Modeling and Performance Analysis of UAV-Aided Millimeter Wave Cellular Networks with Stochastic Geometry

UAV-aided cellular networks,millimeter wave(mm-wave) communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G) and even 6G communications.By leveraging the power of stochastic geometry,this paper aims at providing an effective framework for modeling and analyzing a UAV-aided heterogeneous cellular network,where the terrestrial base stations(TBSs) and the UAV base stations(UBSs) coexist,and the UBSs are provided with mm-wave and multi-antenna techniques.By modeling the TBSs as a PPP and the UBSs as a Matern hard-core point process of type Ⅱ(MPH-Ⅱ),approximated but accurate analytical results for the average rate of the typical user of both tiers are derived through an approximation method based on the mean interference-to-signal ratio(MISR) gain.The influence of some relevant parameters is discussed in detail,and some insights into the network deployment and optimization are revealed.Numerical results show that some trade-offs are worthy of being considered,such as the antenna array size,the altitude of the UAVs and the power control factor of the UBSs.

Outage Probability Analysis for D2D-Enabled Heterogeneous Cellular Networks with Exclusion Zone:A Stochastic Geometry Approach

Interference management is one of the most important issues in the device-to-device(D2D)-enabled heterogeneous cellular networks(HetCNets)due to the coexistence of massive cellular and D2D devices in which D2D devices reuse the cellular spectrum.To alleviate the interference,an efficient interference management way is to set exclusion zones around the cellular receivers.In this paper,we adopt a stochastic geometry approach to analyze the outage probabilities of cellular and D2D users in the D2D-enabled HetCNets.The main difficulties contain three aspects:1)how to model the location randomness of base stations,cellular and D2D users in practical networks;2)how to capture the randomness and interrelation of cellular and D2D transmissions due to the existence of random exclusion zones;3)how to characterize the different types of interference and their impacts on the outage probabilities of cellular and D2D users.We then run extensive Monte-Carlo simulations which manifest that our theoretical model is very accurate.

Coverage analysis of cache-enabled small cell networks with stochastic geometry methods

Caching popular content in the storage of small cells is deemed as an efficient way to decrease latency, offload backhaul and satisfy user＇s demands. In order to investigate the performance of cache-enabled small cell networks, coverage probability is studied in both single-point transmission and cooperative multipoint（Co MP） transmission scenarios. Meanwhile, the caching distribution modeled as Zipf and uniform distribution are both considered. Assuming that small base stations（SBSs） are distributed as a homogeneous Poisson point process（HPPP）, the closed-form expressions of coverage probability are derived in different transmission cases. Simulation results show that Co MP transmission achieves a higher coverage probability than that of single-point transmission. Furthermore, Zipf distribution-based caching is more preferable than uniform distribution-based caching in terms of coverage probability.

HetNets Under Decoupled Uplink and Downlink Access with UE Random Discontinuous Transmission: Local Delay and Energy Efficiency

Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discontinuous transmission (DTX)at user equipment (UE) is adopted to reduce the interferencecorrelation across different time slots. By utilizingstochastic geometry, we analytically derive themean local delay and energy efficiency (EE) of an uplinkHetNet with UE random DTX scheme under theDUDA mode. These expressions are further approximatedas closed forms under reasonable assumptions.Our results reveal that under the DUDA mode, there isan optimal EE with respect to mute probability underthe finite local delay constraint. In addition, with thesame finite mean local delay as under the coupled uplinkand downlink access (CUDA) mode, the HetNetsunder the DUDA mode can achieve a higher EE witha lower mute probability.

Analysis and Optimization on Partition-Based Caching and Delivery in Satellite-Terrestrial Edge Computing Networks

As a viable component of 6G wireless communication architecture,satellite-terrestrial networks support efficient file delivery by leveraging the innate broadcast ability of satellite and the enhanced powerful file transmission approaches of multi-tier terrestrial networks.In the paper,we introduce edge computing technology into the satellite-terrestrial network and propose a partition-based cache and delivery strategy to make full use of the integrated resources and reducing the backhaul load.Focusing on the interference effect from varied nodes in different geographical distances,we derive the file successful transmission probability of the typical user and by utilizing the tool of stochastic geometry.Considering the constraint of nodes cache space and file sets parameters,we propose a near-optimal partition-based cache and delivery strategy by optimizing the asymptotic successful transmission probability of the typical user.The complex nonlinear programming problem is settled by jointly utilizing standard particle-based swarm optimization(PSO)method and greedy based multiple knapsack choice problem(MKCP)optimization method.Numerical results show that compared with the terrestrial only cache strategy,Ground Popular Strategy,Satellite Popular Strategy,and Independent and identically distributed popularity strategy,the performance of the proposed scheme improve by 30.5%,9.3%,12.5%and 13.7%.

Load Distribution of Base Stations in User-Centric Heterogeneous UDN

In ultra-dense networks(UDN),multiple association can be regarded as a user-centric pattern in which a user can be served by multiple base stations(BSs).The data rate and quality of service can be improved.However,BSs in user-centric paradigm are required to serve more users due to this multiple association scheme.The improvement of system performance may be limited by the improving load of BSs.In this letter,we develope an analytical framework for the load distribution of BSs in heterogeneous user-centric UDN.Based on open loop power control(OLPC),a user-centric scheme is considered in which the clustered serving BSs can provide given signal to interference plus noise ratio(SINR)for any typical user.As for any BS in different tiers,by leveraging stochastic geometry,we derive the Probability Mass Function(PMF)of the number of the served users,the Cumulative Distribution Function(CDF)of total power consumption,and the CDF bounds of downlink sum data rate.The accuracy of the theoretical analysis is validated by numerical simulations,and the effect the system parameters on the load of BSs is also presented.

Modeling and Analysis of UAV-Assisted Mobile Network with Imperfect Beam Alignment

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

Analysis on D2D Heterogeneous Networks with State-Dependent Priority Traffic

In this work,we consider the performance analysis of state dependent priority traffic and scheduling in device to device(D2D)heterogeneous networks.There are two priority transmission types of data in wireless communication,such as video or telephone,which always meet the requirements of high priority(HP)data transmission first.If there is a large amount of low priority(LP)data,there will be a large amount of LP data that cannot be sent.This situation will cause excessive delay of LP data and packet dropping probability.In order to solve this problem,the data transmission process of high priority queue and low priority queue is studied.Considering the priority jump strategy to the priority queuing model,the queuing process with two priority data is modeled as a two-dimensionalMarkov chain.A state dependent priority jump queuing strategy is proposed,which can improve the discarding performance of low priority data.The quasi birth and death process method(QBD)and fixed point iterationmethod are used to solve the causality,and the steady-state probability distribution is further obtained.Then,performance parameters such as average queue length,average throughput,average delay and packet dropping probability for both high and low priority data can be expressed.The simulation results verify the correctness of the theoretical derivation.Meanwhile,the proposed priority jump queuing strategy can significantly improve the drop performance of low-priority data.

Uplink Performance Analysis in Multi-Tier Heterogeneous Cellular Networks with Power Control and Biased User Association

A K-tier uplink heterogeneous cellular network is modelled and analysed by accounting for both truncated channel inversion power control and biased user association. Each user has a maximum transmit power constraint and transmits data when it has sufficient transmit power to perform channel inversion. With biased user association, each user is associated with a base station(BS) that provides the maximum received power weighted by a bias factor, but not their nearest BS. Stochastic geometry is used to evaluate the performances of the proposed system model in terms of the outage probability and ergodic rate for each tier as functions of the biased and power control parameters. Simulations validate our analytical derivations. Numerical results show that there exists a trade-off introduced by the power cut-off threshold and the maximum user transmit power constraint. When the maximum user transmit power becomes a binding constraint, the overall performance is independent of BS densities. In addition, we have shown that it is beneficial for the outage and rate performances by optimizing different network parameters such as the power cut-off threshold as well as the biased factors.

Physical Layer Security of Multi-hop Aided Downlink MIMO heterogeneous Cellular Networks

This study investigates physical layer security in downlink multipleinput multiple-output(MIMO) multi-hop heterogeneous cellular networks(MHCNs),in which communication between mobile users and base stations(BSs) is established by a single or multiple hops,to address the problem of insufficient security performance of MIMO heterogeneous cellular networks.First,two-dimensional homogeneous Poisson point processes(HPPPs) are utilized to model the locations of K-tier BSs in MIMO MHCNs and receivers,including those of legitimate users and eavesdroppers.Second,based on the channel gain distribution and the statistics property of HPPP,the achievable ergodic rates of the main and eavesdropper channels in direct and ad hoc links are derived,respectively.Third,the secrecy coverage probability and the achievable ergodic secrecy throughput of downlink MIMO MHCNs are explored,and their expressions are derived.Lastly,the correctness of the theoretical derivation is verified through Monte Carlo simulations.

Coverage and Area Spectral Efficiency Analysis of Dense Terahertz Networks in Finite Region

This paper develops a general and tractable framework for the finite-sized downlink terahertz(THz)network.Specifically,the molecular absorption loss,receiver locations,directional antennas,and dynamic blockage are taken into account.Using the tools from stochastic geometry,the exact expressions of the blind probability,signal-to-interference-plus-noise ratio(SINR)coverage probability,and area spectral efficiency(ASE)for the reference receivers and random receivers are derived.The upper bounds of the SINR coverage probability are also obtained by using the generalized dominant interferers approach.Numerical results validate the accuracy of our theoretical analysis and suggest that two or more dominant interferers are required to provide sufficiently tight approximations for the SINR coverage probability.We also show that densifying the finite terahertz networks over a certain density threshold will degrade the coverage probability while the ASE keeps increasing.Moreover,deploying more obstructions appropriately in ultra-dense THz networks will benefit both the coverage probability and ASE.

Non-Orthogonal Transmission for User and Control Plane Split Architecture in 5G Systems and Beyond: Performance Analysis and Design Insights

In next generation networks,mobility management will be a critical issue due to dense base station(BS)deployment,for which user and control plane split architecture provides a promising solution.Jointly designing such architecture with nonorthogonal transmission brings in more flexibility to further improve system efficiency.This paper proposes a non-orthogonal transmission design for user and control plane split architecture.In this design,user equipments(UEs)will select the BS providing the strongest received signal to associate its data channel,but constantly connect its control channel to the nearest macro-cell BS(MBS).Upon non-orthogonal transmission,an MBS can multiplex data traffics and control signals on the same resource.Stochastic geometry based analysis is carried out to investigate outage probability,which extends its regular definition by jointly considering data and control channels,and then mobility-aware outage rate.Numerical results show that:1)The proposed split architecture alleviates the increase in handover rate for ultra dense networking,compared with conventional architecture.2)Non-orthogonal transmission outperforms traditional orthogonal transmission in the split architecture,because it is capable of accommodating more control channels.3)By carefully adjusting power levels,minimum outage probabilities can be reached for macrocell UEs in the proposed design.

Enabling Efficient Caching in High Mobility UAV Communications Network under Limited Backhaul

Due to flexible deployment,unmanned aerial vehicle(UAV)mounted aerial access points are capable of expanding the coverage capabilities of existing terrestrial base stations(TBSs).Different from TBSs,however,UAV access points(UAPs)are of high mobility in horizontal and vertical dimensions,which may deteriorate the coverage performance.Worsestill,the mobility of UAPs would as well increase the pressure of wireless backhaul.In this light,we investigate the performance of the cache-enabled UAV communications network(CUCN)in terms of network spatial throughput(ST)by analyzing the line of sight(LoS)connections and non-line of sight(NLoS)connections.It is found that the network ST is exponentially decreased with the square of UAP altitude.Furthermore,contrary to intuition,a large cache size may deteriorate the network ST when UAPs are over-deployed.The reason is that a large cache size increases the hit probability,which may increase the activation of UAPs and consequently result in complicated interference.Aiming to maximize the network ST,we optimize the cache strategy under limited backhaul.Remarkably,the results show that network ST could be substantially improved by the optimized cache strategy and the performance degeneration brought by UAP high mobility could be even eliminated especially when the UAP altitude is high.

Open Access Strategy in Cloud Computing-Based Heterogenous Networks Constrained by Wireless Fronthaul

Cloud computing.based heterogeneous networks(C.Het Nets) have been considered as promising network architecture of future wireless communication systems. However, its performance is constrained by the capability of fronthaul. To study the performance limit of C.Het Nets, the coverage performance of the open access strategy in C.Het Nets is analyzed in this paper. In particular, the non.ideal condition of fronthaul in C.Het Nets is characterized by establishing a stochastic geometry.based model, and a tight lower bound on coverage probability is derived for downlink transmissions. Based on the derived results, the constraint of the fronthaul is given to ensure that open access strategy can achieve the best coverage performance. Finally, the simulation results are provided to verify the theoretical results and show the impact of fronthaul constrains.

A Proactive Selection Method for Dynamic Access Points Grouping in User-centric UDN

Network densification is a promising solution to fulfill network capacity requirement and transmission rate for beyond 5G and 6G wireless communications.Ultra-dense network(UDN)integrates heterogeneous network resources and coordinates technologies on quality of service controlling,to provide users with flexible service.However,dense deployment reduces coverage radius of the cell,resulting in an increase on handover frequency,which makes a serious impact on service continuity.In this paper,we propose a proactive selection method for dynamic access points grouping(DAPGing)in accordance with“user-centric”philosophy,which selects target Access Points(AP)and reduces handover times to ensure communication continuity.This method includes two criteria:1)the user’s sojourn time,which is determined by analyzing the AP coverage area;2)neighbor relationship between APs,which is determined by coverage area and signal strength characteristics between neighboring APs.Therefore,candidate APs become the proactive selected ones to update the AP group.Stochastic geometry is used to build system model and performance metrics are analyzed,including AP group coverage probability and average update frequency.Experimental analysis shows that the proposed proactive selection method brings similar coverage probability to traditional handover method,while average update frequency is reduced more than 20%selection criteria.

Coverage Analyses on Directional Transmissions Ultra-Dense Networks with Imperfect Beam Alignment

Blockage and imperfect beam alignment are two principal difficulties in high-frequency bands directional transmissions.In this paper,the coverage performance of downlink directional transmissions in ultra-dense networks is analyzed,with the consideration of beam alignment error and link blockage through stochastic geometry.Numerical experiments demonstrate that narrower beam leads to higher coverage probability with perfect beam alignment,but it is not the case with imperfect beam alignment.Therefore,the optimal beamwidth that maximize the coverage probability is characterized and a closed-form approximation of the optimal beamwidth is derived under imperfect beam alignment,accordingly.Furthermore,the optimal beamwidth is a monotonically increasing function of the standard deviation of the beam alignment error,and a monotonically decreasing function of the beamwidth of correspondent communication end,indicating that the beamwidth of the communication pairs ought to be jointly designed.

Optimization Processes of Tangible and Intangible Networks through the Laplace Problems for Regular Lattices with Multiple Obstacles along the Way

A systematic approach is proposed to the theme of safety,reliability and global quality of complex networks(material and immaterial)by means of special mathematical tools that allow an adequate geometric characterization and study of the operation,even in the presence of multiple obstacles along the path.To that end,applying the theory of graphs to the problem under study and using a special mathematical model based on stochastic geometry,in this article we consider some regular lattices in which it is possible to schematize the elements of the network,with the fundamental cell with six,eight or 2(n+2)obstacles,calculating the probability of Laplace.In this way it is possible to measure the“degree of impedance”exerted by the anomalies along the network by the obstacles examined.The method can be extended to other regular and/or irregular geometric figures,whose union together constitutes the examined network,allowing to optimize the functioning of the complex system considered.

Resource Allocation for Channel Estimation in Reconfigurable Intelligent Surface-Aided Multi-Cell Networks

Reconfigurable intelligent surface(RIS)is a promising solution to deal with the blockage-sensitivity of millimeter wave band and reduce the high energy consumption caused by network densification. However, deploying large scale RISs may not bring expected performance gain due to significant channel estimation overhead and non-negligible reflected interference.In this paper,we derive the analytical expressions of the coverage probability, area spectrum efficiency(ASE)and energy efficiency (EE)of a downlink RIS-aided multi-cell network.In order to optimize the network performance, we investigate the conditions for the optimal number of training symbols of each antenna-to-antenna and antenna-to-element path (referred to as the optimal unit training overhead) in channel estimation.Our study shows that:1)RIS deployment is not“the more, the better”, only when blockage objects are dense should one deploy more RISs;2) the coverage probability is maximized when the unit training overhead is designed as large as possible;3)however,the ASE-and-EE-optimal unit training overhead exists. It is a monotonically increasing function of the frame length and a monotonically decreasing function of the average signal-to-noise-ratio (in the high signal-to-noise-ratio region). Additionally,the optimal unit training overhead is smaller when communication nodes deploy particularly few or many antennas.

Spatio-Temporal Service Analysis in Multi-Layer Non-Terrestrial Networks

In the advent of the 6G era, non-terrestrial networks (NTN) with expansive coverage are being increasingly recognized as a vital supplement to cellular networks for facilitating seamless communication. The intricate interplay between network performance and service quality necessitates a thorough investigation into the modeling and analysis of services for efficient construction of NTN.Previous studies on service analysis, predominantly focused on terrestrial networks,fall short in addressing the unique challenges posed by NTN,particularly those related to platform distribution and antenna gain modeling. This deficiency in research,coupled with the varying preferences of users for different network types, forms the basis of this study. This paper explores the spatio-temporal characteristics of services within a multi-layered NTN framework.In this context,the spatial distribution of the platforms is modeled using a binomial point process, and the antennas are characterized by a sectorized beam pattern. We derive the closed-form expressions for the association probability,the number of accessed users, and the arrival rate of services with certain delay requirements towards different types of NTN. Simulation results are provided to evaluate the influence of various parameters on the association probability, the number of accessed users, and the total arrival rate of services. The number of satellites can be determined to achieve the optimal system utility,balancing the accessed services, offloading effects, and launching costs. This initial investigation lays the groundwork for further theoretical progress in the service analysis and platform deployment of NTN.

Spectrum allocation for wireless backhaul in heterogeneous ultra-dense networks

Wireless ultra-dense network （UDN） is one of the important technologies to solve the burst of throughput demand in the forthcoming fifth generation （SG） cellular networks. Reusing spectrum resource for the backhaul of small base stations （SBSs） is a hotspot research because of lower cost and rapid implementation with macro base stations （MBSs） in recent years. In heterogeneous UDN, the problem of spectrum allocation for wireless backhaul is investigated. In particular, two different spectrum resource reusing strategies for wireless backhaul are proposed in heterogeneous UDN with the limited bandwidth condition. Using a stochastic geometry-based heterogeneous UDN model, the success probabilities that mobile users communicate with SBSs or MBSs are derived under two different spectrum resource reusing strategies. In addition, the network throughput＇s analytical expressions and the optimal ratio of spectrum allocation are derived. Numeral results are provided to evaluate the performance of the proposed strategies at throughput. Thus, the effectiveness of the strategy that mobile users can only communicate with SBSs is validated.