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

Solutions to Integrals Involving the Marcum Q-Function and Applications

Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals. The offered expressions are both convenient and versatile, which is particularly useful in applications relating to natural sciences and engineering, including wireless cpmmunications and signal processing. To this end, they are employed in the derivation of the channel capacity for fixed rate and channel inversion in the case of correlated multipath fading and switched diversity.Comment: 15 Pages, 2 Figure

Razvoj metoda i algoritama za procenu performansi komunikacionih sistema primenom aproksimacija specijalnih funkcija

The intensive development of wireless communication systems has been accompanied by the need to develop methods and algorithms for implementing appropriate approximations of special functions in order to efficiently estimate the corresponding performance of these services through their application. In order to evaluate the behavior of digital communications systems, it is necessary to estimate standard performance measures for the observed wireless communications systems, various modulation types application, detection types, as well as channel models, and observe relations between performance and key values of system parameters. The analysis of the average bit error rate at reception for the applied modulation format is one of the tools for assessing service performance, that describes the nature of the wireless communication system in the best manner. In order to analytically evaluate the average bit error rate for the applied modulation format, it is necessary to perform the most accurate implementation of the approximation of special functions erfc(x), erf (x), Marcum Q, in the widest input range values. The dissertation will present composite methods of the special functions’ approximations. In addition to the simplicity of realization in approximating the observed functions, the aspect of robustness of approximations absolute and relative error values in a wide range of input parameters values will be considered. The advantages of the proposed solutions will be highlighted by direct comparison with the absolute and relative errors obtained by using the known special functions’ approximations from the literature. Furthermore, when transferring information through fading communication channels, for cases of application of proposed special functions’ approximations, it will be proved that system performance can be determined more easily by applying solutions proposed in the dissertation. In this way, it would be easier to determine the probability of the error of communication systems due to different types of fading existance in the channel. By comparing predicted values of the average bit error rate at reception, when transmitting signals through various communication channels medias, for cases of application of existing, previously proposed special functions’ approximations, with the average bit error rate at reception obtained by calculation based on the proposed approximation solutions, it will be shown that communication performances can be calculated more precisely. Proposed approximations could also be used in the source coding of the signal and could simplify design and realization of the quantizers