Skip to main content

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 289))

  • 683 Accesses

Abstract

Compared with conventional regular hexagonal cellular models, random cellular network models resemble real cellular networks much more closely. However, most studies of random cellular networks are based on the Poisson point process (PPP) and do not take into account the fact that adjacent base stations (BSs) should be separated with a minimum distance to avoid strong interference among each other BSs. Moreover, the user distribution in ultra-dense networks (UDNs) plays a crucial role in affecting the performance of UDNs due to the essential coupling between the traffic and the service provided by the networks. Existing studies are mostly based on the assumption that users are uniformly distributed in space. The non-uniform user distribution has not been widely considered despite that it is much closer to the real scenario. This chapter proposes a multi-user multi-antenna random cellular network model with the aforementioned minimum distance constraint for adjacent BSs, based on the hardcore point process (HCPP). A spectrum efficiency model and an energy efficiency model are presented based on the random cellular network model, and the maximum achievable energy efficiency of the considered multi-user multi-antenna HCPP random cellular networks is investigated. Moreover, a radiation and absorbing model (R&A model) is first adopted to analyze the impact of the nonuniformly distributed users on the performance of 5G UDNs. Based on the R&A model and queueing network theory, the stationary user density in each hot area is investigated. Simulation results demonstrate that the energy efficiency of conventional PPP cellular networks is underestimated when the minimum distance between adjacent BSs is ignored. Furthermore, the simulation results indicate that non-uniform user distribution has a significant impact on the performance of UDNs, compared with the uniformly distributed assumption.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ge, X., et al.: 5G ultra-dense cellular networks. IEEE Wirel. Commun. 23(1), 72–79 (2016) (Art. no. 7422408)

    Google Scholar 

  2. Larsson, E.G., et al.: Antenna count for massive MIMO: 1.9 GHz vs. 60 GHz. IEEE Commun. Mag. 56(9), 132–137 (2018)

    Article  Google Scholar 

  3. Ge, X., et al.: Energy efficiency of small cell backhaul networks based on Gauss-Markov mobile models. IET Netw. 4(2), 158–167 (2015)

    Article  Google Scholar 

  4. Zhong, Y., et al.: Traffic matching in 5G ultra-dense networks. IEEE Commun. Mag. 56(8), 100–105 (2018)

    Article  Google Scholar 

  5. Hasan, Z., et al.: Green cellular networks: a survey, some research issues and challenges, (in English). IEEE Commun. Surv. Tutor. 13(4), 524–540 (2011)

    Article  Google Scholar 

  6. Demestichas, P., et al.: 5G on the horizon: key challenges for the radio-access network. IEEE Veh. Technol. Mag. 8(3), 47–53 (2013) (Art. no. 6568922)

    Google Scholar 

  7. Shafi, M., et al.: 5G: a tutorial overview of standards, trials, challenges, deployment, and practice. IEEE J. Sel. Areas Commun. 35(6), 1201–1221 (2017)

    Article  Google Scholar 

  8. Andrews, J.G., et al.: What will 5G be? IEEE J. Select. Areas Commun. 32(6), 1065–1082 (2014) Art. no. 6824752

    Google Scholar 

  9. Ge, X., et al.: User mobility evaluation for 5G small cell networks based on individual mobility model. IEEE J. Select. Areas Commun. 34(3), 528–541 (2016) (Art. no. 7399689)

    Google Scholar 

  10. Zhong, Y., et al.: QoE and cost for wireless networks with mobility under spatio-temporal traffic. IEEE Access 7, 47206–47220 (2019)

    Article  Google Scholar 

  11. Héliot, F., et al.: An accurate closed-form approximation of the energy efficiency-spectral efficiency trade-off over the MIMO Rayleigh fading channel. In: IEEE International Conference on Communications (2011)

    Google Scholar 

  12. Héliot, F., et al.: On the energy efficiency gain of MIMO communication under various power consumption models. In: 2011 Future Network and Mobile Summit, FutureNetw 2011 (2011)

    Google Scholar 

  13. Liu, W., et al.: Energy efficiency of MIMO transmissions in wireless sensor networks with diversity and multiplexing gains. In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing—Proceedings, vol. IV, pp. 897–900 (2005)

    Google Scholar 

  14. Belmega, E.V., Lasaulce, S.: An information-theoretic look at MIMO energy-efficient communications. In: VALUETOOLS 2009—4th International Conference on Performance Evaluation Methodologies and Tools (2009)

    Google Scholar 

  15. Xu, J., et al.: Improving energy efficiency through multimode transmission in the downlink MIMO systems. Eurasip J. Wirel. Commun. Netw. 2011(1) (Art. no. 200) (2011)

    Google Scholar 

  16. Xu, J., Qiu, L.: Energy efficiency optimization for MIMO broadcast channels. IEEE Trans. Wireless Commun. 12(2), 690–701(Art. no. 6409501) (2013)

    Google Scholar 

  17. Miao, G., Zhang, J.: On optimal energy-efficient multi-user MIMO. In: GLOBECOM—IEEE Global Telecommunications Conference (2011)

    Google Scholar 

  18. Ngo, H.Q., et al.: Energy and spectral efficiency of very large multiuser MIMO systems. IEEE Trans. Commun. 61(4), 1436–1449(Art. no. 6457363) (2013)

    Google Scholar 

  19. Chen, M., et al.: On the computation offloading at ad hoc cloudlet: architecture and service modes. IEEE Commun. Mag. 53(6), 18–24 (Art. no. 7120041) (2015)

    Google Scholar 

  20. Chen, M., et al.: EMC: emotion-aware mobile cloud computing in 5G. IEEE Netw. 29(2), 32–38 (Art. no. 7064900) (2015)

    Google Scholar 

  21. Chen, M., et al.: AIWAC: affective interaction through wearable computing and cloud technology. IEEE Wirel. Commun. 22(1), 20–27 (Art. no. 7054715) (2015)

    Google Scholar 

  22. Elsawy, H., et al.: Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: a survey. IEEE Commun. Surv. Tutor. 15(3), 996–1019 (Art. no. 6524460) (2013)

    Google Scholar 

  23. Andrews, J.G., et al.: A tractable approach to coverage and rate in cellular networks. IEEE Trans. Commun. 59(11), 3122–3134 (Art. no. 6042301) (2011)

    Google Scholar 

  24. Ge, X., et al.: 5G wireless backhaul networks: challenges and research advances. IEEE Netw. 28(6), 6–11 (Art. no. 6963798) (2014)

    Google Scholar 

  25. Chan, C.C., Hanly, S.V.: Calculating the outage probability in a CDMA network with spatial poisson traffic. IEEE Trans. Veh. Technol. 50(1), 183–204 (2001)

    Article  Google Scholar 

  26. Yu, S.M., Kim, S.L.: Downlink capacity and base station density in cellular networks. In: 2013 11th International Symposium and Workshops on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2013, pp. 119–124 (2013)

    Google Scholar 

  27. Guidotti, A., et al.: Simplified expression of the average rate of cellular networks using stochastic geometry. In: IEEE International Conference on Communications, pp. 2398–2403 (2012)

    Google Scholar 

  28. Renzo, M.D., et al.: Average rate of downlink heterogeneous cellular networks over generalized fading channels: a stochastic geometry approach. IEEE Trans. Commun. 61(7), 3050–3071 (Art. no. 6516171) (2013)

    Google Scholar 

  29. Mukherjee, S.: Distribution of downlink SINR in heterogeneous cellular networks. IEEE J. Select. Areas Commun. 30(3), 575–585 (Art. no. 6171998) (2012)

    Google Scholar 

  30. Govindasamy, S., et al.: Asymptotic spectral efficiency of the uplink in spatially distributed wireless networks with multi-antenna base stations. IEEE Trans. Commun. 61(7), 100–112 (Art. no. 6528073) (2013)

    Google Scholar 

  31. Dhillon, H.S., et al.: Downlink MIMO HetNets: modeling, ordering results and performance analysis. IEEE Trans. Wirel. Commun. 12(10), 5208–5222 (Art. no. 6596082) (2013)

    Google Scholar 

  32. Soh, Y.S., et al.: Energy efficient heterogeneous cellular networks, (in English). Ieee J. Select. Areas Commun. 31(5), 840–850 (2013)

    Article  Google Scholar 

  33. Srinivasa, S., Haenggi, M.: Modeling interference in finite uniformly random networks. In: Proceedings of International Workshop on Information Theory for Sensor Networks (WITS'07), pp. 1–12 (2007)

    Google Scholar 

  34. Ganti, R.K., Haenggi, M.: Interference and outage in clustered wireless ad hoc networks. IEEE Trans. Inf. Theory 55(9), 4067–4086 (2009)

    Article  Google Scholar 

  35. Elsawy, H., et al.: Characterizing random CSMA wireless networks: a stochastic geometry approach. In: IEEE International Conference on Communications, pp. 5000–5004 (2012)

    Google Scholar 

  36. Guo, A., Haenggi, M.: Spatial stochastic models and metrics for the structure of base stations in cellular networks. IEEE Trans. Wireless Commun. 12(11), 5800–5812 (2013)

    Article  Google Scholar 

  37. Win, M.Z., et al.: A mathematical theory of network interference and its applications. Proc. IEEE 97(2), 205–230 (Art. no. 4802198) (2009)

    Google Scholar 

  38. Haenggi, M.: Mean interference in hard-core wireless networks. IEEE Commun. Lett. 15(8), 792–794 (Art. no. 5934671) (2011)

    Google Scholar 

  39. Matérn, B.: Spatial Variation. Springer Science & Business Media (1986)

    Google Scholar 

  40. Chiu, S.N., et al.: Stochastic Geometry and Its Applications. Wiley (2013)

    Google Scholar 

  41. Elsawy, H., Hossain, E.: Modeling random CSMA wireless networks in general fading environments. In: IEEE International Conference on Communications, pp. 5457–5461 (2012)

    Google Scholar 

  42. Frost, V.S., Melamed, B.: Traffic modeling for telecommunications networks as new communications services evolve, professionals must create better models to predict system performance. IEEE Commun. Mag. 32(3), 70–81 (1994)

    Article  Google Scholar 

  43. Lilith, N., Doǧançay, K.: Using reinforcement learning for call admission control in cellular environments featuring self-similar traffic. In: IEEE Region 10 Annual International Conference, Proceedings/TENCON, vol. 2007 (2005)

    Google Scholar 

  44. Ramakrishnan, P.: Self-similar traffic model. Technical Report CSHCN T.R.99–5 (ISR T.R. 99–12) (1997)

    Google Scholar 

  45. Norros, I.: On the use of fractional brownian motion in the theory of connectionless networks. IEEE J. Sel. Areas Commun. 13(6), 953–962 (1995)

    Article  Google Scholar 

  46. Karasaridis, A., Hatzinakos, D.: Network heavy traffic modeling using α-stable self-similar processes. IEEE Trans. Commun. 49(7), 1203–1214 (2001)

    Article  Google Scholar 

  47. Ge, X., et al.: Spatial spectrum and energy efficiency of random cellular networks. IEEE Trans. Commun. 63(3), 1019–1030 (Art. no. 7015548) (2015)

    Google Scholar 

  48. Andrews, J.G., et al.: Overcoming interference in spatial multiplexing mimo cellular networks. IEEE Wirel. Commun. 14(6), 95–104 (2007)

    Article  Google Scholar 

  49. Cho, B., et al.: Bounding the mean interference in Matern Type II hard-core wireless networks. IEEE Wirel. Commun. Lett. 2(5), 563–566 (Art. no. 6574907) (2013)

    Google Scholar 

  50. Simon, M.K., Alouini, M.S.: Digital Communication over Fading Channels: A Unified Approach to Performance Analysis. Wiley (2002)

    Google Scholar 

  51. Cui, S., et al.: Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks. IEEE J. Sel. Areas Commun. 22(6), 1089–1098 (2004)

    Article  Google Scholar 

  52. Arnold, O., et al.: Power consumption modeling of different base station types in heterogeneous cellular networks. In: 2010 Future Network and Mobile Summit (2010)

    Google Scholar 

  53. Chen, C.J., Wang, L.C.: Performance analysis of scheduling in multiuser MIMO systems with zero-forcing receivers. IEEE J. Sel. Areas Commun. 25(7), 1435–1445 (2007)

    Article  Google Scholar 

  54. Wang, L.C., Yeh, C.J.: Scheduling for multiuser MIMO broadcast systems: transmit or receive beamforming? IEEE Trans. Wirel. Commun. 9(9), 2779–2791 (Art. no. 5529760) (2010)

    Google Scholar 

  55. Telatar, E.: Capacity of multi-antenna Gaussian channels. Eur. Trans. Telecommun. 10(6), 585–595 (1999)

    Article  MathSciNet  Google Scholar 

  56. Ge, X., et al.: Capacity analysis of a multi-cell multi-antenna cooperative cellular network with co-channel interference. IEEE Trans. Wireless Commun. 10(10), 3298–3309 (Art. no. 6064713) (2011)

    Google Scholar 

  57. Masouros, C., et al.: Large-scale MIMO transmitters in fixed physical spaces: the effect of transmit correlation and mutual coupling. IEEE Trans. Commun. 61(7), 2794–2804 (Art. no. 6522419) (2013)

    Google Scholar 

  58. Paulraj, A., et al.: Introduction to space-time wireless communications. In: Introduction to Space-Time Wireless Communications, pp. 1–270 (2003)

    Google Scholar 

  59. Baccelli, F., Blaszczyszyn, B.: Stochastic Geometry and Wireless Networks-Volume I : Theory. Now Publishers Inc (2009)

    Google Scholar 

  60. Cioffi, J.M.: A Multicarrier Primer (1991)

    Google Scholar 

  61. Marzetta, T.L.: Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans. Wirel. Commun. 9(11), 3590–3600 (Art. no. 5595728) (2010)

    Google Scholar 

  62. Humar, I., et al.: Rethinking energy efficiency models of cellular networks with embodied energy. IEEE Netw. 25(2), 40–49 (Art. no. 5730527) (2011)

    Google Scholar 

  63. Wu, G., et al.: Recent advances in energy-efficient networks and their application in 5G systems. IEEE Wirel. Commun. 22(2), 145–151 (Art. no. 7096297) (2015)

    Google Scholar 

  64. Stefanatos, S., Alexiou, A.: Access point density and bandwidth partitioning in ultra dense wireless networks. IEEE Trans. Commun. 62(9), 3376–3384 (Art. no. 6883156) (2014)

    Google Scholar 

  65. Samarakoon, S., et al.: Ultra dense small cell networks: turning density into energy efficiency. IEEE J. Select. Areas Commun. 34(5), 1267–1280 (Art. no. 7439746) (2016)

    Google Scholar 

  66. López-Pérez, D., et al.: Towards 1 Gbps/UE in cellular systems: understanding ultra-dense small cell deployments. IEEE Commun. Surv. Tutor. 17(4), 2078–2101 (Art. no. 7126919) (2015)

    Google Scholar 

  67. Tseng, F.H., et al.: Ultra-dense small cell planning using cognitive radio network toward 5g (in English). IEEE Wirel. Commun. 22(6), 76–83 (2015)

    Article  Google Scholar 

  68. Zhou, F., et al.: Energy-efficient optimal power allocation for fading cognitive radio channels: ergodic capacity, outage capacity, and minimum-rate capacity. IEEE Trans. Wirel. Commun. 15(4), 2741–2755 (Art. no. 7358164) (2016)

    Google Scholar 

  69. Zhong, Y., et al.: On the stability of static poisson networks under random access. IEEE Trans. Commun. 64(7), 2985–2998 (Art. no. 7486114) (2016)

    Google Scholar 

  70. Zhong, Y., et al.: Heterogeneous cellular networks with spatio-temporal traffic: delay analysis and scheduling. IEEE J. Select. Areas Commun. 35(6), 1373–1386 (Art. no. 7886285) (2017)

    Google Scholar 

  71. Zhang, T., et al.: Energy efficiency of base station deployment in ultra dense HetNets: a stochastic geometry analysis. IEEE Wirel. Commun. Lett. 5(2), 184–187 (Art. no. 7377022) (2016)

    Google Scholar 

  72. Ding, M., et al.: Performance impact of LoS and NLoS transmissions in dense cellular networks. IEEE Trans. Wireless Commun. 15(3), 2365–2380 (Art. no. 7335646) (2016)

    Google Scholar 

  73. Yunas, S., et al.: Spectral and energy efficiency of ultra-dense networks under different deployment strategies. IEEE Commun. Mag. 53(1), 90–100 (Art. no. 7010521) (2015)

    Google Scholar 

  74. Park, J., et al.: Tractable resource management with uplink decoupled millimeter-wave overlay in ultra-dense cellular networks. IEEE Trans. Wirel. Commun. 15(6), 4362–4379 (Art. no. 7430349) (2016)

    Google Scholar 

  75. Gao, Z., et al.: MmWave massive-MIMO-based wireless backhaul for the 5G ultra-dense network. IEEE Wirel. Commun. 22(5), 13–21 (Art. no. 7306533) (2015)

    Google Scholar 

  76. Galinina, O., et al.: 5G multi-RAT LTE-WiFi ultra-dense small cells: performance dynamics, architecture, and trends. IEEE J. Sel. Areas Commun. 33(6), 1224–1240 (2015)

    Article  Google Scholar 

  77. Ghazanfari, A., et al.: Ambient RF energy harvesting in ultra-dense small cell networks: performance and trade-offs. IEEE Wirel. Commun. 23(2), 38–45 (Art. no. 7462483) (2016)

    Google Scholar 

  78. Ge, X., et al.: Millimeter wave communications with OAM-SM scheme for future mobile networks. IEEE J. Select. Areas Commun. 35(9), 2163–2177 (Art. no. 7968418) (2017)

    Google Scholar 

  79. Wu, Q., et al.: Energy-efficient resource allocation for wireless powered communication networks. IEEE Trans. Wirel. Commun. 15(3), 2312–2327 (Art. no. 7332956) (2016)

    Google Scholar 

  80. Chen, S., et al.: User-centric ultra-dense networks for 5G: challenges, methodologies, and directions. IEEE Wirel. Commun. 23(2), 78–85 (Art. no. 7462488) (2016)

    Google Scholar 

  81. Kim, J., et al.: Virtual cell beamforming in cooperative networks. IEEE J. Select. Areas Commun. 32(6), 1126–1138 (Art. no. 6827165) (2014)

    Google Scholar 

  82. Wang, J., Dai, L.: Downlink rate analysis for virtual-cell based large-scale distributed antenna systems. IEEE Trans. Wirel. Commun. 15(3), 1998–2011 (Art. no. 7317799) (2016)

    Google Scholar 

  83. Nie, W., et al.: User-centric cross-tier base station clustering and cooperation in heterogeneous networks: rate improvement and energy saving. IEEE J. Select. Areas Commun. 34(5), 1192–1206 (Art. no. 7448831) (2016)

    Google Scholar 

  84. Hong, M., et al.: Joint base station clustering and beamformer design for partial coordinated transmission in heterogeneous networks. IEEE J. Select. Areas Commun. 31(2), 226–240 (Art. no. 6415394) (2013)

    Google Scholar 

  85. Feng, Z., et al.: An effective approach to 5G: wireless network virtualization. Commun. Mag. IEEE 53(12), 53–59 (2015)

    Article  Google Scholar 

  86. Song, C., et al.: Limits of predictability in human mobility. Science 327(5968), 1018–1021 (2010)

    Article  MathSciNet  Google Scholar 

  87. Song, C., et al.: Modelling the scaling properties of human mobility. Nat. Phys. 6(10), 818–823 (2010)

    Article  Google Scholar 

  88. Zipf, G.K.: The P1P2/D hypothesis: on the intercity movement of persons. Am. Sociol. Rev. 11(6), 677–686 (1946)

    Article  Google Scholar 

  89. Simini, F., et al.: A universal model for mobility and migration patterns. Nature 484(7392), 96–100 (2012)

    Article  Google Scholar 

  90. Jackson, J.R.: Networks of waiting lines. Oper. Res. 5(4), 518–521 (1957)

    Article  MathSciNet  Google Scholar 

  91. Santaló, L.A.: Integral geometry and geometric probability. In: Encyclopedia of mathematics and its applications, vol. 1. Cambridge University Press, Cambridge, U.K. (1976)

    Google Scholar 

  92. Guo, J., et al.: Outage probability in arbitrarily-shaped finite wireless networks. IEEE Trans. Commun. 62(2), 699–712 (Art. no. 6712183) (2014)

    Google Scholar 

  93. Abate, J., Whitt, W.: Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7(1), 36–43 (1995)

    Article  Google Scholar 

  94. O'Cinneide, C.A.: Euler summation for Fourier series and Laplace transform inversion. Commun. Stat. Part C Stochastic Mod. 13(2), 315–337 (1997)

    Google Scholar 

  95. Auer, G., et al.: Energy efficiency analysis of the reference systems, areas of improvements and target breakdown. INFSO-ICT-247733 EARTH2012. Available: http://www.ict-earth.eu/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to X. Ge .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ge, X., Yang, J., Ye, J. (2022). 5G Green Network. In: Nicopolitidis, P., Misra, S., Yang, L.T., Zeigler, B., Ning, Z. (eds) Advances in Computing, Informatics, Networking and Cybersecurity. Lecture Notes in Networks and Systems, vol 289. Springer, Cham. https://doi.org/10.1007/978-3-030-87049-2_13

Download citation

Publish with us

Policies and ethics