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We present an analytic, quasi-local model for accretion discs threaded by net, vertical magnetic flux. In a simple slab geometry and ignoring stochastic mean-field dynamo effects, we calculate the large-scale field resulting from the balance between kinematic field amplification and turbulent diffusion. The ability of the disc to accumulate magnetic flux is sensitive to a single parameter dependent on the ratio of the vertical diffusion time to the Alfvén crossing time, and we show how the saturation levels of magnetorotational and other instabilities can govern disc structure and evolution. Under wide-ranging conditions, inflow is governed by large-scale magnetic stresses rather than internal viscous stress. We present models of such 'magnetically boosted' discs and show that they lack a radiation pressure-dominated zone. Our model can account for 'magnetically elevated' discs as well as instances of midplane outflow and field reversals with height that have been seen in some global simulations. Using the time-dependent features of our model, we find that the incorporation of global transport effects into disc structure can lead to steady or episodic 'magnetically arrested discs' that maximize the concentration of magnetic flux in their central regions. [ABSTRACT FROM AUTHOR]

This paper presents a resource allocation scheme that fulfills the maximum possible aggregate rate of the capacity region by targeting the corner points of the multiple-input multiple-output multiple access channel. This corner points of the channel's capacity region are attainable whenever each user's transmission has minimum possible interference among other users. This work aims to investigate the non-singularity of such situations by the exploitation of users' geographic location seeking the opportunity of getting users' transmission spatially multiplexed. The developed model demonstrates that similar results can be achieved with partial channel state information knowledge under certain conditions throughout the operational signal to noise ratio range. The proposed resource allocation scheme is designed for a shotgun cellular system with a random distribution of users over a circular coverage area. The proposed model uses stochastic geometry to prove that when number of users grows up within the coverage area, the probability of achieving the corner points sum rate increases rapidly. The developed model was evaluated, and the results show that for a circular coverage area with a radius of 10 km, the probability of having users whose transmissions can be spatially multiplexed with minimum interference increases as the number of users grows to 300 users. [ABSTRACT FROM AUTHOR]

A stochastic, prey–predator model of the low to high confinement transition is presented. The model concerns the interaction of a turbulent fluctuation amplitude, zonal flow shear, and the ion density gradient. Delta-correlated noise terms are used to construct Langevin equations for each of the three variables, and a Fokker–Planck equation is subsequently derived. A time-dependent probability distribution function is solved and a number of diagnostic quantities are calculated from it, including the information rate and length. We find the marginal probability distribution functions to be strongly non-Gaussian and frequently multi-modal, showing the coexistence of dithering and H-mode solutions over time. The information rate and length are shown to be useful diagnostics to investigate self-regulation between the variables, particularly the turbulence and zonal flow shear. [ABSTRACT FROM AUTHOR]

This study focuses on the performance of device-to-device (D2D) communications in underlay cellular networks by analyzing key metrics such as successful transmission probability, coverage probability, and throughput. Under the homogeneous Poisson point process (PPP) spatial distribution of full-duplex (FD)-D2D users in cellular networks, stochastic geometry tools are used to derive approximate expressions for D2D users’ coverage probability and throughput. In comparison to the conventional half-duplex (HD) communication mode, when the self-interference cancellation factor β reaches −95 dB, there is a substantial improvement in the throughput of FD-D2D users, nearly doubling their gain. Additionally, experimental results demonstrate that the Newton iterative algorithm can be used to optimize the targeted signal-to-interference-plus-noise-ratio (SINR) threshold of users within the range of (10, 20) dB. [ABSTRACT FROM AUTHOR]

Geometric properties of exceedance regions above a given quantile level provide meaningful theoretical and statistical characterizations for stochastic processes defined on Euclidean domains. Many theoretical results have been obtained for excursions of Gaussian processes and include expected values of the so-called Lipschitz–Killing curvatures (LKCs), such as the area, perimeter and Euler characteristic in two-dimensional Euclidean space. In this paper, we derive novel results for the expected LKCs of excursion sets of more general processes whose construction is based on location or scale mixtures of a Gaussian process, which means that the mean or the standard deviation, respectively, of a stationary Gaussian process is a random variable. We first present exact formulas for peaks-over-threshold-stable limit processes (so-called Pareto processes) arising from the use of Gaussian or log-Gaussian spectral functions in the spectral construction of max-stable processes. These peaks-over-threshold limits are known to arise for Gaussian location or scale mixtures if the mixing distributions satisfies certain regular-variation properties. As a second important result, we show that expected LKCs of excursion sets of such general mixture processes converge to the corresponding expressions of their Pareto process limits. We further provide exact subasymptotic formulas of expected LKCs for various specific choices of the distribution of the mixing variable. Finally, we discuss consistent empirical estimation of LKCs of exceedance regions and implement numerical experiments to illustrate the rate of convergence towards asymptotic expressions. An application to daily temperature data simulated by climate models for the period 1951–2005 over a regular pixel grid covering continental France showcases the practical utility of the new results. [ABSTRACT FROM AUTHOR]

Summary: Low Earth Orbit (LEO) satellite‐based Internet of Things (IoT) has become a hot topic in IoT networks due to the ability of global coverage, especially in remote areas. How to design a commercial LEO satellite‐based constellation to meet the IoT traffic requirement remains an open problem. In this paper, we propose a throughput optimization algorithm for LEO satellite‐based IoT networks meanwhile reducing the number of LEO satellite. Based on stochastic geometry theory, a closed‐form expression is derived for the throughput of a dynamic LEO satellite‐based IoT networks when LEO satellite equips with capture effect (CE) receiver and successive interference cancelation (SIC) receiver, respectively. Furthermore, a joint altitude and beamwidth optimization problem is formulated under the constraint of Walker constellation to optimize the throughput and the number of LEO satellites. To solve this multi‐objective optimization problem, we design an iterative non‐dominated sorting genetic algorithm II (NSGA‐II) for the rapid development of IoT traffic. Simulation results show that our proposed algorithm can effectively improve the throughput performance of random access (RA) protocol in LEO satellite‐based IoT networks compared to benchmark problems. [ABSTRACT FROM AUTHOR]

Fifth-generation networks are facing coverage problems due to the vulnerability of millimeter-wave bands caused by blockage and penetration loss phenomena, resulting in shadow zones commonly called isolated regions (IRs). Unmanned aerial vehicles (UAVs) acting as aerial base stations, can be rapidly applied to provide communications coverage in IR. Existing research mainly adopts UAVs with conventional beamforming, but this scheme simply neglects the array gain in the vertical plane, and interference coordination becomes complicated. Considering a 3D beamforming approach that adjusts the tilt angle, this paper explores the coverage and network spectral efficiency (NSE) analysis using stochastic geometry, where UAVs are distributed as a binomial point process within a bounded circular area over the IR. Specifically, the association probability of an arbitrarily-located typical user in the finite region is computed based on the strongest averaged received power in line-of-sight/non-line-of-sight propagation. Furthermore, the signal-to-interference-plus-noise ratio coverage probability and NSE expressions are obtained under the hypothesis of Nakagami-m fading. Monte Carlo simulations are performed to illustrate the effectiveness of the proposed analysis method. Through the results we show the impact of antenna elevation on the coverage, the optimal tilt angle and the optimal number of simultaneously active UAVs to maximize performance. [ABSTRACT FROM AUTHOR]

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.

Training defect detection algorithms for visual surface inspection systems requires a large and representative set of training data. Often there is not enough real data available which additionally cannot cover the variety of possible defects. Synthetic data generated by a synthetic visual surface inspection environment can overcome this problem. Therefore, a digital twin of the object is needed, whose micro-scale surface topography is modeled by texture synthesis models. We develop stochastic texture models for sandblasted and milled surfaces based on topography measurements of such surfaces. As the surface patterns differ significantly, we use separate modeling approaches for the two cases. Sandblasted surfaces are modeled by a combination of data-based texture synthesis methods that rely entirely on the measurements. In contrast, the model for milled surfaces is procedural and includes all process-related parameters known from the machine settings. [ABSTRACT FROM AUTHOR]

Decoupling uplink and downlink access (DUDA) has latterly proven to effectively enhance transmission efficiency in wireless communication systems, with particular effectiveness observed in both terrestrial and unmanned aerial vehicle (UAV) systems. In this paper, we propose an innovative DUDA approach specifically designed for non-geostationary orbit (NGEO) multi-layer satellite systems (MSS), integrating strategies to mitigate in-line interference to ensure spectral coexistence between geostationary Earth orbit (GEO) and NGEO satellites. Notably, the interference from the main lobe of directional antennas on NGEO satellites is meticulously characterized using a spherical surface model based on the geocentric angle. Within the framework of proposed DUDA method, a user terminal (UT) can establish communication with the satellite which provides the highest average power of received signal in compliance with the unique exclusion angle constraints of NGEO satellites. The association probability of DUDA is analyzed based on stochastic geometry. The performance evaluation, conducted in terms of transmission rate, reveals that the proposed DUDA methodology yields significant improvements when compared to conventional access schemes. [ABSTRACT FROM AUTHOR]

The magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long. [ABSTRACT FROM AUTHOR]

Since the groundbreaking work by Cleveland and McGill in 1984, studies have revealed the difficulties humans have extracting quantitative data from visualizations as simple as bar graphs. As a first step toward understanding this situation, this paper proposes a mathematical model of the interpretation effort of a bar graph using concepts drawn from eye tracking. First, three key areas of interest (AOIs) are identified, and fixations are modeled as random point clouds within the AOIs. Stochastic geometry is introduced via random triangles connecting fixations within the adjacent key visual regions. The so-called landmark methodology provides the basis for the probabilistic analysis of the constructed system. It is found that the random length of interest in a stochastic triangle has a noncentral chi distribution with a known mean. Unique to this model, in terms of previous landmark applications, is the inclusion of a correlation between fixations, which is justified by physiological studies of the eyes. This approach introduces several model parameters, such as the noncentrality parameter, variance of the fixation cloud, correlation between fixations, and a visualization scale. A detailed parametric analysis examining the dependence of the mean on these parameters is conducted. The paper ties this work to the visualization via a definition of the expected visual measurement error. An asymptotic analysis of the visual error is performed, and a simple expression is found to relate the expected visual measurement error to the key model parameters. From this expression, the influence these parameters have on a visualization's interpretation is considered. [ABSTRACT FROM AUTHOR]

This research endeavors to advance energy efficiency (EE) within heterogeneous networks (HetNets) through a comprehensive approach. Initially, we establish a foundational framework by implementing a two-tier network architecture based on Poisson process distribution from stochastic geometry. Through this deployment, we develop a tailored EE model, meticulously analyzing the implications of random base station and user distributions on energy efficiency. We formulate joint base station and user densities that are optimized for EE while adhering to stringent quality-of-service (QoS) requirements. Subsequently, we introduce a novel dynamically distributed opportunistic sleep strategy (D-DOSS) to optimize EE. This strategy strategically clusters base stations throughout the network and dynamically adjusts their sleep patterns based on real-time traffic load thresholds. Employing Monte Carlo simulations with MATLAB, we rigorously evaluate the efficacy of the D-DOSS approach, quantifying improvements in critical QoS parameters, such as coverage probability, energy utilization efficiency (EUE), success probability, and data throughput. In conclusion, our research represents a significant step toward optimizing EE in HetNets, simultaneously addressing network architecture optimization and proposing an innovative sleep management strategy, offering practical solutions to maximize energy efficiency in future wireless networks. [ABSTRACT FROM AUTHOR]

Gibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many random fields with a strongly dependent spatial structure. In this work, we provide a very general framework for approximate Gibbsian structure for strongly correlated random point fields, including those with a highly singular spatial structure. These include processes that exhibit strong spatial rigidity, in particular, a certain one‐parameter family of analytic Gaussian zero point fields, namely the α$\alpha$‐GAFs, that are known to demonstrate a wide range of such spatial behavior. Our framework entails conditions that may be verified via finite particle approximations to the process, a phenomenon that we call an approximate Gibbs property. We show that these enable one to compare the spatial conditional measures in the infinite volume limit with Gibbs‐type densities supported on appropriate singular manifolds, a phenomenon we refer to as a generalized Gibbs property. Our work provides a general mechanism to rigorously understand the limiting behavior of spatial conditioning in strongly correlated point processes with growing system size. We demonstrate the scope and versatility of our approach by showing that a generalized Gibbs property holds with a logarithmic pair potential for the α$\alpha$‐GAFs for any value of α$\alpha$. In this vein, we settle in the affirmative an open question regarding the existence of point processes with any specified level of rigidity. In particular, for the α$\alpha$‐GAF zero process, we establish the level of rigidity to be exactly ⌊1α⌋$\lfloor \frac{1}{\alpha} \rfloor$, a fortiori demonstrating the phenomenon of spatial tolerance subject to the local conservation of ⌊1α⌋$\lfloor \frac{1}{\alpha} \rfloor$ moments. For such processes involving complex, many‐body interactions, our results imply that the local behavior of the random points still exhibits 2D Coulomb‐type repulsion in the short range. Our techniques can be leveraged to estimate the relative energies of configurations under local perturbations, with possible implications for dynamics and stochastic geometry on strongly correlated random point fields. [ABSTRACT FROM AUTHOR]

This paper studies a random caching design in multi-tier cache-enabled Internet of Things (IoT) networks. A cross-tier base station (BS) cooperation scheme is proposed, where the user equipment (UE) is jointly served by the BSs that cache the requested file with the maximal long-term averaged received power form each tier. The goal is to design a caching strategy to improve the network performance by taking successful transmission probability (STP) as the metric. We first derive the expression of the STP in integral form for the M-tier networks. Then, as special cases, an optimal caching strategy for the single-tier networks and a sub-optimal caching strategy (SCS) for the two-tier networks are obtained by solving two optimization problems where the caching probability matrix is optimized to maximize the STP, respectively. The former problem is solved by the Lagrangian method, based on which and combining with the gradient projection method, an algorithm is designed for the latter problem. Simulation results show that the SCS outperforms some existing strategies in terms of STP. [ABSTRACT FROM AUTHOR]

The performance of 5G/6G cellular systems operating in millimeter wave (mmWave, 30–100 GHz) and sub-terahertz (sub-THz, 100–300 GHz) bands is conventionally assessed by utilizing the static distributions of user locations. The rationale is that the use of the beam tracking procedure allows for keeping the beams of a base station (BS) and user equipment (UE) aligned at all times. However, by introducing 3GPP Reduced Capability (RedCap) UEs utilizing the Radio Resource Management (RRM) Relaxation procedure, this may no longer be the case, as UEs are allowed to skip synchronization signal blocks (SSB) to improve energy efficiency. Thus, to characterize the performance of such UEs, methods explicitly accounting for UE mobility are needed. In this paper, we will utilize the tools of the stochastic geometry and random walk theory to derive signal-to-noise ratio (SNR), spectral efficiency, and rate as an explicit function of time by accounting for mmWave/sub-THZ specifics, including realistic directional antenna radiation patterns and micro- and macro-mobilities causing dynamic antenna misalignment. Different from other studies in the field that consider time-averaged performance measures, these metrics are obtained as an explicit function of time. Our numerical results illustrate that the macro-mobility specifies the overall trend of the time-dependent spectral efficiency, while local dynamics at 1–3 s scales are mainly governed by micro-mobility. The difference between spectral efficiency corresponding to perfectly synchronized UE and BS antennas and time-dependent spectral efficiency in a completely desynchronized system is rather negligible for realistic cell coverages and stays within approximately 5–10% for a wide range of system parameters. These conclusions are not affected by the utilized antenna array at the BS side. However, accounting for realistic radiation patterns is critical for a time-dependent performance analysis of 5G/6G mmWave/sub-THz systems. [ABSTRACT FROM AUTHOR]

With the increasing demand for data exchange between nearby devices in proximity-based services, enhancing the security of wireless mutual broadcast (WMB) networks is crucial. However, WMB networks are inherently vulnerable to eavesdropping due to the open broadcast nature of their communication. This paper investigates the improvement of secrecy performance in random-access-based WMB (RA-WMB) networks by integrating physical layer security (PLS) techniques with hybrid duplex (HBD) operations under a stochastic geometry framework. The HBD method balances half-duplex (HD) receiving and full-duplex (FD) transceiving, utilizing self-interference cancellation (SIC) to enhance PLS performance. Key operational parameters, including transmission probability (TxPr), friendly jammer density, and conditions for FD operation, are designed to maximize secrecy performance. The analytical and numerical results demonstrate significant improvements in PLS performance, with SIC playing a critical role, particularly in scenarios with dense legitimate nodes, and with TxPr adjusted to balance HD receiving and FD transceiving based on SIC imperfections. The proposed design principles provide a comprehensive framework for enhancing the security of WMB networks, addressing the complex interplay of interference and SIC in various network configurations. [ABSTRACT FROM AUTHOR]

Processes of random tessellations of the Euclidean space $\mathbb{R}^d$ , $d\geq 1$ , are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation processes are a reference model. In the present paper a generalization concerning the life time distributions is introduced, a sufficient condition for the existence of such cell division tessellation processes is provided, and a construction is described. In particular, for the case that the random dividing hyperplanes have a Mondrian distribution—which means that all cells of the tessellations are cuboids—it is shown that the intrinsic volumes, except the Euler characteristic, can be used as the parameter for the exponential life time distribution of the cells. [ABSTRACT FROM AUTHOR]

The average transmit power and coverage probability (Pcov) of uplink energy harvesting-enabled long-range networks are investigated in the present paper. Particularly, we model the end-device (EDs) according to the homogeneous Poisson point process while the power beacon is randomly distributed on the circle in the middle of the network. All EDs rely on the harvested energy to perform their operations and transmissions. Under this context, the upper bound of the average transmit power of an end-device is derived in the closed-form expression. The signal-to-noise-ratio condition of the coverage probability is given in the closed-form expression as well. Simulation results are provided to corroborate the accuracy of the derived mathematical framework as well as to feature the impact of some key parameters on the considered metrics. Our findings unveil that increasing either the number of power beacons or their transmit power will monotonically ameliorate the Pcov. Nevertheless, rising the average number of EDs will significantly decline the Pcov's performance. [ABSTRACT FROM AUTHOR]

Satellite-terrestrial integrated wireless network (STIN) is a pivotal approach in achieving worldwide wireless connectivity. To guide base stations deployment of STIN, an analysis of the uplink coverage probability was conducted. Stochastic geometry was used to modeled the STIN under a setting of distinct frequencies. The satellite stations modeled as a one-dimensional Poisson point process (PPP) on orbit, base stations and users were represented as two-dimensional PPP. The expression for the uplink coverage probability was derived in terms of parameters such as base station density and orbital inclination. The correctness of the derived expression was verified through experimental simulations, and the impact of network parameters on the uplink coverage probability were analyzed.

Summary: In the rapidly evolving landscape of fifth generation Internet of Things (5G‐IoT) networks, Device‐to‐Device (D2D) communication has emerged as a promising paradigm to enhance secrecy transmission rate (STR) and connectivity. However, the security of D2D communications in the presence of eavesdroppers remains a critical challenge. This article investigates the problem of optimizing D2D transmit power to achieve secure D2D communication while considering the presence of random eavesdroppers in 5G‐IoT networks. We propose a novel secrecy‐based power control approach (SRMWPCA) approach to model the random distribution of eavesdroppers in the network, taking into account their varying distances from D2D pairs and deliberately increasing interference at the eavesdropper's link. By leveraging tools from stochastic geometry, we derive an analytical expression for the secrecy transmission probability (STP), which quantifies the probability of eavesdroppers successfully decoding the D2D transmission. In this analysis, we have incorporated practical considerations such as channel fading, path loss, and interference from other devices. To enhance the security of D2D communication, we formulate an optimization problem to determine the optimal transmit power levels for D2D pairs, subject to constraints on the secrecy transmission probability and interference to the cellular network. We propose an efficient algorithm to find the power allocation that maximizes the secrecy outage performance while meeting these constraints. Simulation results demonstrate the effectiveness of the proposed approach in achieving secure D2D communication in 5G‐IoT networks with random eavesdroppers. The performance of the proposed SRMWPCA approach improved by 23.25% and 20.9% compared with standard approaches in terms of the secrecy rate and throughput of the users from malicious attacks. [ABSTRACT FROM AUTHOR]

The hierarchical local-fog-cloud computing-enabled paradigm applied in fog radio access networks (F-RANs) has been considered as a promising architecture to cope with the surge of mobile intelligent applications. Meanwhile, non-orthogonal multiple access (NOMA) technology with superior spectrum efficiency has been widely utilized to provide transmission services for offloading tasks in F-RANs. A comprehensive understanding of the computation offloading performance of NOMA-based F-RANs is thus essential to provide guidelines for F-RANs planning and resources scheduling. In this paper, we first develop a mathematical framework to analyze the ability of NOMA to support computation offloading in F-RANs. Then, the expression for a lower bound of the average computation offloading probability is provided based on stochastic geometry and order statistics, and the relation between the computation offloading probability and the average task execution latency as well as energy consumption is further derived by queuing theory. Finally, extensive numerical simulations are executed to verify the accuracy of our theoretical results. The numerical results show that the average computation offloading probability is nearly linear with most of key network parameters, such as the coverage radius of cellular networks, the density of fog radio access points (F-APs), the number of users sharing the same spectrum resources, and the task request rate, respectively. [ABSTRACT FROM AUTHOR]

Vehicle -to-vehicle (V2V) communications are crucial for enhancing road network safety and efficiency. With the increasing demand for bandwidth in V2V services, exploring innovative solutions has become imperative. This study explores a comparative analysis of mmWave and WiFi transmission technologies, with a specific focus on line-of-sight (LoS) and non-line-of-sight (NLoS) scenarios in both 2D and 3D modeling environments. The use of stochastic geometry tools allows a realistic modeling of the random positioning of vehicles within the V2V system framework, resulting in accurate expressions for the successful transmission probability (STP) and average throughput (AT) for both communication systems. To validate our analytical findings, Monte Carlo simulations have been employed, offering a comprehensive evaluation of mmWave and WiFi performance. Simulation results highlight that mmWave systems outperform in scenarios with short transmission distances and low vehicle density while WiFi systems demonstrate greater efficiency for longer transmission distances. [ABSTRACT FROM AUTHOR]

In the present paper, we propose a method for controlling the interval of safety message transmissions in a fully distributed manner that maximizes the number of successful transmissions to vehicles located a set target distance away. In the proposed method, each vehicle estimates the density of vehicles in its vicinity, and, based on the estimated vehicle density, each vehicle calculates an optimal message transmission interval in order to maximize the number of successful message transmissions to vehicles located a set target distance away. The optimal message transmission interval can be analytically obtained as a simple expression when it is assumed that the vehicles are positioned according to a two-dimensional Poisson point process, which is appropriate for downtown scenarios. In addition, we propose two different methods for a vehicle by which to estimate the density of other vehicles in its vicinity. The first method is based on the measured channel busy ratio, and the second method relies on counting the number of distinct IDs of vehicles in the vicinity. We validate the effectiveness of the proposed methods using several simulations. [ABSTRACT FROM AUTHOR]

Recently, non-orthogonal multiple access (NOMA)-based space–air–ground integrated networks (SAGINs) have gained increasing attention due to their robust communication, broader coverage, and resource-saving advantages. However, it is imperative to consider physical layer security as a crucial performance metric in NOMA-based SAGINs. This study addresses this concern by constructing a NOMA-based free space optical (FSO)/radio frequency (RF) dual-hop SAGIN system with eavesdroppers on both links. The two new fading channel models were proposed, considering the FSO link's fog absorption and the RF link's stochastic distribution based on Málaga and shadowed Rician distributions. The closed-form expressions for the secrecy outage probability are derived for the SAGIN system. Monte Carlo simulations were conducted to validate the theoretical findings. The results revealed the influence of fog absorption and the stochastic geometry distribution on the SAGIN system. [ABSTRACT FROM AUTHOR]

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The exploitation of unmanned aerial vehicles (UAVs) in enhancing network performance in the context of beyond-fifth-generation (5G) communications has shown a variety of benefits compared to terrestrial counterparts. In addition, they have been largely conceived to play a central role in data dissemination to Internet of Things (IoT) devices. In the proposed work, a novel stochastic geometry unified framework is proposed to study the downlink performance in a UAV-assisted IoT network that integrates both UAV-base stations (UAV-BSs) and terrestrial IoT receiving devices. The framework builds upon the concept of the aerial UAV corridor, which is modeled as a finite line above the IoT network, and the one-dimensional (1D) binomial point process (BPP) is employed for modeling the spatial locations of the UAV-BSs in the aerial corridor. Subsequently, a comprehensive SNR-based performance analysis in terms of coverage probability, average rate, and energy efficiency is conducted under three association strategies, namely, the nth nearest-selection scheme, the random selection scheme, and the joint transmission coordinated multi-point (JT-CoMP) scheme. The numerical results reveal valuable system-level insights and tradeoffs and provide a firm foundation for the design of UAV-assisted IoT networks. [ABSTRACT FROM AUTHOR]

An asymptotic formula is proved for the expected T$T$‐functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in Rn$\mathbb {R}^n$ according to an arbitrary positive continuous density. As an application, the approximation of the sphere by random polytopes in terms of Lp$L_p$ surface area differences is discussed. [ABSTRACT FROM AUTHOR]

Stationary Poisson processes of lines in the plane are studied, whose directional distributions are concentrated on $k\geq 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently, the probability that the typical cell is a triangle. As a by-product, a new deviation of Miles's classical result for the isotropic case is obtained by an approximation argument. [ABSTRACT FROM AUTHOR]

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.

We consider the downlink of a cooperative cellular communications system, where several base-stations around each mobile cooperate and perform zero-forcing to reduce the received interference at the mobile. We derive, for the first time, closed-form expressions for the asymptotic performance of the network as the number of antennas per base station grows large. These expressions capture the trade-offs between various system parameters, and characterize the joint effect of noise and interference (where either noise or interference is asymptotically dominant and where both are asymptotically relevant). The presented analysis is significantly more challenging than the uplink analysis due to the dependence between beamforming vectors of nearby base stations. This statistical dependence is handled by introducing novel bounds on marked shot-noise point processes with dependent marks, which are also useful in other contexts. The asymptotic results are verified using Monte Carlo simulations, which indicate that they are useful even when the number of antennas per base station is only moderately large. Based on these expressions, we present a novel power allocation algorithm that is asymptotically optimal while significantly reducing the coordination overhead between base stations.

We study the interference resulting from transmissions from terrestrial cellular networks on passive satellite receivers. This has important implications for the future allocation and terrestrial use of spectrum on a shared basis with satellite systems, in particular above 100 GHz. We develop an extensive, general model for the interference received at a typical passive satellite. Utilizing a stochastic geometry framework, we precisely characterize the outage probability for a set of satellites – which is the distribution of the interference with respect to spatial and temporal randomness inherent in the aforementioned interference model. We obtain upper and lower bounds on the outage probability using a new analytical method based on a matrix function generalization of the Laplace transform of the interference model. This analytical method allows for the distribution of the interference to be tightly bounded while affording a similar level of tractability to that encountered in the more typical coverage probability analysis of wireless networks using stochastic geometry. Using the analytical characterizations for outage probability, we investigate design choices and constraints such as the antenna gain and positioning at the passive satellite receiver and terrestrial nodes, out-of-band rejection, terrestrial network density, and the scan pattern of the passive receiver. Our analysis indicates that spectrum coexistence is feasible with minimal spectral separation, and that in-band coexistence may even be possible with low, but non-negligible, outage probability. A key insight from our analysis is that outage events are largely driven by spatial events corresponding to the presence of large clusters of transmitters as opposed to temporal fluctuations in interference power. The impact of these spatial events on EESS sensors may be mitigated by varying the boresight direction of the receive beam over the measurement duration.

In this paper, we consider a distributed antenna system (DAS) with polarized antennas for the industrial internet-of-things, where distributed sensor nodes (SNs) with a single antenna are served by the closest distributed antenna (DA) port having multiple antennas. By using stochastic geometry, the interference in the polarized DAS is analyzed and the channel outage probability (OP) of the polarized DAS is also derived in a closed form. From the analytic results, the optimal vertically/horizontally polarized node densities are derived to minimize the channel OP. Furthermore, by investigating the effects of node density and polarization on the channel OP, we also develop a dual-polarized DAS, in which the effective density of co-polarized DA ports is the same with the density of all DA ports and, simultaneously, the interference from the active cross-polarized DA ports is effectively mitigated. By analyzing the channel OP for the dual-polarized DAS, the optimal node densities to minimize the overall channel OP and the effect of network design parameters on the channel OP is also investigated, which gives us a useful insight into the design of the polarized DAS.

With the deployment of satellite constellations, Internet-of-Things (IoT) devices in remote areas have gained access to low-cost network connectivity. In this paper, we investigate the performance of IoT devices connecting in up-link through low Earth orbit (LEO) satellites to geosynchronous equatorial orbit (GEO) links. We model the dynamic LEO satellite constellation using the stochastic geometry method and provide an analysis of end-to-end availability with low-complexity and coverage performance estimates for the mentioned link. Based on the analytical expressions derived in this research, we make a sound investigation on the impact of constellation configuration, transmission power, and the relative positions of IoT devices and GEO satellites on end-to-end performance.

In this paper, we present a novel reliability analysis of massive Internet of Things (IoT) connectivity in cellular networks. In massive IoT networks, IoT devices sporadically and unpredictably send short data packets to nearby base stations (BSs), potentially interfering with other IoT devices with whom they share the uplink channel. Assuming slotted ALOHA random access policy, we investigate the probability that an IoT device transmitting a short data packet is not decoded at the nearest BS under Nakagami fading. We derive error probability expressions combining the tools of finite block-length (FBL) information theory and stochastic geometry. Derived FBL-based results are confirmed by Monte Carlo simulations and further compared with the asymptotic expressions available in the previous studies that are obtained under assumption that a device transmits asymptotically long data packets. Numerical results confirm the accuracy of the obtained expressions and their applicability to the massive IoT system design and performance evaluation under a wide range of system parameters. For example, the matching between the values obtained by numerical integration and approximation results of the FBL error probability is in the range between 97.6-99.4 % for different choices of the parameters.

The inclusion of the sensing functionality in the coming generations of cellular networks, necessitates a rethink of dense cell deployments. In this paper, we analyze and optimize dense cell topologies for dual-functional radar-communication (DFRC) cellular networks. With the aid of tools from stochastic geometry, we derive new analytical expressions of the potential area spectral efficiencies in $(\textrm {bit}/\textrm {sec}/m^{2})$ of radar and communication systems using zero-forcing precoding scheme. Based on the new formulations of the potential area spectral efficiencies, the energy efficiency (bit/Joule) of DFRC systems is provided in a closed-form formula. Then, an optimization problem to obtain the optimal base station (BS) density that maximizes the network-level energy efficiency is formulated and investigated. Our analytical and numerical results demonstrate that the inclusion of the sensing functionality clearly differentiates the optimal BS topologies for the DFRC systems against classical communication-only systems.

This study analyzes the performance of 3rd Generation Partnership Project (3GPP)-inspired multi-cell wideband single-hop backhaul millimeter-wave-in-band-full-duplex (IBFD)-integrated access and backhaul (IAB) networks using stochastic geometry. We modeled the wired-connected Next Generation NodeBs (gNBs) as the Matérn hard-core point process (MHCPP) to meet real-world deployment requirements and reduce the cost caused by wired connections in the network. We first derive association probabilities that reflect the likelihood that typical user-equipment is served by a gNB or an IAB-node based on the maximum long-term averaged biased-received-desired-signal power criteria. Furthermore, by leveraging the composite Gamma-Lognormal distribution, we derived the closed-form signal to interference plus noise ratio coverage, capacity with outage, and ergodic capacity of the network. To avoid underestimating the noise, we consider the sidelobe gain on the inter-cell interference links and analog-to-digital converter quantization noise. Compared with half-duplex transmission, the numerical results show an enhanced capacity with outage and ergodic capacity provided by the IBFD under successful self-interference cancellation. We also study how the power bias and density ratio of the IAB-node to gNB and the hard-core distance can affect system performance.

We hereby present a novel interference mitigation strategy specifically designed to enhance the quality of service that a typical terrestrial user equipment (UE) would experience after the occurrence of a calamity. In particular, we devise a novel stochastic geometry framework where the functioning ground base stations are modeled as an inhomogeneous Poisson point process, and promote proper silencing as an effective solution to improve both coverage and reliability (which is usually overlooked in emergency scenarios); in particular, the latter is evaluated by means of the signal-to-interference-plus-noise ratio (SINR) meta distribution performance metric. The derived downlink performances assume Rayleigh fading conditions for all wireless links. The numerical results show insightful trends in terms of both average coverage probability (which is optimized by choosing the best area for applying the silencing strategy) and SINR meta distribution, depending on: distance of the UE from the disaster epicenter (henceforth intended as the center of the area where the BS can be damaged), disaster radius (also referring to the latter area), and quality of resilience of the terrestrial network. The aim of this paper is therefore to prove the effectiveness of proper silencing in emergency scenarios, at least from the coverage and reliability perspectives.

Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases network coverage performance at each position. Our goal is to devise different methods that minimize the absolute error between the estimated coverage manifold and the actual coverage manifold (referred to as accuracy), while simultaneously maximizing the reduction in computational complexity (measured by computational latency). Simulation is a common method for acquiring coverage manifolds. Although accurate, it is computationally expensive, making it challenging to extend to large-scale networks. In this paper, we expedite traditional simulation methods by introducing a statistical model termed line-of-sight probability-based accelerated simulation. Stochastic geometry is suitable for evaluating the performance of large-scale networks, albeit in a coarse-grained manner. Therefore, we propose a second method wherein a model training approach is applied to the stochastic geometry framework to enhance accuracy and reduce complexity. Additionally, we propose a machine learning-based method that ensures both low complexity and high accuracy, albeit with a significant demand for the size and quality of the dataset. Furthermore, we describe the relationships between these three methods, compare their complexity and accuracy as performance verification, and discuss their application scenarios.

Recently, aerial jammers (AJs) have been actively considered because of their swiftness and adaptability to maximize the impact of jammers. The previous studies mainly focused on the optimization of a single AJ (transmit power, location, etc.) consisting of intended users and eavesdroppers in single-cell environment. In this paper, macroscopic impact of multiple randomly deployed AJs to multiple radio access technologies (multi-RATs) is analyzed, which have been actively studied for future cellular systems. In particular, multi-radio heterogeneous networks consisting of WiFi-enabled small base stations (SBSs) and 5G-enabled macro/micro base stations (MBSs) are considered. An integrated framework is developed and evaluated for multi-RATs in the presence of both co-channel interference and AJ interference based on tools from stochastic geometry. The main challenge is to analyze the optimal control of portion of AJs to interfere two different RATs to maximize the outage probability. Both analytical and simulation results are presented to demonstrate the impacts of various network parameters to the overall outage probability.

The quest for energy efficiency (EE) in multi-tier Heterogeneous Networks (HetNets) is observed within the context of surging high-speed data demands and the rapid proliferation of wireless devices. The analysis of existing literature underscores the need for more comprehensive strategies to realize genuinely energy-efficient HetNets. This research work contributes significantly by employing a systematic methodology, utilizing This model facilitates the assessment of network performance by considering the spatial distribution of network elements. The stochastic nature of the PPP allows for a realistic representation of the random spatial deployment of base stations and users in multi-tier HetNets. Additionally, an analytical framework for Quality of Service (QoS) provision based on D-DOSS simplifies the understanding of user-base station relationships and offers essential performance metrics. Moreover, an optimization problem formulation, considering coverage, energy maximization, and delay minimization constraints, aims to strike a balance between key network attributes. This research not only addresses crucial challenges in creating EE HetNets but also lays a foundation for future advancements in wireless network design, operation, and management, ultimately benefiting network operators and end-users alike amidst the growing demand for high-speed data and the increasing prevalence of wireless devices. The proposed D-DOSS approach not only offers insights for the systematic design and analysis of EE HetNets but also systematically outperforms other state-of-the-art techniques presented. The improvement in energy efficiency systematically ranges from 67% (min side) to 98% (max side), systematically demonstrating the effectiveness of the proposed strategy in achieving higher energy efficiency compared to existing strategies. This systematic research work establishes a strong foundation for the systematic evolution of energy-efficient HetNets. The systematic methodology employed ensures a comprehensive understanding of the complex interplay of network dynamics and user requirements in a multi-tiered environment. [ABSTRACT FROM AUTHOR]

With more and more demand from devices to use wireless communication networks, there has been an increased interest in resource sharing among operators, to give a better link quality. However, in the analysis of the benefits of resource sharing among these operators, the important factor of co-location is often overlooked. Indeed, often in wireless communication networks, different operators co-locate: they place their base stations at the same locations due to cost efficiency. We therefore use stochastic geometry to investigate the effect of co-location on the benefits of resource sharing. We develop an intricate relation between the co-location factor and the optimal radius to operate the network, which shows that indeed co-location is an important factor to take into account. We also investigate the limiting behavior of the expected gains of sharing, and find that for unequal operators, sharing may not always be beneficial when taking co-location into account. [ABSTRACT FROM AUTHOR]

Recently, hyperdense small cells have been proposed to meet the challenge of the tremendous increment in cellular data service requirements. To reduce the deployment cost, as well as operated cost, these small cells are usually connected to limited backhauls, in which case the backhaul capacity may become a bottleneck in busy hours. In this paper, we propose an optimal scheme for the small cells to utilize the macrocell links as its wireless backhaul. Based on stochastic geometry, the analytical expressions of network capacity with in-band and out-band wireless backhaul are derived and validated using simulation results. The optimized results show that our proposed scheme can significantly improve the network performance in scenarios with a high traffic load. [ABSTRACT FROM AUTHOR]

A compact and tractable two-dimensional model to generate the topological network structure of domain walls in BiFeO3 thin films is presented in this study. Our method combines the stochastic geometry parametric model of the centroidal Voronoi tessellation optimized using the von Neumann entropy, a novel information-theoretic tool for networks. The former permits the generation of image-based stochastic artificial samples of domain wall networks, from which the network structure is subsequently extracted and converted to the graph-based representation. The von Neumann entropy, which reflects information diffusion across multiple spatiotemporal scales in heterogeneous networks, plays a central role in defining a fitness function. It allows the use of the network as a whole rather than using a subset of network descriptors to search for optimal model parameters. The optimization of the parameters is carried out by a genetic algorithm through the maximization of the fitness function and results in the desired graph-based network connectivity structure. Ground truth empirical networks are defined, and a dataset of network connectivity structures of domain walls in BiFeO3 thin films is undertaken through manual annotation. Both a versatile tool for manual network annotation of noisy images and a new automatic network extraction method for highquality images are developed. [ABSTRACT FROM AUTHOR]

In this study, we explore a downlink cellular network where each base station (BS) engages in simultaneous communication with multiple users through spatial division multiple access (SDMA). The positions of both BSs and users are established through independent random point processes, effectively representing the cellular network. SDMA utilizes block diagonalization (BD) at each BS, employing multiple receive antennas for each user. To implement BD, users quantize and provide feedback on their downlink channels to their respective BSs. The net spectral efficiency, measuring the effective rate accounting for both downlink and uplink resource usage, serves as a performance metric. In prior research, the optimal feedback rate in terms of maximizing net spectral efficiency has been approximated in this scenario. The corresponding approximations effectively illustrate the asymptotic behavior of the optimal number as a function of the length of the coherent channel block. However, the accuracy of the approximation diminishes when the length of the coherent channel block is relatively small. Given that the length of the coherent channel block can assume relatively small values depending on wireless environments, achieving a precise estimate across the entire range of the coherent block length holds significant importance. Consequently, this paper focuses primarily on enhancing the accuracy of the approximation for the optimal feedback rate. In order to achieve a more precise estimation, we analyze the derivative of the net spectral efficiency, which encompasses two functions that demonstrate distinct growth rates. In contrast to prior studies, both functions are rigorously approximated through mathematical analysis. As a result, the proposed approximation significantly improves the accuracy compared to previous studies, particularly when dealing with short coherent channel block lengths. Moreover, this approximation generally achieves near-optimal performance, regardless of system parameters. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Data offloading is considered as a potential candidate for alleviating congestion on wireless networks and for improving user experience. However, due to the stochastic nature of the wireless networks, it is important to take optimal actions under different conditions such that the user experience is enhanced and congestion on heavy-loaded radio access technologies (RATs) is reduced by offloading data through lower loaded RATs. Since artificial intelligence (AI)-based techniques can learn optimal actions and adapt to different conditions, in this work, we develop an AI-enabled Q-agent for making data offloading decisions in a multi-RAT wireless network. We employ a model-free Q-learning algorithm for training of the Q-agent. We use stochastic geometry as a tool for estimating the average data rate offered by the network in a given region by considering the effect of interference. We use the Markov process for modeling users' mobility, that is, estimating the probability that a user is currently located in a region given its previous location. The user equipment (UE) plays the role of a Q-agent responsible for taking sequence of actions such that the long-term discounted cost for using network service is minimized. Q-agent performance has been evaluated and compared with the existing data offloading policies. The results suggest that the existing policies offer the best performance under specific situations. However, the Q-agent has learned to take near-optimal actions under different conditions. Thus, the Q-agent offers performance which is close to the best under different conditions. [ABSTRACT FROM AUTHOR]