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Mehdi Molu, N. Görtz:
"Performance Analysis of Amplify-and-Forward Relaying Using Fractional Calculus";
Vortrag: Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA; 04.11.2012 - 07.11.2012; in: "Proceedings Asilomar Conference on Signals, Systems, and Computers", (2012), ISSN: 1058-6393; S. 1346 - 1350.

The paper provides a simple approach for analysing the performance of Amplify-and-Forward relaying systems that are subject to block Rayleigh fading. The PDF of equivalent Source-to-Relay-to-Destination (S-R-D) link SNR involves modified Bessel functions of the second kind. Using fractional calculus mathematics, a simple, yet novel approach is introduced to rewrite the modified Bessel functions in series form using simple elementary functions. Then, we derive a novel S-R-D link SNR model which is mathematically convenient to work with. By obtaining a simple SNR model for S-R-D link, we derive the PDF of the equivalent total SNR which is observed by the destination (including both the S-R-D and S-D channels). By having a simple expression for the equivalent total SNR, performance analysis of the relaying system turns to be a simple task. Finally, we derive novel theoretical expressions for bit error probability of the system using simple elementary functions. The theoretical results are confirmed with Monte-Carlo simulations.

The paper provides a simple approach for analysing the performance of Amplify-and-Forward relaying systems that are subject to block Rayleigh fading. The PDF of equivalent Source-to-Relay-to-Destination (S-R-D) link SNR involves modified Bessel functions of the second kind. Using fractional calculus mathematics, a simple, yet novel approach is introduced to rewrite the modified Bessel functions in series form using simple elementary functions. Then, we derive a novel S-R-D link SNR model which is mathematically convenient to work with. By obtaining a simple SNR model for S-R-D link, we derive the PDF of the equivalent total SNR which is observed by the destination (including both the S-R-D and S-D channels). By having a simple expression for the equivalent total SNR, performance analysis of the relaying system turns to be a simple task. Finally, we derive novel theoretical expressions for bit error probability of the system using simple elementary functions. The theoretical results are confirmed with Monte-Carlo simulations.

Relaying, Amplify and Forward, Bessel functions

http://dx.doi.org/10.1109/ACSSC.2012.6489244

http://publik.tuwien.ac.at/files/PubDat_211708.pdf