Offloading in Heterogeneous Networks: Modeling, Analysis, and Design
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Abstract

Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the over-loaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of \(M\) different RATs, each deploying up to \(K\) different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize \(\SINR\) coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate.

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A Tractable Approach to Coverage and Rate in Cellular Networks

, , (2011)

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.

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Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks

, , … (2012)

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given SINR, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.

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Heterogeneous Cellular Networks with Flexible Cell Association: A Comprehensive Downlink SINR Analysis

Han-Shin Jo, Young Sang, Ping Xia … (2011)

In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function. The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the \emph{average ergodic rate} of the typical user, and the \emph{minimum average user throughput} -- the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics.