Independent Poisson Point Processes Research Articles

Evaluating energy harvesting UAV-NOMA network with random user pairing in the finite blocklength regime

This study proposes an integrated system that combines energy harvesting (EH) enabled unmanned aerial vehicles (UAVs) with non-orthogonal multiple access (NOMA) to enhance communication system performance within a cellular network. Addressing the limitations of existing analyses that often assume an infinite blocklength scenario, we explore EH-enabled UAV-NOMA systems within a cellular framework under a finite blocklength (FBL) scenario. The study investigates the complex interactions and advantages resulting from the integration of EH, NOMA, and UAV technologies, aiming to assess whether EH can sustain communication within this framework. The network model considers base stations (BSs), UAVs, and terrestrial devices distributed with independent Poisson point processes (PPPs) over a large area. In this network, BSs employ NOMA to serve cell center devices directly, while cell edge devices, which are nor in direct contact with BS, are served via simultaneous wireless information and power transfer (SWIPT) enabled UAVs. The study derives metrics including joint harvesting and decoding probability for a randomly selected UAV, coverage probability (CP) for cell devices, and end-to-end block error rate (BLER) probabilities for typical device pairs. The findings demonstrate that the proposed scheme effectively supplies all the necessary transmit power for communication purposes through EH, achieving reasonable reliability. Additionally, the study highlights the importance of considering a combination of blocklengths from different phases to achieve optimal performance, rather than solely relying on an increment in blocklength. Finally, the effects of parameter variations on network performance are examined.

Nonlinear wireless energy harvesting based uplink transmission in K-tier heterogeneous networks over Nakagami-m fading channels

With the widespread application of various battery-powered devices, it is very challenging to sustainably meet the tremendous wireless transmission requirements over limited spectrum. We propose a wireless energy harvesting (EH) based uplink transmission scheme for the K-tier heterogeneous cellular network (HCN) with all the channels undergoing Nakagami-m fading. The locations of base stations (BSs) in each tier, mobile users (MUs), and power beacons (PBs) are properly modeled as independent homogeneous Poisson point processes. Each MU can be associated with a BS in any tier that provides the maximum averaged received signal power. MUs can harvest wireless energy from all the PBs in a nonlinear fashion, and then transmit data to the associated BS by using the harvested energy. We properly model the energy statuses of MUs by defining a series of unequally spaced energy levels according to the probability distribution of EH amount. Through properly modeling the aggregate interference, we analyze the outage probability and the area throughput of the multi-tier HCN. Numerical results show that our proposed scheme can greatly outperform the benchmark scheme in terms of outage probability and area throughput. The impacts of key parameters are revealed through extensive simulations, which can guide the network deployment.

Clustered jamming and antenna beam-width fluctuations for UAV-assisted cellular networks

Jamming devices have the capability to deliberately disrupt legitimate communications. Clustered jamming pertains to the deployment of jammers that are concentrated within specific clusters to amplify the interference. This paper models the impact of clustered jamming interference on unmanned aerial vehicles (UAV)-assisted cellular networks, taking into account fluctuations of the 3-dimensional (3D) beam-width of low altitude platform (LAP) antennas. The distribution of UAVs and macro base station (MBS) is modeled by independent 3D and 2D homogeneous Poisson point processes, respectively, while jammers are modeled using an independent Matern cluster process. Antenna 3D beam-width fluctuations are modeled according to Normal distribution. The modeling centers on the probability of association as well as coverage and spectral efficiency for line-of-sight LAP, non-line-of-sight LAP, and MBS links. This modeling investigation is conducted under multiple jamming clusters and the antenna 3D beam-width fluctuations of UAV. Analytical expressions are derived to characterize association, coverage, and SE performance in the context of clustered jamming and UAV beam-width variation. The obtained results indicate that UAV-assisted cellular networks experience a notable decline in the proximity of clustered jammers. Furthermore, this performance degradation is significantly exacerbated when the antenna 3D beam-width exhibits fluctuations. Consequently, to enhance the performance of UAV-assisted cellular networks, it is imperative for system designers to consider the implementation of robust anti-jamming techniques.

Properties of a Random Bipartite Geometric Associator Graph Inspired by Vehicular Networks.

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in R2 as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed.

Analysis of Fluctuating Antenna Beamwidth in UAV-Assisted Cellular Networks

This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability and spectral efficiency (SE) in the presence of fluctuations of 3D antenna beamwidth. Within this analytical framework, the macro base stations (MBSs) are meticulously characterized through the application of an independent 2D homogeneous Poisson point process (PPP), while the low-altitude platforms (LAPs) are described using an independent 3D PPP. The study entails the derivation of association probabilities, determining the likelihood of the T-UE associating with MBSs, line-of-sight LAPs, and non-line-of-sight LAPs. Through rigorous mathematical analysis, the paper formulates precise analytical expressions that encapsulate the association and coverage probabilities, taking into account the inherent variability in the UAV antenna beamwidth. This research focuses on a thorough performance evaluation of the T-UE across diverse network configurations, encompassing LAP density, the transmission power of LAPs, and the critical signal-to-interference ratio threshold. The outcomes of this study distinctly underscore the substantial disruptive impact resulting from fluctuating beamwidth on the performance of the T-UE within the UAV-assisted cellular network. Additionally, this performance is further impacted by larger densities and transmission power of the LAP. Hence, it is imperative to take into account the influence of these fluctuations on network association, coverage, and SE whenever contemplating a UAV-assisted cellular network.

Heterogeneous Ultradense Networks With Traffic Hotspots: A Unified Handover Analysis

With the ever-growing communication demands and the unceasing miniaturization of mobile devices, the Internet of Things is expanding the amount of mobile terminals to an enormous level. To deal with such numbers of communication data, plenty of base stations (BSs) need to be deployed. However, denser deployments of heterogeneous networks (HetNets) lead to more frequent handovers, which could increase network burden and degrade the users experience, especially in traffic hotspot areas. In this paper, we develop a unified framework to investigate the handover performance of wireless networks with traffic hotspots. Using the stochastic geometry, we derive the theoretical expressions of average distances and handover metrics in HetNets, where the correlations between users and BSs in hotspots are captured. Specifically, the distributions of macro cells are modeled as independent Poisson point processes (PPPs), and the two tiers of small cells outside and inside the hotspots are modeled as PPP and Poisson cluster process (PCP) separately. A modified random waypoint (MRWP) model is also proposed to eliminate the density wave phenomenon in traditional models and to increase the accuracy of handover decision. By combining the PCP and MRWP model, the distributions of distances from a typical terminal to the BSs in different tiers are derived. Afterwards, we derive the expressions of average distances from a typical terminal to different BSs, and reveal that the handover rate, handover failure rate, and ping-pong rate are deduced as the functions of BS density, scattering variance of clustered small cell, user velocity, and threshold of triggered time. Simulation results verify the accuracy of the proposed analytical model and closed-form theoretical expressions.

Analysis of fluctuations of antenna pattern in U-V2X communications

The third-generation partnership project (3GPP) defined several scenarios of vehicle-to-everything (V2X) networks such as vehicle-to-vehicle, vehicle-to-pedestrian, and vehicle-to-infrastructure. Unmanned aerial vehicles (UAVs) exploiting such scenarios for vehicular applications like vehicular-platooning, autonomous driving, and traffic management have shown improved networks’ performance in UAV-V2X (U-V2X) communications. This promising performance is typically obtained by considering high directional UAV antennas. However, the UAV vibration makes UAV antennas’ beam-width sensitive to UAV fluctuations which results in degrading the networks’ performance. Thus, in this paper, the performance of a U-V2X network in the presence of UAV fluctuations is investigated. The UAVs are modeled using an independent homogeneous Poisson Point Process and the vehicular-nodes are modeled using an independent Poisson Line Process. To this end, the association probability and success probability of various links such as vehicular-node connected to a UAV link, vehicular-node connected to a near-by vehicular-node link, and the overall U-V2X link are derived. In addition, the effect of different network settings such as the number of vehicular-nodes, UAVs, roads, and antennas is quantified. Moreover, the spectral efficiency of a U-V2X network is evaluated. Extensive simulations revealed that V2X networks facilitate UAVs and that for less dense areas with fewer roads, buildings, and crowds; UAVs provide more reliable links for connectivity than vehicular-nodes. Furthermore, it is also revealed that UAVs provide less reliable connection for V2X networks with larger UAV antenna fluctuations.

A Factor Matching of Optimal Tail Between Poisson Processes

Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension d at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., a measurable function of the point configurations that commutes with translations), and with the property that the distance between two matched configuration points has a tail distribution that decays as fast as possible in magnitude, namely, as bexp (-cr^d) with suitable constants b,c>0. This settles the most difficult version of such matching problems: bicolored (versus unicolored) and deterministic (versus randomized). Our proof relies on two earlier results: an allocation (“land-division”) rule of similar tail for a Poisson point process by Markó and the author, and a recent breakthrough result of Bowen, Kun and Sabok that enables one to obtain perfect matchings from fractional perfect matchings under suitable conditions.

Cell-Free Massive MIMO With Finite Fronthaul Capacity: A Stochastic Geometry Perspective

In this work, we analyze the downlink performance of a cell-free massive multiple-input-multiple-output system with finite capacity fronthaul links between the centralized baseband unit and the access point (APs). Conditioned on the user and AP locations, we first derive an achievable rate for a randomly selected user in the network that captures the effect of finite fronthaul capacity as a compression error. From this expression, we establish that for the traditional cell-free architecture where each AP serves all the users in the network, the achievable rate becomes zero as the network size grows. Hence, to have a meaningful analysis, for the traditional architecture, we model the user and AP locations as two independent binomial point processes over a finite region and provide an accurate theoretical result to determine the user rate coverage. In contrast, for an asymptotically large network, we consider a user-centric architecture where each user in the network is served by a specified number of nearest APs that limits the fronthaul load. For this architecture, we model the AP and user locations as two independent Poisson point processes (PPPs). Since the rate expression is a function of the number of users served by an AP, we statistically characterize the load in terms of the number of users per AP. As the exact derivation of the probability mass function of the load is intractable, we first present the exact expressions for the first two moments of the load. Next, we approximate the load as a negative binomial random variable through the moment matching method. Using the load results along with appropriate distance distributions of a PPP, we present an accurate theoretical expression for the rate coverage of the typical user. From the analyses, we conclude that for the traditional architecture when the AP transmit power is relatively high, a more collocated antenna deployment is preferred. Further, for the user-centric architecture, the energy efficiency of the system is a concave function of the number of antennas per AP.

Directional antennas modelling and coverage analysis for UAV networks with blockage effects in urban environment

AbstractIn recent years, the use of unmanned aerial vehicles (UAVs) as flying base stations (BSs) has attracted widespread attention in both academia and industry. Most of the existing research on UAV networks in dense urban environment focus on omnidirectional antenna patterns, which results in severe interference and overlapping between coverage area due to dominant line‐of‐sight (LOS) links. This paper proposed a directional antennas model with tunable beamwidth and blockage effects in urban UAV networks, and derive the coverage probability of UAV networks in dense urban environment by stochastic geometry tools, where UAVs and users are deployed according to independent Poisson point process (PPP). Specifically, a realistic and mathematically tractable directional antenna pattern is adopted and radiation gain is modelled by a continuous function of the elevation angle . In addition, the blockage effects of the buildings are considered by establishing a three‐dimensional blockage model where buildings are distributed according to PPP with heights followed by Rayleigh distribution. Numerical results match well with simulations and provide optimal deployment parameters for UAV deployments.

RIS-Assisted mmWave Networks With Random Blockages: Fewer Large RISs or More Small RISs?

Reconfigurable intelligent surface (RIS), which provides indirect line-of-sight (LoS) transmission paths between the receiver and its blocked transmitter, has been proposed as one of the promising technologies for network performance enhancement. Recent works indicate that both the numbers of RISs and unit cells per RIS have a significant impact on network performance. However, with a given total number of unit cells, the joint analysis of these two factors considering blockage effect has not been investigated. In this paper, the coverage probability of a three-dimensional downlink millimeter wave RIS-assisted network is analyzed. We first derive the acceptable area where a LoS RIS is capable to satisfy the signal-to-noise ratio threshold at the receiver. Next, we model the centers of building blockages and human-body blockages as two independent Poisson point processes and derive the probability that indirect LoS transmissions exist. Then, we derive and validate the analytical upper and lower bounds of the coverage probability as the functions of network parameters and blockage densities. We also derive and validate the closed-form coverage probability when RISs are much closer to UE than BS. Finally, we propose a general network cost model for RIS-assisted network. Results show that in terms of coverage enhancement, densely deployed small-scale RISs outperform sparsely deployed large-scale RISs in scenarios with dense blockages or short transmission distances, while sparsely deployed large-scale RISs are preferable in scenarios with sparse blockages or long transmission distances.

Analytical modeling of cache-enabled heterogeneous networks using Poisson cluster processes

The dual frequency Heterogeneous Network (HetNet), including sub-6 GHz networks together with Millimeter Wave (mmWave), achieves the high data rates of user in the networks with hotspots. The cache-enabled HetNets with hotspots are investigated using an analytical framework in which Macro Base Stations (MBSs) and hotspot centers are treated as two independent homogeneous Poisson Point Processes (PPPs), and locations of Small Base Stations (SBSs) and users are modeled as two Poisson Cluster Processes (PCPs). Under the PCP-based modeling method and the Most Popular Caching (MPC) scheme, we propose a cache-enabled association strategy for HetNets with limited storage capacity. The performance of association probability and coverage probability is explicitly derived, and Monte Carlo simulation is utilized to verify that the results are correct. The outcomes of the simulation present the influence of antenna configuration and cache capacities of MBSs and SBSs on network performance. Numerical optimization of the standard deviation ratio of SBSs and users of association probability is enabled by our analysis.

Secrecy Performance Evaluation of Scalable Cell-Free Massive MIMO Systems: A Stochastic Geometry Approach

This paper presents the first performance analysis of physical layer downlink secure transmissions in a scalable cell-free massive MIMO (SCF-mMIMO) system. A stochastic geometry approach is used to model the locations of the access points (APs), user equipments (UEs) and eavesdroppers (Eves) as independent homogeneous Poisson point processes (HPPPs). In addition to applying maximum ratio transmission (MRT) to send the confidential messages, null-space artificial noise is also injected for secrecy enhancement. We analytically characterize the secrecy performance in terms of both the outage-based secrecy transmission rate (STR) and the ergodic secrecy rate (ESR), appropriate for slow quasi-static fading channels and fast block-fading channels, respectively. By utilizing moment matching and Gil-Pelaez inversion theorem, we are able to obtain mathematically tractable approximations for the performance metrics. These approximations are shown to have high accuracy as compared to simulation results. Our numerical results reveal useful design insights that cannot be inferred from existing studies. These insights answer important questions such as whether it is best to deploy as many APs each with fewer antennas and to what extent the artificial noise insertion is beneficial.

Poisson limit theorems for the Robinson–Schensted correspondence and for the multi-line Hammersley process

We consider the Robinson–Schensted–Knuth algorithm applied to a random input and study the growth of the bottom rows of the corresponding Young diagrams. We prove a multidimensional Poisson limit theorem for the resulting Plancherel growth process. In this way we extend the result of Aldous and Diaconis to more than just one row. This result can be interpreted as convergence of the multi-line Hammersley process to its stationary distribution which is given by a collection of independent Poisson point processes.

Modeling and Analysis of the Local Delay in an MEC-Based VANET for an Urban Area

This article studies the local delay modeling and analysis in a mobile edge computing (MEC) based vehicular ad hoc network (VANET) for an urban scenario where vehicle nodes request for computing services from an edge node. Based on stochastic geometry, theoretical local delay models are derived for uplink transmission of a service request and downlink transmission of a computing result, respectively. In deriving the theoretical models, the road distribution of an urban area is modeled as a Poisson line process (PLP), the spatial distribution of vehicle nodes on each street are modeled as an independent one-dimensional homogeneous Poisson point process (PPP), and edge nodes are deployed along each street with a certain probability. Moreover, a carrier sense multiple access (CSMA) mechanism is considered for channel access, and independent Nakagami-m fading is considered over all wireless links. Based on the derived models, the impacts of major parameters on the local delay are investigated through numerical results. The derived local delay models can be used to help parameter settings in the deployment of edge nodes in an urban area.

Stochastic Geometry Analysis of Sojourn Time in RF/VLC Hybrid Networks

The spectrum scarcity in the radio frequency (RF) communication in indoor environments motivates the integration of an alternative technology like visible light communication (VLC) with the existing RF architecture that results in a hybrid RF/VLC network. While VLC helps offloading the congested RF spectrum by offering capacity-per-area improvements, the resulting heterogeneity and narrow coverage areas of optical base stations (BSs) impose several challenges for user mobility such as unnecessary handovers. To help addressing these challenges, in this paper, we derive the mean and the distribution of sojourn time in RF/VLC hybrid networks. The mathematical analysis conducted in this paper makes use of the tools from stochastic geometry and abstracting the BSs’ locations via two independent homogeneous Poisson point processes (PPPs). Since PPP modeling is yet to be well established for RF/VLC hybrid networks, we compare the PPP based analytical results to those obtained for an actual deployment, a Matérn hard-core point process (MHCPP) based deployment, and a deterministic square lattice deployment of VLC luminaries. Furthermore, we utilize the sojourn time distribution to calculate the unnecessary handover probability. Our numerical results show the interplay between the sojourn time and the receiver field of view as a function of BS density and they highlight the cost of BS densification in terms of unnecessary handovers.

Performance Analysis of Blockchain-Enabled Data-Sharing Scheme in Cloud-Edge Computing-Based IoT Networks

Blockchain and cloud-edge computing techniques are promising technologies for next-generation, secure, and privacy-preserving data-sharing systems. By integrating these technologies, the data demands of many data users, such as research institutes, hospitals, manufacturers, etc., can be met. Despite this promising integration, it is yet to be understood how the vulnerability and uncertainties of wireless communication links between the data producers, blockchain systems, cloud-edge computing-based platforms, and data users, as well as unstable validation parameters can affect the overall performance of such blockchain-enabled data-sharing systems. In this article, we considered a collaborative data-sharing scheme, where multiple data providers and data users collaborate to accomplish data-sharing tasks through the proposed blockchain and cloud-edge computing schemes. We considered the spatial distribution of data providers and data users to follow the independent homogeneous Poisson point process, while the transactions generation rate at each node was also modeled using an independent Bernoulli process. We then obtained analyses for some selected performance metrics of interest and evaluate the performance of the system. The obtained results showed that the proposed analyses can be useful in investigating the performance of any blockchain-enabled data-sharing system. This will aid successful deployments of effective data-sharing systems.

Fine-Grained Analysis of Reconfigurable Intelligent Surface-Assisted mmWave Networks

Reconfigurable intelligent surfaces (RISs) have emerged as a promising technology for millimeter wave (mmWave) networks. In this paper, we utilize tools from stochastic geometry to study the performance of a RIS-assisted mmWave cellular network. Specifically, the locations of the base stations (BSs) and the midpoints of the blockage are modeled as two independent Poisson point processes (PPPs), where the blockages are modeled by a Boolean model and a fraction of the blockages are coated with RISs. The particular characteristics of mmWave communications, i.e., directional beamforming and different path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) propagation, are incorporated into our analysis. We derive analytical expressions for the success probability and the area spectral efficiency. The success probability under the special case where the blockage parameter is sufficiently small is also derived. Numerical results demonstrate that better coverage performance and higher energy efficiency can be achieved by a large-scale deployment of RISs. In addition, the tradeoff between the BS and RIS densities is investigated and the results show that the RISs can indeed enable the traditional networks to improve the success probability, especially for the cell-edge region, with limited power consumption.

Interference Characterization in Cellular-Assisted Vehicular Communications With Jamming

The automobile industry has been evolving with rapid growth over the last two decades. Conventionally, the narrow band dedicated short-range communications is used for the wireless connectivity of vehicular networks in the automobile industry. However, due to its shorter wireless range, higher latency, and lower capacity; cellular-assisted vehicular communications can be adopted to improve networks performance by disrupting the nearby infrastructure. The performance of cellular-assisted vehicular communications is typically compromised if jammers are present in their vicinity. Thus, it is important to characterize the interference in cellular-assisted vehicular communications with jammers. In this paper, we investigate jamming interference due to clustered-jammers for vehicular networks by considering that vehicles, road-side units, and pedestrians are modeled using an independent one-dimensional Poisson line process while cellular base stations are modeled using an independent two-dimensional homogeneous Poisson point process. The results show that jamming disrupts the performance of the vehicular networks and that this performance is severely compromised by increasing the density of jamming clusters and their transmission power. Therefore, the prime focus of the system designers should be to introduce anti-jamming scenario, when the transmission power and the number of jamming clusters in a network increase.

Coverage probability of aerial heterogeneous networks disrupting dual connectivity in the Presence of Jammers

The coverage performance of the target user in dual connectivity-enabled heterogeneous networks is adversely affected depending upon the presence and distribution of wide-band jammers (WBJs). Thus, we deploy WBJs with uniform distribution using an independent homogeneous Poisson point process (IHPPP) and in clusters using the Matern cluster process (MCP). Results show that the coverage performance of the target user in the presence of IHPPP-distributed WBJs is larger than the MCP-distributed WBJs. Thus, to reduce the severity of jamming attacks, network designers should focus on the anti-jamming of clustered jammers relative to uniformly distributed jammers.