arXiv subjects

Orestis Georgiou

Publications and source records attributed to Orestis Georgiou.

At least 37 records · Page 2Linked to original sources

arXiv2016

Isolation probabilities in dynamic soft random geometric graphs

We consider soft random geometric graphs, constructed by distributing points (nodes) randomly according to a Poisson Point Process, and forming links between pairs of nodes with a probability that depends on their mutual distance, the "connection function." Each node has a probability of being isolated depending on the locations of the other nodes; we give analytic expressions for the distribution of isolation probabilities. Keeping the node locations fixed, the links break and reform over time, making a dynamic network; this is a good model of a wireless ad-hoc network with communication channels undergoing rapid fading. We use the above isolation probabilities to investigate the distribution of the time to transmit information to all the nodes, finding good agreement with numerics.

cond-mat.dis-nn↗

arXiv2016

Connectivity of Soft Random Geometric Graphs Over Annuli

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as a dense-network limit is approached. This extends recent work modelling ad hoc networks in non-convex domains.

math.CO↗

arXiv2016

Betweenness Centrality in Dense Random Geometric Networks

Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how often all paths in the network characterisable as topologically `shortest' contain a given node (betweenness centrality), deriving an expression in terms of a known integral whenever 1) the network boundary is the perimeter of a disk and 2) the network is extremely dense. Our method shows how similar formulas can be obtained for any convex geometry. Numerical corroboration is provided, as well as a discussion of our formula's potential use for cluster head election and boundary detection in densely deployed wireless ad hoc networks.

cs.SI↗

arXiv2016

Counting Geodesic Paths in 1D VANETs

In the IEEE 802.11p standard addressing vehicular communications, Basic Safety Messages (BSMs) can be bundled together and relayed as to increase the effective communication range of transmitting vehicles. This process forms a vehicular ad hoc network (VANET) for the dissemination of safety information. The number of "shortest multihop paths" (or geodesics) connecting two network nodes is an important statistic which can be used to enhance throughput, validate threat events, protect against collusion attacks, infer location information, and also limit redundant broadcasts thus reducing interference. To this end, we analytically calculate for the first time the mean and variance of the number of geodesics in 1D VANETs.

cs.NI↗

arXiv2016

Distributed Power Allocation and Channel Access Probability Assignment for Cognitive Radio

In this paper, we present a framework for distributively optimizing the transmission strategies of secondary users in an ad hoc cognitive radio network. In particular, the proposed approach allows secondary users to set their transmit powers and channel access probabilities such that, on average, the quality of service of both the primary and secondary networks are satisfied. The system under consideration assumes several primary and secondary transceiver pairs and assumes no cooperation or information exchange between neither primary and secondary users nor among secondary users. The outage probability, and consequently the connection probability, is derived for the system and is used in defining a new performance metric in the optimization problem using tools from stochastic geometry. We refer to this metric as the spatial density of successful transmission. We corroborate our derivations through numerical evaluations. We further demonstrate that even in the absence of any form of cooperation, an acceptable quality of service can be attained in the cognitive radio environment.

cs.NI↗

arXiv2016

Connectivity of Cooperative Ad hoc Networks

The connectivity properties of ad hoc networks have been extensively studied over the past few years, from local observables, to global network properties. In this paper we introduce a novel layer of network dynamics which lives and evolves on top of the ad hoc network. Nodes are assumed selfish and a snow-drift type game is defined dictating the way nodes decide to allocate their cooperative resource efforts towards other nodes in the network. The dynamics are strongly coupled with the physical network causing the cooperation network topology to converge towards a stable equilibrium state, a global maximum of the total pay-off. We study this convergence from a connectivity perspective and analyse the inherent parameter dependence. Moreover, we show that direct reciprocity can be an efficient incentive to promote cooperation within the network and discuss the analogies between our simple yet tractable framework with D2D proximity based services such as LTE-Direct. We argue that cooperative network dynamics have many application in ICT, not just ad hoc networks, and similar models as the one described herein can be devised and studied in their own right.

cs.NI↗

arXiv2016

Connectivity Scaling Laws in Wireless Networks

We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas exploited for diversity coding and/or beamforming at each node. We demonstrate that the local probability of connectivity scales like $\mathcal{O}(z^\mathcal C)$ in these parameters, where $\mathcal C$ is the ratio of the dimension of the network domain to the path loss exponent, thus enabling efficient boundary effect mitigation and network topology control.

cs.NI↗

arXiv2016

Random geometric graphs with general connection functions

In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected, that is every node is linked to every other node in a multihop fashion. Here, the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components, for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.

cond-mat.stat-mech↗

arXiv2015

Directional antennas improve the link-connectivity of interference limited ad hoc networks

We study wireless ad hoc networks in the absence of any channel contention or transmit power control and ask how antenna directivity affects network connectivity in the interference limited regime. We answer this question by deriving closed-form expressions for the outage probability, capacity and mean node degree of the network using tools from stochastic geometry. These novel results provide valuable insights for the design of future ad hoc networks. Significantly, our results suggest that the more directional the interfering transmitters are, the less detrimental are the effects of interference to individual links. We validate our analytical results through computer simulations.

cs.NI↗

arXiv2015

More is less: Connectivity in fractal regions

Ad-hoc networks are often deployed in regions with complicated boundaries. We show that if the boundary is modeled as a fractal, a network requiring line of sight connections has the counterintuitive property that increasing the number of nodes decreases the full connection probability. We characterise this decay as a stretched exponential involving the fractal dimension of the boundary, and discuss mitigation strategies. Applications of this study include the analysis and design of sensor networks operating in rugged terrain (e.g. railway cuttings), mm-wave networks in industrial settings and vehicle-to-vehicle/vehicle-to-infrastructure networks in urban environments.

cs.NI↗

arXiv2015

Location, location, location: Border effects in interference limited ad hoc networks

Wireless networks are fundamentally limited by the intensity of the received signals and by their inherent interference. It is shown here that in finite ad hoc networks where node placement is modelled according to a Poisson point process and no carrier sensing is employed for medium access, the SINR received by nodes located at the border of the network deployment/operation region is on average greater than the rest. This is primarily due to the uneven interference landscape of such networks which is particularly kind to border nodes giving rise to all sorts of performance inhomogeneities and access unfairness. Using tools from stochastic geometry we quantify these spatial variations and provide closed form communication-theoretic results showing why the receiver's location is so important.

cs.NI↗

arXiv2015

Multihop connectivity of ad hoc networks with randomly oriented directional antennas

Directional antennas and beamforming can significantly improve point-to-point wireless links when perfectly aligned. In this letter we investigate the extreme opposite where antenna orientations and positions are chosen at random in the presence of Rayleigh fading. We show that while the 1-hop network connectivity is deteriorated, the multihop routes improve, especially in the dense regime. We derive closed form expressions for the expectation of the $1$-hop and $2$-hop degree which are verified through computer simulations. We conclude that node density does not greatly affect the number of hops required between stations whilst simple random beamforming schemes do, thus returning substantial network performance benefits due to the existence of shorter multi-hop paths.

cs.NI↗

arXiv2015

Maximum Likelihood based Multihop Localization in Wireless Sensor Networks

For data sets retrieved from wireless sensors to be insightful, it is often of paramount importance that the data be accurate and also location stamped. This paper describes a maximum-likelihood based multihop localization algorithm called kHopLoc for use in wireless sensor networks that is strong in both isotropic and anisotropic network deployment regions. During an initial training phase, a Monte Carlo simulation is utilized to produce multihop connection density functions. Then, sensor node locations are estimated by maximizing local likelihood functions of the hop counts to anchor nodes. Compared to other multihop localization algorithms, the proposed kHopLoc algorithm achieves higher accuracy in varying network configurations and connection link-models.

cs.NI↗

arXiv2014

Network connectivity in non-convex domains with reflections

Recent research has demonstrated the importance of boundary effects on the overall connection probability of wireless networks but has largely focused on convex deployment regions. We consider here a scenario of practical importance to wireless communications, in which one or more nodes are located outside the convex space where the remaining nodes reside. We call these `external nodes', and assume that they play some essential role in the macro network functionality e.g. a gateway to a dense self-contained mesh network cloud. Conventional approaches with the underlying assumption of only line-of-sight (LOS) or direct connections between nodes, fail to provide the correct analysis for such a network setup. To this end we present a novel analytical framework that accommodates for the non-convexity of the domain and explicitly considers the effects of non-LOS nodes through reflections from the domain boundaries. We obtain analytical expressions in 2D and 3D which are confirmed numerically for Rician channel fading statistics and discuss possible extensions and applications.

cs.NI↗

arXiv2014

Escape through a time-dependent hole in the doubling map

We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the sides of the hole are moving in or out of phase respectively. We find out that the escape rate is well described by the overlap of the hole with its images, for holes centred at periodic orbits.

nlin.CD↗

arXiv2014

Connectivity in Dense Networks Confined within Right Prisms

We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries that can be found in practice. To maximize practicality and applicability, we adopt a general point-to-point link model based on outage probability, and present example analytical and numerical results for a network employing $2 \times 2$ multiple-input multiple-output (MIMO) maximum ratio combining (MRC) link level transmission confined within particular bounding geometries. Furthermore, we provide suggestions for extending the approach detailed herein to more general convex geometries.

cs.NI↗

arXiv2014

Network Connectivity: Stochastic vs. Deterministic Wireless Channels

We study the effect of stochastic wireless channel models on the connectivity of ad hoc networks. Unlike in the deterministic geometric disk model where nodes connect if they are within a certain distance from each other, stochastic models attempt to capture small-scale fading effects due to shadowing and multipath received signals. Through analysis of local and global network observables, we present conclusive evidence suggesting that network behaviour is highly dependent upon whether a stochastic or deterministic connection model is employed. Specifically we show that the network mean degree is lower (higher) for stochastic wireless channels than for deterministic ones, if the path loss exponent is greater (lesser) than the spatial dimension. Similarly, the probability of forming isolated pairs of nodes in an otherwise dense random network is much less for stochastic wireless channels than for deterministic ones. The latter realisation explains why the upper bound of $k$-connectivity is tighter for stochastic wireless channels. We obtain closed form analytic results and compare to extensive numerical simulations.

cs.NI↗

arXiv2013

Connectivity of confined 3D Networks with Anisotropically Radiating Nodes

Nodes in ad hoc networks with randomly oriented directional antenna patterns typically have fewer short links and more long links which can bridge together otherwise isolated subnetworks. This network feature is known to improve overall connectivity in 2D random networks operating at low channel path loss. To this end, we advance recently established results to obtain analytic expressions for the mean degree of 3D networks for simple but practical anisotropic gain profiles, including those of patch, dipole and end-fire array antennas. Our analysis reveals that for homogeneous systems (i.e. neglecting boundary effects) directional radiation patterns are superior to the isotropic case only when the path loss exponent is less than the spatial dimension. Moreover, we establish that ad hoc networks utilizing directional transmit and isotropic receive antennas (or vice versa) are always sub-optimally connected regardless of the environment path loss. We extend our analysis to investigate boundary effects in inhomogeneous systems, and study the geometrical reasons why directional radiating nodes are at a disadvantage to isotropic ones. Finally, we discuss multi-directional gain patterns consisting of many equally spaced lobes which could be used to mitigate boundary effects and improve overall network connectivity.

cs.IT↗