Skip to main content
Log in

Stochastic geometry modeling and analysis of downlink coverage and rate in small cell network

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

Due to the massive wireless traffic demand in fifth generation (5G) network, small cell have been attracted growing attention as a key solution and scalable approach for 5G deployments. However, to provide appropriate Quality of Service (QoS), mobile service providers need to study and analyze coverage with and without interference coordination. In this paper, we provide an analytical framework based on Stochastic Geometry to investigate downlink coverage analysis by taking into account mmWave and Nakagami fading. These metrics are analyzed with path loss laws in both cases namely; Line of Site (LOS) and Non Line of Site (NLOS). we derive a general expression of coverage probability according to signal-to-interference-plus-noise ratio (SINR) by assuming directional Beamforming. Then, downlink rate probability is obtained for good network reliability. Moreover, we propose an efficient approach to explore the coverage characteristics under cognitive interference coordination strategies. Finally, simulations results are verified using Monte Carlo Simulations.

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Chen, J., Ge, X., & Ni, Q. (2019). Coverage and handoff analysis of 5G fractal small cell networks. IEEE Transactions on Wireless Communications, 18(2), 1263–1276.

    Article  Google Scholar 

  2. Ge, X., Tian, X., Qiu, Y., et al. (2018). Small cell networks with fractal coverage characteristics. IEEE Transactions on Communications, 66(11), 5457–5469.

    Article  Google Scholar 

  3. Yang, B., Yang, X., Ge, X., & Li, Q. (2018). Coverage and handover analysis of ultra-dense millimeter-wave networks with control and user plane separation architecture. IEEE Access, 6, 54739–54750.

    Article  Google Scholar 

  4. Ding, M., Wang, P., López-Pérez, D., et al. (2016). Performance impact of LoS and NLoS transmissions in dense cellular networks. IEEE Transactions on Wireless Communications, 15(3), 2365–2380.

    Article  Google Scholar 

  5. Rappaport, T., Sun, S., Mayzus, R., Zhao, H., Azar, Y., Wang, K., Wong, G. N., Schulz, J. K., Samimi, M., & Gutierrez, F. (2013). Millimeter wave mobile communications for 5G cellular: It will work! IEEE Access, 1, 335–349.

    Article  Google Scholar 

  6. Akdeniz, M. R., Liu, Y., Samimi, M. K., Sun, S., Rangan, S., Rappaport, T. S., & Erkip, E. (2014). Millimeter wave channel modeling and cellular capacity evaluation. IEEE Journal on Selected Areas in Communications, 32, 1164–1179.

    Article  Google Scholar 

  7. Belbase, K., Zhang, Z., Jiang, H., & Tellambura, C. (2018). Coverage analysis of millimeter wave decode-and-forward networks with best relay selection. IEEE Access, 6, 22670–22683.

    Article  Google Scholar 

  8. Ouamri, M. A., Oteşteanu, M.-E., Isar, A., & Aznia, M. (2020). Coverage, handoff and cost optimization for 5G heterogeneous network. Physical communication, 39, 1–8.

    Article  Google Scholar 

  9. Kpojime, H. O., & Safdar, G. A. (2015). Interference mitigation in cognitive-radio-based femtocells. IEEE Communication Surveys and Tutorials, 17(3), 1511–1534.

    Article  Google Scholar 

  10. Jafari, A. H., Pérez, D. L., Ding, M., & Zhang, J. (2017). Performance analysis of dense small cell networks with practical antenna heights under rician fading. IEEE Access, 6, 9960–9974.

    Article  Google Scholar 

  11. Bai, T., & Heath, R. W. (2015). Coverage and rate analysis for millimeter-wave cellular networks. IEEE Transactions on Wireless Communication, 14(2), 1100–1114.

    Article  Google Scholar 

  12. Chen, C., Elliott, R. C., Krzymień, W. A., & Melzer, J. (2018). Modeling of cellular networks using stationary and nonstationary point processes. IEEE Access, 6, 47144–47162.

    Article  Google Scholar 

  13. He Wang, X., Zhou, M. C., & Reed, . (2014). Coverage and throughput analysis with a non-uniform small cell deployment. IEEE Transactions on Wireless Communication, 13(4), 2047–2059.

    Article  Google Scholar 

  14. Ding, M., Wang, P., Pérez, D. L., Mao, G., & Lin, Z. (2016). Performance impact of LoS and NLoS transmissions in dense cellular networks. IEEE Transactions on Wireless Communications, 15(3), 2365–2380.

    Article  Google Scholar 

  15. Cheng, M., Wang, J.-B., Yongpeng, Wu., Xia, X.-G., Wong, K.-K., & Lin, M. (2018). Coverage analysis for millimeter wave cellular networks with imperfect beam alignment. IEEE Transactions on Vehicular Technology, 63(9), 8302–8314.

    Article  Google Scholar 

  16. Yoon, J., & Hwang, G. (2018). Distance-based inter-cell interference coordination in small cell networks: stochastic geometry modeling and analysis. IEEE Transactions on Wireless Communications, 17(6), 4089–4103.

    Article  Google Scholar 

  17. Wang, X. Y., Ho, P.-H., & Chen, K. C. (2012). Interference analysis and mitigation for cognitive-empowered femtocells through stochastic dual control. IEEE Transactions on Wireless Communications, 11(6), 2065–2075.

    Article  Google Scholar 

  18. Di Renzo, M. (2015). Stochastic geometry modeling and analysis of multi-tier millimeter wave cellular networks. IEEE Transactions on Communications, 14(9), 5038–5057.

    Google Scholar 

  19. Andrews, J. G., Bai, T., Kulkarni, M. N., et al. (2017). Modeling and analyzing millimeter wave cellular systems. IEEE Transactions on Communications., 65(1), 403–430.

    Google Scholar 

  20. Di Renzo, M., Guidotti, A., & Corazza, G. E. (2013). Average rate of downlink heterogeneous cellular networks over generalized fading channels – Astochastic geometry approach. IEEE Transactions on Communications, 61(7), 3050–3071.

    Article  Google Scholar 

  21. Bai, T., Vaze, R., & Heath, R. W., Jr. (2014). Analysis of blockage effects on urban cellular networks. IEEE Transactions on Wireless Communications, 13(9), 5070–5083.

    Article  Google Scholar 

  22. Keith, Q. T. (2016). Zhang, Wireless Communications: Principles, Theory and Methodology (1st ed.). Published: Wiley.

    Google Scholar 

  23. Yi, W., Liu, Y., Nallanathan, A., & Elkashlan, M. (2019). Clustered Millimeter-Wave Networks With Non-Orthogonal Multiple Access. IEEE Transactions on Communications, 67(6), 4350–4364.

    Article  Google Scholar 

  24. W. Lu and M. Di Renzo (2015) “Stochastic geometry modeling of cellular networks: analysis, simulation and experimental validation, ACM MSWiM, 179–188,

  25. B. Błaszczyszyn, Mohamed Kadhem Karray, H. P. Keeler (April 2013) Using Poisson processes to model lattice cellular networks, Proceedings IEEE INFOCOM.

  26. Di Renzo, M., & Lu, W. (2017). System-Level Analysis/Optimization of Cellular Networks with Simultaneous Wireless Information and Power Transfer: Stochastic Geometry Modeling. IEEE Transactions on Vehicular Technology, 66, 2251–2275.

    Article  Google Scholar 

  27. Wildemeersch, M., Quek, T. Q. S., Slump, C. H., & Rabbachin, A. (2013). Cognitive small cell networks: Energy efficiency and trade-offs. IEEE Transactions on Communications, 61(9), 4016–4029.

    Article  Google Scholar 

  28. Jo, H.-S., Sang, Y. J., Xia, P., & Andrews, J. G. (2012). Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis. IEEE Transactions on Wireless Communications, 11(10), 3484–3495.

    Article  Google Scholar 

  29. H. Alzer, “On Some inequalities for the incomplete Gamma function,” Math. Comput., vol. 66, no. 218, pp. 771–778, 1997. [Online]. Available: http://www.jstor.org/stable/2153894.

  30. Błaszczyszyn, B., Haenggi, M., & Keeler, P. (2018). Stochastic geometry analysis of cellular networks. Cambridge University Press.

    Book  Google Scholar 

  31. 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 

  32. ElSawy, H., Hossain, E., & Haenggi, M. (2013). Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: a survey. IEEE Communications Surveys and Tutorials, 15(3), 996–1019.

    Article  Google Scholar 

  33. Yan, Z., Zhou, W., Chen, S., & Liu, H. (2016). Modeling and analysis of two-tier hetnets with cognitive small cells. IEEE Access, 5, 2904–2912.

    Article  Google Scholar 

  34. Huang, Li., Zhu, G., & Xiaojiang, Du. (2013). Cognitive femtocell networks: an opportunistic spectrum access for future indoor wireless coverage. IEEE Wireless Communications, 20(2), 44–51.

    Article  Google Scholar 

  35. Yulin, Hu., Cenk Gursoy, M., & Schmeink, A. (2018). Relaying-Enabled Ultra-Reliable Low-Latency Communications in 5G”. IEEE Network, 32(2), 62–68.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohamed Amine Ouamri.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ouamri, M.A. Stochastic geometry modeling and analysis of downlink coverage and rate in small cell network. Telecommun Syst 77, 767–779 (2021). https://doi.org/10.1007/s11235-021-00770-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-021-00770-5

Keywords

Navigation