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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Very recent studies showed that in a fully loaded dense small cell network (SCN), the coverage probability performance will continuously decrease with the network densification. Such new results were captured in IEEE ComSoc Technology News with an alarming title of "Will Densification Be the Death of 5G?". In this paper, we revisit this issue from more practical views of realistic network deployment, such as a finite number of active base stations (BSs) and user equipments (UEs), a decreasing BS transmission power with the network densification, etc. Particularly, in dense SCNs, due to an oversupply of BSs with respect to UEs, a large number of BSs can be put into idle modes without signal transmission, if there is no active UE within their coverage areas. Setting those BSs into idle modes mitigates unnecessary inter-cell interference and reduces energy consumption. In this paper, we investigate the performance impact of such BS idle mode capability (IMC) on dense SCNs. Different from existing work, we consider a realistic path loss model incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions. Moreover, we obtain analytical results for the coverage probability, the area spectral efficiency (ASE) and the energy efficiency (EE) performance for SCNs with the BS IMC and show that the performance impact of the IMC on dense SCNs is significant. As the BS density surpasses the UE density in dense SCNs, the coverage probability will continuously increase toward one, addressing previous concerns on "the death of 5G". Finally, the performance improvement in terms of the EE performance is also investigated for dense SCNs using practical energy models developed in the Green-Touch project. 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. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math .