3,047 research outputs found
Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation
In this article, a framework is presented for the joint optimization of the
analog transmit and receive filter with respect to a parameter estimation
problem. At the receiver, conventional signal processing systems restrict the
two-sided bandwidth of the analog pre-filter to the rate of the
analog-to-digital converter to comply with the well-known Nyquist-Shannon
sampling theorem. In contrast, here we consider a transceiver that by design
violates the common paradigm . To this end, at the receiver, we
allow for a higher pre-filter bandwidth and study the achievable
parameter estimation accuracy under a fixed sampling rate when the transmit and
receive filter are jointly optimized with respect to the Bayesian
Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we
propose to approximate the required Fisher information matrix and solve the
transceiver design problem by an alternating optimization algorithm. The
presented approach allows us to explore the Pareto-optimal region spanned by
transmit and receive filters which are favorable under a weighted mean squared
error criterion. We also discuss the computational complexity of the obtained
transceiver design by visualizing the resulting ambiguity function. Finally, we
verify the performance of the optimized designs by Monte-Carlo simulations of a
likelihood-based estimator.Comment: 15 pages, 16 figure
Induced decay of composite JPC=1++ particles in atomic Coulomb fields
The electron-positron pairs observed in heavy-ion collisions at Gesellschaft fĂĽr Schwerionen-forschung Darmstadt mbH have been interpreted as the decay products of yet unknown particles with masses around 1.8 MeV. The negative results of resonant Bhabha scattering experiments, however, do not support such an interpretation. Therefore we focus on a more complex decay scenario, where the e+e- lines result from a two-collision process. We discuss the induced decay of a metastable 1++ state into e+e- pairs. For most realizations of a 1++ state such a decay in leading order can only take place in the Coulomb field of a target atom. This fact has the attractive consequence that for such a state the Bhabha bounds are no longer valid. However, the absolute value of the e+e- production cross section turns out to be unacceptably small
Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients
Subsurface flows are commonly modeled by advection-diffusion equations.
Insufficient measurements or uncertain material procurement may be accounted
for by random coefficients. To represent, for example, transitions in
heterogeneous media, the parameters of the equation are spatially
discontinuous. Specifically, a scenario with coupled advection- and diffusion
coefficients that are modeled as sums of continuous random fields and
discontinuous jump components are considered. For the numerical approximation
of the solution, an adaptive, pathwise discretization scheme based on a Finite
Element approach is introduced. To stabilize the numerical approximation and
accelerate convergence, the discrete space-time grid is chosen with respect to
the varying discontinuities in each sample of the coefficients, leading to a
stochastic formulation of the Galerkin projection and the Finite Element basis
Class number approximation in cubic function fields
We develop explicitly computable bounds for the order of the
Jacobian of a cubic function field. We use approximations via
truncated Euler products and thus derive effective methods
of computing the order of the Jacobian of a cubic function field.
Also, a detailed discussion of the zeta function of a cubic
function field extension is included
Stochastic Transport with L\'evy Noise -- Fully Discrete Numerical Approximation
Semilinear hyperbolic stochastic partial differential equations have various
applications in the natural and engineering sciences. From a modeling point of
view the Gaussian setting may be too restrictive, since applications in
mathematical finance and phenomena such as porous media or pollution models
indicate an influence of noise of a different nature. In order to capture
temporal discontinuities and allow for heavy-tailed distributions, Hilbert
space-valued L\'evy processes (or L\'evy fields) as driving noise terms are
considered. The numerical discretization of the corresponding SPDE involves
several difficulties: Low spatial and temporal regularity of the solution to
the problem entails slow convergence rates and instabilities for
space/time-discretization schemes. Furthermore, the L\'evy process admits
values in a possibly infinite-dimensional Hilbert space, hence projections onto
a finite-dimensional subspace for each discrete point in time are necessary.
Finally, unbiased sampling from the resulting L\'evy field may not be possible.
We introduce a novel fully discrete approximation scheme that addresses all of
these aspects. Our central contribution is a novel discontinuous
Petrov-Galerkin scheme for the spatial approximation that naturally arises from
the weak formulation of the SPDE. We prove optimal convergence of this approach
and couple it with a suitable time stepping scheme to avoid numerical
oscillations. Moreover, we approximate the driving noise process by truncated
Karhunen-Lo\'eve expansions. The latter essentially yields a sum of scaled and
uncorrelated one-dimensional L\'evy processes, which may be simulated with
controlled bias by Fourier inversion techniques
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