The aggressive spatial spectrum reuse (SSR) by network densification using smaller cells has successfully driven the wireless communication industry onward in the past decades. In our future journey toward ultra-dense networks (UDNs), a fundamental question needs to be answered. Is there a limit to SSR? In other words, when we deploy thousands or millions of small cell base stations (BSs) per square kilometer, is activating all BSs on the same time frequency resource the best strategy? In this paper, we present theoretical analyses to answer such question. In particular, we find that both the signal and interference powers become bounded in practical UDNs with a non-zero BS-to-UE antenna height difference and a finite UE density, which leads to a constant capacity scaling law. As a result, there exists an optimal SSR density that can maximize the network capacity. Hence, the limit to SSR should be considered in the operation of future UDNs.
Recently, a few noteworthy studies have followed and revisited the network performance analysis of UDNs using more practical assumptions @cite_8 @cite_18 @cite_9 @cite_10 @cite_12 @cite_3 , such as a general multi-piece path loss model with probabilistic line-of-sight (LoS) and non-LoS (NLoS) transmissions, a non-zero BS-to-UE antenna height difference @math , and a non-fully-loaded network with a finite UE density @math .
@cite_18 @cite_8 @cite_9 @cite_3 @cite_10 @cite_12
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In this paper, we introduce a sophisticated path loss model incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions to study their impact on the performance of dense small cell networks (SCNs). Analytical results are obtained for the coverage probability and the area spectral efficiency (ASE), assuming both a general path loss model and a special case with a linear LoS probability function. The performance impact of LoS and NLoS transmissions in dense SCNs in terms of the coverage probability and the ASE is significant, both quantitatively and qualitatively, compared with the previous work that does not differentiate LoS and NLoS transmissions. Our analysis demonstrates that the network coverage probability first increases with the increase of the base station (BS) density, and then decreases as the SCN becomes denser. This decrease further makes the ASE suffer from a slow growth or even a decrease with network densification. The ASE will grow almost linearly as the BS density goes ultra dense. For practical regime of the BS density, the performance results derived from our analysis are distinctively different from previous results, and thus shed new insights on the design and deployment of future dense SCNs. In this paper, we investigate the downlink performance of dense cellular networks with elevated base stations (BSs) using a channel model that incorporates line-of-sight (LOS) non-line-of-sight (NLOS) propagation into both small-scale and large-scale fading. Modeling LOS fading with Nakagami- @math fading, we provide a unified framework based on stochastic geometry that encompasses both closest and strongest BS association. This paper is particularized to two distance-dependent LOS NLOS models of practical interest. Considering the effect of LOS propagation alone, we derive closed-form expressions for the coverage probability with Nakagami- @math fading, showing that the performance for strongest BS association is the same as in the case of Rayleigh fading, whereas for closest BS association it monotonically increases with the shape parameter @math . Then, focusing on the effect of elevated BSs, we show that network densification eventually leads to near-universal outage even for moderately low BS densities: in particular, the maximum area spectral efficiency is proportional to the inverse of the square of the BS height. The concept of Ultra Dense Networks (UDN) is often seen as a key enabler of the next generation mobile networks. However, existing analysis of UDNs, including Stochastic Geometry, has not been able to fully determine the potential gains and limits of densification. In this paper we study performance of UDNs in downlink and provide new insights on the impact of antenna height and careful site selection on the network performance. We focus our investigation on the probability of coverage, average cell rate and average area spectral efficiency for networks with regular and random BS deployments. We show that under a path-loss model which considers antenna height there exists an upper limit on network performance which is dependent on the path-loss model parameters. Our analysis shows an interesting finding that even for over-densified networks a non-negligible system performance can be achieved. This paper presents an analytically tractable stochastic geometry model for urban wireless networks, where the locations of the nodes and the shadowing are highly correlated and different path loss functions can be applied to line-of-sight (LOS) and non-line-of-sight (NLOS) links. Using a distance-based LOS path loss model and a blockage (shadowing)-based NLOS path loss model, we are able to derive the distribution of the interference observed at a typical location and the joint distribution at different locations. When applied to cellular networks, this model leads to tractable expressions for the coverage probability (SINR distribution). We show that this model captures important features of urban wireless networks, which cannot be analyzed using existing models. The numerical results also suggest that even in the presence of significant penetration loss, ignoring the NLOS interference can lead to erroneous estimations on coverage. They also suggest that allowing users to be associated with NLOS BSs may provide a non-trivial gain on coverage.