Coverage analysis for millimeter wave cellular networks with blockage effects

In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.

Coverage probability of uplink millimeter wave cellular network with non-homogeneous interferers’ point process

In this paper, a new mathematical approach for the analysis and optimization of cellular-enabled low-energy mobile devices with simultaneous wireless information and power transfer capabilities is introduced. The proposed methodology relies on modeling the locations of the base stations as points of a spatial Poisson point process, and it leverages stochastic geometry for system-level analysis. The tradeoffs emerging from simultaneous wireless information and power transfer transmission are characterized through the concept of “feasibility regions” and are quantified through the joint cumulative distribution function of harvested power and rate. To gain insight on the achievable performance, in addition, an upper bound is proposed, and its accuracy is discussed. The system model encompasses a realistic channel model that accounts for line-of-sight (LOS) and non-LOS (NLOS) links, different cell association criteria, practical receivers based on time switching and power splitting schemes, and directional beamforming. The analysis shows that optimal values for the time switching and power splitting ratios exist and that directional beamforming and network densification are capable of enhancing system performance. More specifically, high directional antennas lead cellular networks to operate in the noise-limited regime, which is proved to provide optimal performance, and because of the existence of LOS and NLOS links, an optimal deployment density for the base stations is proven to exist for typical system setups.

In indoor environments, the performance of ultra-dense cellular networks is significantly affected by blockages, especially for ultra-high frequencies. However, previous works either ignore or simplify such effects for analysing the networks. On the basis of stochastic geometry, this paper proposes a mathematically tractable approach to analyse ultra-dense networks in indoors, which considers both the effects of wall blockages and the distance-based path loss. The effects of wall blockages are firstly investigated by modelling the walls as a Boolean scheme of straight lines on a finite plane. Then a path loss model incorporating both the blockage-based and distance-based path loss is applied to analyse the performance of indoor networks. Finally, the analytical result is validated by comparing it with Monte Carlo simulations. The simulation results also show that the optimum transmitter density is finite for indoor ultra-dense networks with blockages, although the coverage probability benefits from the increase of transmitter density.

Since millimeter wave (mmWave) and sub-terahertz bands are highly vulnerable to blockage and penetration loss effects, wireless coverage enhancement is one of the critical challenges in indoor mmWave deployments. In particular, when the line-of-sight (LoS) link is blocked, a strong non-LoS (NLoS) path can provide a stable link quality. One of the efficient ways to improve the NLoS link is the use of strategically placed passive reflectors. In this letter, we study the indoor coverage improvement by using a transparent passive reflector attached on a wall. We consider an indoor open-door scenario, where the LoS link is blocked by the walls for receivers inside the room, and the coverage can only be achieved via an NLoS link through a passive reflector. We analytically derive closed-form equations of the reflection visibility probability and the coverage probability. By simulation and analytical results, we show the coverage dependency on the location and size of the reflector.

A K-tier heterogeneous downlink millimeter wave (mmWave) cellular network with user-centric small cell deployments is studied in this paper. In particular, we consider a heterogeneous network model with user equipments (UEs) being deployed according to a Poisson Cluster Process (PCP), i.e., Thomas cluster process, where the UEs are clustered around the base stations (BSs) and the distances between UEs and the BS are modeled as Gaussian distributed. In addition, distinguishing features of mmWave communications including directional beamforming and a sophisticated path loss model incorporating both line-of-sight (LOS) and non-line-of-sight (NLOS) transmissions, are taken into account. In this paper, the complementary cumulative distribution function (CCDF) and probability density function (PDF) of the path loss are provided. Also, using tools from stochastic geometry, we derive a general expression of the signal-to-interference-plus-noise ratio (SINR) coverage probability. Our results demonstrate that coverage probability can be improved by decreasing the size of UE clusters around BSs, and interference has noticeable influence on the coverage performance of our model.

With the rapid development of emerging 5G and beyond (B5G), Unmanned Aerial Vehicles (UAVs) are increasingly important to improve the performance of dense cellular networks. As a conventional metric, coverage probability has been widely studied in communication systems due to the increasing density of users and complexity of the heterogeneous environment. In recent years, stochastic geometry has attracted more attention as a mathematical tool for modeling mobile network systems. In this paper, an analytical approach to the coverage probability analysis of UAV-assisted cellular networks with imperfect beam alignment has been proposed. An assumption was considered that all users are distributed according to Poisson Cluster Process (PCP) around base stations, in particular, Thomas Cluster Process (TCP). Using this model, the impact of beam alignment errors on the coverage probability was investigated. Initially, the Probability Density Function (PDF) of directional antenna gain between the user and its serving base station was obtained. Then, association probability with each tier was achieved. A tractable expression was derived for coverage probability in both Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) condition links. Numerical results demonstrated that at low UAVs altitude, beam alignment errors significantly degrade coverage performance. Moreover, for a small cluster size, alignment errors do not necessarily affect the coverage performance.

Spectrum sharing is a promising technology that improves the spectral utilization efficiency and provides the foundation stone to build up future drone cellular networks. This chapter presents an efficient transmission scheme and to optimally allocate resources in an underlay spectrum sharing between drone networks and cellular networks. Taking advantage of the stochastic geometry, the 3D blockage effect by random shape theory is determined. Under a blockage model with volume, the exact expression of the signal‐to‐noise ratio (SNR) meta‐distribution is derived. The chapter focuses on the deployment of aerial base stations in drone small cells (DSCs) while sharing the spectrum with cellular networks. Starting with a consideration of the spectrum sharing of single‐tier DSCs in a 3D network, the optimal DSC base station density by maximizing the DSC network throughput is derived. UAVs can act as aerial base stations or relays, namely DSCs, to provide communication services to areas after natural disasters.

The continuously growing mobile traffic demand is pushing wireless networks to dense heterogeneous architectures with different types of base stations (BSs). In such dense heterogeneous networks (HetNets), especially in the high-rise building 3-D environment, the users need to determine which BS to be associated with before communication. Different user association schemes lead to different system performance. In this paper, a maximum instantaneous signal-to-interference-plus-noise ratio (MISINR) user association scheme is studied in the dense urban environment. A general 3-D model is utilized to model the dense urban HetNets deployed in the high-rise buildings. The coverage probability and average user rate are theoretically derived by using stochastic geometry in a general case and an interference-limited case, respectively. Numerical and simulation results demonstrate that the MISINR user association scheme has the best performance compared with other two association schemes in 3-D HetNets. From the results, it is interesting to observe that the expressions of coverage probability and average user rate can be simplified to closed-forms in the interference-limited case.

Performance analysis of coverage-centric heterogeneous cellular networks using dual-slope path loss model

In cellular networks, all base stations (BSs) do not continuously transmit i.e., the BSs transmit only when their queues are non-empty. This implies that the system resources are only partially loaded, and the dynamics of such a network differs significantly from that of a fully-loaded system. The coverage probability in a fully- and partially-loaded cellular network is analysed. We consider a regular spatial arrangement of base stations, and obtain the coverage probability in the presence of interference. More specifically, expressions for coverage probability are obtained for square and hexagonal lattices with full and partial loading. The coverage probability is obtained using properties of lattice sums which were first used in physics to analyse potentials in crystal structures.

Millimeter wave (mmwave) is a potential technology to cater to the data requirements of future cellular networks through its wider spectrum and directional beamforming. With such directional communication, exact alignment of communicating beams is crucial. In this paper, the directivity gains with an antenna model having a Gaussian main lobe is used and the impact of beam alignment error due to random movement of the user are investigated on the uplink system performance of mmwave cellular network. Using stochastic geometry, we have derived Signal-to-Interference-plus-Noise Ratio (SINR) coverage probability. Numerical results show that an optimal number of base station beams exist that maximizes coverage probability at different user velocities and cell radii.

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.

Stochastic geometry has recently become a very attractive tool to model wireless systems because it provides a clear insight in the statistical performance of systems. In this paper, we present a stochastic analysis of the autonomous uplink power allocation scheme we proposed in [1]. This scheme hinges on defining interference limits to the amount of interference produced by each cell. Since the probability of coverage is a major metric to evaluate the performance of wireless systems, we develop herein a theoretical formula for the probability of coverage in an OFDMA wireless system using that proposed uplink power allocation. The provided theoretical formula is shown to be a good approximation to the actual probability of coverage at low interference limits, while at high interference limits it serves as a lower bound to the probability of coverage. The developed formula helps predicting the performance of the system at different interference limits.

Heterogeneous network (HetNet) has been studied as a promising technology to boost the system throughput. A new upper boundary of coverage probability (CP) is derived, which is the one of cooperative communication between two base stations (BSs) for downlink HetNet. For the tractability, only the cooperation between two base stations in the same tier of HetNet is considered and a model is set up, in which each randomly chosen user located in the cooperation zones can communicate with at most one couple of BSs, due to the threshold of Signal-to-Interference-Ratio (SIR). Stochastic geometry theory is used to establish the model of HetNet. Simulation results show that the upper boundary of CP for cooperative communication between two BSs in the same tier is decreasing when the SIR threshold for macrocell tier is increasing. The increasing density of low power BSs can increase the performance of cooperative communication in the same tier, as well as reducing the cooperative SIR threshold for low power BSs tier.