Performance analysis of amplify-and-forward relaying using fractional calculus

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.