Skip to main content
SpringerLink
Log in

Ranking and candidacy probabilities of signal-to-noise ratio random variables under rayleigh fading

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

In design and analysis problems of wireless communication systems, a set of signal-to-noise ratio random variables may have to be dealt with. For example, this applies to transmit and/or receive diversity systems, and to scheduling and resource allocation problems. In such cases, it can be important to know how a given signal-to-noise ratio random variable ranks among the whole set of random variables. For example, in opportunistic multiuser systems, allocating resources to a user depends strongly on the probability of that user’s signal-to-noise ratio being larger than those of all (or most) other users. Considering a set of signal-to-noise ratio random variables, ranking probability is defined in this paper as the probability of a signal-to-noise ratio random variable being smaller than a given number of signal-to-noise ratio random variables in the set. Candidacy probability is defined as the probability of a signal-to-noise ratio random variable belonging to a subset of signal-to-noise ratio random variables with highest values. Closed form expressions for ranking and candidacy probabilities of signal-to-noise ratio random variables are derived, assuming Rayleigh fading. The derived probabilities are compared to those found by simulation. Comparisons confirm the correctness of the derived expressions. Simulations have been performed assuming a cellular base station that is serving a number of users. In several experiments, different levels of variation in the average signal-to-noise ratios of the users have been assumed. Results confirm the need for applying some fairness constraints in signal-to-noise ratio order-based scheduling algorithms to prevent situations where some users may not get enough access to system resources.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Liu, X., Chong, E.K., Shroff, N.B. (2001). Transmission scheduling for efficient wireless utilization. In: Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No. 01CH37213), vol. 2, pp. 776–785. IEEE.

  2. Tse, D., & Viswanath, P. (2005). Fundamentals of Wireless Communication. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  3. Liu, X., Edwin, K., Chong, K. P., & Shroff, N. B. (2001). Opportunistic transmission scheduling with resource-sharing constraints in wireless networks. IEEE Journal on Selected Areas in Communications, 19(5), 2053–2064.

    Article  Google Scholar 

  4. Goldsmith, A. (2005). Wireless Communications. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  5. Svensson, A. (2007). An introduction to adaptive QAM modulation schemes for known and predicted channels. Proceedings of the IEEE, 95(12), 2322–2336.

    Article  Google Scholar 

  6. Asadi, A., & Mancuso, V. (2013). A survey on opportunistic scheduling in wireless communications. IEEE Communications Surveys & Tutorials, 15(4), 1671–1688.

    Article  Google Scholar 

  7. Zhang, H. (1995). Service disciplines for guaranteed performance service in packet-switching networks. Proceedings of the IEEE, 83(10), 1374–1396.

    Article  Google Scholar 

  8. Knopp, R., Humblet, P. (1995). Information capacity and power control in single-cell multiuser communications. In: Proceedings of the IEEE International Conference on Communications ICC ’95, vol. 1. Seattle, WA, USA, pp. 331–335.

  9. Viswanath, P., Tse, D. N. C., & Laroia, R. (2002). Opportunistic beamforming using dumb antennas. IEEE Transactions on Information Theory, 48(6), 1277–1294.

    Article  Google Scholar 

  10. Liu, X., Chong, E.K.P., Shroff, N.B. (2003). Optimal opportunistic scheduling in wireless networks. In: Proceedings of the 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall, vol. 3. Orlando, FL, USA, pp. 1417–1421.

  11. Viswanath, P., Tse, D. N. C., & Laroia, R. (2002). Opportunistic beamforming using dumb antennas. IEEE Transactions on Information Theory, 48(6), 1277–1294.

    Article  Google Scholar 

  12. Zheng, K., Liu, F., Zheng, Q., Xiang, W., & Wang, W. (2013). A graph-based cooperative scheduling scheme for vehicular networks. IEEE Transactions on Vehicular Technology, 62(4), 1450–1458.

    Article  Google Scholar 

  13. Jalali, A., Padovani, R., Pankaj, R. (2000). Data throughput of CDMA-HDR a high efficiency-high data rate personal communication wireless system. In: Proceedings of the 2000 IEEE 51st Vehicular Technology Conference. VTC 2000-Spring, vol. 3. Tokyo, Japan, pp. 1854–1858.

  14. Mansouri, W., Ali, K.B., Zarai, F., Obaidat, M.S. (2015). Radio resource management for heterogeneous wireless networks: Schemes and simulation analysis. In: Modeling and Simulation of Computer Networks and Systems, pp. 767–792. Elsevier.

  15. Hadzi-Velkov, Z., Nikoloska, I., Chingoska, H., & Zlatanov, N. (2016). Proportional fair scheduling in wireless networks with rf energy harvesting and processing cost. IEEE Communications Letters, 20(10), 2107–2110.

    Article  Google Scholar 

  16. Cheng, Y., Fu, P., Ding, Y., Li, B., & Yuan, X. (2017). Proportional fairness in cognitive wireless powered communication networks. IEEE Communications Letters, 21(6), 1397–1400.

    Article  Google Scholar 

  17. Li, X., Shankaran, R., Orgun, M. A., Fang, G., & Xu, Y. (2018). Resource allocation for underlay D2D communication with proportional fairness. IEEE Transactions on Vehicular Technology, 67(7), 6244–6258.

    Article  Google Scholar 

  18. Nguyen, T.T.N., Brun, O., Prabhu, B.J. (2019). An algorithm for improved proportional-fair utility for vehicular users. In: International Conference on Analytical and Stochastic Modeling Techniques and Applications, pp. 115–130. Springer

  19. Liu, F., Mähönen, P., Petrova, M. (2016). Proportional fairness-based power allocation and user set selection for downlink noma systems. In: 2016 IEEE International Conference on Communications (ICC), pp. 1–6. IEEE.

  20. Al-Wani, M.M., Sali, A., Ali, B.M., Salah, A.A., Navaie, K., Leow, C.Y., Noordin, N.K., Hashim, S.J. (2019). On short term fairness and throughput of user clustering for downlink non-orthogonal multiple access system. In: 2019 IEEE 89th Vehicular Technology Conference (VTC2019-Spring), pp. 1–6. IEEE

  21. Banat, M.M., Shatnawi, R. (2021) Round opportunistic fair downlink scheduling in wireless communications networks. In: Proceedings of the 1st International Congress on Engineering Technologies: EngiTek 2020, 16-18 June 2020, Irbid, Jordan, p. 116. CRC Press.

  22. Banat, M.M., Shatnawi, R.F. (2022). Round opportunistic fair wireless downlink scheduling with performance guarantees. In: 2022 13th International Conference on Information and Communication Systems (ICICS), pp. 448–45. IEEE

  23. Wolfe, D. A. (2012). Nonparametrics: Statistical Methods Based on Ranks and Its Impact on the Field of Nonparametric Statistics (pp. 1101–1110). Boston, MA: Springer. https://doi.org/10.1007/978-1-4614-1412-4_96

    Book  Google Scholar 

  24. Morsi, R., Michalopoulos, D. S., & Schober, R. (2015). Multiuser scheduling schemes for simultaneous wireless information and power transfer over fading channels. IEEE Transactions on Wireless Communications, 14(4), 1967–1982.

  25. Almekhlafi, M., Arfaoui, M.A., Elhattab, M., Assi, C., Ghrayeb, A. (2021). Joint scheduling of embb and urllc services in ris-aided downlink cellular networks. In: 2021 International Conference on Computer Communications and Networks (ICCCN), pp. 1–9. IEEE.

  26. Zhang, Z., Sun, Y., Sabharwal, A., Chen, Z. (2018). Impact of channel state misreporting on multi-user massive mimo scheduling performance. In: IEEE INFOCOM 2018-IEEE Conference on Computer Communications, pp. 917–925. IEEE

  27. Pawar, A. R., Kashyap, S., & Chouhan, S. (2021). Impact of max-min power control, channel estimation and user grouping strategies on uplink massive mimo-noma systems. IEEE Transactions on Vehicular Technology, 70(8), 7858–7869.

    Article  Google Scholar 

  28. Dommel, J., Faehse, S., Thiele, L. (2017). On power allocation and user grouping for sparse coded non-orthogonal multiple access in the downlink. In: 2017 IEEE 86th Vehicular Technology Conference (VTC-Fall), pp. 1–4. IEEE

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, Jordan University of Science and Technology, PO Box 3030, Irbid, 22110, Jordan

    Mohammad M. Banat

  2. Department of Electrical Engineering and Information Technology, Faculty of Computer Science, Electrical Engineering and Mathematics, Paderborn University, 33098, Paderborn, Germany

    Osamah K. El-Radaideh

Authors
  1. Mohammad M. Banat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Osamah K. El-Radaideh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad M. Banat.

Ethics declarations

Conflicts of interest

The authors have not disclosed any competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banat, M.M., El-Radaideh, O.K. Ranking and candidacy probabilities of signal-to-noise ratio random variables under rayleigh fading. Telecommun Syst 83, 357–364 (2023). https://doi.org/10.1007/s11235-023-01020-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-023-01020-6

Keywords

Search

Navigation