Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks

TLDR

Cellular networks are transitioning from planned large tower‑mounted base stations to irregular deployments of heterogeneous infrastructure, including micro, pico, femtocells, and distributed antennas. The paper develops a tractable, flexible, and accurate model for a downlink heterogeneous cellular network comprising K tiers of randomly located base stations with varying transmit power, data rate, and density. The authors derive a closed‑form expression for coverage probability under both open and closed access, validate the model against an actual LTE tier‑1 network with the remaining tiers modeled as independent Poisson point processes, and compute the average rate and load per tier for a randomly located mobile. The model achieves accuracy within 1–2 dB and reveals that, for interference‑limited open‑access networks with equal target‑SINR across tiers, adding more tiers or base stations does not change the coverage probability or outage rate.

Abstract

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.