Laplace Functional Ordering of Point Processes in Large-scale Wireless Networks

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte-Carlo simulations are used to supplement our analytical results.Comment: 30 pages, 5 figures, Submitted to Hindawi Wireless Communications and Mobile Computin

Downlink Coverage and Rate Analysis of Low Earth Orbit Satellite Constellations Using Stochastic Geometry

As low Earth orbit (LEO) satellite communication systems are gaining increasing popularity, new theoretical methodologies are required to investigate such networks' performance at large. This is because deterministic and location-based models that have previously been applied to analyze satellite systems are typically restricted to support simulations only. In this paper, we derive analytical expressions for the downlink coverage probability and average data rate of generic LEO networks, regardless of the actual satellites' locality and their service area geometry. Our solution stems from stochastic geometry, which abstracts the generic networks into uniform binomial point processes. Applying the proposed model, we then study the performance of the networks as a function of key constellation design parameters. Finally, to fit the theoretical modeling more precisely to real deterministic constellations, we introduce the effective number of satellites as a parameter to compensate for the practical uneven distribution of satellites on different latitudes. In addition to deriving exact network performance metrics, the study reveals several guidelines for selecting the design parameters for future massive LEO constellations, e.g., the number of frequency channels and altitude.Comment: Accepted for publication in the IEEE Transactions on Communications in April 202

Stochastic Geometry Modeling and Analysis of Single- and Multi-Cluster Wireless Networks

This paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-cluster wireless networks. We first define finite homogeneous Poisson point processes to model the number and locations of the transmitters in a confined region as a single-cluster wireless network. We study the coverage probability for a reference receiver for two strategies; closest-selection, where the receiver is served by the closest transmitter among all transmitters, and uniform-selection, where the serving transmitter is selected randomly with uniform distribution. Second, using Matern cluster processes, we extend our model and analysis to multi-cluster wireless networks. Here, the receivers are modeled in two types, namely, closed- and open-access. Closed-access receivers are distributed around the cluster centers of the transmitters according to a symmetric normal distribution and can be served only by the transmitters of their corresponding clusters. Open-access receivers, on the other hand, are placed independently of the transmitters and can be served by all transmitters. In all cases, the link distance distribution and the Laplace transform (LT) of the interference are derived. We also derive closed-form lower bounds on the LT of the interference for single-cluster wireless networks. The impact of different parameters on the performance is also investigated

Stochastic Geometry Modeling and Analysis of Finite Millimeter Wave Wireless Networks

This paper develops a stochastic geometry-based approach for the modeling and analysis of finite millimeter wave (mmWave) wireless networks where a random number of transmitters and receivers are randomly located inside a finite region. We consider a selection strategy to serve a reference receiver by the transmitter providing the maximum average received power among all transmitters. Considering the unique features of mmWave communications such as directional transmit and receive beamforming and having different channels for line-of-sight (LOS) and non-line-of-sight (NLOS) links according to the blockage process, we study the coverage probability and the ergodic rate for the reference receiver that can be located everywhere inside the network region. As key steps for the analyses, the distribution of the distance from the reference receiver to its serving LOS or NLOS transmitter and LOS and NLOS association probabilities are derived. We also derive the Laplace transform of the interferences from LOS and NLOS transmitters. Finally, we propose upper and lower bounds on the coverage probability that can be evaluated easier than the exact results, and investigate the impact of different parameters including the receiver location, the beamwidth, and the blockage process exponent on the system performance

Optimal Deployment of Tethered Drones for Maximum Cellular Coverage in User Clusters

Unmanned aerial vehicle (UAV) assisted cellular communication is gaining significant interest recently. Although it offers several advantages over terrestrial communication, UAV communication suffers from two main shortcomings. The typical untethered UAV (uUAV) has a limited battery power supply and therefore limited flying time, and it needs an extra wireless backhaul link to connect users to the core network. In this paper, we propose the utilization of the tethered UAV (tUAV) to assist the cellular network, where the tether provides power supply and connects the tUAV to the core network through high capacity link. The tUAV however has a limited mobility due to the limited tether length. A stochastic geometry-based analysis is provided for the coverage probability of an UAV-assisted cellular network where the mobile users located within a circular hot-spot. For that setup, we analyze and compare two scenarios: (i) utilizing uUAV and (ii) utilizing tUAV, for offloading the terrestrial base station (TBS). We capture the aforementioned limitations of each of the uUAV and the tUAV in our analysis. A novel user association analysis is provided given the TBS and the UAV locations. Next, we study the optimal locations of the uUAV and the tUAV to maximize the coverage probability. Multiple useful insights are revealed. For instance, numerical results show that tUAVs outperform uUAVs when the tether length is above 75 m, given that the uUAV is available for 80% of the time due to its battery limitations.Comment: Accepted at the IEEE Transaction on Wireless Communication

Outage Performance of Uplink Rate Splitting Multiple Access with Randomly Deployed Users

With the rapid proliferation of smart devices in wireless networks, more powerful technologies are expected to fulfill the network requirements of high throughput, massive connectivity, and diversify quality of service. To this end, rate splitting multiple access (RSMA) is proposed as a promising solution to improve spectral efficiency and provide better fairness for the next-generation mobile networks. In this paper, the outage performance of uplink RSMA transmission with randomly deployed users is investigated, taking both user scheduling schemes and power allocation strategies into consideration. Specifically, the greedy user scheduling (GUS) and cumulative distribution function (CDF) based user scheduling (CUS) schemes are considered, which could maximize the rate performance and guarantee scheduling fairness, respectively. Meanwhile, we re-investigate cognitive power allocation (CPA) strategy, and propose a new rate fairness-oriented power allocation (FPA) strategy to enhance the scheduled users' rate fairness. By employing order statistics and stochastic geometry, an analytical expression of the outage probability for each scheduling scheme combining power allocation is derived to characterize the performance. To get more insights, the achieved diversity order of each scheme is also derived. Theoretical results demonstrate that both GUS and CUS schemes applying CPA or FPA strategy can achieve full diversity orders, and the application of CPA strategy in RSMA can effectively eliminate the secondary user's diversity order constraint from the primary user. Simulation results corroborate the accuracy of the analytical expressions, and show that the proposed FPA strategy can achieve excellent rate fairness performance in high signal-to-noise ratio region.Comment: 38 pages,8 figure

Optimizing the number of fog nodes for finite fog radio access networks under multi-slope path loss model

Fog Radio Access Network (F-RAN) is a promising technology to address the bandwidth bottlenecks and network latency problems, by providing cloud-like services to the end nodes (ENs) at the edge of the network. The network latency can further be decreased by minimizing the transmission delay, which can be achieved by optimizing the number of Fog Nodes (FNs). In this context, we propose a stochastic geometry model to optimize the number of FNs in a finite F-RAN by exploiting the multi-slope path loss model (MS-PLM), which can more precisely characterize the path loss dependency on the propagation environment. The proposed approach shows that the optimum probability of being a FN is determined by the real root of a polynomial equation of a degree determined by the far-field path loss exponent (PLE) of the MS-PLM. The results analyze the impact of the path loss parameters and the number of deployed nodes on the optimum number of FNs. The results show that the optimum number of FNs is less than 7% of the total number of deployed nodes for all the considered scenarios. It also shows that optimizing the number of FNs achieves a significant reduction in the average transmission delay over the unoptimized scenarios