489 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.
Only slight formatting modification
An Approximation of the First Order Marcum -Function with Application to Network Connectivity Analysis
An exponential-type approximation of the first order Marcum -function is
presented, which is robust to changes in its first argument and can easily be
integrated with respect to the second argument. Such characteristics are
particularly useful in network connectivity analysis. The proposed
approximation is exact in the limit of small first argument of the Marcum
-function, in which case the optimal parameters can be obtained
analytically. For larger values of the first argument, an optimization problem
is solved, and the parameters can be accurately represented using regression
analysis. Numerical results indicate that the proposed methods result in
approximations very close to the actual Marcum -function for small and
moderate values of the first argument. We demonstrate the accuracy of the
approximation by using it to analyze the connectivity properties of random ad
hoc networks operating in a Rician fading environment.Comment: 6 pages, 4 figures, 1 tabl
- β¦