A Novel Equivalent Definition of Modified Bessel Functions for Performance Analysis of Multi-Hop Wireless Communication Systems

• Published in: IEEE access Vol. 5; pp. 7594 - 7605
• Main Authors: Molu, Mehdi M., Pei Xiao, Khalily, Mohsen, Lei Zhang, Tafazolli, Rahim
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: amplify and forward (AF); Analytical models; Bessel functions; Capacity planning; Codes; Equivalence; Mathematical analysis; maximum ratio combining (MRC); Modified bessel function of second kind; Probability; Probability density function; Probability density functions; Receivers; Relay; Relaying; Relays; Signal processing; Signal to noise ratio; Statistical analysis; Statistical models; Wireless communication systems; Wireless communications
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2017.2685085

A statistical model is derived for the equivalent signal-to-noise ratio of the Source-to-Relay-to-Destination (S-R-D) link for Amplify-and-Forward (AF) relaying systems that are subject to block Rayleigh-fading. The probability density function and the cumulated density function of the S-R-D link SNR involve modified Bessel functions of the second kind. Using fractional-calculus mathematics, a novel approach is introduced to rewrite those Bessel functions (and the statistical model of the S-R-D link SNR) in series form using simple elementary functions. Moreover, a statistical characterization of the total receive-SNR at the destination, corresponding to the S-R-D and the S-D link SNR, is provided for a more general relaying scenario in which the destination receives signals from both the relay and the source and processes them using maximum ratio combining (MRC). Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained. The analytical results presented in this paper provide a theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver.