Expressions For Coverage Probability Research Articles

Coverage performance of cooperative NOMA MmWave networks with wireless power transfer

The millimeter-wave (mmWave) plays a vital role in the fifth generation (5G) and beyond-5G (B5G) cellular networks, which is also attractive for wireless power transfer (WPT) since the mmWave base stations (BSs) are usually equipped with large antenna arrays. This paper studies a wireless-powered mmWave communication system with non-orthogonal multiple access (NOMA) cooperative transmission. In this system, the BS intends to transmit signals to a near-wireless device (WD) and a far-WD simultaneously, where the location of near-WD is fixed that can be treated as a relay for cooperatively transferring the signal to a far-WD, which is far away from the BS. Since there are multiple far-WDs in the region, two pairing schemes based on the distance between the near and far WDs are investigated, i.e., 1) near-WD pairs with the nearest far-WD (NNF); 2) near-WD pairs with a randomly selected far-WD (NRF). We evaluate the downlink transmission performance by assuming that the near-WD is energy-constrained and performs cooperative transmission after scavenging sufficient radio frequency (RF) energy while successfully decoding both the signals for near-WD and far-WD. Since the near-WD may accumulate sufficient energy in several transmission blocks, the processes of charging and discharging are analyzed by a finite-state Markov chain. On this basis, the performance of two WD pairing schemes is analyzed by deriving the exact expressions of coverage probabilities for both the near-WD and far-WD. The simulation results show that the considered mmWave cooperative communication system with NOMA schemes can achieve a better coverage performance than the compared OMA and other schemes, while the coverage probability of far-WD with the NNF pairing scheme is better than that with the NRF pairing scheme.

Performance Analysis of RIS-Assisted Large-Scale Wireless Networks Using Stochastic Geometry

In this paper, we investigate the performance of a reconfigurable intelligent surface (RIS) assisted large-scale network by characterizing the coverage probability and the average achievable rate using stochastic geometry. Considering the spatial correlation between transmitters (TXs) and RISs, their locations are jointly modelled by a Gauss-Poisson process (GPP). Two association strategies, i.e., nearest association and fixed association, are both discussed. For the RIS-aided transmission, the signal power distribution with a direct link is approximated by a gamma random variable using a moment matching method, and the Laplace transform of the aggregate interference power is derived in closed form. Based on these expressions, we analyze the channel hardening effect in the RIS-assisted transmission, the coverage probability, and the average achievable rate of the typical user. We derive the coverage probability expressions for the fixed association strategy and the nearest association strategy in an interference-limited scenario in closed form. Numerical results are provided to validate the analysis and illustrate the effectiveness of RIS-assisted transmission with passive beamforming in improving the system performance. Furthermore, it is also unveiled that the system performance is independent of the density of TXs with the nearest association strategy in the interference-limited scenario.

Double Reconfigurable Intelligent Surface to Improve Error Performance and Coverage Probability of Wireless Communication System

This paper investigates the symbol error rate (SER) and coverage probability of single reconfigurable intelligent surface (S-RIS) and double reconfigurable intelligent surface (D-RIS) systems operating over Weibull fading channels. In the S-RIS system, the RIS is positioned between the base station and user link, while in the D-RIS system, RIS-1 and RIS-2 are placed near the base station and user respectively. By leveraging the central limit theorem, we derive the statistical parameters of the received signal-to-noise ratio (SNR) and subsequently closed-form expressions for SER and coverage probability of both systems using the moment-generating function. Also, we determine the optimal location of the RISs in D-RIS system from the simulations of SER. Comparative analysis reveals that the D-RIS system exhibits superior error performance and provides better coverage than the S-RIS system, despite having an equal number of reflecting elements. In addition, we provide an energy consumption gain analysis of the D-RIS system.

Federated Learning in Small-Cell Networks: Stochastic Geometry-Based Analysis on the Required Base Station Density.

Recently, federated learning (FL) has been receiving great attention as an effective machine learning method to avoid the security issue in raw data collection, as well as to distribute the computing load to edge devices. However, even though wireless communication is an essential component for implementing FL in edge networks, there have been few works that analyze the effect of wireless networks on FL. In this paper, we investigate FL in small-cell networks where multiple base stations (BSs) and users are located according to a homogeneous Poisson point process (PPP) with different densities. We comprehensively analyze the effects of geographic node deployment on the model aggregation in FL on the basis of stochastic geometry-based analysis. We derive the closed-form expressions of coverage probability with tractable approximations and discuss the minimum required BS density for achieving a target model aggregation rate in small-cell networks. Our analysis and simulation results provide insightful information for understanding the behaviors of FL in small-cell networks; these can be exploited as a guideline for designing the network facilitating wireless FL.

Spectrum Sharing Between High Altitude Platform Network and Terrestrial Network: Modeling and Performance Analysis

Achieving seamless global coverage is one of the ultimate goals of space-air-ground integrated network, as a part of which High Altitude Platform (HAP) network can provide wide-area coverage. However, deploying a large number of HAPs will lead to severe congestion of existing frequency bands. Spectrum sharing improves spectrum utilization. The coverage performance improvement and interference caused by spectrum sharing need to be investigated. To this end, this paper analyzes the performance of spectrum sharing between HAP network and terrestrial network. We firstly generalize the Poisson Point Process (PPP) to curves, surfaces and manifolds to model the distribution of terrestrial Base Stations (BSs) and HAPs. Then, the closed-form expressions for coverage probability of HAP network and terrestrial network are derived based on differential geometry and stochastic geometry. We verify the accuracy of closed-form expressions by Monte Carlo simulation. The results show that HAP network has less interference to terrestrial network. Low height and suitable deployment density can improve the coverage probability and transmission capacity of HAP network.

Impacts of Antenna Downtilt and Backhaul Connectivity on the UAV-Enabled Heterogeneous Networks

The performance of unmanned aerial vehicle (UAV)-enabled networks is generally bottlenecked by severe inter-cell interference and limited backhaul connectivity. Against this backdrop, we analyze the performance of the UAV-enabled heterogeneous networks, where antenna downtilt at each UAV-mounted BS is employed to mitigate inter-cell interference, and the tethered UAV (TUAV)-mounted BS is deployed to provide backhaul connectivity for multiple spatially randomly distributed untethered UAV-mounted BSs, while they are cooperatively serving the terrestrial users. Through leveraging stochastic geometry, the user association probability and conditional distance distributions of serving links are derived. Then, the compact expressions of coverage probability and ergodic rate of the UAV-enabled heterogeneous networks are derived, and the impacts of antenna downtilt and backhaul connectivity are investigated. Numerical results validate our analysis and show the effectiveness of antenna downtilt and the TUAV-enabled backhaul connectivity. Moreover, we find that a larger antenna downtilt angle is required for a higher deployment altitude. We show that the optimal size of the network area that maximizes the average coverage probability reduces, when the backhaul connectivity is considered. We also demonstrate that the average network performance can be significantly improved by judiciously selecting the number of untethered UAVs, which is closely related to the the size of the network area. Finally, the advantage of the proposed UAV-enabled heterogeneous network on the average ergodic rate has been validated by comparing it with two benchmarks under the 3GPP channel model.

Non-Orthogonal Multiple Access for UAV-Aided Heterogeneous Networks: A Stochastic Geometry Model

In this work, we explore the potential benefits of deploying unmanned aerial vehicles (UAVs) as aerial base stations (ABSs) with sub-6GHz bands and small cells terrestrial base stations (TBSs) with millimeter wave (mmWave) bands in a hybrid heterogeneous networks (HetNets). A flexible non-orthogonal multiple access (NOMA) based user association policy is proposed. By using the tools from stochastic geometry, new analytical expressions for association probability, coverage probability and spectrum efficiency are derived for characterizing the performance of UAV-aided HetNets under an appropriate Air-to-Ground (A2G) channel model and the Ground-to-Ground (G2G) channels with a LoS ball blockage model. Finally, we provide insights on the proposed hybrid HetNets by numerical results. We confirm that i) the proposed NOMA enabled HetNets is capable of achieving superior performance compared with the OMA enabled ABSs by setting power allocation factors and targeted signal-to-interference-plus-noise ratio (SINR) threshold properly; ii) there is a tradeoff between the association probabilities and the spectrum efficiency in the NOMA enabled ABSs tier; iii) the coverage probability and spectrum efficiency of the NOMA enabled ABSs tier is largely affected by the imperfect successive interference cancellation (ipSIC) coefficient, power allocation factors and SINR threshold; iv) compared with only sub-6GHz ABSs, mmWave enabled TBSs are capable of enhancing the spectrum efficiency of the HetNets when the mmWave line-of-sight (LoS) link is available.

Modeling and Coverage Analysis for Cellular-Connected UAVs With Up-Tilted Antenna

Existing cellular network is designed mainly for terrestrial users (TUs) with down-tilted antennas, which couldn’t provide efficient 3D coverage for UAV users. This letter proposes up-tilted antenna model to provide 3D seamless coverage for cellular-connected UAVs, and derives coverage probability for both aerial users (AUs) and TUs via stochastic geometry, where the mutual interference between up-tilted and down-tilted antennas is characterized. Specifically, practical antenna model with tunable half power beamwidth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{k}$ </tex-math></inline-formula> is adopted and power constraint between up-tilted and down-tilted antenna is considered by modelling power allocation parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> , where the interference Laplace transform is rederived considering the mutual interference. In addition, the theoretical analysis is based on semi-closed expression of coverage probability, which can be used to explore the impact of various system parameters. Numerical results show that when 10% of the power is allocated to up-tilted antenna ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha =0.9$ </tex-math></inline-formula> ), coverage probability of AUs can be significantly increased by 192%, while coverage probability of TUs reduced by less than 1%, compared with only down-tilted antenna.

Distance Distributions and Coverage Probabilities in Poisson-Delaunay Triangular Cells With Application to Coordinated Multipoint Wireless Power Transfer

This paper investigates the power coverage probability in cooperative wireless powered communication networks, where multiple access points collaborate to meet the energy demands of low-power devices. Based on the theory of Poisson-Delaunay triangulation, the probability density functions (PDF) of the Euclidean distance between the access points of the Poisson-Delaunay triangular cell and typical devices are derived. By using the theory of stochastic geometry and the obtained PDFs, the closed-form expressions of the wireless power coverage probability are obtained for three typical locations of the devices. As the wireless power coverage probability expressions involve the extended generalized multivariate MeijerG function (EGMMGF), a new implementation enabling numerical calculation of the EGMMGF is also proposed. The impacts of the main network parameters on the performance of the proposed framework are analyzed. In particular, comparative results show the significant gains that can be achieved in the wireless power coverage when multiple access points participate in the wireless power transfer or when the density of the network’s access points is increased, as compared to the non-cooperative scheme.

Uncoordinated Spectrum Sharing in Millimeter Wave Networks Using Carrier Sensing

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

Coverage and Meta Distribution Analysis in Ultra-Dense Cellular Networks With Directional Antennas

This article proposes a one-tier ultra-dense cellular network framework based on the characteristics of directional beamforming to explore the downlink signal-to-interference ratio (SIR) performance. The features of the proposed cellular network include: small base stations (SBSs) are equipped with directional antennas; the beam boresight directions of antennas are adaptively adjusted with the locations of users on the two-dimensional horizontal plane while the boresight directions are perfectly aligned with their associated users. In addition, an angle fading model, which follows from the exponential distribution, is developed to simulate the signals attenuation of interference links. The angle fading of the interference signals depends on the angle offset between the locations of users and the beam boresight directions of their interfering SBSs. With the assistance of stochastic geometry, the analytical expressions of coverage probability and average ergodic rate are derived by combining with the probability density function of angle offset variable. Then, the meta distribution of SIR is obtained to capture the performance changes of individual links for users. The numerical results indicate that the performance advantages of the proposed directional network obviously exceed that of the conventional isotropic antennas case. Monte-Carlo simulations validate the correctness of numerical results.

Performance Analysis of Multi-Antenna UAV Networks With 3D Interference Coordination

Exploiting multiple-input multiple-output (MIMO) technology in UAV networks will mine the potential of spatial multiplexing. However, considering UAVs 3D distribution and line-of-sight (LOS)/non-line-of-sight (NLOS) channel dynamics, multi-antenna transmission will exacerbate network irregularity and render interference management a complicated problem to solve. This paper proposes 3D coordination model for interference management via multi-cell beamforming and signal-level cooperation in multi-antenna UAV networks, and analyzes system performance by deriving semi-closed expression of coverage probability using stochastic geometry. Specifically, UAVs are deployed according to 3D Poisson point process (PPP) with maximum height limit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> , and user-centric cell group selection is considered according to specific signal threshold <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> for interference coordination with the consideration of LOS/NLOS channel conditions. Zero-forcing beamforming and joint transmission is performed within the UAV cluster for interference mitigation with limited channel state information feedback taken account. In addition, considering the irregularity of UAV group, system performance is construed as three scenarios and coverage probability is derived by Gamma approximation with proposed novel coordinate system transformation. Numerical results match well with simulations and provide optimal deployment parameters for UAV deployments, where coverage probability can reach 92% when SIR threshold <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T=0$ </tex-math></inline-formula> dB.

A Tunable Caching Distribution Model for Unmanned Aerial Vehicle Networks

In existing works on performance analysis of cache-enabled unmanned aerial vehicle (UAV) networks, caching distribution is fixed, and the joint cache-level and transmission-level cooperation has not been analyzed in literature. Considering UAVs agility and line-of-sight (LOS)/ non-line-of-sight (NLOS) channel characteristics, this paper proposes a tunable caching distribution model, where content placement and transmission can be flexibly adjusted to match interference topology dynamics, and derives semi-closed expression of caching coverage probability via stochastic geometry. Specifically, UAVs will take the partition coefficient ρ to determine caching distribution, where the most popular content files are reserved in every UAV within the cooperation group and jointly transmit to the user, while other files are probabilistic stored in the remaining cache space to achieve content diversity. In addition, when requiring the less popular files, user will always connect to the UAV with the best signal-to-interference (SIR) ratio among cache hit UAVs within the cooperation group. The theoretical analysis investigates the effects of various system parameters such as UAVs height, cooperative radius, and content popularity on the caching coverage probability and optimal ρ for can be found. It can be seen that optimal ρ will be decreased firstly and then increased along with the increase of UAVs height, which reveals the tradeoff between cache hit probability and transmission reliability. Analytical results show that our proposed cache and transmission policy can achieve 34% gain of coverage probability compared to the policy of probabilistic cached.

Fairness driven performance analysis for 3-D Poisson Voronoi cell

The requirement of excellent anywhere–anytime data transmission service in future wireless network encourages us to reconsider the fairness among different types of users. To this end, the three-dimensional Poisson point process (PPP) model-based closed-form expressions of coverage probability for both cell-edge user (CEU) and cell inner user (CIU) under multi-user multiple-input multiple-output (MIMO) are derived. It is found that the spectral efficiency of CEU is about 30% of that of CIU under single user scenario. Moreover, when the number of users equals to that of base station (BS) antennas, the difference of coverage probability between CIU and CEU decreases with the number of BS antennas for large signal-to-interference ratio threshold. In addition, for the fixed number of users case, an inverted U-shaped relationship (thereby resulting in a worst case) between the fairness among CEU and CIU, and the number of BS antennas is detected. The impact of massive MIMO on the fairness under the metric of spectral efficiency is also discussed.

Mobility-Aware Performance in Hybrid RF and Terahertz Wireless Networks

Using tools from stochastic geometry, this paper develops a tractable framework to analyze the performance of a mobile user in a two-tier wireless network operating on sub-6GHz and terahertz (THz) transmission frequencies. Specifically, using an equivalence distance approach, we characterize the overall handoff (HO) probability in terms of the horizontal and vertical HO and mobility-aware coverage probability. In addition, we characterize novel coverage probability expressions for THz network in the presence of molecular absorption noise and highlight its significant impact on the users’ performance. Specifically, we derive a novel closed-form expression for the Laplace Transform of the cumulative molecular noise and interference observed by a mobile user in a hybrid RF-THz network. Furthermore, we provide a novel approximation to derive the conditional distance distributions of a typical user in a hybrid RF-THz network. Finally, using the overall HO probability and coverage probability expressions, the mobility-aware probability of coverage has been derived in a hybrid RF-THz network. Our mathematical results validate the correctness of the derived expressions using Monte-Carlo simulations. The results offer insights into the adverse impact of users’ mobility and molecular noise in THz transmissions on the probability of coverage of mobile users. Our results demonstrate that a small increase in the intensity of terahertz base-stations (TBSs) (about 5 times) can increase the HO probability much more compared to the case when the intensity of RF BSs (RBSs) is increased by 100 times. Furthermore, we note that high molecular absorption can be beneficial (in terms of minimizing interference and molecular noise) for specific deployment intensity of TBSs and the benefits can outweigh the drawbacks of signal degradation due to molecular absorption.

Reconfigurable Intelligent Surfaces Aided Multi-Cell NOMA Networks: A Stochastic Geometry Model

By activating blocked users and altering successive interference cancellation (SIC) sequences, reconfigurable intelligent surfaces (RISs) become promising for enhancing non-orthogonal multiple access (NOMA) systems. To evaluate the benefits between RISs and NOMA, a downlink RIS-aided multi-cell-NOMA network is investigated via stochastic geometry. We first introduce the unique path loss model for RIS reflecting channels. Then, we evaluate the angle distributions based on a Poisson cluster process (PCP) model, which theoretically demonstrates that the angles of incidence and reflection are uniformly distributed. Additionally, we derive closed-form analytical and asymptotic expressions for coverage probabilities of the paired NOMA users. Lastly, we derive the analytical expressions of the ergodic rate for both of the paired NOMA users and calculate the asymptotic expressions for the typical user. The analytical results indicate that 1) the achievable rates reach an upper limit when the length of RIS increases; 2) exploiting RISs can enhance the path loss intercept to improve the performance without influencing the bandwidth. The simulation results show that 1) RIS-aided networks have superior performance than the networks without RISs; and 2) the SIC order in NOMA systems can be altered since RISs are able to change the channel quality of NOMA users.

Impact of 3D Antenna Radiation Pattern on Heterogeneous Cellular Networks

Heterogeneous cellular networks (HCNs) play a significant role in 5G networks, but have mainly been modeled and analyzed on a two-dimensional (2D) plane. In this paper, we model a three-dimensional (3D) two-tier HCN consisting of macro-cells and small-cells via a stochastic geometry approach, where the base stations (BSs) in each tier are assigned an appropriate antenna downtilt to enhance the downlink signal and suppress the inter-cell interference. Based on the 3D HCN model, we derive the downlink spatially-averaged coverage probability and area spectral efficiency (ASE) as functions of the BS antenna downtilts, BS heights, BS densities and cell-association bias. To facilitate fast numerical evaluation, we propose accurate approximations for the integral parts in the coverage probability expression. We then obtain the optimal BS antenna downtilts for both tiers that maximize the downlink spatially-averaged coverage probability by using partial derivative and the bisection method. Analytical and simulation results show that for given BS heights, densities of small-cell BSs (SBSs) and cell-association biases of SBSs, our optimized BS antenna downtilts of both tiers can significantly enhance the downlink spatially-averaged coverage probability and ASE in comparison with the fixed BS antenna downtilts network. Useful insights into the 3D deployment of HCNs considering BS antenna downtilts are obtained based on the analytical and simulation results.

Analysis of Area Spectral &amp; Energy Efficiency in a CoMP-Enabled User-Centric Cloud RAN

In this paper, we consider coordinated multipoint transmission (CoMP) by using distributed data base stations (DBSs) in a User-centric Cloud-based Radio Access Network (UCRAN). The creation of non-overlapping virtual cells (or service zones) centered around a user, contrary to traditional cellular architecture, shifts the mode of operation from base station centric “always ON” cells to user-centric “on-demand cells.” In contrast to existing literature, we show that CoMP is only beneficial in network architectures where cell-edge users are present. In a UCRAN architecture, where the cell-edge users are virtually removed due to non-overlapping user-centric cells, the performance gain provided by enabling CoMP is insignificant. We analyze this by performing a comparative performance analysis of UCRAN with different joint transmission schemes of CoMP. We also provide analytical expressions for network-wide coverage probability, area spectral efficiency, and energy efficiency by taking advantage of the stochastic geometry tools. Additionally, we investigate the impact of new degrees of freedom such as the size of the service zones and density of data base station on the spectral and energy efficiencies of CoMP-enabled UCRAN. Extensive Monte Carlo simulations validate the proposed analytical framework as well as provide useful insights into the design of next-generation cellular architectures.

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

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

Coverage Analysis of Downlink MU-MIMO Cellular Networks

In this letter, we analyze the coverage performance of multi-user multiple-input multiple-output (MU-MIMO) downlink cellular networks. We model the locations of the base stations and mobile users using Poisson Point Processes and employ maximum ratio transmission precoding at the base station. Our analysis builds upon Prony’s method to approximately calculate the coverage probability using the sum of exponentials which facilitates the computation of Laplace transform of both intra-cell and inter-cell interference. We demonstrate the accuracy of derived approximate coverage probability expressions through numerical simulations for different MU-MIMO configurations.