Search Results (8)

Bistatic radar exhibits spatial isomerism and diverse configurations, leading to unique clutter characteristics distinct from those of monostatic radar. The clutter rank serves as a pivotal indicator of clutter characteristics, enabling the quantification of clutter severity. Space-time adaptive processing (STAP) is a critical technique to detect moving targets, and clutter rank determines the number of independent and identically distributed (IID) training samples and the degree of freedom (DOF) for effective suppression of clutter that STAP requires. Therefore, the accurate estimation of clutter rank for bistatic radar can provide a crucial indicator for designing and constructing STAP processors, thereby facilitating fast and efficient clutter suppression in bistatic radar systems. This study is based on the idea that clutter rank is the number of prolate spheroidal wave function (PSWF) orthogonal bases utilized for approximating the clutter signal. Firstly, the challenge of utilizing PSWF orthogonal bases for approximating the clutter signal in bistatic radar is elucidated. This pertains to the fact that, unlike monostatic radar clutter, bistatic radar clutter is not capable of being expressed as a single-frequency signal. The clutter rank estimation for bistatic radar is thus derived as the frequency bandwidth estimation. Secondly, to achieve this estimation, the frequency distribution of each individual scattering unit is investigated, thereby determining their extending frequency broadening (EFB) as compared to that of single-frequency. Subsequently, the integral average of EFB across the entire range bin is computed, ultimately enabling the acquisition of bistatic radar’s frequency bandwidth. Finally, the estimation method is extended to non-side-looking mode and limited observation areas with pattern modulation. Simulation experiments confirm that our proposed method provides accurate clutter rank estimations, surpassing 99% proportions of large eigenvalues across various bistatic configurations, observation modes, and areas. Full article

This study explores efficient methods for computing eigenvalues and function values associated with Chebyshev-type prolate spheroidal wave functions (CPSWFs). Applying the expansion of the factor $e^{\mathrm{i}cxy}$ and the inherent properties of Chebyshev polynomials, we present an exact and stable numerical approximation for the exact eigenvalues of the integral operator to CPSWFs. Additionally, we illustrate the efficiency of employing fast Fourier transform and barycentric interpolation techniques for computing CPSWF values and related quantities, which are essential for various numerical applications based on these functions. The analysis is supported by numerical examples, providing validation for the accuracy and reliability of our proposed approach. Full article

Near-field acoustic holography (NAH) based on compressing sensing (CS) theory enables accurate reconstruction of sound fields using a limited number of sampling points. However, the successful implementation of this technique depends on two crucial factors: (1) the appropriate selection or construction of the spatial basis and (2) an effective sparse regularization process. To enhance reconstruction performance for elongated sound sources, this paper proposes a novel sound field reconstruction method that combines prolate spheroidal wave functions (PSWFs) with the orthogonal matching pursuit (OMP) algorithm. In this method, PSWFs serve as a sparse spatial basis for representing the radiated sound field. The sparse coefficients are determined by the OMP algorithm in a linear subspace composed of basic functions that best match the residual error. The OMP algorithm effectively identifies significant components before potentially selecting incorrect ones by setting an appropriate stopping rule. Numerical simulations are conducted using a line-array source model. The results show that the proposed method can accurately reconstruct the sound pressures of the elongated source model using a relatively small number of samplings. In addition, the proposed method exhibits robustness across a wide frequency range, diverse array configurations and various sampling numbers. The experimental results further validate the feasibility and reliability of the proposed method. Full article

In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one of its axes, which is also known as a spheroid. We have developed a fast and ad hoc code to solve the electromagnetic scattering problem, using spheroidal vector wave functions, which are special functions used to describe physical problems in which a prolate or oblate spheroidal reference system is considered. Numerical results are presented, both for TE and TM polarization of the incident wave, and are validated by a comparison with results obtained by a commercial electromagnetic simulator. Full article

Direction-of-arrival (DOA) estimation in a spatially isotropic white noise background has been widely researched for decades. However, in practice, such as underwater acoustic ambient noise in shallow water, the ambient noise can be spatially colored, which may severely degrade the performance of DOA estimation. To solve this problem, this paper proposes a DOA estimation method based on sparse Bayesian learning with the modified noise model using acoustic vector hydrophone arrays. Firstly, an applicable linear noise model is established by using the prolate spheroidal wave functions (PSWFs) to characterize spatially colored noise and exploiting the excellent performance of the PSWFs in extrapolating band-limited signals to the space domain. Then, using the proposed noise model, an iterative method for sparse spectrum reconstruction is developed under a sparse Bayesian learning (SBL) framework to fit the actual noise field received by the acoustic vector hydrophone array. Finally, a DOA estimation algorithm under the modified noise model is also presented, which has a superior performance under spatially colored noise. Numerical results validate the effectiveness of the proposed method. Full article

We consider a communication system whereby T-seconds time-limited codewords are transmitted over a W-Hz band-limited additive white Gaussian noise channel. In the asymptotic regime as $WT\to \infty$, it is known that the maximal achievable rates with such a scheme converge to Shannon’s capacity with the presence of $2WT$ degrees of freedom. In this work we study the degrees of freedom and the achievable information rates for finite values of $WT$. We use prolate spheroidal wave functions to obtain an information lossless equivalent discrete formulation and then we apply Polyanskiy’s results on coding in the finite block-length regime. We derive upper and lower bounds on the achievable rates and the corresponding degrees of freedom and we numerically evaluate them for sample values of $2WT$. The bounds are asymptotically tight and numerical computations show the gap between them decreases as $2WT$ increases. Additionally, the possible decrease from $2WT$ in the available degrees of freedom is upper-bounded by a logarithmic function of $2WT$. Full article

The aim of this paper is to introduce a new methodology for the fault diagnosis of induction machines working in the transient regime, when time-frequency analysis tools are used. The proposed method relies on the use of the optimized Slepian window for performing the short time Fourier transform (STFT) of the stator current signal. It is shown that for a given sequence length of finite duration, the Slepian window has the maximum concentration of energy, greater than can be reached with a gated Gaussian window, which is usually used as the analysis window. In this paper, the use and optimization of the Slepian window for fault diagnosis of induction machines is theoretically introduced and experimentally validated through the test of a 3.15-MW induction motor with broken bars during the start-up transient. The theoretical analysis and the experimental results show that the use of the Slepian window can highlight the fault components in the current’s spectrogram with a significant reduction of the required computational resources. Full article

The method of angular correlations recovers quantities from diffraction patterns of randomly oriented particles, as expected to be measured with an X-ray free electron laser (XFEL), proportional to quadratic functions of the spherical harmonic expansion coefficients of the diffraction volume of a single particle. We have previously shown that it is possible to reconstruct a randomly oriented icosahedral or helical virus from the average over all measured diffraction patterns of such correlations. We point out in this paper that a structure of even simpler particles of 50 Å or so in diameter and consisting of heavier atomic elements (to enhance scattering) that has been used as a test case for reconstructions from XFEL diffraction patterns can also be solved by this technique. Even though there has been earlier work on similar objects (prolate spheroids), one advantage of the present technique is its potential to also work with diffraction patterns not only due to single particles as has been suggested on the basis on nonoverlapping delta functions of angular scattering. Accordingly, we calculated from the diffraction patterns the angular momentum expansions of the pair correlations and triple correlations for general particle images and reconstructed those images in the standard way. Although the images looked pretty much the same, it is not totally clear to us that the angular correlations are exactly the same as different numbers of particles due to the possibility of constructive or destructive interference between the scattered waves from different particles. It is of course known that, for a large number of particles contributing to a diffraction parttern, the correlations converge to that of a single particle. It could be that the lack of perfect agreement between the images reconstructed with one and two particles is due to uncancelling constructive and destructive conditions that are not found in the case of solution scattering. Full article