370 research outputs found
On Association Cells in Random Heterogeneous Networks
Characterizing user to access point (AP) association strategies in
heterogeneous cellular networks (HetNets) is critical for their performance
analysis, as it directly influences the load across the network. In this
letter, we introduce and analyze a class of association strategies, which we
term stationary association, and the resulting association cells. For random
HetNets, where APs are distributed according to a stationary point process, the
area of the resulting association cells are shown to be the marks of the
corresponding point process. Addressing the need of quantifying the load
experienced by a typical user, a "Feller-paradox" like relationship is
established between the area of the association cell containing origin and that
of a typical association cell. For the specific case of Poisson point process
and max power/SINR association, the mean association area of each tier is
derived and shown to increase with channel gain variance and decrease in the
path loss exponents of the corresponding tier
A Tractable Approach to Coverage and Rate in Cellular Networks
Cellular networks are usually modeled by placing the base stations on a grid,
with mobile users either randomly scattered or placed deterministically. These
models have been used extensively but suffer from being both highly idealized
and not very tractable, so complex system-level simulations are used to
evaluate coverage/outage probability and rate. More tractable models have long
been desirable. We develop new general models for the multi-cell
signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under
very general assumptions, the resulting expressions for the downlink SINR CCDF
(equivalent to the coverage probability) involve quickly computable integrals,
and in some practical special cases can be simplified to common integrals
(e.g., the Q-function) or even to simple closed-form expressions. We also
derive the mean rate, and then the coverage gain (and mean rate loss) from
static frequency reuse. We compare our coverage predictions to the grid model
and an actual base station deployment, and observe that the proposed model is
pessimistic (a lower bound on coverage) whereas the grid model is optimistic,
and that both are about equally accurate. In addition to being more tractable,
the proposed model may better capture the increasingly opportunistic and dense
placement of base stations in future networks.Comment: Submitted to IEEE Transactions on Communication
Towards a generalisation of formal concept analysis for data mining purposes
In this paper we justify the need for a generalisation of Formal
Concept Analysis for the purpose of data mining and begin the
synthesis of such theory. For that purpose, we first review semirings and
semimodules over semirings as the appropriate objects to use in abstracting
the Boolean algebra and the notion of extents and intents, respectively.
We later bring to bear powerful theorems developed in the field
of linear algebra over idempotent semimodules to try to build a Fundamental
Theorem for K-Formal Concept Analysis, where K is a type of
idempotent semiring. Finally, we try to put Formal Concept Analysis in
new perspective by considering it as a concrete instance of the theory
developed
Series Expansion for Interference in Wireless Networks
The spatial correlations in transmitter node locations introduced by common
multiple access protocols makes the analysis of interference, outage, and other
related metrics in a wireless network extremely difficult. Most works therefore
assume that nodes are distributed either as a Poisson point process (PPP) or a
grid, and utilize the independence properties of the PPP (or the regular
structure of the grid) to analyze interference, outage and other metrics.
But,the independence of node locations makes the PPP a dubious model for
nontrivial MACs which intentionally introduce correlations, e.g. spatial
separation, while the grid is too idealized to model real networks. In this
paper, we introduce a new technique based on the factorial moment expansion of
functionals of point processes to analyze functions of interference, in
particular outage probability. We provide a Taylor-series type expansion of
functions of interference, wherein increasing the number of terms in the series
provides a better approximation at the cost of increased complexity of
computation. Various examples illustrate how this new approach can be used to
find outage probability in both Poisson and non-Poisson wireless networks.Comment: Submitted to IEEE Transactions on Information Theor
Análisis exploratorio de las dificultades de alumnado de ingenierÃa en la resolución de problemas de optimización
En este trabajo se presenta un análisis exploratorio descriptivo de las dificultades de los alumnos para resolver problemas de optimización, dicho análisis se realiza a fin de mejorar las estrategias de enseñanza de este tema. Se analizaron las producciones de alumnos de la primera asignatura de Análisis Matemático de la Facultad de IngenierÃa de la Universidad Nacional de Mar del Plata utilizando conceptos del enfoque Ontosemiótico de la instrucción y la cognición Matemática. Los resultados del análisis muestran que las dificultades detectadas, en la mayorÃa de las resoluciones, se encuentran en algunos de los procedimientos empleados al resolver dichos problemas. La identificación de dichos procedimientos permitirá intervenir sobre ellos para lograr un mejor desempeño a la hora de resolver problemas de optimización
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