  An exponential-type approximation of the first order Marcum $Q$-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
$Q$-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 $Q$-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.
