Downlink Coverage Probability Research Articles

Downlink Coverage Probability and Rate Analysis Based on Backhaul-Access Pair in Moving Networks

Downlink Coverage Probability and Rate Analysis Based on Backhaul-Access Pair in Moving Networks

UAV-Aided Post-Disaster Cellular Networks: A Novel Stochastic Geometry Approach

Motivated by the need for ubiquitous and reliable communications in post-disaster emergency management systems (EMSs), we hereby present a novel and efficient stochastic geometry (SG) framework. This mathematical model is specifically designed to evaluate the quality of service (QoS) experienced by a typical ground user equipment (UE) residing either inside or outside a generic area affected by a calamity. In particular, we model the functioning terrestrial base stations (TBSs) as an inhomogeneous Poisson point process (IPPP), and assume that a given number of uniformly distributed unmanned aerial vehicles (UAVs) equipped with cellular transceivers is deployed in order to compensate for the damage suffered by some of the existing TBSs. The downlink (DL) coverage probability is then derived based on the maximum average received power association policy and the assumption of Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading conditions for all wireless links. The proposed numerical results show insightful trends in terms of coverage probability, depending on: distance of the UE from the disaster epicenter, disaster radius, quality of resilience (QoR) of the terrestrial network, and fleet of deployed ad-hoc aerial base stations (ABSs). The aim of this paper is therefore to prove the effectiveness of vertical heterogeneous networks (VHetNets) in emergency scenarios, which can both stimulate the involved authorities for their implementation and inspire researchers to further investigate related problems.

Performance of Indoor Small-Cell Networks Under Interior Wall Penetration Losses

The performance of indoor small-cell networks (SCNs) is affected by the indoor environment, such as walls, blockages, etc. In this paper, we investigate the effect of interior wall attenuation on the performance of an indoor SCN. Specifically, the spatial distribution of interior walls is modelled based on the random shape theory and the indoor base stations (BSs) are distributed following a homogeneous Poisson point process. The channel model includes the path loss, Rayleigh fading, and wall attenuation. We analytically derive the downlink coverage probability under the strongest received signal user association strategy, which is validated by Monte Carlo simulations for three typical interior wall layouts (i.e., random layout, binary orientation layout, and Manhattan grid). The analytical results show that for a given density of interior walls and signal strength attenuation per wall, there is an optimal BS density that maximises the coverage probability, and the optimal BS density increases as the wall attenuation increases.

Coverage Analysis of mmWave and THz-Enabled Aerial and Terrestrial Heterogeneous Networks

Heterogeneous networks (HetNets) are becoming a promising solution for future wireless systems to satisfy the high data rate requirements. This paper introduces a stochastic geometry framework for the analysis of the downlink coverage probability in a multi-tier HetNet consisting of a macro-base station (MBS) operating at sub-6 GHz, millimeter wave (mmWave)-enabled unmanned aerial vehicles (UAVs) operating at 28 GHz, and small BSs operating both at mmWave and THz frequencies. The analytical expressions for the coverage probability for each tier have been derived in the paper. Monte Carlo simulations are then performed to validate the analytical expressions. The effectiveness of the HetNet is analyzed on various performance metrics including association and coverage probabilities for different network parameters. We show that the mmWave and THz-enabled cells provide significant improvement in the achievable data rates because of their high available bandwidths, however, they have a degrading effect on the coverage probability due to their high propagation losses.

Uncoordinated Spectrum Sharing in Millimeter Wave Networks Using Carrier Sensing

We propose using Carrier Sensing (CS) for distributed interference management in millimeter-wave (mmWave) cellular networks where spectrum is shared by multiple operators that do not coordinate among themselves. In addition, even the base station sites can be shared by the operators. We describe important challenges in using traditional CS in this setting and propose enhanced CS protocols to address these challenges. Using stochastic geometry, we develop a general framework for downlink coverage probability analysis of our shared mmWave network in the presence of CS and derive the downlink coverage probability expressions for several CS protocols. Our work is the first to investigate and analyze (using stochastic geometry) CS for mmWave networks with spectrum and BS sites shared among non-coordinating operators. We evaluate the downlink coverage probability of our shared mmWave network using simulations as well as numerical examples based on our analysis. Our evaluations show that our proposed approach leads to an improvement in coverage probability, compared to the coverage probability with no CS, for higher values of signal-to-interference and noise ratio (SINR). Interestingly, our evaluations also reveal that for lower values of SINR, not using any CS is the best strategy in terms of the downlink coverage probability.

Nonhomogeneous Stochastic Geometry Analysis of Massive LEO Communication Constellations

Providing truly ubiquitous connectivity requires development of low Earth orbit (LEO) satellite Internet, whose theoretical study is lagging behind network-specific simulations. In this paper, we derive analytical expressions for the downlink coverage probability and average data rate of a massive inclined LEO constellation in terms of total interference power’s Laplace transform in the presence of fading and shadowing, ergo presenting a stochastic geometry-based analysis. We assume the desired link to experience Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading, which serves to represent different fading scenarios by varying integer <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> , while the interfering channels can follow any fading model without an effect on analytical tractability. To take into account the inherent non-uniform distribution of satellites across different latitudes, we model the LEO network as a nonhomogeneous Poisson point process with its intensity being a function of satellites’ actual distribution in terms of constellation size, the altitude of the constellation, and the inclination of orbital planes. From the numerical results, we observe optimum points for both the constellation altitude and the number of orthogonal frequency channels; interestingly, the optimum user’s latitude is greater than the inclination angle due to the presence of fewer interfering satellites. Overall, the presented study facilitates general stochastic evaluation and planning of satellite Internet constellations without specific orbital simulations or tracking data on satellites’ exact positions in space.

On the Optimal Base-Station Height in mmWave Small-Cell Networks Considering Cylindrical Blockage Effects

Small-cell networks (SCNs), especially those operating in millimeter-wave bands, are sensitive to blockages. In this letter, we develop a three-dimensional (3D) SCN model considering blockages to investigate the impact of base-station (BS) height, BS density and blockage density on the downlink coverage probability. More specifically, we model the blockages as cylinders whose locations follow a Poisson point process and model the locations of BSs as a Poisson hole process. We assume that all the BSs are of the same height and the blockage height follows an exponential distribution. Based on the 3D SCN model, we derive the exact integral expression of coverage probability for general SCNs and the closed-form expression of coverage probability for ultra-dense SCNs. Our analytical results are verified to be reliable through simulations. The numerical results quantify the impact of the blockage density and the BS height on the coverage probability. For a small blockage density, elevated BSs always degrade the coverage probability, while the coverage probability first increases and then decreases with the BS height when the blockage density becomes sufficiently large.

Fractional Frequency Reuse in Random Hybrid FD/HD Small Cell Networks With Fractional Power Control

Small cells are regarded as a promising solution for improving the coverage and spectral efficiency of the fifth generation (5G) cellular networks. Small cell networks utilize low transmission power levels and thus, are appropriate for deploying full-duplex (FD) technology. In this paper, a hybrid full/half duplex (FD/HD) small cell network exploiting fractional frequency reuse (FFR) and fractional power control (FPC) for interference mitigation is considered. Theoretical expressions for the coverage probability and the average sum-rate in uplink and downlink directions are derived for systems that make use of conventional frequency reuse, hard FFR, and soft FFR. The impact of various system parameters, such as power control parameter, small base station (SBS) density, and self-interference cancellation (SIC) parameters on system performance are investigated. The numerical experiments show that SBSs tend to operate in FD mode for large values of SBS density and SIC level. Also, interestingly, the optimal sum-rate is achieved when all SBSs operate either in FD or in HD mode. Finally, it is observed that exploiting FFR techniques in FD networks making use of FPC, significantly improves downlink coverage probability.

An Analytic Approach for Modeling the Coverage Performance of Dense Satellite Networks

Connectivity provided from space is the ultimate method for a true and uninterrupted global coverage, where there are several massive satellite constellations that are currently undergoing rapid deployment. This letter lays a tractable analytic approach for modeling the downlink coverage probability in such dense satellite networks. The presented framework utilizes tools from stochastic geometry leveraging recent developments in Satellite-to-Ground path-loss modeling, and in Line-of-Sight probability formulation. Simulation results show a very good match to the presented analytic forms even for lower number of satellites, suggesting that the obtained insights can be used by system designers to analytically predict and optimize the expected downlink coverage performance.

Downlink Coverage and Rate Analysis of an Aerial User in Vertical Heterogeneous Networks (VHetNets)

In this paper, we analyze the downlink coverage probability and rate of an aerial user in vertical HetNets (VHetNets) comprising aerial base stations (aerial-BSs) and terrestrial-BSs. The locations of terrestrial-BSs are modeled as an infinite 2-D Poisson Point Process (PPP), while the locations of aerial-BSs are modeled as a finite 2-D Binomial Point Process (BPP). Our cellular-to-air (C2A) channel model incorporates line-of-sight (LoS) and non-LoS transmissions between terrestrial-BSs and a typical aerial user, while we assume LoS transmissions for all aerial links. We assume that the aerial user is associated with an aerial-BS or terrestrial-BS that provides the strongest average received power. Using stochastic geometry, we derive exact and approximate expressions of the coverage probability and rate in terms of interference power’s Laplace transform. The expressions are simplified assuming only LoS transmissions for the C2A channels. This enables easy-to-compute equations with good accuracy at elevated aerial user heights. We find that aerial users hovering at low altitudes tend to connect to aerial-BSs in denser terrestrial environments. Employing directive beamforming at aerial-BSs guarantees an acceptable performance at the aerial user by reducing interference signals received from the aerial-BSs. In denser terrestrial networks, the performance at the aerial user degrades substantially despite beamforming.

On the Performance of Indoor Multi-Story Small-Cell Networks

Mobile data traffic has been largely generated indoors. However, indoor cellular networks have been studied either on a two-dimensional (2D) plane or as an intractable optimization problem for a multi-story building. In this paper, we develop a tractable three-dimensional small-cell network model for a multi-story building. On each story, the small-cell base stations (BS) are distributed following a 2D homogeneous Poisson point process. We analytically derive the downlink coverage probability, spectral efficiency (SE) and area spectral efficiency for the indoor network as functions of the story height, the penetration loss of the ceiling and the BS density. Our tractable expressions show that a higher penetration loss of the ceiling leads to a higher coverage probability and a higher SE. Meanwhile, with the increase of the story height or the BS density, the downlink coverage probability first decreases and then increases after reaching a minimum value, indicating that certain values of story height and BS density should be avoided for good indoor wireless coverage.

Downlink Coverage and Rate Analysis of Low Earth Orbit Satellite Constellations Using Stochastic Geometry

As low Earth orbit (LEO) satellite communication systems are gaining increasing popularity, new theoretical methodologies are required to investigate such networks' performance at large. This is because deterministic and location-based models that have previously been applied to analyze satellite systems are typically restricted to support simulations only. In this paper, we derive analytical expressions for the downlink coverage probability and average data rate of generic LEO networks, regardless of the actual satellites' locality and their service area geometry. Our solution stems from stochastic geometry, which abstracts the generic networks into uniform binomial point processes. Applying the proposed model, we then study the performance of the networks as a function of key constellation design parameters. Finally, to fit the theoretical modeling more precisely to real deterministic constellations, we introduce the effective number of satellites as a parameter to compensate for the practical uneven distribution of satellites on different latitudes. In addition to deriving exact network performance metrics, the study reveals several guidelines for selecting the design parameters for future massive LEO constellations, e.g., the number of frequency channels and altitude.

Performance Analysis of Cell-Free Massive MIMO Systems: A Stochastic Geometry Approach

Cell-free (CF) massive multiple-input-multiple-output (MIMO) has emerged as an alternative deployment for conventional cellular massive MIMO networks. As revealed by its name, this topology considers no cells, while a large number of multi-antenna access points (APs) serves simultaneously a smaller number of users over the same time/frequency resources through time-division duplex (TDD) operation. Prior works relied on the strong assumption (quite idealized) that the APs are uniformly distributed, and actually, this randomness was considered during the simulation and not in the analysis. However, in practice, ongoing and future networks become denser and increasingly irregular. Having this in mind, we consider that the AP locations are modeled by means of a Poisson point process (PPP) which is a more realistic model for the spatial randomness than a grid or uniform deployment. In particular, by virtue of stochastic geometry tools, we derive both the downlink coverage probability and achievable rate. Notably, this is the only work providing the coverage probability and shedding light on this aspect of CF massive MIMO systems. Focusing on the extraction of interesting insights, we consider small-cells (SCs) as a benchmark for comparison. Among the findings, CF massive MIMO systems achieve both higher coverage and rate with comparison to SCs due to the properties of favorable propagation, channel hardening, and interference suppression. Especially, we showed for both architectures that increasing the AP density results in a higher coverage which saturates after a certain value and increasing the number of users decreases the achievable rate but CF massive MIMO systems take advantage of the aforementioned properties, and thus, outperform SCs. In general, the performance gap between CF massive MIMO systems and SCs is enhanced by increasing the AP density. Another interesting observation concerns that a higher path-loss exponent decreases the rate while the users closer to the APs affect more the performance in terms of the rate.

Stochastic Analysis of Downlink Heterogeneous Cellular Networks: Based on Spatial Hybrid Model

In this paper, a hybrid model for heterogeneous cellular networks (HCNs) is proposed based on the differences in the distribution characteristics, path loss models and transmit power of macro and micro base stations (BSs). The macro base stations in HCNs are modelled as 2-D PPP which obeys certain parameters, and the small base stations are modelled as 3-D PPP. According to the stochastic geometry theory and the relevant knowledge of probability theory, the interference characteristics in HCNs are analysed, and the downlink coverage probability of the target users in the network are derived. Compared the hybrid interference model proposed in this paper with the traditional model, simulation shows that the hybrid interference model can illustrate the distribution characteristics of each kind of base station in HCNs more accurately, and the network performance based on model proposed in this paper is more accurate.

Downlink Coverage Probability in Cellular Networks With Poisson–Poisson Cluster Deployed Base Stations

Poisson-Poisson cluster processes (PPCPs) are a class of point processes exhibiting attractive point patterns. Recently, PPCPs are actively studied for modeling and analysis of heterogeneous cellular networks or device-to-device networks. However, surprisingly, to the best knowledge of the author, there is no exact derivation of downlink coverage probability in a numerically computable form for a cellular network with base stations (BSs) deployed according to a PPCP within the most fundamental setup such as single-tier, Rayleigh fading and nearest BS association. In this paper, we consider this fundamental model and derive a numerically computable form of coverage probability. To validate the analysis, we compare the results of numerical computations with those by Monte Carlo simulations and confirm the good agreement.

Coverage and Cell-Edge Sum-Rate Analysis of mmWave Massive MIMO Systems With ORP Schemes and MMSE Receivers

In this study, we consider the downlink of millimeter-wave massive multiple-input multiple-output systems that employ orthogonal random precoding (ORP) and minimum-mean-square-error (MMSE) receivers. In the ORP scheme, a precoding matrix consisting of orthogonal vectors is utilized at the transmitter, which provides beamforming gains to enhance the maximum signal-to-interference-plus-noise ratio (SINR) at the receivers. In this study, the ability of the ORP scheme with MMSE receivers to extend the cell coverage and its sum-rate performance for cell-edge users are investigated. In particular, we first derive the approximate distribution of the maximum SINR at the output of the MMSE receiver. Then, to analyze and optimize the ORP scheme with MMSE receivers in terms of coverage and sum-rate performance, the analytical expressions for the downlink coverage probability and sum rate are derived. It is shown that there is a tradeoff between coverage and sum-rate performance in the ORP scheme. In particular, a smaller number of precoding vectors provides larger coverage; however, it leads to a lower sum rate. To achieve optimal tradeoff between coverage and sum rate for the ORP scheme, we propose using multiple random precoder groups over multiple time slots. It is shown that the proposed scheme is capable of significantly enhancing coverage performance while preserving an acceptable sum rate for cell-edge users. The simulation results validate the analytical findings.

Coverage Analysis of User-Centric Wireless Network in a Comprehensive Fading Environment

This letter analyzes the downlink coverage probability of user-centric wireless network in a comprehensive fading environment. The comprehensive fading environment consists of two types of fading models: 1) a long-term shadowed fading, where all signals experience an identical and independent lognormal shadowing and 2) an instantaneous fading, where the desired signal experiences $\kappa $ – $\mu $ shadowed fading with integer fading parameters and the interfering signals experience arbitrary fading. Based on the Gaussian–Hermit quadrature, a tractable and accurate expression for the serving distance with lognormal shadowing is obtained. Under a general cell association rule, a simple and generic expression for the downlink coverage probability of user-centric wireless network in the comprehensive fading scenario is successfully derived and verified through simulation. The derived expression reveals that there is no need for the coverage analysis with respect to the instantaneous interfering fading channels in terms of the independence assumption between network model and fading channels.

3GPP-Inspired HetNet Model Using Poisson Cluster Process: Sum-Product Functionals and Downlink Coverage

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated a variety of user and base station (BS) configurations to be considered for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models proposed by standardization bodies, such as the 3rd Generation Partnership Project (3GPP). Complementary to these simulation models, stochastic geometry-based approach, modeling the locations of the users, and the $K$ tiers of BSs as independent and homogeneous Poisson point processes (PPPs), has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based $K$ -tier HetNet model is not rich enough to capture spatial coupling between user and BS locations that exists in real-world HetNet deployments and is included in 3GPP simulation models. In this paper, we demonstrate that modeling a fraction of users and arbitrary number of BS tiers alternatively with a Poisson cluster process (PCP) captures the aforementioned coupling, thus bridging the gap between the 3GPP simulation models and the PPP-based analytic model for HetNets. We further show that the downlink coverage probability of a typical user under maximum signal-to-interference-ratio ( $ \mathtt {SIR}$ ) association can be expressed in terms of the sum-product functionals over PPP, PCP, and its associated offspring point process, which are all characterized as a part of our analysis. We also show that the proposed model converges to the PPP-based HetNet model as the cluster size of the PCPs tends to infinity. Finally, we specialize our analysis based on general PCPs for Thomas and Matern cluster processes. Special instances of the proposed model closely resemble the different configurations for BS and user locations considered in 3GPP simulations.

Improving the Coverage and Spectral Efficiency of Millimeter-Wave Cellular Networks Using Device-to-Device Relays

The susceptibility of millimeter waveform propagation to blockages limits the coverage of millimeter-wave (mmWave) signals. To overcome blockages, we propose to leverage two-hop device-to-device (D2D) relaying. Using stochastic geometry, we derive expressions for the downlink coverage probability of relay-assisted mmWave cellular networks when the D2D links are implemented in either uplink mmWave or uplink microwave bands. We further investigate the spectral efficiency (SE) improvement in the cellular downlink, and the effect of D2D transmissions on the cellular uplink. For mmWave links, we derive the coverage probability using dominant interferer analysis while accounting for both blockages and beamforming gains. For microwave D2D links, we derive the coverage probability considering both line-of-sight (LOS) and non-line-of-sight (NLOS) propagation. Numerical results show that downlink coverage and SE can be improved using two-hop D2D relaying. Specifically, microwave D2D relays achieve better coverage because D2D connections can be established under NLOS conditions. However, mmWave D2D relays achieve better coverage when the density of interferers is large because blockages eliminate interference from NLOS interferers. The SE on the downlink depends on the relay mode selection strategy, and mmWave D2D relays use a significantly smaller fraction of uplink resources than microwave D2D relays.

Enriched $K$ -Tier HetNet Model to Enable the Analysis of User-Centric Small Cell Deployments

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing $K$ -tier Poisson point process (PPP) HetNet model by considering user locations as Poisson Cluster Process with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. The derived results are specialized for two cases of interest: 1) Thomas cluster process , where the locations of the users around BSs are Gaussian distributed and 2) Matern cluster process , where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: 1) uniformly distributed and 2) clustered around certain tiers.