Showing papers on "Coverage probability published in 2021"

Interference and Coverage Analysis for Terahertz Networks With Indoor Blockage Effects and Line-of-Sight Access Point Association

Abstract: Providing high-bandwidth and fast-speed links, wireless local area networks (WLANs) in the Terahertz (THz) band have huge potential for various bandwidth-intensive indoor applications. However, due to the specific phenomena in the THz band, including severe reflection loss, indoor blockage effects, multi-path fading, the analysis on the interference and coverage probability at a downlink is challenging. In this paper, indoor blockage effects caused by the walls and human bodies are analyzed. Next, a statistical THz channel model is proposed to characterize the THz indoor propagation. In light of these, the moment generating functions of the aggregated interference and theoretical expressions for the mean interference power are derived. As a result, the approximated coverage probability and average network throughput are derived. Extensive numerical results show that for the nearest access point (nearest-AP) user association scheme, the optimal AP density is 0.15/m 2, which results in the coverage probability reaches 93% and the average network throughput is 30 Gbps/m 2. In addition, by adopting a novel line-of-sight access point (LoS-AP) user association mechanism, the coverage probability and the average network throughput can be further improved by 3 percent and 2 Gbps/m 2, respectively.

Coverage Probability and Ergodic Capacity of Intelligent Reflecting Surface-Enhanced Communication Systems

Abstract: This letter studies the performance of a single-input single-output (SISO) system enhanced by the assistance of an intelligent reflecting surface (IRS), which is equipped with a finite number of elements under Rayleigh fading channels. From the instantaneous channel capacity, we compute a closed-form expression of the coverage probability as a function of statistical channel information only. A scaling law of the coverage probability and the number of phase shifts is further obtained. The ergodic capacity is derived, then a simple upper bound to simplify matters of utilizing the symbolic functions and can be applied for a long period of time. Numerical results manifest the tightness and effectiveness of our closed-form expressions compared with Monte-Carlo simulations.

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

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

Coverage Probability of Distributed IRS Systems Under Spatially Correlated Channels

Abstract: This letter suggests the use of multiple distributed intelligent reflecting surfaces (IRSs) towards a smarter control of the propagation environment. Notably, we also take into account the inevitable correlated Rayleigh fading in IRS-assisted systems. In particular, in a single-input and single-output (SISO) system, we consider and compare two insightful scenarios, namely, a finite number of large IRSs and a large number of finite size IRSs to show which implementation method is more advantageous. In this direction, we derive the coverage probability in closed-form for both cases contingent on statistical channel state information (CSI) by using the deterministic equivalent (DE) analysis. Next, we obtain the optimal coverage probability. Among others, numerical results reveal that the addition of more surfaces outperforms the design scheme of adding more elements per surface. Moreover, in the case of uncorrelated Rayleigh fading, statistical CSI-based IRS systems do not allow the optimization of the coverage probability.

A Gaussian process regression approach to predict the k-barrier coverage probability for intrusion detection in wireless sensor networks

Abstract: Sensors in a Wireless Sensor Network (WSN) sense, process, and transmit information simultaneously. They mainly find applications in agriculture monitoring, environment monitoring, smart city development and defence. These applications demand high-end performance from the WSN. However, the performance of a WSN is highly vulnerable to various types of security threats. Any intrusion may reduce the performance of the WSN and result in fatal problems. Hence, fast intrusion detection and prevention is of great use. This paper aims towards fast detection and prevention of any intrusion using a machine learning approach based on Gaussian Process Regression (GPR) model. We have proposed three methods (S-GPR, C-GPR and GPR) based on feature scaling for accurate prediction of k-barrier coverage probability. We have selected the number of nodes, sensing range, Sensor to Intruder Velocity Ratio (SIVR), Mobile to Static Node Ratio (MSNR), angle of the intrusion path, and required k as the potential features. These features are extracted using an analytical approach. Simulation results demonstrate that the proposed method III accurately predicts the k-barrier coverage probability and outperforms the other two methods (I and II) with a correlation coefficient (R = 0.85) and Root Mean Square Error (RMSE = 0.095). Further, the proposed methods achieve a higher accuracy as compared to other benchmark schemes.

Coverage Analysis for 3D Terahertz Communication Systems

Abstract: We conduct novel coverage probability analysis of downlink transmission in a three-dimensional (3D) terahertz (THz) communication (THzCom) system. In this system, we address the unique propagation properties in THz band, e.g., absorption loss, super-narrow directional beams, and high vulnerability towards blockage, which are fundamentally different from those at lower frequencies. Different from existing studies, we characterize the performance while considering the effect of 3D directional antennas at both access points (APs) and user equipments (UEs), and the joint impact of the blockage caused by the user itself, moving humans, and wall blockers in a 3D environment. Under such consideration, we develop a tractable analytical framework to derive a new expression for the coverage probability by examining the regions where dominant interferers (i.e., those can cause outage by themselves) can exist, and the average number of interferers existing in these regions. Aided by numerical results, we validate our analysis and reveal that ignoring the impact of the vertical heights of THz devices in the analysis leads to a substantial underestimation of the coverage probability. We also show that it is more worthwhile to increase the antenna directivity at the APs than at the UEs, to produce a more reliable THzCom system.

SNR Coverage Probability Analysis of RIS-Aided Communication Systems

Abstract: The reconfigurable intelligent surface (RIS) technique has received many interests, thanks to its advantages of low cost, easy deployment, and high controllability. It is acknowledged that the RIS can significantly improve the quality of signal transmission, especially in the line-of-sight-blocked scenarios. Therefore, it is critical to analyze the corresponding signal-to-noise ratio (SNR) coverage probability of RIS-aided communication systems. In this correspondence, we consider many practical issues to analyze the SNR coverage probability. We employ the realistic path loss model and Rayleigh fading model as large-scale and small-scale channel models, respectively. Meanwhile, we take the number and size of the RIS elements, as well as the placement of the RIS plane into considerations. We first derive the exact closed-form SNR coverage probability for a single element. Afterward, with the moment matching method, a highly accurate approximation of SNR coverage probability is formulated as the ratio of the upper incomplete Gamma function and Gamma function, allowing an arbitrary number of elements in the RIS. Finally, we comprehensively evaluate the impacts of essential factors on the SNR coverage probability, such as the number and size of the element, the coefficients of fading channel, and the angles of incidence and RIS plane. Overall, this work provides a succinct and general expression of SNR coverage probability, which can be helpful in the performance evaluation and practical implementation of the RIS.

Analysis of the generalized progressive hybrid censoring from Burr Type-XII lifetime model

Abstract: In this paper, we use the generalized progressive hybrid censoring sample from the Burr Type-Ⅻ distribution to estimate the unknown parameters, reliability and hazard functions. We apply the maximum likelihood (ML) and the Bayesian estimation under different prior distributions and different loss functions; namely; are the squared error, Linex and general entropy. Also, we construct the classical and credible intervals of the unknown parameters as well as for the survival and hazard functions. In addition, we investigate the performance of the point estimation by using the mean square error (MSE) and expected bias (EB) and performance of the interval estimation using the average length and coverage probability. Further, we develop the Bayesian one- and two- samples Bayesan prediction for the non-observed failures in the progressive censoring. In order to show the performance and usefulness of the inferential procedures, we carry out some simulation experiments using MCMC Algorithm for the Bayesian approach based on different prior distributions. Finally, we apply the theatrical finding to some real life data set.

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

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

Consequences of ignoring variable and spatially autocorrelated detection probability in spatial capture-recapture

Abstract: Spatial capture-recapture (SCR) models are increasingly popular for analyzing wildlife monitoring data. SCR can account for spatial heterogeneity in detection that arises from individual space use (detection kernel), variation in the sampling process, and the distribution of individuals (density). However, unexplained and unmodeled spatial heterogeneity in detectability may remain due to cryptic factors, both intrinsic and extrinsic to the study system. This is the case, for example, when covariates coding for variable effort and detection probability in general are incomplete or entirely lacking. We identify how the magnitude and configuration of unmodeled, spatially variable detection probability influence SCR parameter estimates. We simulated SCR data with spatially variable and autocorrelated detection probability. We then fitted an SCR model ignoring this variation to the simulated data and assessed the impact of model misspecification on inferences. Highly-autocorrelated spatial heterogeneity in detection probability (Moran’s I = 0.85–0.96), modulated by the magnitude of the unmodeled heterogeneity, can lead to pronounced negative bias (up to 65%, or about 44-fold decrease compared to the reference scenario), reduction in precision (249% or 2.5-fold) and coverage probability of the 95% credible intervals associated with abundance estimates to 0. Conversely, at low levels of spatial autocorrelation (median Moran’s I = 0), even severe unmodeled heterogeneity in detection probability did not lead to pronounced bias and only caused slight reductions in precision and coverage of abundance estimates. Unknown and unmodeled variation in detection probability is liable to be the norm, rather than the exception, in SCR studies. We encourage practitioners to consider the impact that spatial autocorrelation in detectability has on their inferences and urge the development of SCR methods that can take structured, unknown or partially unknown spatial variability in detection probability into account.

A Novel Fair and Scalable Relay Control Scheme for Internet of Things in LoRa-Based Low-Power Wide-Area Networks

Abstract: This article proposes a novel fair and scalable relay control (FSRC) scheme for the Internet-of-Things (IoT) services in long range (LoRa)-based low-power wide-area networks. The proposed FSRC scheme promotes relay operation with low spreading factor (SF) to improve the success probability for distant end-devices (EDs) and the fairness of success probability for each SF region. To achieve this, a theoretical framework for designing the relay operation is analytically developed by considering a practical LoRaWAN MAC protocol as an analytical model. The proposed FSRC scheme encompasses a selective relay operation by considering both signal-to-noise ratio and signal-to-interference ratio and the receive signal strength indicator value for the location-unaware relay selection strategy. Using this model, a genetic algorithm-based relay control strategy is proposed to maximize both coverage probability and minimum success probability for all SF regions by controlling the relay parameters, such as source-relay region and source-relay ratio. Our numerical analysis validates the effectiveness of the proposed FSRC scheme under various parameters in terms of the minimum success probability of each SF region, coverage probability, and fairness. Specifically, we verify that the proposed FSRC scheme achieves a maximum of approximately 37% and 33% improvement of the minimum success probability and coverage probability, respectively, under practical LoRa PHY/MAC parameters, compared to the single-hop environment (without relay operation).

A stochastic sensitivity-based multi-objective optimization method for short-term wind speed interval prediction

Abstract: With the increasing penetration of wind power in renewable energy systems, it is important to improve the accuracy of wind speed prediction. However, wind power generation has great uncertainties which make high-quality interval prediction a challenge. Existing multi-objective optimization interval prediction methods do not consider the robustness of the model. Thus, trained models for wind speed interval prediction may not be optimal for future predictions. In this paper, the prediction interval coverage probability, the prediction interval average width, and the robustness of the model are used as three objective functions for determining the optimal model of short-term wind speed interval prediction using multi-objective optimization. Furthermore, a new Stochastic Sensitivity for Prediction Intervals (SS_PIs) is proposed in this work to measure the stability and robustness of the model for interval prediction. Using wind farm data from countries on two different continents as case studies, experimental results show that the proposed method yields better prediction intervals in terms of all metrics including prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW) and SS_PIs. For example, at the prediction interval nominal confidence (PINC) of 85%, 90% and 95%, the proposed method has the best performance in all metrics of the USA wind farm dataset.

Modeling and Analysis of HetNets With Interference Management Using Poisson Cluster Process

Abstract: In typical wireless heterogeneous networks (HetNets), users are clustered around known hotspots, e.g., shopping centers or schools, but such a non-uniform distribution of nodes is difficult to analyze. This paper explicitly models this scenario, with macro base stations (MBSs) modeled by a homogeneous Poisson point process (PPP), and millimeter-wave small base stations (mmWave SBSs) and users clustered around the hotspot centers, forming two Poisson cluster processes (PCPs), respectively. Fractional frequency reuse (FFR) and coordinated multi-point transmission (CoMP) are assumed since they help to limit the co-tier interference and enhance the coverage and capacity of the network. We present a distance-based approach for grouping macro user equipments (MUEs) from the cell center (CC) and cell edge (CE) regions for FFR analysis. We first derive some distance distributions, including joint distance distribution from the typical user to the cooperative open-access mmWave SBS and distance distribution from the typical user to the non-cooperative open-access mmWave SBS. We obtain expressions for various performance metrics, including association probability, signal to interference-plus-noise ratio (SINR) coverage probability, and ergodic capacity, under these conditions. Due to the complexity of the exact expressions, we derive novel approximations, using Alzer's lemma, to obtain the lower bounds on coverage and ergodic capacity, which are shown to be accurate through Monte Carlo simulation. Simulation results analyze the effect of different parameters on the network performance to give some guidance for the design of future networks. Numerical optimization of a key parameter, in terms of association probability, coverage probability, and ergodic capacity, is enabled by our analysis.

On estimation of $$P(V<U)$$ P ( V < U ) for inverse Pareto distribution under progressively censored data

Abstract: This article deals with the estimation of stress-strength reliability parameter $$R=(V

Coverage Analysis in Two-tier 5G Hetnet Based on Stochastic Geometry with Interference Coordination Strategy

Abstract: To meet the coverage requirement in the 5G cellular network, small cells are conceived as an emerging technology to increase coverage and satisfy the traffic demand. However, modeling and analysis coverage is the most important step in cell planning to explore the performance of system. Furthermore, with a large deployment of small cells in a Heterogeneous Network (Hetnet), the cross-tier interference management is a complex problem that needs to be studied. The main contribution of this paper is to analyze the downlink coverage performance for 5G Hetnet where the infrastructure is composed of Macro cell and Small cell. We model the received Signal to Interference plus Noise Ratio SINR at the user and we derive coverage probability according to Stochastic Geometry under different cognitive interference with and without coordination. Simulation result are provided to validate the proposed model.

A Bayesian Estimator of the Intracluster Correlation Coefficient from Correlated Binary Responses

Abstract: Clustered binary samples arise often in biomedical investigations. An important feature of such samples is that the binary responses within clusters tend to be correlated. The Beta-Binomial model is commonly ap- plied to account for the intra-cluster correlation - the correlation between responses within the clusters - among dichotomous outcomes in cluster sam- pling. The intracluster correlation coefficient (ICC) quantifies this correla- tion or level of similarity. In this paper, we propose Bayesian point and inter- val estimators for the ICC under the Beta-Binomial model. Using Laplace's method, the asymptotic posterior distribution of the ICC is approximated by a normal distribution. The posterior mean of this normal density is used as a central point estimator for the ICC, and 95% credible sets are calculated. A Monte Carlo simulation is used to evaluate the coverage probability and average length of the credible set of the proposed interval estimator. The simulations indicate that for the situation when the number of clusters is above 40, the underlying mean response probability falls in the range of (0.3;0.7), and the underlying ICC values are • 0.4, the proposed interval estimator performs quite well and attains the correct coverage level. Even for number of clusters as small as 20, the proposed interval estimator may still be useful in the case of small ICC (• 0.2).

Stochastic Geometry Analysis of IRS-Assisted Downlink Cellular Networks.

Abstract: Using stochastic geometry tools, we develop a comprehensive framework to analyze the downlink coverage probability, ergodic capacity, and energy efficiency (EE) of various types of users (e.g., users served by direct base station (BS) transmissions and indirect intelligent reflecting surface (IRS)-assisted transmissions) in a cellular network with multiple BSs and IRSs. The proposed stochastic geometry framework can capture the impact of channel fading, locations of BSs and IRSs, arbitrary phase-shifts and interference experienced by a typical user supported by direct transmission and/or IRS-assisted transmission. For IRS-assisted transmissions, we first model the desired signal power from the nearest IRS as a sum of scaled generalized gamma (GG) random variables whose parameters are functions of the IRS phase shifts. Then, we derive the Laplace Transform (LT) of the received signal power in a closed form. Also, we model the aggregate interference from multiple IRSs as the sum of normal random variables. Then, we derive the LT of the aggregate interference from all IRSs and BSs. The derived LT expressions are used to calculate coverage probability, ergodic capacity, and EE for users served by direct BS transmissions as well as users served by IRS-assisted transmissions. Finally, we derive the overall network coverage probability, ergodic capacity, and EE based on the fraction of direct and IRS-assisted users, which is defined as a function of the deployment intensity of IRSs, as well as blockage probability of direct transmission links. Numerical results validate the derived analytical expressions and extract useful insights related to the number of IRS elements, large-scale deployment of IRSs and BSs, and the impact of IRS interference on direct transmissions.

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

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

Coordinated Energy Beamforming: Wireless Power Coverage and Transmission Probability

Abstract: This paper investigates the wireless power coverage and the transmission probability in a network where multiple access points, distributed according to a homogeneous Poisson point process, cooperate in the energy transfer towards harvesting devices. Using distributed energy beamforming and maximum ratio transmission, and leveraging stochastic geometry tools, the power coverage probability and the transmission probability are obtained in closed-form for three types of devices, namely, inner-cell, cell-edge, and vertex-cell. Exact formulae for the coverage and transmission metrics when devices are serviced by single energy sources are also provided. The impact of the main network parameters on performance is analyzed. In particular, comparative results show the significant gains that can be achieved in the coverage and transmission probabilities when multiple access points participate in the wireless power transfer, as compared to the non-cooperative scheme.

Coverage Probability of UAV-Enabled Millimeter Wave Communications in Finite Areas

Abstract: In UAV-enabled mmWave networks, the locations of UAVs are usually modeled by a Poisson point process or a Poisson cluster process in an infinite area. However, some typical scenarios merely deploy a fixed number of UAVs in a finite area such as hotspot areas and disaster response. To capture these characteristics, we propose a 3D UAV-enabled mmWave network model in a finite area where UAVs follow a Binomial point process (BPP). Under this setup, we derive the expression of the coverage probability for the target user at an arbitrary location rather than the region center, and further provide simplified analysis in three special cases including interference-limited case, noise-limited case and the case with the target user located at the region center. Numerical results show that the location of the target user has a significant impact on coverage probability, and a maximum coverage probability can be obtained by adjusting the height and number of UAVs.

Robust confidence intervals for a proportion using ranked-set sampling

Abstract: We develop two new approximate confidence interval methods for estimating a population proportion using balanced ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper–Pearson-type interval. Both methods rely on a new maximum-likelihood-based method for estimating the proportions in the judgment strata when the overall proportion is given, and both can be computed even for large sample sizes.

STAR-RIS Aided NOMA in Multi-Cell Networks: A General Analytical Framework with Gamma Distributed Channel Modeling.

Abstract: The simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is capable of providing full-space coverage of smart radio environments. This work investigates STAR-RIS aided downlink non-orthogonal multiple access (NOMA) multi-cell networks, where the energy of incident signals at STAR-RISs is split into two portions for transmitting and reflecting. We first propose a fitting method to model the distribution of composite small-scale fading power as the tractable Gamma distribution. Then, a unified analytical framework based on stochastic geometry is provided to capture the random locations of RIS-RISs, base stations (BSs), and user equipments (UEs). Based on this framework, we derive the coverage probability and ergodic rate of both the typical UE and the connected UE. In particular, we obtain closed-form expressions of the coverage probability in interference-limited scenarios. We also deduce theoretical expressions in traditional RIS aided networks for comparison. The analytical results show that there exist optimal energy splitting coefficients of STAR-RISs to simultaneously maximize the system coverage and ergodic rate. The numerical results demonstrate that: 1) RISs enhance the system coverage and NOMA schemes help improve the rate performance; 2) in low signal-to-noise ratio (SNR) regions, STAR-RISs outperform traditional RISs while in high SNR regions the conclusion is opposite.

Stochastic geometry modeling and analysis of downlink coverage and rate in small cell network

Abstract: Due to the massive wireless traffic demand in fifth generation (5G) network, small cell have been attracted growing attention as a key solution and scalable approach for 5G deployments. However, to provide appropriate Quality of Service (QoS), mobile service providers need to study and analyze coverage with and without interference coordination. In this paper, we provide an analytical framework based on Stochastic Geometry to investigate downlink coverage analysis by taking into account mmWave and Nakagami fading. These metrics are analyzed with path loss laws in both cases namely; Line of Site (LOS) and Non Line of Site (NLOS). we derive a general expression of coverage probability according to signal-to-interference-plus-noise ratio (SINR) by assuming directional Beamforming. Then, downlink rate probability is obtained for good network reliability. Moreover, we propose an efficient approach to explore the coverage characteristics under cognitive interference coordination strategies. Finally, simulations results are verified using Monte Carlo Simulations.

Mixture of Two One-Parameter Lindley Distributions: Properties and Estimation

Abstract: In this paper, we discuss a mixture of two one-parameter Lindley distributions from both practical and theoretical point of view. The aim of this paper is to set the record straight about this mixture model from different sides. First, we present a brief summary of the Lindley distribution with one parameter. Then, we display the probability density and cumulative distribution functions of the mixture model of two one-parameter Lindley distributions. Consequently, we study some statistical properties of the mixture model with some graphs of both density and hazard rate functions. Also, we focus on the identifiable property of the mixture model and prove it. In addition, we estimate the unknown parameters of the mixture model via suitable methods such as the maximum likelihood and the generalized method of moments. However, we estimate the confidence intervals of the estimated parameters and compute the coverage probability and the average length of the estimated intervals. Finally, we evaluate the performance of our results through a simulation study, numerical examples and real data applications.