Skip to main content
Log in

Generalized carrier to interference ratio analysis for shotgun cellular systems in multiple dimensions over composite Rayleigh–Lognormal (Suzuki) fading

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

This paper analyzes the carrier-to-interference ratio (CIR) of the so-called shotgun cellular systems (SCSs) in \(\tau \) dimensions (\(\tau =1, 2,\) and 3). SCSs are wireless communication systems with randomly placed base stations (BSs) over the entire plane according to a Poisson point process in \(\tau \) dimensions. Such a system can model a dense cellular or wireless data network deployment, where locations of BSs end up being close to random due to constraints other than optimal coverage. In this paper we apply SCSs in \(\tau \) dimensions and also, in addition to path-loss and shadow fading, consider Rayleigh fading as a most commonly used distribution to model multi-path fading, and analyze the CIR over the composite fading channel [i.e., Rayleigh–Lognormal (or Suzuki) fading channel], and determine a generalized expression for the distribution of CIR and obtain the tail probability of CIR.

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

Access this article

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
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Al-Ahmadi, S., & Yanikomeroglu, H. (2009). On the approximation of the generalized-K PDF by a gamma PDF using the moment matching method. In Proceedings of the IEEE wireless communications and networking conference (WCNC’09), Budapest, Hungary. https://doi.org/10.1109/WCNC.2009.4917849.

  2. Andrews, J. G., Baccelli, F., & Ganti, R. K. (2011). A tractable approach to coverage and rate in cellular networks. IEEE Transactions on Communications, 59(11), 3122–3134.

    Article  Google Scholar 

  3. Atapattu, S., Tellambura, C., & Jiang, H. (2010). Representation of composite fading and shadowing distributions by using mixtures of Gamma distributions. In Proceedings of the wireless communications and networking conference (WCNC’10), Sydney, Australia. https://doi.org/10.1109/WCNC.2010.5506173.

  4. Blanc, S. (2016). Physical layer security of wireless transmissions over fading channels. Ann Arbor: ProQuest Dissertations Publishing.

    Google Scholar 

  5. Brown, T. X. (1998). Analysis and coloring of a shotgun cellular system. In Proceedings of the IEEE radio and wireless conference (RAWCON), Colorado Springs, USA. https://doi.org/10.1109/RAWCON.1998.709134.

  6. Brown, T. X. (1999). Dynamic channel assignment in shotgun cellular systems. In Proceedings of the IEEE radio and wireless conference (RAWCON), Denver, USA. https://doi.org/10.1109/RAWCON.1999.810951.

  7. Brown, T. X. (2000). Practical cellular performance bounds via shotgun cellular systems. IEEE Journal on Selected Areas in Communications, 18(11), 2443–2455.

    Article  Google Scholar 

  8. 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, 99(2), 695–716.

    Article  Google Scholar 

  9. 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. AEU-International Journal of Electronics and Communications, 82, 397–405.

    Article  Google Scholar 

  10. Dhillon, H. S., & Andrews, J. G. (2014). Downlink rate distribution in heterogeneous cellular networks under generalized cell selection. IEEE Wireless Communications Letters, 3(1), 42–45.

    Article  Google Scholar 

  11. Dinh, T. M. T., Nguyen, Q. T., & Sandrasegaran, K. (2017). A closed-form of cooperative detection probability using EGC-based soft decision under Suzuki fading. In Proceedings of the 11th international conference on signal processing and communication systems (ICSPCS’17), Surfers Paradise, Australia. https://doi.org/10.1109/ICSPCS.2017.8270508.

  12. El-Bahaie, E. H., & Al-Hussaini, E. K. (2017). Novel results for the performance of single and double stages cognitive radio systems through Nakagami-m fading and log-normal shadowing. Telecommunication Systems, 65(4), 729–737.

    Article  Google Scholar 

  13. Hansen, F., & Meno, F. I. (1977). Mobile fading-rayleigh and lognormal superimposed. IEEE Transactions on Vehicular Technology, 26(4), 332–335.

    Article  Google Scholar 

  14. Keeler, H. P., BÅaszczyszyn, B. & Karray, M. K. (2013). SINR-based k-coverage probability in cellular networks with arbitrary shadowing. In Proceedings of the IEEE international symposium on information theory proceedings (ISIT’13), Istanbul, Turkey. https://doi.org/10.1109/ISIT.2013.6620410.

  15. Khodadoust, A. M., & Hodtani, G. A. (2018). Carrier to interference ratio analysis in shotgun cellular systems over a generalized shadowing distribution. Wireless Networks. https://doi.org/10.1007/s11276-018-1742-z.

  16. Kibria, Mirza G., Villardi, G. P., Liao, W. S., Nguyen, K., Ishizu, K., & Kojima, F. (2017). Outage analysis of offloading in heterogeneous networks: Composite fading channels. IEEE Transactions on Vehicular Technology, 66(10), 8990–9004.

    Article  Google Scholar 

  17. Krstić, D., Suljović, S., Milić, D., Panić, S., & Stefanović, M. (2018). Outage probability of macrodiversity reception in the presence of Gamma long-term fading, Rayleigh short-term fading and Rician co-channel interference. Annals of Telecommunications. https://doi.org/10.1007/s12243-017-0593-4.

  18. Kumar, N., & Bhatia, V. (2018). Performance evaluation of QAM schemes for multiple AF relay network under Rayleigh fading channels. Wireless Personal Communications, 99(1), 567–580.

    Article  Google Scholar 

  19. Lam, S. C., Sandrasegaran, K., & Ghosal, P. (2017). Performance analysis of frequency reuse for PPP networks in composite Rayleigh–Lognormal fading channel. Wireless Personal Communications, 96(1), 989–1006.

    Article  Google Scholar 

  20. Laourine, Amine, Alouini, M. S., Affes, S., & Stephenne, A. (2009). On the performance analysis of composite multi-path/shadowing channels using the G-distribution. IEEE Transactions on Communications, 57(4), 1162–1170.

    Article  Google Scholar 

  21. Macdonald, V. (1979). The cellular concept. The Bell System Technical Journal, 58, 15–41.

    Article  Google Scholar 

  22. Madhusudhanan, P., Restrepo, J. G., Liu, Y. E., Brown, T. X., & Baker, K. (2009). Carrier to interference ratio analysis for the shotgun cellular system. In Proceeding of the global telecommunications conference (GLOBECOM’09), Honolulu, USA. https://doi.org/10.1109/GLOCOM.2009.5425785.

  23. Madhusudhanan, P., Restrepo, J. G., Liu, Y., Brown, T. X., & Baker, K. (2010). Generalized carrier to interference ratio analysis for the shotgun cellular system in multiple dimensions. CoRR. arXiv:1002.3943.

  24. Madhusudhanan, P., Restrepo, J. G., Liu, Y., Brown, T. X., & Baker, K. R. (2011). Multi-tier network performance analysis using a shotgun cellular system. In Proceedings of the global telecommunications conference (GLOBECOM’11), Kathmandu, Nepal. https://doi.org/10.1109/GLOCOM.2011.6134293.

  25. Madhusudhanan, P., Restrepo, J. G., Liu, Y. E., Brown, T. X., & Baker, K. R. (2012). Stochastic ordering based carrier-to-interference ratio analysis for the shotgun cellular systems. IEEE Wireless Communications Letters, 1(6), 565–568.

    Article  Google Scholar 

  26. Madhusudhanan, P., Restrepo, J. G., Liu, Y., Brown, T. X., & Baker, K. R. (2014). Downlink performance analysis for a generalized shotgun cellular system. IRE Transactions on Wireless Communications, 13(12), 6684–6696.

    Article  Google Scholar 

  27. Populis, A. (1984). Probability, random variables and stochastic processes. New York: McGraw-Hill.

    Google Scholar 

  28. Reig, J., & Rubio, L. (2013). Estimation of the composite fast fading and shadowing distribution using the log-moments in wireless communications. IEEE Transactions on Wireless Communications, 12(8), 3672–3681.

    Article  Google Scholar 

  29. Shah, S. M., Samar, R., & Raja, M. A. Z. (2018). Fractional-order algorithms for tracking Rayleigh fading channels. Nonlinear Dynamics, https://doi.org/10.1007/s11071-018-4122-4.

  30. Singh, R., & Rawat, M. (2016). Closed-form distribution and analysis of a combined nakagami-Lognormal shadowing and unshadowing fading channel. Journal of Telecommunications and Information Technology, 4, 81–87.

    Google Scholar 

  31. Sofotasios, P. C., & Freear, S. (2015). A generalized non-linear composite fading model. CoRR. arXiv:1505.03779.

  32. Tepedelenlioglu, C., Rajan, A., & Zhang, Y. (2011). Applications of stochastic ordering to wireless communications. IEEE Transactions on Wireless Communications, 10(12), 4249–4257.

    Article  Google Scholar 

  33. Tiwari, D., Soni, S., & Chauhan, P. S. (2017). A new closed-form expressions of channel capacity with MRC, EGC and SC over Lognormal fading channel. Wireless Personal Communications, 97(3), 4183–4197.

    Article  Google Scholar 

  34. Yilmaz, F., & Alouini, M. S. (2010). A new simple model for composite fading channels: Second order statistics and channel capacity. In Proceedings of the 7th international symposium on wireless communication systems (ISWCS’10), York, UK. https://doi.org/10.1109/ISWCS.2010.5624350.

  35. Yilmaz, F., & Alouini, M. S. (2010). Extended generalized-K (EGK): a new simple and general model for composite fading channels. CoRR. arXiv:1012.2598.

  36. Yoo, S.K., Sofotasios, P. C., Cotton, S. L., Matthaiou1, M., Valkama, M., & Karagiannidis, G. K. (2015). The \(\eta \) \(\mu \) / inverse gamma composite fading model. In Proceedings of the IEEE 26th annual international symposium on personal, indoor, and mobile radio communications (PIMRC’15), Hong Kong, China. https://doi.org/10.1109/PIMRC.2015.7343288.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ali Mohammad Khodadoust.

Ethics declarations

Conflict of interest

All authors declare that they have no competing interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khodadoust, A.M., Khodadoust, J. Generalized carrier to interference ratio analysis for shotgun cellular systems in multiple dimensions over composite Rayleigh–Lognormal (Suzuki) fading. Telecommun Syst 70, 171–183 (2019). https://doi.org/10.1007/s11235-018-0478-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-018-0478-5

Keywords

Navigation