G. Bienvenu

Bio: G. Bienvenu is an academic researcher from ASM International. The author has contributed to research in topics: Eigenvalues and eigenvectors & Gaussian. The author has an hindex of 1, co-authored 1 publications receiving 357 citations.

Optimality of high resolution array processing using the eigensystem approach

Abstract: In the classical approach to underwater passive listening, the medium is sampled in a convenient number of "look-directions" from which the signals are estimated in order to build an image of the noise field. In contrast, a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously. In a Gaussian context, it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels. This paper aims to compute such estimators when the wavefront shapes are not assumed known a priori. This justifies results previously found using the asymptotical properties of the eigenvalue-eigenvector decomposition of the estimated spectral density matrix of the sensor signals: they have led to a variety of "high resolution" array processing methods. More specifically, a covariance matrix test for equality of the smallest eigenvalues is presented for source detection. For source localization, a "best fit" method and a test of orthogonality between the "smallest" eigenvectors and the "source" vectors are discussed.

The Geometry of Algorithms with Orthogonality Constraints

Abstract: In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.

MUSIC, maximum likelihood, and Cramer-Rao bound

Abstract: The performance of the MUSIC and ML methods is studied, and their statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established. The relationship between the MUSIC and ML estimators is investigated as well. A numerical study is reported of the statistical efficiency of the MUSIC estimator for the problem of finding the directions of two plane waves using a uniform linear array. An exact description of the results is included. >

Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations

Abstract: Array processing involves manipulation of signals induced on various antenna elements. Its capabilities of steering nulls to reduce cochannel interferences and pointing independent beams toward various mobiles, as well as its ability to provide estimates of directions of radiating sources, make it attractive to a mobile communications system designer. Array processing is expected to play an important role in fulfilling the increased demands of various mobile communications services. Part I of this paper showed how an array could be utilized in different configurations to improve the performance of mobile communications systems, with references to various studies where feasibility of apt array system for mobile communications is considered. This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them. This paper brings together almost all aspects of array signal processing.

Performance study of conditional and unconditional direction-of-arrival estimation

Abstract: A numerical and analytical study of conditional and unconditional direction-of-arrival (DOA) estimation is presented. Explicit expressions for the unconditional Cramer-Rao bounds on the DOA estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given. It is shown that many DOA estimation methods have the same asymptotic statistical properties under conditional and unconditional models. The situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed. >

The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise

Abstract: This paper presents an asymptotic statistical analysis of the null-spectra of two eigen-assisted methods, MUSIC [1] and Minimum-Norm [2], for resolving independent closely spaced plane waves in noise. Particular attention is paid to the average deviation of the null-spectra from zero at the true angles of arrival for the plane waves. These deviations are expressed as functions of signal-to-noise ratios, number of array elements, angular separation of emitters, and the number of snapshots. In the case of MUSIC. an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise. This result is validated by Monte Carlo simulations.