Analytic expressions and bounds for special functions and applications in communication theory

Paschalis C. Sofotasios, Theodoros A. Tsiftsis, Yury A. Brychkov, Steven Freear, Mikko Valkama, George K. Karagiannidis

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

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 Kampéde 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.

Original languageEnglish
Article number6911973
Pages (from-to)7798-7823
Number of pages26
JournalIEEE Transactions on Information Theory
Volume60
Issue number12
DOIs
Publication statusPublished - Dec 1 2014
Externally publishedYes

Fingerprint

communication theory
Information theory
Fading channels
communication system
Communication systems
Channel capacity
Optical communication
Cognitive radio
Outages
Signal to noise ratio
radio
communications
Radar
Antennas

Keywords

  • emerging wireless technologies
  • fading channels
  • multiantenna systems
  • outage probability
  • Special functions
  • truncated channel inversion
  • wireless communication theory

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Cite this

Sofotasios, P. C., Tsiftsis, T. A., Brychkov, Y. A., Freear, S., Valkama, M., & Karagiannidis, G. K. (2014). Analytic expressions and bounds for special functions and applications in communication theory. IEEE Transactions on Information Theory, 60(12), 7798-7823. [6911973]. https://doi.org/10.1109/TIT.2014.2360388

Analytic expressions and bounds for special functions and applications in communication theory. / Sofotasios, Paschalis C.; Tsiftsis, Theodoros A.; Brychkov, Yury A.; Freear, Steven; Valkama, Mikko; Karagiannidis, George K.

In: IEEE Transactions on Information Theory, Vol. 60, No. 12, 6911973, 01.12.2014, p. 7798-7823.

Research output: Contribution to journalArticle

Sofotasios, PC, Tsiftsis, TA, Brychkov, YA, Freear, S, Valkama, M & Karagiannidis, GK 2014, 'Analytic expressions and bounds for special functions and applications in communication theory', IEEE Transactions on Information Theory, vol. 60, no. 12, 6911973, pp. 7798-7823. https://doi.org/10.1109/TIT.2014.2360388
Sofotasios PC, Tsiftsis TA, Brychkov YA, Freear S, Valkama M, Karagiannidis GK. Analytic expressions and bounds for special functions and applications in communication theory. IEEE Transactions on Information Theory. 2014 Dec 1;60(12):7798-7823. 6911973. https://doi.org/10.1109/TIT.2014.2360388
Sofotasios, Paschalis C. ; Tsiftsis, Theodoros A. ; Brychkov, Yury A. ; Freear, Steven ; Valkama, Mikko ; Karagiannidis, George K. / Analytic expressions and bounds for special functions and applications in communication theory. In: IEEE Transactions on Information Theory. 2014 ; Vol. 60, No. 12. pp. 7798-7823.
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