Asymptotic Deployment Gain: A Simple Approach to Characterize the SINR Distribution in General Cellular Networks

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the outage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) is smaller than a threshold) as the threshold goes to zero. We show that, remarkably, the slope of the outage probability (in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the success probabilities of the PPP and another point process in the high-reliability regime (where the success probability is near 1). To demonstrate the usefulness of the ADG for the characterization of the SINR distribution, we investigate the outage probabilities and the ADGs for different point processes and fading statistics by simulations.

[1]  Jeffrey G. Andrews,et al.  A Tractable Approach to Coverage and Rate in Cellular Networks , 2010, IEEE Transactions on Communications.

[2]  Jeffrey G. Andrews,et al.  Analytical Evaluation of Fractional Frequency Reuse for OFDMA Cellular Networks , 2011, IEEE Transactions on Wireless Communications.

[3]  Martin Haenggi,et al.  Interference in ad hoc networks with general motion-invariant node distributions , 2008, 2008 IEEE International Symposium on Information Theory.

[4]  Jeffrey G. Andrews,et al.  A primer on spatial modeling and analysis in wireless networks , 2010, IEEE Communications Magazine.

[5]  F.I. Meno,et al.  Mobile fading—Rayleigh and lognormal superimposed , 1977, IEEE Transactions on Vehicular Technology.

[6]  Martin Haenggi,et al.  Spatial Stochastic Models and Metrics for the Structure of Base Stations in Cellular Networks , 2013, IEEE Transactions on Wireless Communications.

[7]  Martin Haenggi,et al.  Asymptotic deployment gain: A new approach to characterize coverage probability , 2014, 2014 IEEE International Conference on Communications (ICC).

[8]  Shu Lin,et al.  Error Control Coding , 2004 .

[9]  Wuyang Zhou,et al.  The Ginibre Point Process as a Model for Wireless Networks With Repulsion , 2014, IEEE Transactions on Wireless Communications.

[10]  Esko Valkeila,et al.  An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure, 2nd Edition by Daryl J. Daley, David Vere‐Jones , 2008 .

[11]  Lazaros F. Merakos,et al.  Energy-efficient and interference-aware handover decision for the LTE-Advanced femtocell network , 2013, 2013 IEEE International Conference on Communications (ICC).

[12]  Martin Haenggi,et al.  Outage Probability of General Ad Hoc Networks in the High-Reliability Regime , 2010, IEEE/ACM Transactions on Networking.

[13]  Ulrike Goldschmidt,et al.  An Introduction To The Theory Of Point Processes , 2016 .

[14]  BaccelliFrançois,et al.  Stochastic geometry and random graphs for the analysis and design of wireless networks , 2009 .

[15]  Yi Zhong,et al.  Multi-Channel Hybrid Access Femtocells: A Stochastic Geometric Analysis , 2013, IEEE Transactions on Communications.

[16]  Jeffrey G. Andrews,et al.  Stochastic geometry and random graphs for the analysis and design of wireless networks , 2009, IEEE Journal on Selected Areas in Communications.

[17]  N. Miyoshi,et al.  A cellular network model with Ginibre configurated base stations , 2012 .

[18]  Marco Di Renzo,et al.  Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels: A Stochastic Geometry Approach , 2013, IEEE Transactions on Communications.

[19]  Martin Haenggi,et al.  Mean Interference in Hard-Core Wireless Networks , 2011, IEEE Communications Letters.

[20]  Tony Q. S. Quek,et al.  Throughput Optimization, Spectrum Allocation, and Access Control in Two-Tier Femtocell Networks , 2012, IEEE Journal on Selected Areas in Communications.

[21]  Jeffrey G. Andrews,et al.  A new method for computing the transmission capacity of non-Poisson wireless networks , 2010, 2010 IEEE International Symposium on Information Theory.

[22]  Jeffrey G. Andrews,et al.  Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks , 2011, IEEE Journal on Selected Areas in Communications.

[23]  Kenji Nakagawa,et al.  Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable , 2006, IEEE Transactions on Information Theory.

[24]  Martin Haenggi,et al.  Stochastic Geometry for Wireless Networks , 2012 .

[25]  M. Haenggi,et al.  Interference in Large Wireless Networks , 2009, Found. Trends Netw..

[26]  S. Weber,et al.  A stochastic geometry approach to wideband ad hoc networks with channel variations , 2006, 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks.

[27]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[28]  A. Turkmani.  Probability of error for M-branch macroscopic selection diversity , 1992 .

[29]  Jeffrey G. Andrews,et al.  Transmission capacity of wireless ad hoc networks with outage constraints , 2005, IEEE Transactions on Information Theory.

[30]  Ekram Hossain,et al.  A Modified Hard Core Point Process for Analysis of Random CSMA Wireless Networks in General Fading Environments , 2013, IEEE Transactions on Communications.

[31]  Edward J. Coyle,et al.  An energy efficient hierarchical clustering algorithm for wireless sensor networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[32]  Jeffrey G. Andrews,et al.  High-SIR Transmission Capacity of Wireless Networks With General Fading and Node Distribution , 2011, IEEE Transactions on Information Theory.

[33]  Martin Haenggi,et al.  Interference and Outage in Clustered Wireless Ad Hoc Networks , 2007, IEEE Transactions on Information Theory.

[34]  Holger Paul Keeler,et al.  Using Poisson processes to model lattice cellular networks , 2013, 2013 Proceedings IEEE INFOCOM.

[35]  Janne Riihijärvi,et al.  A spatial statistics approach to characterizing and modeling the structure of cognitive wireless networks , 2012, Ad Hoc Networks.