Abstract
Relying on the fact that, cascaded \(\alpha\)–\(\mu\) distribution provide simplified and excellent fitting to the measurement data compared to the other composite fading model. This work investigates the performance of versatile cascaded non-identical \(\alpha\)–\(\mu\) fading channel. The \(\alpha\)–\(\mu\)/\(\alpha\)–\(\mu\) model has emerged as a generalization of the cascaded line-of-sight multipath fading channels such as Rayleigh, Weibull, and Nakagami-m etc., by appropriately choosing the values of \(\alpha\) and \(\mu\) parameters. More specifically, we present novel closed-form formulations for some of the interested fundamental statistics of the wireless communication system, namely, generalized moment, moment generating function, Error rate (coherent/non-coherent), channel capacity under different transmission policy. The results are expressed in terms of easily implementable well-known Fox’s H function. Also, an asymptotic investigation of all the mentioned metrics is performed, so as to gain more insights of the impact of the key system parameters. The proposed expressions provide flexibility to satisfy different propagation scenarios.
References
Yacoub, M. D. (2007). The \(\kappa\)–\(\mu\) distribution and the \(\eta\)–\(\mu\) distribution. IEEE Antennas and Propag Magazine, 49(1), 68–81.
Yacoub, M. D. (2007). The \(\alpha\)–\(\mu\) distribution: A physical fading model for the Stacy distribution. IEEE Transactions on Vehicular Technology, 56(1), 27–34.
Fathi, Y., & Tawfik, M. H. (2012). Versatile performance expression for energy detector over \(\alpha\)–\(\mu\) generalised fading channels. Electronics Letters, 48(17), 1081–1082.
Leonardo, E. J., & Yacoub, M. D. (2015). The product of two \(\alpha\)-\(-\mu\) variates and the composite \(\alpha\)–\(\mu\) multipath-shadowing model. IEEE Transactions on Vehicular Technology, 64(6), 2720–2725.
Bhargav, N., Nogueira da Silva, C. R., et al. (2017). The product of two \(\kappa\)–\(\mu\) variates and the \(\kappa\)–\(\mu\)/\(\kappa\)–\(\mu\) composite fading model. In2017 In Proceedings IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC) (pp. 1–5).
Bhargav, N., Nogueira da Silva, C. R., et al. (2018). On the product of two \(\kappa\)–\(\mu\) random variables and its application to double and composite fading channels. IEEE Transactions on Wireless Communications, 17(4), 2457–2470.
Leonardo, E. J., & Yacoub, M. D. (2015). Product of \(\alpha\)–\(\mu\) variates. IEEE Wireless Communication Letters, 1(1), 1–4.
Nogueira da Silva, C. R., Leonardo, E. J., & Yacoub, M. D. (2018). Product of two envelopes taken from \(\alpha\)–\(\mu\), \(\kappa\)–\(\mu\), and \(\eta\)-\(\mu\) distributions. IEEE Transactions on Communications, 63(3), 1284–1295.
Huang, H., & Yuan, C. (2018). Product of \(\kappa\)–\(\mu\) and \(\alpha\)–\(\mu\) distributions and their composite fading distributions. In IEEE/CIC International Conference on Communications in China (ICCC) (pp. 389–393).
Badarneh, O. S., & da Costa, D. B. (2019). Cascaded fluctuating two-ray fading channels. IEEE Communications Letters, 23(9), 1497–1500.
Huang, H., & Yuan, C., (2019). Ergodic capacity of composite fading channels in cognitive radios with series formula for product of \(\kappa\)–\(\mu\) and \(\alpha\)–\(\mu\) fading distributions. IEICE Transactions on Communications, E103.B(4), 458–466.
Badarneh, O. S. (2016). The \(\alpha\)–\(\mu\)/\(\alpha\)-\(-\mu\) composite multipath-shadowing distribution and its connection with the extended generalized-K distribution. International Journal of Electronic Communications, 70, 1211–1218.
Kundu, M. K., & Badrudduza, A. S. M. (2019). Information theoretic security over \(\alpha\)–\(\mu\)/\(\alpha\)–\(\mu\) composite multipath fading channel. Proceedings IEEE International Conference on Telecommunications and Photonics (ICTP), 2019, 1–4.
Kong, L., Kaddoum, G., & da Costa, D. B. (2018). Cascaded \(\alpha {-}\mu\) fading channels: reliability and security analysis. IEEE Access, 6, 41978–41992.
Leonardo, E. J., Yacoub, M. D., & de Souza, R. A. A. (2016). Ratio of products of \(\alpha\)–\(\mu\) variates. IEEE Communications Letters, 20(5), 1022–1025.
Boddiscatz, C. D. (1992). Finding an H-function distribution for the sum of independent H-function variates. Ph.D. dissertation, The University of Texas, Austin.
Mathai, A., Saxena, R. K., & Haubold, H. J. (2010). The H-function: Theory and Applications, 1st edn. Springer, Berlin.
Chauhan, P. S., Rana, V., Kumar, S., Soni, S. K., & Pant, D. (2019). Performance analysis of wireless communication system over non-identical cascaded generalised gamma fading channels. International Journal of of Communications System (pp. 1–15).
Chauhan, P. S., Tiwari, D., & Soni, S. K. (2017). New analytical expressions for the performance metrics of wireless communication system over Weibull/Lognormal composite fading. International Journal of Electronic Communications, 82, 397–405.
Badarneh, O. S., & Aloqlah, M. S. (2016). Performance analysis of digital communication systems over \(\alpha\)–\(\eta\)–\(\mu\) fading channels. IEEE Transactions of Vehicular Technlogy, 65(10), 7972–7981.
Chauhan, P. S., Kumar, S., & Soni, S. K. (2019). New approximate expressions of average symbol error probability, probability of detection and AUC with MRC over generic and composite fading channels. International Journal of Electronic Communications, 99, 119–129.
Chauhan, P. S., & Soni, S. K. (2018). New analytical expressions for ASEP of modulation techniques with diversity over Lognormal fading channels with application to interference-limited environment. Wireless Personal Communications, 92(2), 695–716.
Al-Hmood, H., & Al-Raweshidy, H. S. (2018). Unified approaches based effective capacity analysis over composite \(\alpha\)–\(\eta\)–\(\mu\)/gamma fading channels. Electronic Letters, 54(13), 852–853.
Prodnikov, A. P., Brychkov, Yu. A., & Marichev, O. I. (1986). Integral and Series Volume 3: More special function. Gordon and Breach Science Publisher.
Gradshteyn, I. S., & Ryzhik, I. M. (2007). Table of Integrals, Series, and Products (7th ed.). San Diego, CA: Academic Press.
Prudnikov, A. P., Brychkov, Y. A., & Marichev, O. I. (1986). Integrals and series volume 2: Special functions, 1st edn. Gordon and Breach Science Publishers.
Soulimani, A., Benjillali, M., Chergui, H., & B. da Costa, D. (2015). Performance analysis of MQAM multihop relaying over mm wave Weibull fading channels. In International conference on wireless networks and mobile communications (WINCOM15) (pp. 1–19).
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Chauhan, P.S., Kumar, S. & Soni, S.K. Performance Analysis of Non-identical Cascaded \(\alpha\)–\(\mu\) Fading Channels. Wireless Pers Commun 116, 3553–3566 (2021). https://doi.org/10.1007/s11277-020-07864-4
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DOI: https://doi.org/10.1007/s11277-020-07864-4