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.

Optimal AP Deployment in Cell-Free Massive MIMO Systems with LoS/NLoS Transmissions:A Stochastic Geometry Approach

Cell-free massive multiple-input multipleoutput(MIMO)is a promising technology for future wireless communications,where a large number of distributed access points(APs)simultaneously serve all users over the same time-frequency resources.Since users and APs may locate close to each other,the line-of-sight(Lo S)transmission occurs more frequently in cell-free massive MIMO systems.Hence,in this paper,we investigate the cell-free massive MIMO system with Lo S and non-line-of-sight(NLo S)transmissions,where APs and users are both distributed according to Poisson point process.Using tools from stochastic geometry,we derive a tight lower bound for the user downlink achievable rate and we further obtain the energy efficiency(EE)by considering the power consumption on downlink payload transmissions and circuitry dissipation.Based on the analysis,the optimal AP density and AP antenna number that maximize the EE are obtained.It is found that compared with the previous work that only considers NLo S transmissions,the actual optimal AP density should be much smaller,and the maximized EE is actually much higher.

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.

Capacity Research in Cluster-Based Underwater Wireless Sensor Networks Based on Stochastic Geometry

Underwater wireless sensor networks(UWSNs) have attracted wide attention in recent years.The capacity research on it is still in the initial stage,lacking adequate performance evaluation for network construction.This paper will focus on this subject by theoretical analysis and simulation,aiming to provide some insights for the actual UWSNs construction.According to the structure features of cluster-based UWSNs and the propagation characteristics of underwater acoustic signal,with the combination of signal to interference plus noise ratio,we define some capacity performance metrics,such as outage probability and transmission capacity.Based on the theory of stochastic geometry,a network capacity analytical model used in the cluster-based UWSNs is presented.The simulation results verify the validity of the theoretical analysis,and the cause of error between theoretical and simulation results has also been clearly explained.

Energy Efficiency Analysis of Cellular Networks with Cooperative Relays via Stochastic Geometry

Cooperative relaying is a promising technology that can improve the spectral and energy efficiency of cellular networks. However, the deployed relays consume a lot of energy and system resources. To improve the energy efficiency of the relay-assisted cellular networks, this paper considers the use of energy harvesting(EH) on relay nodes. A random sleeping strategy is also introduced in macro base stations(MBS) as a possible method to reduce energy consumption. In this paper, an analytical model is proposed to investigate the energy efficiency of cellular networks with EH relays and sleep mode strategy. Numerical results confirm a significant energy efficiency gain of the proposed networks comparing to the cellular networks with non-EH relays and MBSs without sleep mode strategy. The effects of the density and transmit power of MBSs on energy efficiency are also given through simulations.

A Non-Stationary Beam-Enabled Stochastic Channel Model and Characterization over Non-Reciprocal Beam Patterns

The multiple-input multiple-output(MIMO)-enabled beamforming technology offers great data rate and channel quality for next-generation communication.In this paper,we propose a beam channel model and enable it with time-varying simulation capability by adopting the stochastic geometry theory.First,clusters are generated located within transceivers'beam ranges based on the Mate?rn hardcore Poisson cluster process.The line-of-sight,singlebounce,and double-bounce components are calculated when generating the complex channel impulse response.Furthermore,we elaborate on the expressions of channel links based on the propagation-graph theory.A birth-death process consisting of the effects of beams and cluster velocities is also formulated.Numerical simulation results prove that the proposed model can capture the channel non-stationarity.Besides,the non-reciprocal beam patterns yield severe channel dispersion compared to the reciprocal patterns.

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.

Stochastic Geometric Analysis of the Uplink Throughput in Cognitive Radio Cellular Networks

This paper investigates the uplink throughput of Cognitive Radio Cellular Networks(CRCNs).As oppose to traditional performance evaluation schemes which mainly adopt complex system level simulations,we use the theoretical framework of stochastic geometry to provide a tractable and accurate analysis of the uplink throughput in the CRCN.By modelling the positions of User Equipments(UEs)and Base Stations(BSs)as Poisson Point Processes(PPPs),we analyse and derive expressions for the link rate and the cell throughput in the Primary(PR)and Secondary(SR)networks.The expressions show that the throughput of the CRCN is mainly affected by the density ratios between the UEs and the BSs in both the PR and SR networks.Besides,a comparative analysis of the link rate between random and regular BS deployments is concluded,and the results confirm the accuracy of our analysis.Furthermore,we define the cognitive throughput gain and derive an expression which is dominated by the traffic load in the PR network.

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.

Relay selection region and system performance analysis for interfered cooperative ad-hoc networks

The performance of interfered cooperative ad-hoc networks is analyzed by stochastic geometry analysis and a selection region of relay is presented. First, assuming that the distribution of nodes in the random network follows the Poisson point process （PPP）, a closed-form expression of the outage probability is derived for the best relay selection （BRS） scheme. Secondly, the capacity of the network is presented for this scheme. Finally, a performance factor is defined to evaluate the performance gain obtained from the BRS. By using this factor, a relay selection region is found to guarantee the performance gain from the BRS. The analysis and simulation results show that the performance of the BRS not only depends on the densities of source nodes and relay nodes but also on the factors of networks such as the path loss factor and the decoding threshold. And the BRS has a greater advantage than direct transmission （DT） in hush environments such as the long transmission distances, much interference and the high decoding thresholds.

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.

Asymptotic Analysis of Transmission Capacities for Overlaid Spread-Spectrum Wireless Networks

We study the transmission capacities of two coexisting spread-spectrum wireless networks (a primary network vs. a secondary network) that operate in the same geographic region and share the same spectrum. We defi ne transmission capacity as the product among the density of transmissions, the transmission rate, and the successful transmission probability. The primary (PR) network has a higher priority to access the spectrum without particular considerations for the secondary (SR) network, while the SR network limits its interference to the PR network by carefully controlling the density ofits transmitters. Considering two types of spread-spectrum transmission schemes (FH-CDMA and DS-CDMA) and the channel inversion power control mechanism, we quantify the transmission capacities for these two networks based on asymptotic analysis. Our results show that if the PR network permits a small increase ofits outage probability, the sum transmission capacities of the two networks (i.e., the overall spectrumefficiency per unit area) will be boosted significantly over that of a single network.

Downlink SINR and Rate Distribution of Ultra-Dense Het Nets with Burst Traffic

SINR distribution and rate overage distribution are crucial for optimization of deployment of Ultra-dense Het Nets.Most existing literatures assume that BSs have full queues and full-buffer traffic.In fact,due to ultra-dense deployment of small cells,traffic in small cell varies dramatically in time and space domains.Hence,it is more practical to investigate scenario with burst traffic.In this paper,we consider a two-tier non-uniform ultra-dense Het Net with burst traffic,where macro BSs are located according to Poisson Point Process(PPP),and pico BSs are located according to Poisson Hole Process(PHP).The closed-form expressions of SINR distribution and rate distribution are derived,and then validated through simulation.Our study shows that different from the result of full buffer case,the SINR distribution and rate distribution of users depend on the average transmission probabilities of BSs in burst traffic case.

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.