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EC Analysis of Multi-Antenna System over 5G and Beyond Networks and its Application to IRS-Assisted Wireless Systems

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Abstract

Recently, the theory of effective rate has attracted much attention, since it can take the delay aspect into account when performing channel capacity analysis. In this paper, we study the effective throughput performance of the multi-antenna system over the Beaulieu-Xie fading channel. Both the probability density function-based approach and the moment generating function-based approaches are used to derive the closed-form expressions of the effective throughput for the multi-antenna system. The application of the proposed solution for the IRS-assisted indoor wireless system over the Beaulieu-Xie fading channel is also discussed. Interesting insights related to the channel fading parameters and the number of reflecting elements on the system performance are drawn and discussed conclusively. In addition to this, we also derived the simplified high-power and low-power approximation that enables direct interpretation of the system performance concerning system fading parameters. The accuracy of the derived theoretical expressions is validated through Monte-Carlo simulation results. The results presented in this study can be used in designing the communication system for real-time applications in femtocells and high-speed trains.

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References

  1. Kaur, M., & Yadav, R. K. (2021). Effective capacity analysis over Fisher-Snedecor F fading channels with MRC reception. Wireless Personal Communications, 121, 1693–1705.

    Article  Google Scholar 

  2. Wu, D., & Negi, R. (2003). Effective capacity: A wireless link model for support of quality of service. IEEE Transactions on Wireless Communications, 2(4), 630–643.

    Google Scholar 

  3. Khalek, A., & Dawy, Z. (2012). Energy-efficient cooperative video distribution with statistical QoS provisions over wireless networks. IEEE Transactions on Mobile Computing, 11(7), 1223–1236.

    Article  Google Scholar 

  4. Balasubramanian, A., & Miller, S. (2010). The effective capacity of a time division downlink scheduling system. IEEE Transactions on Communications, 58(1), 73–78.

    Article  Google Scholar 

  5. Agarwal, S., De, S., Kumar, S., & Gupta, H. (2015). QoS-aware downlink cooperation for cell-edge and handoff users. IEEE Transactions on Vehicular Technology, 64(6), 2512–2527.

    Article  Google Scholar 

  6. Qiao, D., Gursoy, M., & Velipasalar, S. (2013). Effective capacity of two hop wireless communication systems. IEEE Transactions on Information Theory, 59(2), 873–885.

    Article  MathSciNet  Google Scholar 

  7. Chauhan, P. S., Kumar, S. K., Upadhayay, V. K., & Soni, S. K. (2021). Unified approach to effective capacity for generalised fading channels. Physical Communication, 45, 101278.

    Article  Google Scholar 

  8. Benkhelifa, F., Rezki, Z., Alouini, M. S., (2013) Effective capacity of nakagami-m fading channels with full channel state information in the low power regime. In IEEE 24th Annual Int Symp Personal, Indoor, and Mobile Radio Commun (PIMRC), 2013, pp. 1883–1887.

  9. Yadav, P., Kumar, S., Kumar, R., (2021) Analysis of EC over Gamma shadowed α–η–μ fading channel. In IOP Conference series: Material Science & Engineering, Nirjuli, India, p. 012010.

  10. Yadav,P., Kumar, S., Kumar, R. (2020) Effective capacity analysis over α–κ–μ/Gamma composite fading channel. In IEEE Internatational Conference on Advances in Computing,Communication Control and Networking (ICACCCN), Greater Noida, India, pp. 587–592.

  11. Yadav, P., Kumar, S., & Kumar, R. (2020). Effective capacity analysis over generalized lognormal shadowed composite fading channels. Internet Technology Letters, 3(5), e171.

    Article  Google Scholar 

  12. Yoo, S. K., Cotton, S., Sofotasios, P., Muhaidat, S., & Karagiannidis, G. (2020). Effective capacity analysis over generalized composite fading channels. IEEE Access, 8, 123756–123764.

    Article  Google Scholar 

  13. Singh,R., & Rawat, M. (2019) On the performance analysis of effective capacity of double shadowed κ – μ fading channels. In IEEE Region 10 Conference (TENCON), Kochi, India, pp. 806–810.

  14. You, M., Sun, H., Jiang, J., & Zhang, J. (2016). Effective rate analysis in weibull fading channels. IEEE Wireless Communication Letters, 5(4), 340–343.

    Article  Google Scholar 

  15. Matthaiou, M., Alexandropoulos, G. C., Ngo, H. Q., & Larsson, E. G. (2012). Analytic framework for the effective rate of MISO fading channels. IEEE Transactions on Communications, 60(6), 1741–1751.

    Article  Google Scholar 

  16. Zhang, J., Dai, L., Wang,Z., Ng, D., Gerstacke, W. (2015) Effective rate analysis of MISO systems over α-μ fading channels. In Proceeding Global Communications Conference (GLOBECOM), San Diego, CA, 2015, pp. 1–6.

  17. Yilmaz, F., & Alouini, M. (2012). A unified MGF-based capacity analysis of diversity combiners over generalized fading channels. IEEE Transactions on Communications, 60(3), 862–875.

    Article  Google Scholar 

  18. Larsson, E. G., Edfors, O., Tufvesson, F., & Marzetta, T. L. (2014). Massive MIMO for next generation wireless systems. IEEE Communications Magazine, 52(2), 186–195.

    Article  Google Scholar 

  19. Wu, Q., & Zhang, R. (2019). Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless network. IEEE Communications Magazine, 58(1), 106–112.

    Article  Google Scholar 

  20. Hou, T., et al. (2020). Reconfigurable intelligent surface aided NOMA networks. IEEE Journal on Selected Areas in Communications, 38(11), 2575–2588.

    Article  Google Scholar 

  21. Pan, C., et al. (2020). Intelligent reflecting surface aided MIMO broadcasting for simultaneous wireless information and power transfer. IEEE Journal on Selected Areas in Communications, 38(8), 1719–1734.

    Article  Google Scholar 

  22. Yang, L., et al. (2020). Secrecy performance analysis of RIS-aided wireless communication systems. IEEE Transactions on Vehicular Technology, 69(10), 12296–12300.

    Article  Google Scholar 

  23. Yang, L., Guo, W., & Ansari, I. S. (2020). Mixed dual-hop FSO-RF communication systems through reconfigurable intelligent surface. IEEE Communications Letters, 24(7), 1558–1562.

    Article  Google Scholar 

  24. Li, S., Duo, B., Yuan, X., Liang, Y. C., & Di Renzo, M. (2020). Reconfigurable intelligent surface assisted UAV communication: Joint trajectory design and passive beamforming. IEEE Wireless Communications Letters, 9(5), 716–720.

    Article  Google Scholar 

  25. Odeyemi, K. O., Owolawi, P. A., & Olakanmi, O. O. (2020). Reconfigurable intelligent surface assisted mobile network with randomly moving user over fisher-snedecor fading channel. Physical Communication, 43, 101186.

    Article  Google Scholar 

  26. Nagarajan, D., & Balakrisnan, R. (2021). Error probability and throughput analysis of IRS-assisted wireless system over generalized κ–μ fading channels. Wireless Personal Communications. https://doi.org/10.1007/s11277-021-08740-5 [Online].

    Article  Google Scholar 

  27. Kaur, M., & Yadav, R. K. (2020). Performance analysis of Beaulieu-Xie fading channel. Transactions on Emerging Telecommunications Technologies, 31, e3949.

    Article  Google Scholar 

  28. Beaulieu, N. C., & Jiandong, X. (2015). A novel fading model for channels with multiple dominant specular components. IEEE Wireless Communications Letters, 4(1), 54–57.

    Article  Google Scholar 

  29. Chauhan, P. S., Kumar, S., & Soni, S. K. (2020). On the physical layer security over Beaulieu-Xie fading channel. AEU—International Journal of Electronics and Communications, 113, 152940.

    Google Scholar 

  30. Gradshteyn, I. S., & Ryzhik, I. M. (2007). Table of integrals, series, and products (7th ed.). Academic Press.

  31. Brychkov, Y. A., Marichev, O. I., & Prudnikov, A. P. (1990). Integrals and series: More special functions (3rd ed.). Gordon & Breach Sci. Publ.

  32. Wolfram. (2020) Wolfram function site. [Online]. http://functions.wolfram.com/PDF/MeijerG.pdf

  33. Kang, M., & Alouini, M. S. (2006). Capacity of MIMO Rician channels. IEEE Transactions on Wireless Communications, 5(1), 112–122.

    Article  Google Scholar 

  34. Wolfram. (2020) Wolfram function site. [Online]. http://functions.wolfram.com

  35. You, M., Sun, H., Jiang, J., & Zhang, J. (2017). Unified framework for the effective rate analysis of wireless communication systems over MISO fading channels. IEEE Transactions on Communications, 65(4), 1775–1785.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science & Engineering, Delhi Technological University, Delhi, India

    Manpreet Kaur & Rajesh Kumar Yadav

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  1. Manpreet Kaur
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  2. Rajesh Kumar Yadav
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Correspondence to Manpreet Kaur.

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Appendix

Appendix

The error in (12) by truncating the series by D number of terms can be given by

$$E_{D} = \sum\limits_{d = D}^{\infty } {\frac{{\left( {mkL} \right)^{d} }}{d!}} U\left( {A;A - mL + 1 - d;\frac{\eta L}{\rho }} \right)$$
(38)

Putting g = d−D in the above equation and rearranging we get

$$E_{D} = \left( {mkL} \right)^{D} \sum\limits_{g = 0}^{\infty } {\frac{{\left( {mkL} \right)^{g} }}{{\Gamma \left( {D + g + 1} \right)}}} U\left( {A;A - mL + 1 - D - g;\frac{\eta L}{\rho }} \right)$$
(39)

Since \(U\left( {A;A - mL + 1 - D - g;\frac{\eta L}{\rho }} \right)\) is a monotonically decreasing function with respect to g. Therefore, \(E_{D}\) can be upper bounded as

$$E_{D} \le \left( {mkL} \right)^{D} \sum\limits_{g = 0}^{\infty } {\frac{{\left( {mkL} \right)^{g} }}{{\Gamma \left( {D + g + 1} \right)}}} U\left( {A;A - mL + 1 - D;\frac{\eta L}{\rho }} \right)$$
(40)

Applying Eq. (39) of [15] in the above equation, the closed-form expression of the upper bound of the truncation error can be obtained as Eq. (13)

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Kaur, M., Yadav, R.K. EC Analysis of Multi-Antenna System over 5G and Beyond Networks and its Application to IRS-Assisted Wireless Systems. Wireless Pers Commun 124, 1861–1881 (2022). https://doi.org/10.1007/s11277-021-09434-8

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