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, $\mathcal{Q}_{M,N}$, 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.Comment: Published in IEEE Transactions on Information Theory, August 2009. Only slight formatting modification

A New Framework for the Performance Analysis of Wireless Communications under Hoyt (Nakagami-q) Fading

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI:10.1109/TIT.2017.2655342We present a novel relationship between the distribution of circular and non-circular complex Gaussian random variables. Specifically, we show that the distribution of the squared norm of a non-circular complex Gaussian random variable, usually referred to as the squared Hoyt distribution, can be constructed from a conditional exponential distribution. From this fundamental connection we introduce a new approach, the Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-q) fading in a very simple way. We illustrate that many performance metrics for Hoyt fading can be calculated by leveraging well-known results for Rayleigh fading and only performing a finite-range integral. We use this technique to obtain novel results for some information and communication-theoretic metrics in Hoyt fading channels.Universidad de Málaga. Campus de Execelencia Internacional. Andalucía Tech

Some Useful Collective Properties of Bessel, Marcum Q-Functions and Laguerre Polynomials

Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special functions. These handicaps force researchers to seek new properties of special functions. Many problems that could not be solved so far would be solved by means of these efforts. Therefore in this article, we derived some useful properties and interrelations of each others of Bessel functions, Marcum Q-functions and Laguerre polynomials

Transonic CFD applications at Boeing

The use of computational methods for three dimensional transonic flow design and analysis at the Boeing Company is presented. A range of computational tools consisting of production tools for every day use by project engineers, expert user tools for special applications by computational researchers, and an emerging tool which may see considerable use in the near future are described. These methods include full potential and Euler solvers, some coupled to three dimensional boundary layer analysis methods, for transonic flow analysis about nacelle, wing-body, wing-body-strut-nacelle, and complete aircraft configurations. As the examples presented show, such a toolbox of codes is necessary for the variety of applications typical of an industrial environment. Such a toolbox of codes makes possible aerodynamic advances not previously achievable in a timely manner, if at all

Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory

This paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory. These functions are the well-known Nuttall Q-function, incomplete Toronto function, Rice Ie-function, and incomplete Lipschitz-Hankel integrals. Capitalizing on the offered results, useful identities are additionally derived between the above functions and Humbert, Φ1, function as well as for specific cases of the Kampé de Fériet function. These functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems, such as cognitive radio, cooperative, and free-space optical communications as well as radar, diversity, and multiantenna systems. As an example, new closed-form expressions are derived for the outage probability over nonlinear generalized fading channels, namely, α-η-μ, α-λ-μ, and α-κ-μ as well as for specific cases of the η-μ and λ-μ fading channels. Furthermore, simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal-to-noise ratio for single-antenna and multiantenna communication systems over Rician fading channels. The accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results