Bounded-hop percolation and wireless communication

2016 ◽  
Vol 53 (3) ◽  
pp. 833-845 ◽  
Author(s):  
Christian Hirsch
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Base Station ◽  
Telecommunication Networks ◽  
Base Stations ◽  
Continuum Percolation ◽  
Supercritical Regime ◽  
Close Relationship ◽  
Wireless Telecommunication ◽  
Minimum Number

AbstractMotivated by an application in wireless telecommunication networks, we consider a two-type continuum-percolation problem involving a homogeneous Poisson point process of users and a stationary and ergodic point process of base stations. Starting from a randomly chosen point of the Poisson point process, we investigate the distribution of the minimum number of hops that are needed to reach some point of the base station process. In the supercritical regime of continuum percolation, we use the close relationship between Euclidean and chemical distance to identify the distributional limit of the rescaled minimum number of hops that are needed to connect a typical Poisson point to a point of the base station process as its intensity tends to 0. In particular, we obtain an explicit expression for the asymptotic probability that a typical Poisson point connects to a point of the base station process in a given number of hops.

scholarly journals Investigation of a New Handover Approach in LTE and WiMAX

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Nour Hindia ◽  
Ahmed Wasif Reza ◽  
Kamarul Ariffin Noordin
Keyword(s):  
Mobile Station ◽  
Signal Strength ◽  
Received Signal Strength ◽  
Base Station ◽  
Multiple Criteria ◽  
Base Stations ◽  
Technology Selection ◽  
The Novel ◽  
Vertical Handovers ◽  
Minimum Number

Nowadays, one of the most important challenges in heterogeneous networks is the connection consistency between the mobile station and the base stations. Furthermore, along the roaming process between the mobile station and the base station, the system performance degrades significantly due to the interferences from neighboring base stations, handovers to inaccurate base station and inappropriate technology selection. In this paper, several algorithms are proposed to improve mobile station performance and seamless mobility across the long-term evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX) technologies, along with a minimum number of redundant handovers. Firstly, the enhanced global positioning system (GPS) and the novel received signal strength (RSS) prediction approaches are suggested to predict the target base station accurately. Then, the multiple criteria with two thresholds algorithm is proposed to prioritize the selection between LTE and WiMAX as the target technology. In addition, this study also covers the intercell and cochannel interference reduction by adjusting the frequency reuse ratio 3 (FRR3) to work with LTE and WiMAX. The obtained results demonstrate high next base station prediction efficiency and high accuracy for both horizontal and vertical handovers. Moreover, the received signal strength is kept at levels higher than the threshold, while maintaining low connection cost and delay within acceptable levels. In order to highlight the combination of the proposed algorithms’ performance, it is compared with the existing RSS and multiple criteria handover decision algorithms.

scholarly journals Interference cancelation for high-density fifth-generation relaying network using stochastic geometrical approach

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771985587 ◽  
Author(s):  
MHD Nour Hindia ◽  
Faizan Qamar ◽  
Talib Abbas ◽  
Kaharudin Dimyati ◽  
Mohamad Sofian Abu Talip ◽  
...  
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Process Model ◽  
Success Probability ◽  
Relay Node ◽  
Ergodic Capacity ◽  
Base Station ◽  
High Density ◽  
Geometrical Approach ◽  
Fifth Generation

In order to resolve the issue of coverage limitation for the future fifth-generation network, deploying a relay node within a cell is one of the most capable and cost-effective solution, which not only enhances the coverage but also improves the spectral efficiency. However, this solution leads to the undesired interferences from nearby base station and relay nodes that affects user’s signal-to-interference-plus-noise ratio and can cause the ambiguous received signal at the user end. In this article, we have analyzed a relay-based interference-limited network at millimeter wave frequency and proposed a Poisson point process–based model using a stochastic geometrical approach. The results for the proposed Poisson point process model have been evaluated in terms of success probability, network ergodic capacity, and outage probability, compared with the ideal grid model and conventional multiple-antenna ultra-dense network model. The results proved that the success probability and ergodic capacity for the proposed model are 3.5% and 2.3% higher as compared to the most commonly used model for the high-density network, respectively. Furthermore, the results have been analyzed at different multiple-input-multiple-output antenna configuration, which validates the model in the improvement of overall network performance even for higher number of antennas.

scholarly journals Connectivity of Random Geometric Graphs Related to Minimal Spanning Forests

2013 ◽  
Vol 45 (1) ◽  
pp. 20-36 ◽  
Author(s):  
C. Hirsch ◽  
D. Neuhäuser ◽  
V. Schmidt
Keyword(s):  
Point Process ◽  
Open Problem ◽  
Poisson Point Process ◽  
Point Processes ◽  
Geometric Graphs ◽  
Continuum Percolation ◽  
Random Geometric Graphs ◽  
Spanning Forests ◽  
Percolation Thresholds ◽  
Relative Neighborhood Graph

The almost-sure connectivity of the Euclidean minimal spanning forest MSF(X) on a homogeneous Poisson point process X ⊂ ℝd is an open problem for dimension d>2. We introduce a descending family of graphs (Gn)n≥2 that can be seen as approximations to the MSF in the sense that MSF(X)=∩n=2∞Gn(X). For n=2, one recovers the relative neighborhood graph or, in other words, the β-skeleton with β=2. We show that almost-sure connectivity of Gn(X) holds for all n≥2, all dimensions d≥2, and also point processes X more general than the homogeneous Poisson point process. In particular, we show that almost-sure connectivity holds if certain continuum percolation thresholds are strictly positive or, more generally, if almost surely X does not admit generalized descending chains.

scholarly journals Connectivity of Random Geometric Graphs Related to Minimal Spanning Forests

2013 ◽  
Vol 45 (01) ◽  
pp. 20-36 ◽  
Author(s):  
C. Hirsch ◽  
D. Neuhäuser ◽  
V. Schmidt
Keyword(s):  
Point Process ◽  
Open Problem ◽  
Poisson Point Process ◽  
Point Processes ◽  
Geometric Graphs ◽  
Continuum Percolation ◽  
Random Geometric Graphs ◽  
Spanning Forests ◽  
Percolation Thresholds ◽  
Relative Neighborhood Graph

The almost-sure connectivity of the Euclidean minimal spanning forest MSF(X) on a homogeneous Poisson point processX⊂ ℝdis an open problem for dimensiond>2. We introduce a descending family of graphs (Gn)n≥2 that can be seen as approximations to the MSF in the sense that MSF(X)=∩n=2∞Gn(X). Forn=2, one recovers the relative neighborhood graph or, in other words, the β-skeleton with β=2. We show that almost-sure connectivity ofGn(X) holds for alln≥2, all dimensionsd≥2, and also point processesXmore general than the homogeneous Poisson point process. In particular, we show that almost-sure connectivity holds if certain continuum percolation thresholds are strictly positive or, more generally, if almost surelyXdoes not admit generalized descending chains.

scholarly journals Percolation in the signal to interference ratio graph

2006 ◽  
Vol 43 (2) ◽  
pp. 552-562 ◽  
Author(s):  
Olivier Dousse ◽  
Massimo Franceschetti ◽  
Nicolas Macris ◽  
Ronald Meester ◽  
Patrick Thiran
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Critical Density ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Radio Communications ◽  
Communications Networks ◽  
Infinite Range ◽  
Independent Model

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

scholarly journals Percolation in the signal to interference ratio graph

2006 ◽  
Vol 43 (02) ◽  
pp. 552-562 ◽  
Author(s):  
Olivier Dousse ◽  
Massimo Franceschetti ◽  
Nicolas Macris ◽  
Ronald Meester ◽  
Patrick Thiran
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Critical Density ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Radio Communications ◽  
Communications Networks ◽  
Infinite Range ◽  
Independent Model

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

scholarly journals Cellular coverage probability is independent of base station density under stochastic geometric models

2021 ◽  
Author(s):  
Hamed Nassar
Keyword(s):  
Coverage Probability ◽  
Stochastic Geometry ◽  
Poisson Point Process ◽  
Euclidean Plane ◽  
Base Station ◽  
Base Stations ◽  
Cellular Communications ◽  
Huge Number ◽  
The Past ◽  
Station Density

Stochastic geometry (SG) has been extensively used to model cellular communications, under the assumption that the base stations (BS) are deployed as a Poisson point process in the Euclidean plane. This has spawned a huge number of articles over the past years for different scenarios, culminating in an equally huge number of expressions for the coverage probability in both the uplink (UL) and downink (DL) directions. The trouble is that those expressions include the BS density, $\lambda$, which we prove irrelevant in this article. We start by developing a SG model for a baseline cellular scenario, then prove that the coverage probability is independent of $\lambda$, contrary to popular belief.

scholarly journals Extremal lifetimes of persistent cycles

Extremes ◽  
2021 ◽  
Author(s):  
Nicolas Chenavier ◽  
Christian Hirsch
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
General Feature ◽  
Extreme Values ◽  
Persistent Homology ◽  
Poisson Approximation ◽  
Continuum Percolation ◽  
Coexistence Region ◽  
Death Time ◽  
Topological Features

AbstractPersistent homology captures the appearances and disappearances of topological features such as loops and cavities when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation and the coexistence region. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for cavities in the Čech filtration. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of cavities and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Čech filtration.

DEVELOPMENT OF VALUATION METHOD OF THE STATUS OF BASE STATIONS FOR DETERMINING THE NEED OF THEIR UPGRADING

2017 ◽  
pp. 60-70
Author(s):  
Natalya Ivanovna Shaposhnikova ◽  
Alexander Aleksandrovich Sorokin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Cellular Network ◽  
New Technologies ◽  
Base Station ◽  
Base Stations ◽  
Valuation Method ◽  
The Status ◽  
Telecommunications Services ◽  
Theory Of Fuzzy Sets

The article consideres the problems of determining the need to modernize the base stations of the cellular network based on the mathematical apparatus of the theory of fuzzy sets. To improve the quality of telecommunications services the operators should send significant funding for upgrading the equipment of base stations. Modernization can improve and extend the functions of base stations to provide cellular communication, increase the reliability of the base station in operation and the functionality of its individual elements, and reduce the cost of maintenance and repair when working on a cellular network. The complexity in collecting information about the equipment condition is determined by a large number of factors that affect its operation, as well as the imperfection of obtaining and processing the information received. For a comprehensive assessment of the need for modernization, it is necessary to take into account a number of indicators. In the structure of indicators of the need for modernization, there were introduced the parameters reflecting both the degree of aging and obsolescence(the technical gap and the backlog in connection with the emergence of new technologies and standards). In the process of a problem solving, the basic stages of decision-making on modernization have been allocated. Decision-making on the need for modernization is based not only on measuring information that takes into account the decision-makers, but also on linguistic and verbal information. Therefore, to determine the need for upgrading the base stations, the theory of fuzzy sets is used, with the help of which experts can be attracted to this issue. They will be able to formulate additional fuzzy judgments that help to take into account not only measuring characteristics, but also poorly formalized fuzzy information. To do this, the main indicators of the modernization need have been defined, and fuzzy estimates of the need for modernization for all indicators and a set of indicators reflecting the need for upgrading the base stations have been formulated.

Mobile network synthesis strategy

2019 ◽  
pp. 98-101
Author(s):  
V. Lyandres
Keyword(s):  
Average Distance ◽  
Mobile Network ◽  
Base Station ◽  
Service Area ◽  
Base Stations ◽  
Frequency Assignment ◽  
Network Synthesis ◽  
Universal Method ◽  
Synthesis Strategy ◽  
Adaptive Vector Quantization

Introduction:Effective synthesis of а mobile communication network includes joint optimisation of two processes: placement of base stations and frequency assignment. In real environments, the well-known cellular concept fails due to some reasons, such as not homogeneous traffic and non-isotropic wave propagation in the service area.Purpose:Looking for the universal method of finding a network structure close to the optimal.Results:The proposed approach is based on the idea of adaptive vector quantization of the network service area. As a result, it is reduced to a 2D discrete map split into zones with approximately equal number of service requests. In each zone, the algorithm finds such coordinates of its base station that provide the shortest average distance to all subscribers. This method takes into account the shortage of the a priory information about the current traffic, ensures maximum coverage of the service area, and what is not less important, significantly simplifies the process of frequency assignment.

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