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Stochastic geometry based analysis for heterogeneous networks: a perspective on meta distribution

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Abstract

The meta distribution as a new performance metric can provide much more fine-grained information about the individual link reliability, and is of great value for the analysis and design of the future cellular networks. In this paper, we investigate the stochastic geometry based analysis for heterogeneous networks from the perspective on the meta distribution. The comprehensive overview for the fundamental framework of the meta distribution is provided, which involves the concepts of the meta distribution and its related performance metric (e.g., mean local delay and spatial outage capacity) and the efficient calculation methods of the meta distribution. The insights of the meta distribution are also stated by the comparison with standard success probability. The various applications of the meta distribution to heterogeneous networks are summarized and categorized by different types of technologies. Furthermore, some open issues and future work are discussed to promote the development and application of the meta distribution.

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References

  1. Wang Y F, Yu L, Mudesir A, et al. 5G Unlocks a World of Opportunities. Huawei Whitepaper Technical Report. 2017. https://www.huawei.com/en/industry-insights/outlook/mobile-broadband/insights-reports/5g-unlocks-a-world-of-opportunities

    Google Scholar 

  2. Aguiar R L, Sebanstien-Bedo J, Armada A G, et al. Vision Document for B5G Research. The 5G Infrastructure Public Private Partnership (5G PPP) Technical Report. 2015. https://5g-ppp.eu/wp-content/uploads/2015/12/Beyond5G.pdf

    Google Scholar 

  3. Bhushan N, Li J Y, Malladi D, et al. Network densification: the dominant theme for wireless evolution into 5G. IEEE Commun Mag, 2014, 52: 82–89

    Google Scholar 

  4. Bohli A, Bouallegue R. How to meet increased capacities by future green 5G networks: a survey. IEEE Access, 2019, 7: 42220–42237

    Google Scholar 

  5. Andrews J G, Buzzi S, Choi W, et al. What will 5G be? IEEE J Sel Areas Commun, 2014, 32: 1065–1082

    Google Scholar 

  6. Damnjanovic A, Montojo J, Wei Y B, et al. A survey on 3GPP heterogeneous networks. IEEE Wirel Commun, 2011, 18: 10–21

    Google Scholar 

  7. Peng M G, Li Y, Zhao Z Y, et al. System architecture and key technologies for 5G heterogeneous cloud radio access networks. IEEE Netw, 2015, 29: 6–14

    Google Scholar 

  8. Dhillon H S, Ganti R K, Baccelli F, et al. Modeling and analysis of K-tier downlink heterogeneous cellular networks. IEEE J Sel Areas Commun, 2012, 30: 550–560

    Google Scholar 

  9. Agiwal M, Roy A, Saxena N. Next generation 5G wireless networks: a comprehensive survey. IEEE Commun Surv Tutorials, 2016, 18: 1617–1655

    Google Scholar 

  10. Haenggi M, Ganti R K. Interference in large wireless networks. Found Trends Netw, 2008, 3: 127–248

    MATH  Google Scholar 

  11. Ghosh A, Mangalvedhe N, Ratasuk R, et al. Heterogeneous cellular networks: from theory to practice. IEEE Commun Mag, 2012, 50: 54–64

    Google Scholar 

  12. Andrews J G, Ganti R K, Haenggi M, et al. A primer on spatial modeling and analysis in wireless networks. IEEE Commun Mag, 2010, 48: 156–163

    Google Scholar 

  13. Kleinrock L, Silvester J. Optimum transmission radii for packet radio networks or why six is a magic number. In: Proceedings of the IEEE national telecommunications conference (NTC'78), Birmingham, 1978. 1–4

    Google Scholar 

  14. Weber S, Andrews J G. A stochastic geometry approach to wideband ad hoc networks with channel variations. In: Proceedings of 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt'06), Boston, 2006. 1–6

    Google Scholar 

  15. Hasan A, Andrews J G. The guard zone in wireless ad hoc networks. IEEE Trans Wirel Commun, 2007, 6: 897–906

    Google Scholar 

  16. Andrews J G, Shakkottai S, Heath R, et al. Rethinking information theory for mobile ad hoc networks. IEEE Commun Mag, 2008, 46: 94–101

    Google Scholar 

  17. Baccelli F, Miihlethaler P, Blaszczyszyn B. Stochastic analysis of spatial and opportunistic aloha. IEEE J Sel Areas Commun, 2009, 27: 1105–1119

    Google Scholar 

  18. Ganti R K, Haenggi M. Interference and outage in clustered wireless ad hoc networks. IEEE Trans Inform Theor, 2009, 55: 4067–4086

    MATH  Google Scholar 

  19. Haenggi M, Andrews J G, Baccelli F, et al. Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE J Sel Areas Commun, 2009, 27: 1029–1046

    Google Scholar 

  20. Andrews J G, Baccelli F, Ganti R K. A tractable approach to coverage and rate in cellular networks. IEEE Trans Commun, 2011, 59: 3122–3134

    Google Scholar 

  21. Jo H S, Sang Y J, Xia P, et al. Heterogeneous cellular networks with flexible cell association: a comprehensive downlink SINR analysis. IEEE Trans Wirel Commun, 2012, 11: 3484–3495

    Google Scholar 

  22. Guo A J, Haenggi M. Spatial stochastic models and metrics for the structure of base stations in cellular networks. IEEE Trans Wirel Commun, 2013, 12: 5800–5812

    Google Scholar 

  23. Nigam G, Minero P, Haenggi M. Coordinated multipoint joint transmission in heterogeneous networks. IEEE Trans Commun, 2014, 62: 4134–4146

    Google Scholar 

  24. Haenggi M. Stochastic Geometry for Wireless Networks. New York: Cambridge University Press, 2012

    MATH  Google Scholar 

  25. ElSawy H, Hossain E, Haenggi M. Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: a survey. IEEE Commun Surv Tut, 2013, 15: 996–1019

    Google Scholar 

  26. ElSawy H, Sultan-Salem A, Alouini M S, et al. Modeling and analysis of cellular networks using stochastic geometry: a tutorial. IEEE Commun Surv Tut, 2017, 19: 167–203

    Google Scholar 

  27. Baccelli F, Blaszczyszyn B. Stochastic geometry and wireless networks: volume I: theory. Foundation Trends Network, 2009, 3: 249–449

    MATH  Google Scholar 

  28. Blaszczyszyn B, Haenggi M, Keeler P, et al. Stochastic Geometry Analysis of Cellular Networks. New York: Cambridge University Press, 2018

    MATH  Google Scholar 

  29. Baccelli F, Blaszczyszyn B, Karray M. Random measures, point processes, and stochastic geometry. 2020. https://web.ma.utexas.edu/simons/research topic/preprint-of-a-new-book-on-point-processes-and- stochastic-geometry/

    Google Scholar 

  30. Yu X H, Li C, Zhang J, et al. Stochastic Geometry Analysis of Multi-Antenna Wireless Networks. Singapore: Springer, 2019

    MATH  Google Scholar 

  31. Haenggi M. The meta distribution of the SIR in Poisson bipolar and cellular networks. IEEE Trans Wirel Commun, 2016, 15: 2577–2589

    Google Scholar 

  32. Weber S. The value of observations in predicting transmission success in wireless networks under slotted ALOHA. In: Proceedings of 2017 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt'17), Paris, 2017. 1–8

    Google Scholar 

  33. El Hammouti H, Ghogho M. Air-to-ground channel modeling for UAV communications using 3D building footprints. In: Proceedings of 2018 4th International Symposium on Ubiquitous Networking (UNet'18), Hammamet, 2018. 372–383

    Google Scholar 

  34. Tang J, Chen G, Coon J P. Meta distribution of the secrecy rate in the presence of randomly located eavesdroppers. IEEE Wirel Commun Lett, 2018, 7: 630–633

    Google Scholar 

  35. Ibrahim H, Tabassum H, Nguyen U T. The meta distributions of the SIR/SNR and data rate in coexisting sub-6GHz and millimeter-wave cellular networks. 2019. ArXiv: 190512002

    Google Scholar 

  36. Deng N, Haenggi M. The meta distribution of the SINR and rate in heterogeneous cellular networks. In: Proceedings of 2018 29th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'18), Bologna, 2018. 1–6

    Google Scholar 

  37. Deng N, Haenggi M. SINR and rate meta distributions for HCNs with joint spectrum allocation and offloading. IEEE Trans Commun, 2019, 67: 3709–3722

    Google Scholar 

  38. Hayajneh A M, Zaidi S A R, McLernon D C, et al. Optimal coverage and rate in downlink cellular networks: a SIR meta-distribution based approach. In: Proceedings of 2018 IEEE Global Communications Conference (GLOBE-COM'18), Abu Dhabi, 2018. 1–7

    Google Scholar 

  39. Deng N, Haenggi M. The energy and rate meta distributions in wirelessly powered D2D networks. IEEE J Sel Areas Commun, 2019, 37: 269–282

    Google Scholar 

  40. Luo Y, Shi Z P, Bu F. Analysis of SIR and rate meta distributions for 3D heterogenous ultra-dense networks with joint offloading and resource partitioning. IEEE Access, 2020, 8: 43067–43081

    Google Scholar 

  41. Zhou S Y, Zhao J H, Tan G P, et al. A fine-grained analysis of wireless powered communication with Poisson cluster process. In: Proceedings of 2019 11th International Conference on Wireless Communications and Signal Processing (WCSP'19), Xi'an, 2019. 1–6

    Google Scholar 

  42. Yu X L, Cui Q M, Wang Y J, et al. The joint and product meta distributions of the SIR and their applications to secrecy and cooperation. IEEE Trans Wireless Commun, 2020, 19: 4408–4423

    Google Scholar 

  43. Cui Q M, Jiang X Y, Yu X L, et al. SIR meta distribution in physical layer security with interference correlation. In: Proceedings of 2018 IEEE Global Communications Conference (GLOBECOM'18), Abu Dhabi, 2018. 1–6

    Google Scholar 

  44. Deng N, Haenggi M. A fine-grained analysis of millimeter-wave device-to-device networks. IEEE Trans Commun, 2017, 65: 4940–4954

    Google Scholar 

  45. Kalamkar S S, Haenggi M. The spatial outage capacity of wireless networks. IEEE Trans Wirel Commun, 2018, 17: 3709–3722

    Google Scholar 

  46. Kalamkar S S, Haenggi M. Distributed rate control for high reliability in Poisson bipolar networks. In: Proceedings of 2017 IEEE Global Communications Conference (GLOBECOM'17), Singapore, 2017. 1–6

    Google Scholar 

  47. Kalamkar S S, Haenggi M. Per-link reliability and rate control: two facets of the SIR meta distribution. IEEE Wirel Commun Lett, 2019, 8: 1244–1247

    Google Scholar 

  48. Abd El-Gawad M A, ElSawy H, Sakr A H, et al. Network-wide throughput optimization for highway vehicle-to-vehicle communications. Electronics, 2019, 8: 830

    Google Scholar 

  49. Cui Q M, Song H G, Wang H, et al. Capacity analysis of joint transmission CoMP with adaptive modulation. IEEE Trans Veh Technol, 2016, 66: 1876–1881

    Google Scholar 

  50. Song H G, Cui Q M, Zuo H L, et al. Variable rate and power M-QAM for DPS/DPB CoMP with adaptive modulation. Trans Emerging Tel Tech, 2017, 28: e3185

    Google Scholar 

  51. Cui Q M, Yu X L, Wang Y J, et al. The SIR meta distribution in Poisson cellular networks with base station cooperation. IEEE Trans Commun, 2018, 66: 1234–1249

    Google Scholar 

  52. Salehi M, Mohammadi A, Haenggi M. Analysis of D2D underlaid cellular networks: SIR meta distribution and mean local delay. IEEE Trans Commun, 2017, 65: 2904–2916

    Google Scholar 

  53. Baccelli F, Blaszczyszyn B, Haji-Mirsadeghi M O. Optimal paths on the space-time SINR random graph. Adv Appl Probab, 2011, 43: 131–150

    MathSciNet  MATH  Google Scholar 

  54. Haenggi M. The local delay in Poisson networks. IEEE Trans Inform Theor, 2013, 59: 1788–1802

    MathSciNet  MATH  Google Scholar 

  55. Mankar P D, Dhillon H S. Meta distribution for downlink NOMA in cellular networks with 3GPP-inspired user ranking. In: Proceedings of 2019 IEEE Global Communications Conference (GLOBECOM'19), Waikoloa, 2019. 1–6

    Google Scholar 

  56. Mankar P D, Dhillon H S. Downlink analysis of NOMA-enabled cellular networks with 3GPP-inspired user ranking. IEEE Trans Wirel Commun, 2020, 19: 3796–3811

    Google Scholar 

  57. Salehi M, Tabassum H, Hossain E. Meta distribution of SIR in large-scale uplink and downlink NOMA networks. IEEE Trans Commun, 2019, 67: 3009–3025

    Google Scholar 

  58. Ibrahim H, Tabassum H, Nguyen U T. Meta distribution of SIR in dual-hop Internet-of-Things (IoT) networks. In: Proceedings of 2019 IEEE International Conference on Communications (ICC'19), Shanghai, 2019. 1–7

    Google Scholar 

  59. Wang Y J, Haenggi M, Tan Z H. The meta distribution of the SIR for cellular networks with power control. IEEE Trans Commun, 2018, 66: 1745–1757

    Google Scholar 

  60. Wang Y J, Cui Q M, Haenggi M, et al. On the SIR meta distribution for Poisson networks with interference cancellation. IEEE Wirel Commun Lett, 2018, 7: 26–29

    Google Scholar 

  61. Kalamkar S S. Reliability and local delay in wireless networks: does bandwidth partitioning help? In: Proceedings of 2019 IEEE Global Communications Conference (GLOBECOM'19), Waikoloa, 2019. 1–6

    Google Scholar 

  62. Wang Y J, Haenggi M, Tan Z H. SIR meta distribution of K-tier downlink heterogeneous cellular networks with cell range expansion. IEEE Trans Commun, 2019, 67: 3069–3081

    Google Scholar 

  63. Tang X X, Xu X D, Haenggi M. Meta distribution of the SIR in moving networks. IEEE Trans Commun, 2020. doi: 10.1109/TCOMM.2020.2975996

    Google Scholar 

  64. Hausdorff F. Momentprobleme für ein endliches Intervall. Math Zeitschrift, 1923, 16: 220–248

    MathSciNet  MATH  Google Scholar 

  65. Gil-pelaez J. Note on the inversion theorem. Biometrika, 1951, 38: 481–482

    MathSciNet  MATH  Google Scholar 

  66. Deng N, Haenggi M. The meta distribution of the SINR in mm-wave D2D networks. In: Proceedings of 2017 IEEE Global Communications Conference (GLOBECOM'17), Singapore, 2017. 1–6

    Google Scholar 

  67. Kalamkar S S, Haenggi M. Spatial outage capacity of Poisson bipolar networks. In: Proceedings of 2017 IEEE International Conference on Communications (ICC'17), Paris, 2017. 1–6

    Google Scholar 

  68. Demarchou E, Psomas C, Krikidis I. Asynchronous ad hoc networks with wireless powered cognitive communications. IEEE Trans Cogn Commun Netw, 2019, 5: 440–451

    Google Scholar 

  69. Kalamkar S S, Haenggi M. Simple approximations of the SIR meta distribution in general cellular networks. IEEE Trans Commun, 2019, 67: 4393–4406

    Google Scholar 

  70. Yang H H, Quek T Q S. The meta distribution of SINR for small cell networks with temporal traffic. In: Proceedings of 2019 IEEE International Conference on Communications (ICC'19), Shanghai, 2019. 1–6

    Google Scholar 

  71. Chisci G, ElSawy H, Conti A, et al. On the scalability of uncoordinated multiple access for the Internet of Things. In: Proceedings of 2017 14th International Symposium on Wireless Communication Systems (ISWCS'17), Bologna, 2017. 402–407

    Google Scholar 

  72. ElSawy H, Alouini M S. On the meta distribution of coverage probability in uplink cellular networks. IEEE Commun Lett, 2017, 21: 1625–1628

    Google Scholar 

  73. Ali K, Elsawy H, Alouini M S. Meta distribution of downlink non-orthogonal multiple access (NOMA) in Poisson networks. IEEE Wirel Commun Lett, 2019, 8: 572–575

    Google Scholar 

  74. Chisci G, Elsawy H, Conti A, et al. Uncoordinated massive wireless networks: spatiotemporal models and multiaccess strategies. IEEE/ACM Trans Netw, 2019, 27: 918–931

    Google Scholar 

  75. Emara M, ElSawy H, Bauch G. A spatiotemporal framework for information freshness in IoT uplink networks. 2020. ArXiv: 200111333

    Google Scholar 

  76. Emara M, ElSawy H, Bauch G. A spatiotemporal model for peak AoI in uplink IoT networks: time vs event-triggered traffic. IEEE Internet Things J, 2020. ArXiv: 1912.07855

    Google Scholar 

  77. Kartun-Giles A P, Koufos K, Kim S. Meta distribution of SIR in ultra-dense networks with bipartite Euclidean matchings. 2019. ArXiv: 191013216

    Google Scholar 

  78. Koufos K, Dettmann C P. The meta distribution of the SIR in linear motorway VANETs. IEEE Trans Commun, 2019, 67: 8696–8706

    Google Scholar 

  79. Mankar P D, Dhillon H S, Haenggi M. Meta distribution analysis of the downlink SIR for the typical cell in a Poisson cellular network. In: Proceedings of 2019 IEEE Global Communications Conference (GLOBECOM'19), Waikoloa, 2019. 1–6

    Google Scholar 

  80. Rajanna A, Dettmann C P. Rate statistics in cellular downlink: a per-user analysis of rateless coded transmission. IEEE Commun Lett, 2020, 24: 1221–1225

    Google Scholar 

  81. Yu X L, Cui Q M, Haenggi M. SIR meta distribution for spatiotemporal cooperation in Poisson cellular networks. IEEE Access, 2019, 7: 73617–73626

    Google Scholar 

  82. Feng K, Haenggi M. A location-dependent base station cooperation scheme for cellular networks. IEEE Trans Commun, 2019, 67: 6415–6426

    Google Scholar 

  83. Liu Q S, Zhang Z P. The analysis of coverage probability, ASE and EE in heterogeneous ultra-dense networks with power control. Digital Commun Netw, 2020. doi: 10.1016/j.dcan.2020.02.002

    Google Scholar 

  84. Haenggi M. Efficient calculation of meta distributions and the performance of user percentiles. IEEE Wirel Commun Lett, 2018, 7: 982–985

    Google Scholar 

  85. Wang S S, Di Renzo M. On the meta distribution in spatially correlated non-Poisson cellular networks. EURASIP J Wirel Commun Netw, 2019, 2019: 1–11

    Google Scholar 

  86. Mnatsakanov R, Ruymgaart F H. Some properties of moment-empirical CDF's with application to some inverse estimation problems. Math Methods Stat, 2003, 12: 478–495

    MathSciNet  Google Scholar 

  87. Dettmann C P, Georgiou O. Isolation statistics in temporal spatial networks. Europhys Lett, 2017, 119: 28002

    Google Scholar 

  88. Guruacharya S, Hossain E. Approximation of meta distribution and its moments for Poisson cellular networks. IEEE Wirel Commun Lett, 2018, 7: 1074–1077

    Google Scholar 

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

    MATH  Google Scholar 

  90. Zhou X H, Guo J, Durrani S, et al. Power beacon-assisted millimeter wave ad hoc networks. IEEE Trans Commun, 2017, 66: 830–844

    Google Scholar 

  91. Weber S P, Yang X Y, Andrews J G, et al. Transmission capacity of wireless ad hoc networks with outage constraints. IEEE Trans Inform Theor, 2005, 51: 4091–4102

    MathSciNet  MATH  Google Scholar 

  92. 3GPP. Coordinated Multi-point Operation for LTE Physical Layer Aspects. 3GPP Technical Report, TR 36.819 V11.2.0, 2013. http://www.3gpp.org/DynaReport/36819.htm

    Google Scholar 

  93. Yu X L, Cui Q M, Haenggi M. Coherent joint transmission in downlink heterogeneous cellular networks. IEEE Wirel Commun Lett, 2017, 7: 274–277

    Google Scholar 

  94. Mukherjee A, Fakoorian S A A, Huang J, et al. Principles of physical layer security in multiuser wireless networks: a survey. IEEE Commun Surv Tut, 2014, 16: 1550–1573

    Google Scholar 

  95. Li Y P, Zhang R Q, Zhang J H, et al. Cooperative jamming via spectrum sharing for secure UAV communications. IEEE Wirel Commun Lett, 2020, 9: 326–330

    Google Scholar 

  96. Yang N, Wang L F, Geraci G, et al. Safeguarding 5G wireless communication networks using physical layer security. IEEE Commun Mag, 2015, 53: 20–27

    Google Scholar 

  97. Wu Y P, Khisti A, Xiao C S, et al. A survey of physical layer security techniques for 5G wireless networks and challenges ahead. IEEE J Sel Areas Commun, 2018, 36: 679–695

    Google Scholar 

  98. Li Y P, Zhang R Q, Zhang J H, et al. Cooperative jamming for secure UAV communications with partial eavesdropper information. IEEE Access, 2019, 7: 94593–94603

    Google Scholar 

  99. Cisco. Cisco Annual Internet Report (2018-2023) White Paper. Cisco Technical Report, 2020. https://www.cisco.com/c/en/us/solutions/collateral/executive-perspectives/annual-internet-report/white-paper-c11-741490.html

    Google Scholar 

  100. Haenggi M. The mean interference-to-signal ratio and its key role in cellular and amorphous networks. IEEE Wirel Commun Lett, 2014, 3: 597–600

    Google Scholar 

  101. 3GPP. Study on Non-Orthogonal Multiple Access (NOMA) for NR. 3GPP Technical Report, TR 38.812, 2018. http://www.3gpp.org/ftp/Specs/archive/38_series/38.812/38812-g00.zip

    Google Scholar 

  102. Mankar P D, Parida P, Dhillon H S, et al. Downlink analysis for the typical cell in Poisson cellular networks. IEEE Wirel Commun Lett, 2020, 9: 336–339

    Google Scholar 

  103. Abdulla M, Wymeersch H. Fine-grained vs. average reliability for V2V communications around intersections. In: Proceedings of 2017 IEEE Global Communications Conference Workshops, Singapore, 2017. 1–5

    Google Scholar 

  104. Afshang M, Saha C, Dhillon H S. Equi-coverage contours in cellular networks. IEEE Wirel Commun Lett, 2018, 7: 700–703

    Google Scholar 

  105. Chisci G, ElSawy H, Conti A, et al. Latency in downlink cellular networks with random scheduling. In: Proceedings of 2019 IEEE International Conference on Communications (ICC'19), Shanghai, 2019. 1–6

    Google Scholar 

  106. Cui Q M, Ni W, Li S H, et al. Learning-assisted clustered access of 5G/B5G networks to unlicensed spectrum. IEEE Wirel Commun, 2020, 27: 31–37

    Google Scholar 

  107. Cui Q M, Gong Z Z, Ni W, et al. Stochastic online learning for mobile edge computing: learning from changes. IEEE Commun Mag, 2019, 57: 63–69

    Google Scholar 

  108. Angjelichinoski M, Trillingsgaard K F, Popovski P. A statistical learning approach to ultra-reliable low latency communication. IEEE Trans Commun, 2019, 67: 5153–5166

    Google Scholar 

  109. Singh S, Zhang X C, Andrews J G. Joint rate and SINR coverage analysis for decoupled uplink-downlink biased cell associations in HetNets. IEEE Trans Wirel Commun, 2015, 14: 5360–5373

    Google Scholar 

  110. Haenggi M. User point processes in cellular networks. IEEE Wirel Commun Lett, 2017, 6: 258–261

    Google Scholar 

  111. Kalamkar S S, Haenggi M. A simple approximation of the meta distribution for non-Poisson cellular networks. In: Proceedings of 2018 IEEE International Conference on Communications (ICC'18), Kansas City, 2018. 1–6

    Google Scholar 

  112. Haenggi M. ASAPPP: a simple approximative analysis framework for heterogeneous cellular networks. In: Proceedings of the IEEE 6th International Workshop on Heterogeneous and Small Cell Networks (HetSNets'14), Austin, 2014

    Google Scholar 

  113. Di Renzo M, Wang S S, Xi X J. Inhomogeneous double thinning-modeling and analysis of cellular networks by using inhomogeneous poisson point processes. IEEE Trans Wirel Commun, 2018, 17: 5162–5182

    Google Scholar 

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Acknowledgements

The work was supported by National Natural Science Foundation of China (Grant Nos. 61941114, 61941105, 61971066), Beijing Natural Science Foundation (Grant No. L182038), and National Youth Top-notch Talent Support Program.

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Authors and Affiliations

  1. National Engineering Laboratory for Mobile Network Technologies, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xinlei Yu, Qimei Cui, Na Li & Xiaofeng Tao

  2. National Computer Network Emergency Response Technical Team/Coordination Center of China (CNCERT/CC), Beijing, 100029, China

    Yuanjie Wang

  3. Department of Electrical Engineering, Tampere University, Tampere, 33720, Finland

    Mikko Valkama

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  1. Xinlei Yu
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Yu, X., Cui, Q., Wang, Y. et al. Stochastic geometry based analysis for heterogeneous networks: a perspective on meta distribution. Sci. China Inf. Sci. 63, 223301 (2020). https://doi.org/10.1007/s11432-020-2875-7

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