Outage Probability in Arbitrarily-Shaped Finite Wireless Networks

This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for analytically computing the outage probability at any arbitrary location of an arbitrarily-shaped finite wireless network: (i) a moment generating function-based framework which is based on the numerical inversion of the Laplace transform of a cumulative distribution and (ii) a reference link power gain-based framework which exploits the distribution of the fading power gain between the reference transmitter and receiver. The outage probability is spatially averaged over both the fading distribution and the possible locations of the interferers. The boundary effects are accurately accounted for using the probability distribution function of the distance of a random node from the reference receiver. For the case of the node locations modeled by a Binomial point process and Nakagami-$m$ fading channel, we demonstrate the use of the proposed frameworks to evaluate the outage probability at any location inside either a disk or polygon region. The analysis illustrates the location dependent performance in finite wireless networks and highlights the importance of accurately modeling the boundary effects.Comment: accepted to appear in IEEE Transactions on Communication

Performance Analysis of Arbitrarily-Shaped Underlay Cognitive Networks: Effects of Secondary User Activity Protocols

This paper analyzes the performance of the primary and secondary users (SUs) in an arbitrarily-shaped underlay cognitive network. In order to meet the interference threshold requirement for a primary receiver (PU-Rx) at an arbitrary location, we consider different SU activity protocols which limit the number of active SUs. We propose a framework, based on the moment generating function (MGF) of the interference due to a random SU, to analytically compute the outage probability in the primary network, as well as the average number of active SUs in the secondary network. We also propose a cooperation-based SU activity protocol in the underlay cognitive network which includes the existing threshold-based protocol as a special case. We study the average number of active SUs for the different SU activity protocols, subject to a given outage probability constraint at the PU and we employ it as an analytical approach to compare the effect of different SU activity protocols on the performance of the primary and secondary networks.Comment: submitted to possible IEEE Transactions publicatio

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

The Outage Probability of a Finite Ad Hoc Network in Nakagami Fading

An ad hoc network with a finite spatial extent and number of nodes or mobiles is analyzed. The mobile locations may be drawn from any spatial distribution, and interference-avoidance protocols or protection against physical collisions among the mobiles may be modeled by placing an exclusion zone around each radio. The channel model accounts for the path loss, Nakagami fading, and shadowing of each received signal. The Nakagami m-parameter can vary among the mobiles, taking any positive value for each of the interference signals and any positive integer value for the desired signal. The analysis is governed by a new exact expression for the outage probability, defined to be the probability that the signal-to-interference-and-noise ratio (SINR) drops below a threshold, and is conditioned on the network geometry and shadowing factors, which have dynamics over much slower timescales than the fading. By averaging over many network and shadowing realizations, the average outage probability and transmission capacity are computed. Using the analysis, many aspects of the network performance are illuminated. For example, one can determine the influence of the choice of spreading factors, the effect of the receiver location within the finite network region, and the impact of both the fading parameters and the attenuation power laws.Comment: to appear in IEEE Transactions on Communication

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