2 research outputs found
On the Monotonicity of the Generalized Marcum and Nuttall Q-Functions
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, , 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 . By exploiting these results,
novel upper and lower bounds for \emph{Q}_{M,N} and 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.Comment: Published in IEEE Transactions on Information Theory, August 2009.
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