A Tractable Approach to Coverage and Rate in Cellular Networks

By Jeffrey G. Andrews, François Baccelli, Radha Krishna Ganti. IEEE Transactions on Communications, 2010

3,112 citations recorded by the source corpus.

Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/0bfc3626485953e2d3f87854a00a50f88c62269d

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Citations in the corpus

A Primer on Cellular Network Analysis Using Stochastic Geometry (2016, methodology): “We note that more general fading/shadowing distributions can be accommodated as in [1] and many subsequent papers, but with a loss of tractability and without much change to the results.”
Coverage and capacity of millimeter-wave cellular networks (2014, methodology): “The model of PPP base stations generally provides a lower bound on the network performance in reality [12], as the base stations are randomly dropped without any planning.”
The Meta Distribution of SINR for Small Cell Networks with Temporal Traffic (2019, methodology): “In particular, we compare the simulated SINR coverage probability [21] and the analytical mean computed via the SINR meta distribution in (7) as follows”
Tractable Resource Management With Uplink Decoupled Millimeter-Wave Overlay in Ultra-Dense Cellular Networks (2015, methodology): “Under this interference-limited network, in addition, SE is independent of BS densification and transmission power increase [35].”
Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks (2011, methodology): “Indeed, the recent work [29] showed that for a one-tier network, even with the BS locations drawn from a Poisson Point Process (PPP), the resulting network model is about as accurate as the standard grid model, when compared to an actual 4 G network.”
Towards 1 Gbps/UE in Cellular Systems: Understanding Ultra-Dense Small Cell Deployments (2015, background): “density, contradicting the results in [66], [67] where it is independent of BS density.”
Millimeter-Wave Massive MIMO Communication for Future Wireless Systems: A Survey (2018, background): “System-level performance evaluation of cellular networks is usually performed via numerical simulations or mathematical analyses, both of which are widely regarded as difficult, time-consuming and demanding, with respect to ensuring high confidence levels, employing sufficient and representative dat”
Downlink Cellular Network Analysis With Multi-Slope Path Loss Models (2014, methodology): “Fo r example, using the standard path loss function, [16] shows t hat the network density does not change the SINR distribution in the interference-limited case, which leads to the potent ial throughput growing linearly with the network density and implies a linear scaling for the cellular network a”
Coverage and Rate Analysis for Millimeter-Wave Cellular Networks (2014, methodology): “Moreover, the stochastic model was shown to provide a lower bound of the performance in a real cellular system [16].”
Spatio-Temporal Analysis for SINR Coverage in Small Cell Networks (2019, background): “The intrinsic elegance in modeling and analysis has popularized its application in evaluating performance among various wireless systems, including ad-hoc networks [5], cellular networks [9], or more advanced heterogeneous networks [10], even with device-to-device (D2D) communication [11] and multip”
Throughput Optimization, Spectrum Allocation, and Access Control in Two-Tier Femtocell Networks (2012, methodology): “Motivated by the accuracy and tractability of the PPP macrocell and femtocell models, we capitalize on [25] and [26] and extend them to a two-tier femtocell network model.”
Stochastic Geometry for Modeling, Analysis, and Design of Multi-Tier and Cognitive Cellular Wireless Networks: A Survey (2013, methodology): “Although the idea of modeling the cellular network using the PPP goes back to the late 90’s [52], [53], the work in [54] brought much attention to this modeling approach due to the useful formulas derived for the performance metrics (such as the outage probability and the mean transmission rate), an”
Joint Resource Partitioning and Offloading in Heterogeneous Cellular Networks (2013, background): “The empirical validation in [22] and theoretical validation in [23] for heavily shadowed cellular networks have strengthened the case of modeling macro cellular networks using a PPP. Due to the formation of random association/coverage areas in such network models, load distribution is difﬁcult to…”
Offloading in Heterogeneous Networks: Modeling, Analysis, and Design Insights (2012, methodology): “Lemma 5 reduces to the earlier derived SINR coverage expressions in [24] for M = K = 1 (single tier, single RAT) and those in [22] for M = 1 (single RAT, multiple tiers).”
Analytical Modeling of Mode Selection and Power Control for Underlay D2D Communication in Cellular Networks (2014, background): “That is, in addition to the PPP assumption for the cellular BSs which gives pessimistic bounds on the performance metrics [15], [17], [18], the one channel assumption along with the aggressive spectrum access for the UEs operating in the D2D mode introduce massive cross-mode and intra-mode interfere”
Smart radio environments empowered by reconfigurable AI meta-surfaces: an idea whose time has come (2019, methodology): “In 2011, notably, Poisson point processes were used to formulate the coverage probability in cellular networks [109].”
Cache-enabled small cell networks: modeling and tradeoffs (2014, methodology): “Using recent results from [21], we propose a system model and define performance metrics by taking into account system parameters including signalto-interference-plus-noise ratio (SINR), base station location, target file bitrate, storage size and file popularity distribution.”
Tractable Model for Rate in Self-Backhauled Millimeter Wave Cellular Networks (2014, background): “ged W BS, whose distribution can be expressed as in [26] noting the mean association cell area of a W BS is 1S d(˝ min) . The W network’s SINR coverage P can be derived as in earlier work [36], [42]. E. Validation In the proposed model, the primary geography dependent parameters are C and D. As men”