Downlink Cellular Network Analysis With LOS/NLOS Propagation and Elevated Base Stations

Abstract

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 in both small-scale and large-scale fading. Modeling LOS fading with Nakagami-m fading, we provide a unified framework based on stochastic geometry that encompasses both closest and strongest BS association. Our study 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-m 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 m. 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 squared BS height. Index TermsCoverage probability, elevated base stations, Nakagami-m fading, performance analysis, stochastic geometry, ultra-dense networks, 5G.

A Unified Asymptotic Analysis of Area Spectral Efficiency in Ultradense Cellular Networks

“…In addition, a third definition called the average potential throughput, was proposed in [20], and then used in [18], [19], [22], [42], [43], to study the average ASE in cellular networks as the following:…”

“…Another interesting path loss function is L 4 (r) = A(c 2 0 + r 2 ) −η 2 which captures the case where the elevation difference between the BSs and users is c 0 > 0 [18]. This model has the desired properties in Definition 1 and also satisfies the conditions in Corollary 5 as shown in Table I, which also includes the asymptotic average ASE under this model in a simple closed form that exactly shows how the average ASE scales with the elevation difference c 0 .…”

On the Coverage and Capacity of Ultra-Dense Networks With Directional Transmissions

“…Finally, taking similar steps to the second integral in equality (8) , where θBθU 4π 2 ∈ (0, 1], T 1+T ∈ (0, 1) and ρ(T, β 2 ) ∈ R + . Then we have θBθU For the constrained ASE given in (5), it is obvious that the second term inside the integral monotonically decreases w.r.t θB θU 4π 2 . Denote the partial derivative of the first term w.r.t θB θU 4π 2 by A 1 , and we have: where θB θU 4π 2 ∈ (0, 1], e t −1 e t ∈ (0, 1) and ρ(e t − 1, β 2 ) ∈ R + .…”

“…They find the near-field path loss exponent has a phase transition feature, meaning that the throughput has different asymptotic characteristics depending on whether the nearfield path loss exponent exceeds a threshold. A multi-slope path loss model with line-of-sight (LOS) and non-line-of-sight (NLOS) channels is investigated in [5]. The probability decreases and the constrained area spectrum efficiency (ASE) experiences a slow growth or even a decrease.…”

Optimal Coverage and Rate in Downlink Cellular Networks: A SIR Meta-Distribution Based Approach

“…One of the key observations which follows from these studies is that the BS heights should be lowered as it reduces the path-loss between UE and BS. On a closer inspection it is obvious that the path-loss model used in [14] and [15] does not adequately capture the fact that LoS probability increases with an increase in the BS height along with the path-loss and NLoS probability increases with a decrease in BS height while the path-loss also decreases with a lowering of the BS height. This is indeed adequately captured in [16] and is employed in [17] to investigate optimal height for a low altitude platform empowered with a cellular BS.…”