Stochastic Geometry Approach Research Articles

Theoretical interference analysis of inter-vehicular communication at intersection with power control

Interference problems caused by congestion of vehicles at intersections or on highways may significantly degrade vehicle-to-vehicle (V2V) communications, especially for active-safety assistance systems due to the importance of emergency information. In this paper, we propose a theoretical interference model of V2V communications at an intersection that uses a transmission-power-control method. To evaluate and address the interference problem at an intersection, we derived an analytical expression of the outage probability of a typical vehicle at an intersection and provided guidelines for an optimal power-control method, which cannot be obtained through simulations. We modeled the location of vehicles in queueing and running segments separately and analyzed their interference on the basis of a stochastic geometry approach. In our model, a simple power-control method is used: the transmission power of each vehicle is determined by the status of the vehicle, i.e., stopped or running. By changing the transmission power of vehicles in queueing segments, we can mitigate the interference received at vehicles running closer to an intersection. By using the theoretical results, we obtain an optimal power-control method, which can balance the outage probabilities of vehicles in queueing and running segments. We validated our analytical results and the effect of the power-control method on V2V communications by numerical simulations.

Fractional full duplex cellular network: a stochastic geometry approach

In-band full-duplex (FD) communication has been considered as a promising technology to enhance the spectral efficiency (SE) for the next generation of wireless system. However, the severe interference in FD cellular network may largely degrade the system performance, especially for cell edge users. In this paper, multi-cell cellular network consisting of BSs with FD capability and legacy half duplex (HD) users is studied. In order to relieve the received interference and enhance the system SE, a new resource allocation strategy named fractional FD (FFD) is proposed and its main idea and procedure are described as follows. Firstly, the frequency and time resources are partitioned into FD resource blocks (RBs) and HD RBs based on the network topology. Then all the users are classified into two groups named cell center users (CCUs) and cell edge users (CEUs) based on their channel conditions. At last, in each cell, each FD RB is allocated to a pair of CCUs with one in uplink and the other in downlink transmission direction, while only one CEU in the uplink (or downlink) transmission direction is scheduled over each HD RB. Tractable results of both the coverage probabilities and the ergodic rates of FFD, FD and HD systems are derived using stochastic geometry method. Numerical results show that, FFD can significantly improve the coverage probability of all users especially for CEUs compared with FD cellular system, and higher system SE is obtained compared with FD and HD cellular network. With proper design of the classification criterion and under the simulation settings of this paper, the SE of FFD system outperforms FD and HD system by 1.25 and 1.38 times, respectively.

Toward the Performance Enhancement of Microwave Cellular Networks Through THz Links

Driven by the future need of exploiting the so-called extremely and tremendously high-frequency bands for the rate enhancement of microwave cellular networks, in this paper, we consider the possibility of upgrading the already existing infrastructure of microwave base stations (BSs) by enabling them to convey information through microwave or terahertz (THz) links, depending on the distance and whether a line-of-sight (LOS) link exists between a mobile terminal (MT) and its serving BS. By using a tractable stochastic-geometry approach for the modeling of the position and number of BSs and possible blockages in the radio path, we derive analytical formulas for the achieved coverage probability and average rate, which exhibit a close match with the simulation results and validate the expected significant average-rate gains with respect to the communication only through microwave links. In addition, the results show that the expected tradeoff between the average-rate enhancement and coverage-probability reduction due to the high path-loss attenuation of the THz links can be greatly counteracted by employing highly directional antennas in the THz case, especially for very dense BS setups.

Estimating the medium access probability in large cognitive radio networks

During the last decade we have seen an explosive development of wireless technologies. Consequently the demand for electromagnetic spectrum has been growing dramatically resulting in the spectrum scarcity problem. In spite of this, spectrum utilization measurements have shown that licensed bands are vastly underutilized while unlicensed bands are too crowded. In this context, Cognitive Radio Network emerges as an auspicious paradigm in order to solve those problems. The main question that motivates this work is: what are the possibilities offered by cognitive radio to improve the effectiveness of spectrum utilization? With this in mind, we propose a methodology, based on configuration models for random graphs, to estimate the medium access probability of secondary users. We perform simulations to illustrate the accuracy of our results and we also make a performance comparison between our estimation and one obtained by a stochastic geometry approach.

Robust Relay Selection for Large-Scale Energy-Harvesting IoT Networks

We consider the relay selection problem in large-scale energy harvesting (EH) networks. It is known that if channel state information (CSI) is available at EH relays, a diversity order equal to the number of relays can be obtained, however, at the penalty of a feedback overhead (necessary to obtain accurate CSI) which is not suitable for energy-limited devices intended, e.g., for Internet-of-Things applications. In this paper, we therefore propose a new EH relay selection scheme which is based on the residual energy at each relay’s battery, and on information on the distribution of the channels between relays and the destination. The method thus minimizes both the outage probability and the feedback cost. Where previous work relay selection based on channel distribution information consider only small-scale fading distribution, we employ a stochastic geometry approach to consider jointly the geometrical distribution (i.e., large-scale fading) and small-scale fading yielding a simple relay selection criterion that furthermore utilizes only rough information on the relay’s location, i.e., an ordinal number from the destination. The outage probability of the proposed relay selection scheme is analytically derived, and the achievable diversity order of the proposed approach is investigated. Computer simulations confirm our theoretical analyses and show that our approach is robust against errors in the estimation of the distances between nodes.

Interference Alignment in Two-Tier Randomly Distributed Heterogeneous Wireless Networks Using Stochastic Geometry Approach

With the massive increase in wireless data traffic in recent years, multi-tier wireless networks have been deployed to provide much higher capacities and coverage. However, heterogeneity of wireless networks bring new challenges for interference analysis and coordination due to spatial randomly distributed transmitters. In this paper, we present a distance-dependent interference alignment (IA) approach for a generic two-tier heterogeneous wireless network, where transmitters in the first and second tiers are distributed as poisson point process (PPP) and poisson cluster process, respectively. The feasibility condition of the IA approach is used to find upper bound of the number of interference streams that can be aligned. The proposed IA scheme maximizes the second-tier throughput by using the tradeoff between signal-to-interference ratio and multiplexing gain. It is shown that acquiring accurate knowledge of the distance between the receiver in the second-tier and the nearest cross-tier transmitter only brings insignificant throughput gain compared with statistical knowledge of distance. Furthermore, the remaining cross-tier and intercluster interferences are modeled and analyzed using stochastic geometry technique. Numerical results validate the derived expressions of success probabilities and throughput, and show that the distance-dependent IA scheme significantly outperforms the traditional IA scheme in the presence of path-loss effect.

Performance analysis of cellular networks with mobile relays under different modes

With the popularity of smart phones and tablets, people make intensive use of these devices on public transport. The deployment of mobile relays on public transport may increase the quality of mobile services.The objective of this paper is to study the performance of cellular networks when mobile relays are deployed in public transport vehicles. We consider two modes: in the FDD mobile relay mode, the same spectrum is reused for all links while in the TDD/FDD hybrid mode, a small part of the spectrum is dedicated to the access link between the terminals inside a transport vehicle and the mobile relay. We provide a general analytical model for the two mobile relay modes by using the stochastic geometry approach. Key metrics like the CDF of the SINR and the CDF of the end-to-end rate are computed. Furthermore, the cell total average rate and the energy efficiency in different modes are evaluated. It has been found that penetration loss is a factor that determines how much gain mobile relay can bring. Numerical results show that when the ratio of vehicular UEs in the cell is 0.4 and the penetration loss is 20 dB, the FDD mobile relay mode and the TDD/FDD hybrid mobile relay mode can achieve \(+16.3, +29.1\%\) cell rate gain respectively compared with the direct mode.

Coverage Performance of Joint Transmission for Moving Relay Enabled Cellular Networks in Dense Urban Scenarios

Communication plays a significant role in terms of providing connectivity for urban users as well as sensors in smart cities. It has been shown that better communication capability for vehicular users can be obtained by introducing moving relays (MRs). With MRs, it is possible for macro base stations and moving relays to serve non-vehicular macro-users by performing coordinated multipoint (CoMP) joint transmission (JT). A bias-based CoMP scheme for MR enabled cellular network is analyzed in this paper. Motivated by antenna design constraints, in this paper, we assume that the outdoor antenna system of the MR can only be used for the moving backhaul link, i.e., the in-vehicle antenna system is also serving the non-vehicular macro-users. Using the stochastic geometry approach, a tractable model of the network is proposed. Based on the proposed model, integral expressions for CoMP-JT probability and coverage probability of non-vehicular macro user equipment are derived. Simulations verify the accuracy of the derived expressions. The results show that the probability for macro user equipment to be served with CoMP-JT is up to 70% when the intensity of MRs is ten times that of MBSs. This paper also includes a performance comparison among the analyzed scheme and related works. CoMP-JT with MRs provides better coverage performance for nearby macro user equipment. It can be found that the coverage gain of CoMP increases when the intensity of MRs increases within a certain range. Simulation results provide insights for practical system design in smart cities, such as the optimal MR intensity and the feasibility for opening access of MRs to macro user equipment.

Full-Duplex Small Cells for Next Generation Heterogeneous Cellular Networks: A Case Study of Outage and Rate Coverage Analysis

Full-duplex (FD) technology is currently under consideration for adoption in a range of legacy communications standards due to its attractive features. On the other hand, cellular networks are becoming increasingly heterogeneous as operators deploy a mix of macrocells and small cells. With growing tendency toward network densification, small cells are expected to play a key role in realizing the envisioned capacity objectives of emerging 5G cellular networks. From a practical perspective, small cells provide an ideal platform for deploying FD technology in cellular networks due to its lower transmit power and lower cost for implementation compared with the macrocell counterpart. Motivated by these developments, in this paper, we analyze a two-tier heterogeneous cellular network, wherein the first tier comprises half-duplex macrobase stations and the second tier consists of the FD small cells. Through a stochastic geometry approach, we characterize and derive the closed-form expressions for the outage probability and the rate coverage. Our analysis explicitly accounts for the spatial density, the self-interference cancellation capabilities, and the interference coordination based on enhanced inter-cell interference coordination techniques. Performance evaluation investigates the impact of different parameters on the outage probability and the rate coverage in various scenarios.

Impact of Artificial Noise on Cellular Networks: A Stochastic Geometry Approach

This paper studies the impact of artificial noise (AN) on the secrecy performance of a target cell in multi-cell cellular networks. Although AN turns out to be an efficient approach for securing a pointto-point/single cell confidential transmission, it would increase the inter-cell interference in a multi-cell cellular network, which may degrade the network reliability and secrecy performance. For analyzing the average secrecy performance of the target cell which is of significant interest, we employ a hybrid cellular deployment model, where the target cell is a circle of fixed size and the base stations (BSs) outside the target cell are modeled as a homogeneous Poisson point process (PPP). We investigate the impact of AN on the reliability and security of users in the target cell in the presence of pilot contamination using a stochastic geometry approach. The analytical results of the average connection outage and the secrecy outage of its cellular user (CU) in the target cell are given, which facilitates the evaluation of the average secrecy throughput of a randomly chosen CU in the target cell. It shows that with an optimized power allocation between the desired signals and AN, the AN scheme is an efficient solution for securing the communications in a multi-cell cellular network.

A Stochastic Geometry Approach to the Energy Load of Relaying in Large-Scale Wireless Networks

Multi-hop relaying divides a long radio link into multiple short radio links and thus may reduce the overall energy consumption in wireless networks. But using relaying imposes additional energy load at intermediate relays, the characterization of which is of fundamental interest. In this paper, we propose a novel stochastic geometric model to investigate the energy load of relaying in a random large-scale wireless network. We introduce a notion of relay selection window, defined as the range in which a helping relay is searched for a typical source-destination pair. Under the proposed model, we derive closed form expressions to characterize the dependency of the energy load of relaying on relay selection window and several other key network parameters. The results may have practical implications in the design of wireless networks.

An Analysis Framework for Interuser Interference in IEEE 802.15.6 Body Sensor Networks: A Stochastic Geometry Approach

Interuser interference occurs when multiple body sensor networks (BSNs) are transmitting simultaneously in close proximity to each other. Interference analysis in BSNs is challenging due to the hybrid medium access control (MAC) and the specific channel characteristics of BSNs. This paper presents a stochastic geometry analysis framework for interuser interference in IEEE 802.15.6 BSNs. An extended Matern point process is proposed to model the complex spatial distribution of the interfering BSNs caused by the hybrid MAC defined in IEEE 802.15.6. We employ a stochastic geometry approach to evaluate the performance of BSNs, considering the specific channel characteristics of BSNs near the human body. Performance metrics are derived in terms of outage probability and spatial throughput in the presence of interuser interference. We conduct performance evaluation through extensive simulations and show that the simulation results fit well with the analytic results. Insights are provided on the determination of the interference detection range, the BSN density, and the design of MAC for BSNs.

Modeling Cellular Networks With Full-Duplex D2D Communication: A Stochastic Geometry Approach

A network model is considered, where Poisson distributed base stations transmit to $N$ power-domain non-orthogonal multiple access (NOMA) users (UEs) each that employ successive interference cancellation (SIC) for decoding. We propose three models for the clustering of NOMA UEs and consider two different ordering techniques for the NOMA UEs: mean signal power-based and instantaneous signal-to-intercell-interference-and-noise-ratio-based. For each technique, we present a signal-to-interference-and-noise ratio analysis for the coverage of the typical UE. We plot the rate region for the two-user case and show that neither ordering technique is consistently superior to the other. We propose two efficient algorithms for finding a feasible resource allocation that maximize the cell sum rate $\mathcal {R}_{\mathrm{ tot}}$ , for general $N$ , constrained to: 1) a minimum throughput $\mathcal {T}$ for each UE, 2) identical throughput for all UEs. We show the existence of: 1) an optimum $N$ that maximizes the constrained $\mathcal {R}_{\mathrm{ tot}}$ given a set of network parameters and 2) a critical SIC level necessary for NOMA to outperform orthogonal multiple access. The results highlight the importance in choosing the network parameters $N$ , the constraints, and the ordering technique to balance the $\mathcal {R}_{\mathrm{ tot}}$ and fairness requirements. We also show that interference-aware UE clustering can significantly improve performance.

Physical Layer Security in Three-Tier Wireless Sensor Networks: A Stochastic Geometry Approach

This paper develops a tractable framework for exploiting the potential benefits of physical layer security in three-tier wireless sensor networks (WSNs) using stochastic geometry. In such networks, the sensing data from the remote sensors are collected by sinks with the help of access points, and the external eavesdroppers intercept the data transmissions. We focus on the secure transmission in two scenarios: 1) the active sensors transmit their sensing data to the access points and 2) the active access points forward the data to the sinks. We derive new compact expressions for the average secrecy rate in these two scenarios. We also derive a new compact expression for the overall average secrecy rate. Numerical results corroborate our analysis and show that multiple antennas at the access points can enhance the security of three-tier WSNs. Our results show that increasing the number of access points decreases the average secrecy rate between the access point and its associated sink. However, we find that increasing the number of access points first increases the overall average secrecy rate, with a critical value beyond which the overall average secrecy rate then decreases. When increasing the number of active sensors, both the average secrecy rate between the sensor and its associated access point, and the overall average secrecy rate decrease. In contrast, increasing the number of sinks improves both the average secrecy rate between the access point and its associated sink, and the overall average secrecy rate.

A Stochastic Geometry Approach to the Modeling of DSRC for Vehicular Safety Communication

Vehicle-to-vehicle safety communications based on the dedicated short-range communication technology have the potential to enable a set of applications that help avoid traffic accidents. The performance of these applications, largely affected by the reliability of communication links, stringently ties back to the MAC and PHY layer design, which has been standardized as IEEE 802.11p. The link reliabilities depend on the signal-to-interference-plus-noise ratio (SINR), which, in turn, depends on the locations and transmit power values of the transmitting nodes. Hence, an accurate network model needs to take into account the network geometry. For such geometric models, however, there is a lack of mathematical understanding of the characteristics and performance of IEEE 802.11p. Important questions such as the scalability performance of IEEE 802.11p have to be answered by simulations, which can be very time consuming and provide limited insights to future protocol design. In this paper, we investigate the performance of IEEE 802.11p by proposing a novel mathematical model based on queuing theory and stochastic geometry. In particular, we extend the Matérn hard-core type-II process with a discrete and nonuniform distribution, which is used to derive the temporal states of backoff counters. By doing so, concurrent transmissions from nodes within the carrier sensing ranges of each other are taken into account, leading to a more accurate approximation to real network dynamics. A comparison with Network Simulator 2 (ns2) simulations shows that our model achieves a good approximation in networks with different densities.

Green cell planning and deployment for small cell networks in smart cities

In smart cities, cellular network plays a crucial role to support wireless access for numerous devices anywhere and anytime. The future 5G network aims to build the infrastructure from mobile internet to connected world. Small Cell is one of the most promising technologies of 5G to provide more connections and high data rate. In order to make the best use of small cell technology, smart cell planning should be implemented to guarantee connectivity and performance for all end nodes. It is particularly a challenging task to deploy dense small cells in the presence of dynamic traffic demands and severe co-channel interference. In this paper, we model various traffic patterns using stochastic geometry approach and propose an energy-efficient scheme to deploy and plan small cells according to the prevailing traffic pattern. The simulation results indicate that our scheme can meet dynamic traffic demands with optimized deployment of small cells and enhance the energy efficiency of the system without compromising on quality-of-service (QoS) requirements. In addition, our scheme can achieve very close performance compared with the leading optimization solver CPLEX and find solutions in much less computational times than CPLEX.

Performance Analysis of Outdoor mmWave Ad Hoc Networks

Ad hoc networks provide an on-demand, infrastructure-free means to communicate between soldiers in war zones, aid workers in disaster areas, or consumers in device-to-device (D2D) applications. Unfortunately, ad hoc networks are limited by interference due to nearby transmissions. Millimeter-wave (mmWave) devices offer several potential advantages for ad hoc networks including reduced interference due to directional antennas and building blockages, not to mention huge bandwidth channels for large data rates.. This paper uses a stochastic geometry approach to characterize the one-way and two-way signal-to-interference ratio distribution of a mmWave ad hoc network with directional antennas, random blockages, and ALOHA channel access. The interference-to-noise ratio shows that a fundamental limitation of an ad hoc network, interference, may still be an issue. The performance of mmWave ad hoc networks is bounded by the transmission capacity and area spectral efficiency. The results show that mmWave networks can support much higher densities and larger spectral efficiencies, even in the presence of blockage, compared with lower frequency communication for certain link distances. Due to the increased bandwidth, the rate coverage of mmWave can be much greater than lower frequency devices.

Tilt Angle Optimization in Two-Tier Cellular Networks—A Stochastic Geometry Approach

In this work, we address the antenna tilt optimization problem for a two-tier cellular network consisting of macrocells and femtocells, where both tiers share the same spectrum and their positions are modeled via two independent Poisson point processes (PPPs). First, we derive the coverage probability for a traditional cellular network consisting only of macrocells and obtain the optimum tilt angle that maximizes the overall energy efficiency (EE). Gains of up to 400% in EE were found for a scenario (approximately) equivalent to a hexagonal cell deployment with cell radius of 200 m when the optimum tilt was selected. We then proceed to model the heterogeneous network (HetNet) scenario where femtocells are also deployed in the network's area. We observe that the macrousers performance is highly sensitive to the interference emanating from the femtocell tier. In order to circumvent this issue, interference coordination employing a guard zone for the macrocell user is proposed. Subsequently, we formulate a joint optimization problem where we derive both, the radius of a guard zone protecting the macrouser and the tilt angle that maximize the EE of the network.

Spectrum and Energy Efficiency in Massive MIMO Enabled HetNets: A Stochastic Geometry Approach

This letter focuses on the spectrum efficiency (SE) and energy efficiency (EE) of $K$ -tier heterogeneous networks (HetNets), in which massive multiple-input multiple-output (MIMO) is employed in the macro cells. We consider the impact of massive MIMO on flexible cell association. We develop an analytical approach to examine SE and EE of HetNets. We confirm that using flexible cell association can improve the EE of HetNets by offloading data traffic to small cell. This is due to an increase of EE in the macro cell. Moreover, we show that serving moderate number of users in the macro cells with massive MIMO can boost both SE and EE.

Operational Region of D2D Communications for Enhancing Cellular Network Performance

An important enabler towards the successful deployment of any new element/feature to the cellular network is the investigation and characterization of the operational conditions where its introduction will enhance performance. Even though there has been significant research activity on the potential of device-to-device (D2D) communications, there are currently no clear indications of whether D2D communications are actually able to provide benefits for a wide range of operational conditions, thus justifying their introduction to the system. This paper attempts to fill this gap by taking a stochastic geometry approach on characterizing the set (region) of operational conditions for which D2D communications enhance performance in terms of average user rate. For the practically interesting case of a heavy loaded network, the operational region is provided in closed form as a function of a variety of parameters such as maximum D2D link distances and user densities, reflecting a wide range of operational conditions (points). It is shown that under the appropriate deployment scheme, D2D communications can indeed be beneficial not only for the usually considered regime of "proximal communications" but to a wide range of operational conditions that include D2D link distances comparable to the distance to the cellular access point and considerably large user densities.