TY - JOUR
T1 - A Tractable Framework for the Analysis of Dense Heterogeneous Cellular Networks
AU - Ak, Serkan
AU - Inaltekin, Hazer
AU - Poor, H. Vincent
N1 - Funding Information:
Manuscript received August 26, 2017; revised January 11, 2018; accepted February 10, 2018. Date of publication February 21, 2018; date of current version July 13, 2018. This research was supported in part by the European Union Research Executive Agency Marie Curie FP7-Reintegration-Grants under Grant PCIG10-GA-2011-303713, in part by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant 115E162, and in part by the U.S. National Science Foundation under Grants CNS-1702808 and ECCS-1647198. This work was presented in part at the IEEE International Symposium on Information Theory (ISIT) [1], [2], in Barcelona, Spain, July 2016. The associate editor coordinating the review of this paper and approving it for publication was Z. Dawy. (Corresponding author: Serkan Ak.) S. Ak is with the Wireless Networking and Communications Group, The University of Texas at Austin, Austin, TX 78701 USA (e-mail: serkanak@utexas.edu).
Publisher Copyright:
© 2018 IEEE.
PY - 2018/7
Y1 - 2018/7
N2 - This paper investigates the downlink performance of dense K -tier heterogeneous cellular networks (HCNs) under general settings. First, Gaussian approximation bounds for the standardized aggregate wireless interference (AWI) in dense K -tier HCNs are obtained for when base stations (BSs) in each tier are distributed over the plane according to a spatial and general Poisson point process. The Kolmogorov-Smirnov (KS) distance is used to measure deviations of the distribution of the standardized AWI from the standard normal distribution. An explicit and analytical expression bounding the KS distance between these two distributions is obtained as a function of a broad range of network parameters, such as per-tier transmission power levels, per-tier BS intensity, BS locations, general fading statistics, and general bounded path-loss models. Bounds achieve a good statistical match between the standardized AWI distribution and its normal approximation even for moderately dense HCNs. Second, various spatial performance metrics of interest, such as outage capacity, ergodic capacity, and area spectral efficiency in the downlink of K-tier HCNs for general signal propagation models are investigated by making use of the derived distribution approximation results. Considering two specific BS association policies, it is shown that the derived performance bounds track the actual performance metrics reasonably well for a wide range of BS intensities, with the gap among them becoming negligibly small for denser HCN deployments. Finally, both analytical and numerical results on the area spectral efficiency reveal a non-linear growth trend with diminishing returns of HCN performance. Hence, the SIR invariance property does not hold under bounded path-loss models, which is a critical finding from the HCN design perspective. In particular, it points out a critical BS density beyond which the HCN performance starts to decline due to excessive wireless interference.
AB - This paper investigates the downlink performance of dense K -tier heterogeneous cellular networks (HCNs) under general settings. First, Gaussian approximation bounds for the standardized aggregate wireless interference (AWI) in dense K -tier HCNs are obtained for when base stations (BSs) in each tier are distributed over the plane according to a spatial and general Poisson point process. The Kolmogorov-Smirnov (KS) distance is used to measure deviations of the distribution of the standardized AWI from the standard normal distribution. An explicit and analytical expression bounding the KS distance between these two distributions is obtained as a function of a broad range of network parameters, such as per-tier transmission power levels, per-tier BS intensity, BS locations, general fading statistics, and general bounded path-loss models. Bounds achieve a good statistical match between the standardized AWI distribution and its normal approximation even for moderately dense HCNs. Second, various spatial performance metrics of interest, such as outage capacity, ergodic capacity, and area spectral efficiency in the downlink of K-tier HCNs for general signal propagation models are investigated by making use of the derived distribution approximation results. Considering two specific BS association policies, it is shown that the derived performance bounds track the actual performance metrics reasonably well for a wide range of BS intensities, with the gap among them becoming negligibly small for denser HCN deployments. Finally, both analytical and numerical results on the area spectral efficiency reveal a non-linear growth trend with diminishing returns of HCN performance. Hence, the SIR invariance property does not hold under bounded path-loss models, which is a critical finding from the HCN design perspective. In particular, it points out a critical BS density beyond which the HCN performance starts to decline due to excessive wireless interference.
KW - 5G
KW - Gaussian approximation
KW - Heterogeneous cellular networks
KW - Poisson point processes
KW - downlink interference
KW - outage capacity
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U2 - 10.1109/TCOMM.2018.2808353
DO - 10.1109/TCOMM.2018.2808353
M3 - Article
AN - SCOPUS:85042352504
SN - 1558-0857
VL - 66
SP - 3151
EP - 3171
JO - IEEE Transactions on Communications
JF - IEEE Transactions on Communications
IS - 7
ER -