of digital communications over fading channels, in the information-theoretic analysis of multiple-input multiple-output systems and in the description of stochastic processes in probability theory, among others.
Kapinas Vasilios M.
Karagiannidis George K.
Mihos Sotirios K.
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