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 language | English |
|---|---|
| Article number | 6911973 |
| Pages (from-to) | 7798-7823 |
| Number of pages | 26 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 60 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - Dec 1 2014 |
| Externally published | Yes |
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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
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 journal › Article
}
TY - JOUR
T1 - Analytic expressions and bounds for special functions and applications in communication theory
AU - Sofotasios, Paschalis C.
AU - Tsiftsis, Theodoros A.
AU - Brychkov, Yury A.
AU - Freear, Steven
AU - Valkama, Mikko
AU - Karagiannidis, George K.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - 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.
AB - 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.
KW - emerging wireless technologies
KW - fading channels
KW - multiantenna systems
KW - outage probability
KW - Special functions
KW - truncated channel inversion
KW - wireless communication theory
UR - http://www.scopus.com/inward/record.url?scp=84912098015&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84912098015&partnerID=8YFLogxK
U2 - 10.1109/TIT.2014.2360388
DO - 10.1109/TIT.2014.2360388
M3 - Article
AN - SCOPUS:84912098015
VL - 60
SP - 7798
EP - 7823
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 12
M1 - 6911973
ER -