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Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory
This work 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
function, the incomplete Toronto function, the Rice -function and the
incomplete Lipschitz-Hankel integrals.
Capitalizing on the offered results, useful identities are additionally
derived between the above functions and the Humbert, , function as
well as for specific cases of the Kamp de Friet function. These functions can be considered 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 multi-antenna systems. As an example, new closed-form expressions are
derived for the outage probability over non-linear generalized fading channels,
namely, , and
as well as for specific cases of the and
fading channels. Furthermore, simple expressions are presented
for the channel capacity for the truncated channel inversion with fixed rate
and the corresponding optimum cut-off signal-to-noise ratio for single-and
multi-antenna communication systems over Rician fading channels. The accuracy
and validity of the derived expressions is justified through extensive
comparisons with respective numerical results.Comment: 63 page