8,902 research outputs found
Differentially 4-uniform functions
We give a geometric characterization of vectorial boolean functions with
differential uniformity less or equal to 4
Formal study of plane Delaunay triangulation
This article presents the formal proof of correctness for a plane Delaunay
triangulation algorithm. It consists in repeating a sequence of edge flippings
from an initial triangulation until the Delaunay property is achieved. To
describe triangulations, we rely on a combinatorial hypermap specification
framework we have been developing for years. We embed hypermaps in the plane by
attaching coordinates to elements in a consistent way. We then describe what
are legal and illegal Delaunay edges and a flipping operation which we show
preserves hypermap, triangulation, and embedding invariants. To prove the
termination of the algorithm, we use a generic approach expressing that any
non-cyclic relation is well-founded when working on a finite set
Generalized two-body self-consistent theory of random linear dielectric composites: an effective-medium approach to clustering in highly-disordered media
Effects of two-body dipolar interactions on the effective
permittivity/conductivity of a binary, symmetric, random dielectric composite
are investigated in a self-consistent framework. By arbitrarily splitting the
singularity of the Green tensor of the electric field, we introduce an
additional degree of freedom into the problem, in the form of an unknown
"inner" depolarization constant. Two coupled self-consistent equations
determine the latter and the permittivity in terms of the dielectric contrast
and the volume fractions. One of them generalizes the usual Coherent Potential
condition to many-body interactions between single-phase clusters of
polarizable matter elements, while the other one determines the effective
medium in which clusters are embedded. The latter is in general different from
the overall permittivity. The proposed approach allows for many-body
corrections to the Bruggeman-Landauer (BL) scheme to be handled in a
multiple-scattering framework. Four parameters are used to adjust the degree of
self-consistency and to characterize clusters in a schematic geometrical way.
Given these parameters, the resulting theory is "exact" to second order in the
volume fractions. For suitable parameter values, reasonable to excellent
agreement is found between theory and simulations of random-resistor networks
and pixelwise-disordered arrays in two and tree dimensions, over the whole
range of volume fractions. Comparisons with simulation data are made using an
"effective" scalar depolarization constant that constitutes a very sensitive
indicator of deviations from the BL theory.Comment: 14 pages, 7 figure
Clutter rejection for MTI radar using a single antenna and a long integration time
Moving Target Indicators (MTI) are airborne radar systems
designed to detect and track moving vehicles or aircrafts. In this paper, we address the problem of detecting hazardous collision targets to avoid them. One of the best known solutions to solve this problem is given by the so-called Space-Time Adaptive Processing (STAP) algorithms which optimally filter the target signal from interference and noise exploiting the specific relationship between Direction Of Arrival (DOA) and Doppler for the ground clutter. However, these algorithms require an antenna array and multiple reception channels that increase cost and complexity.
The authors propose an alternative solution using a single antenna only.
In addition to the standard Doppler shift related to the radial speed, the orthoradial speed of any target can be estimated if using a long integration time. Dangerous targets and ground clutter have different signatures in the radial-orthoradial velocity plane. An optimal detector is then proposed based on the oblique projection onto the signal subspace orthogonal to the clutter subspace. The theoretical performances of this detector are derived and a realistic radar scene simulation shows the benefits of this new MTI detector
Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields
A modified Green operator is proposed as an improvement of Fourier-based
numerical schemes commonly used for computing the electrical or thermal
response of heterogeneous media. Contrary to other methods, the number of
iterations necessary to achieve convergence tends to a finite value when the
contrast of properties between the phases becomes infinite. Furthermore, it is
shown that the method produces much more accurate local fields inside
highly-conducting and quasi-insulating phases, as well as in the vicinity of
the phases interfaces. These good properties stem from the discretization of
Green's function, which is consistent with the pixel grid while retaining the
local nature of the operator that acts on the polarization field. Finally, a
fast implementation of the "direct scheme" of Moulinec et al. (1994) that
allows for parcimonious memory use is proposed.Comment: v2: `postprint' document (a few remaining typos in the published
version herein corrected in red; results unchanged
Velocity Dealiased Spectral Estimators of Range Migrating Targets using a Single Low-PRF Wideband Waveform
Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic countermeasures. Unfortunately, classical processing algorithms are challenged by the range-migration phenomenon that occurs then for fast moving targets. We
propose a new approach where the range migration is used rather as an asset to retrieve information about target velocitiesand, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the
level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators
Robustness maximization of parallel multichannel systems
Bit error rate (BER) minimization and SNR-gap maximization, two robustness
optimization problems, are solved, under average power and bit-rate
constraints, according to the waterfilling policy. Under peak-power constraint
the solutions differ and this paper gives bit-loading solutions of both
robustness optimization problems over independent parallel channels. The study
is based on analytical approach with generalized Lagrangian relaxation tool and
on greedy-type algorithm approach. Tight BER expressions are used for square
and rectangular quadrature amplitude modulations. Integer bit solution of
analytical continuous bit-rates is performed with a new generalized secant
method. The asymptotic convergence of both robustness optimizations is proved
for both analytical and algorithmic approaches. We also prove that, in
conventional margin maximization problem, the equivalence between SNR-gap
maximization and power minimization does not hold with peak-power limitation.
Based on a defined dissimilarity measure, bit-loading solutions are compared
over power line communication channel for multicarrier systems. Simulation
results confirm the asymptotic convergence of both allocation policies. In non
asymptotic regime the allocation policies can be interchanged depending on the
robustness measure and the operating point of the communication system. The low
computational effort of the suboptimal solution based on analytical approach
leads to a good trade-off between performance and complexity.Comment: 27 pages, 8 figures, submitted to IEEE Trans. Inform. Theor
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