2,701 research outputs found
Sparse Array Design via Fractal Geometries
Sparse sensor arrays have attracted considerable attention in various fields
such as radar, array processing, ultrasound imaging and communications. In the
context of correlation-based processing, such arrays enable to resolve more
uncorrelated sources than physical sensors. This property of sparse arrays
stems from the size of their difference coarrays, defined as the differences of
element locations. Thus, the design of sparse arrays with large difference
coarrays is of great interest. In addition, other array properties such as
symmetry, robustness and array economy are important in different applications.
Numerous studies have proposed diverse sparse geometries, focusing on certain
properties while lacking others. Incorporating multiple properties into the
design task leads to combinatorial problems which are generally NP-hard. For
small arrays these optimization problems can be solved by brute force, however,
in large scale they become intractable. In this paper, we propose a scalable
systematic way to design large sparse arrays considering multiple properties.
To that end, we introduce a fractal array design in which a generator array is
recursively expanded according to its difference coarray. Our main result
states that for an appropriate choice of the generator such fractal arrays
exhibit large difference coarrays. Furthermore, we show that the fractal arrays
inherit their properties from their generators. Thus, a small generator can be
optimized according to desired requirements and then expanded to create a
fractal array which meets the same criteria. This approach paves the way to
efficient design of large arrays of hundreds or thousands of elements with
specific properties.Comment: 16 pages, 9 figures, 1 Tabl
Fast minimum variance wavefront reconstruction for extremely large telescopes
We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the
reconstruction of the optical wavefront from measurements provided by a
wavefront sensor. As our application is adaptive optics on extremely large
telescopes, our algorithm was designed with speed and best quality in mind. The
latter is achieved thanks to a regularization which enforces prior statistics.
To solve the regularized problem, we use the conjugate gradient method which
takes advantage of the sparsity of the wavefront sensor model matrix and avoids
the storage and inversion of a huge matrix. The prior covariance matrix is
however non-sparse and we derive a fractal approximation to the Karhunen-Loeve
basis thanks to which the regularization by Kolmogorov statistics can be
computed in O(N) operations, N being the number of phase samples to estimate.
Finally, we propose an effective preconditioning which also scales as O(N) and
yields the solution in 5-10 conjugate gradient iterations for any N. The
resulting algorithm is therefore O(N). As an example, for a 128 x 128
Shack-Hartmann wavefront sensor, FRiM appears to be more than 100 times faster
than the classical vector-matrix multiplication method.Comment: to appear in the Journal of the Optical Society of America
Computational strategies for iterative solutions of large fem applications employing voxel data
FE-models for structural solid mechanics analyses can be readily generated from computer images via a 'voxel convesion' method, whereby voxels in a two- or three-dimesional computer image are directly translated to elements in a FE-model. The fact that all elements thus generated are the same creates the possibilities for fast solution algorithm that can compensate for a large number of element. The solving methods described in this paper are based on an iterative solving algorithm in combination with a uniqueelement Element-by-Element (EBE) or with a newly developed Row-by-Row (RBR) matrix-vector multiplication strategy. With these methods it is possible to solve FE-models on the order of 105 3-D brick elements on a workstation and on the order of 106 elements on a Cray computer. The methods are demonstrated for the Boussinesq problem and for FF models that represent a porous trabecular bone structure The results show that the RBR method can be 3.2 times faster than the EBE method. It was concluded that the voxel conversion method in combination with these solving methods not only provides a powerful tool to analyse structures that can not be analysed in another way, but also that this approach can be competitive with traditional meshing and solving techniques
Compressed Sensing - A New mode of Measurement
After introducing the concept of compressed sensing as a complementary
measurement mode to the classical Shannon-Nyquist approach, I discuss some of
the drivers, potential challenges and obstacles to its implementation. I end with a
speculative attempt to embed compressed sensing as an enabling methodology
within the emergence of data-driven discovery. As a consequence I predict the
growth of non-nomological sciences where heuristic correlations will find
applications but often bypass conventional pure basic and use-inspired basic
research stages due to the lack of verifiable hypotheses
Wideband DOA Estimation with Frequency Decomposition via a Unified GS-WSpSF Framework
A unified group sparsity based framework for wideband sparse spectrum fitting (GS-WSpSF) is proposed for wideband direction-of-arrival (DOA) estimation, which is capable of handling both uncorrelated and correlated sources. Then, by making four different assumptions on a priori knowledge about the sources, four variants under the proposed framework are formulated as solutions to the underdetermined DOA estimation problem without the need of employing sparse arrays. As verified by simulations, improved estimation performance can be achieved by the wideband methods compared with narrowband ones, and adopting more a priori information leads to better performance in terms of resolution capacity and estimation accuracy
Sparse Linear Antenna Arrays: A Review
Linear sparse antenna arrays have been widely studied in array processing literature. They belong to the general class of non-uniform linear arrays (NULAs). Sparse arrays need fewer sensor elements than uniform linear arrays (ULAs) to realize a given aperture. Alternately, for a given number of sensors, sparse arrays provide larger apertures and higher degrees of freedom than full arrays (ability to detect more source signals through direction-of-arrival (DOA) estimation). Another advantage of sparse arrays is that they are less affected by mutual coupling compared to ULAs. Different types of linear sparse arrays have been studied in the past. While minimum redundancy arrays (MRAs) and minimum hole arrays (MHAs) existed for more than five decades, other sparse arrays such as nested arrays, co-prime arrays and super-nested arrays have been introduced in the past decade. Subsequent to the introduction of co-prime and nested arrays in the past decade, many modifications, improvements and alternate sensor array configurations have been presented in the literature in the past five years (2015–2020). The use of sparse arrays in future communication systems is promising as they operate with little or no degradation in performance compared to ULAs. In this chapter, various linear sparse arrays have been compared with respect to parameters such as the aperture provided for a given number of sensors, ability to provide large hole-free co-arrays, higher degrees of freedom (DOFs), sharp angular resolutions and susceptibility to mutual coupling. The chapter concludes with a few recommendations and possible future research directions
Maximum Gain, Effective Area, and Directivity
Fundamental bounds on antenna gain are found via convex optimization of the
current density in a prescribed region. Various constraints are considered,
including self-resonance and only partial control of the current distribution.
Derived formulas are valid for arbitrarily shaped radiators of a given
conductivity. All the optimization tasks are reduced to eigenvalue problems,
which are solved efficiently. The second part of the paper deals with
superdirectivity and its associated minimal costs in efficiency and Q-factor.
The paper is accompanied with a series of examples practically demonstrating
the relevance of the theoretical framework and entirely spanning wide range of
material parameters and electrical sizes used in antenna technology. Presented
results are analyzed from a perspective of effectively radiating modes. In
contrast to a common approach utilizing spherical modes, the radiating modes of
a given body are directly evaluated and analyzed here. All crucial mathematical
steps are reviewed in the appendices, including a series of important
subroutines to be considered making it possible to reduce the computational
burden associated with the evaluation of electrically large structures and
structures of high conductivity.Comment: 12 pages, 15 figures, submitted to TA
Uncertainty quantification for fat-tailed probability distributions in aircraft engine simulations
Rare event simulation is vital for industrial design because some events, so-called black swans, can have fatal consequences despite their low probability of occurrence. Finding low-probability events far off the mean design is a challenging task for realistic engineering models because they are characterized by high computational demands, many input variables, and often insufficient statistical information to build parametric probability distributions. Therefore, an adaptive and arbitrary polynomial chaos method, called sparse approximation of moment-based arbitrary polynomial chaos, is suggested in this work. Sparse approximation of moment-based arbitrary polynomial chaos creates custom polynomial basis functions and grids based on statistical moments to avoid incorrect statistical assumptions. The contribution of this work is that it is derived how rare event simulation can conveniently be integrated into adaptive sparse grid methods by calculating polynomial chaos expansions based on the statistical moments of truncated fat-tailed distributions. Moreover, the use of tempered alpha-stable distributions is suggested to avoid discontinuous tail cutoffs. Sparse approximation of moment-based arbitrary polynomial chaos is compared to other statistical methods in two industrial aircraft engine simulations: a simulation of transient cycle temperature in a turbine cavity and hot-gas ingestion in the interwheel region. In both cases, sparse approximation of moment-based arbitrary polynomial chaos agrees with previous results but obtains them with lower computational effort
Antenna Systems
This book offers an up-to-date and comprehensive review of modern antenna systems and their applications in the fields of contemporary wireless systems. It constitutes a useful resource of new material, including stochastic versus ray tracing wireless channel modeling for 5G and V2X applications and implantable devices. Chapters discuss modern metalens antennas in microwaves, terahertz, and optical domain. Moreover, the book presents new material on antenna arrays for 5G massive MIMO beamforming. Finally, it discusses new methods, devices, and technologies to enhance the performance of antenna systems
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