Comparison of generalized Q-function algorithms
IEEE Transactions on Information Theory
Bounds for modified Bessel functions
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the monotonicity of the generalized Marcum and Nuttall Q-functions
IEEE Transactions on Information Theory
New bounds for the Marcum Q-function
IEEE Transactions on Information Theory
On the monotonicity of the generalized Marcum and Nuttall Q-functions
IEEE Transactions on Information Theory
Supertight algebraic bounds on the Gaussian Q-function
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
IEEE Transactions on Information Theory
Hi-index | 754.96 |
In this paper, we study the generalized Marcum Q-function Qν(a,b) where a, ν 0 and b ≥ 0. Our aim is to extend the results of Corazza and Ferrari (IEEE Trans. Inf. Theory, vol. 48, pp. 3003-3008, 2002) to the generalized Marcum Q-function in order to deduce some new tight lower and upper bounds. The key tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind and some classical inequalities, i.e., the Cauchy-Buniakowski-Schwarz and Chebyshev integral inequalities. These bounds are shown to be very tight for large b, i.e., the relative errors of our bounds converge to zero as b increases. Both theoretical analysis and numerical results are provided to show the tightness of our bounds.