A New Capacity Scaling Law in Ultra-Dense Networks

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Abstract

We discover a new capacity scaling law in ultra-dense networks (UDNs) under practical system assumptions, such as a general multi-piece path loss model, a non-zero base station (BS) to user equipment (UE) antenna height difference, and a finite UE density. The intuition and implication of this new capacity scaling law are completely different from that found in year 2011. That law indicated that the increase of the interference power caused by a denser network would be exactly compensated by the increase of the signal power due to the reduced distance between transmitters and receivers, and thus network capacity should grow linearly with network densification. However, we find that both the signal and interference powers become bounded in practical UDNs, which leads to a constant capacity scaling law. As a result, network densification should be stopped at a certain level for a given UE density, because the network capacity will reach its limit due to (i) the bounded signal and interference powers, and (ii) a finite frequency reuse factor because of a finite UE density. Our new discovery on the constant capacity scaling law also resolves the recent concerns about network capacity collapsing in UDNs, e.g., the capacity crash due to a non-zero BS-to-UE antenna height difference, or a bounded path loss model of the near-field (NF) effect, etc.

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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.