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Comparison of music algorithms using gradient- and integral-type mode vectors for direction of arrival and angular spread estimation

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART I-COMMUNICATIONS 2007年第6期90卷 53-64页

作者： Hotta, Hiroyuki Kikuma, Nobuyoshi Sakakibara, Kunio Hirayama, Hiroshi Nagoya Inst Technol Dept Elect & Comp Engn Nagoya Aichi 4668555 Japan

A generalized mode vector that simultaneously uses the differential coefficient component of the mode vector has been proposed for estimating the direction of arrival of incident waves having angular spread. In this paper, the authors first examined this generalized mode vector and proposed a gradient-type music algorithm that uses the differential coefficient component of the mode vector independently for estimating the direction of arrival. Then they used a computer simulation in which the waves having angular spread were considered to be a group of scattered waves to compare this algorithm with regard to the performance for estimating the direction of arrival with an integraltype music algorithm that uses simple integration, which they proposed separately. To improve the estimation precision degradation that occurs when the signal correlation is low among scattered waves that exist within the angular spread when using the integral-type music algorithm, the authors proposed a combined-type music algorithm that incorporated the gradient-type music algorithm in the integral-type music algorithm and used this to examine the performance for estimating the direction of arrival and angular spread again. The results of the comparison of the gradient-type music algorithm and integral-type music algorithm confirmed that the two algorithms have conflicting properties related to the signal correlation among scattered waves that exist within the angular spread. Also, the investigation related to the combined-type music algorithm indicated that estimation precision degradation that occurs when the signal correlation is low among scattered waves when using the integral-type music algorithm was reduced as expected. 0 2007 Wiley Periodicals, Inc.

关键词： gradient-type mode vector integral-type mode vector music algorithm direction of arrival estimation angular spread estimation

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Haar-music: A New Hybrid Method for Frequency Estimation

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2023年第5期42卷 2916-2940页

作者： Yalcin, Nedim Aktan Vatansever, Fahri Bursa Uludag Univ Fac Engn Elect Elect Engn Dept Bursa Turkey

Parameter estimation is very important in signal analysis. In this study, a new hybrid method based on implementation of Multiple Signal Classification (music) method with Discrete Haar transform (DHT) coefficients for frequency estimation of signals is proposed. This method decreases the input data size and sampling frequency and limits noise subspace correlation matrix according to Nyquist criteria. The realized simulations and real test data show that the proposed method converges to signals' frequencies faster than the classical music algorithm and gives accurate results even under high noise.

关键词： Haar transform music algorithm Frequency estimation

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SS-Bmusic algorithm for Space-time 2D signal model 6

SS-BMUSIC algorithm for Space-time 2D signal model

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6th International Conference on Mechanical and Electronics Engineering (ICMEE)

作者： Jun, Yang Feng, Qi Acad Equipment Beijing Beijing Provinc Peoples R China PLA Unit 63812 Haikou 63812 Hainan Peoples R China

ISBN: (纸本)9783038352624

This paper presents a beamforming matrix with spatial smoothing effect, and extends it to the space-time 2D signal model, which not only reduces the computational complexity of the space-time 2D music algorithm and improves the coherence resolution capacity, simulation results show that this algorithm has better performance and effectiveness than music itself.

关键词： beamforming matrix space-time signal model music algorithm coherent resolution

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music for Multidimensional Spectral Estimation: Stability and Super-Resolution

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第23期63卷 6395-6406页

作者： Liao, Wenjing Duke Univ Dept Math Durham NC 27708 USA SAMSI Durham NC 27708 USA

This paper presents a performance analysis of the MUltiple SIgnal Classification (music) algorithm applied on dimensional single-snapshot spectral estimation while true frequencies are located on the continuum of a bounded domain. Inspired by the matrix pencil form, we construct a D-fold Hankel matrix from the measurements and exploit its Vandermonde decomposition in the noiseless case. music amounts to identifying a noise subspace, evaluating a noise-space correlation function, and localizing frequencies by searching the smallest local minima of the noise-space correlation function. In the noiseless case, (2s)(D) measurements guarantee an exact reconstruction by music as the noise-space correlation function vanishes exactly at true frequencies. When noise exists, we provide an explicit estimate on the perturbation of the noise-space correlation function in terms of noise level, dimension, the minimum separation among frequencies, the maximum and minimum amplitudes while frequencies are separated by 2 Rayleigh Length (RL) at each direction. As a by-product the maximum and minimum non-zero singular values of the multidimensional Vandermonde matrix whose nodes are on the unit sphere are estimated under a gap condition of the nodes. Under the 2-RL separation condition, if noise is i.i.d. Gaussian, we show that perturbation of the noise-space correlation function decays like root log(#(N))/#(N) as the sample size #(N) increases. When the separation among frequencies drops below 2 RL, our numerical experiments show that the noise tolerance of music obeys a power law with the minimum separation of frequencies.

关键词： Multidimensional spectral estimation music algorithm singular values of the multidimensional Vandermonde matrix stability super-resolution

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Statistical performance of music-like algorithms in resolving noncircular sources

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第9期56卷 4317-4329页

作者： Abeida, Habti Delmas, Jean-Pierre Inst TELECOM SudParis CNRS Dept CITI UMR 5157 F-91011 Evry France

This paper addresses the resolution of the conventional and noncircular music algorithms for arbitrary circular and noncircular second-order distributions of two uncorrelated closely spaced transmitters observed by an arbitrary array. An explicit closed-form expression of the mean null spectrum of the conventional and noncircular music algorithms is derived using an analysis based on perturbations of the noise projector instead of those of the eigenvectors. Based on these results, theoretical and approximate interpretable closed-form expressions of the threshold array signal-to-noise ratios (ASNR) at which these two algorithms are able to resolve two closely spaced transmitters along the Cox and the Sharman and Durrani criteria are given. It is proved that the threshold ASNRs given by the conventional music algorithm do not depend on the distribution of the sources including their noncircularity, in contrast to the noncircular music algorithm for which they are very sensitive to the noncircularity phase separation of the sources. This threshold ASNR given by the noncircular music algorithm is proven to be comfortably lower than that given by the conventional music algorithm except for weak phase separations of the sources for which the resolving powers of these two algorithms are very close. Finally, these results are analyzed through several illustrations and Monte Carlo simulations.

关键词： circular and noncircular signal direction of arrival (DOA) music algorithm threshold of resolution

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Bias analysis of music in the presence of mutual coupling

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IET SIGNAL PROCESSING 2009年第1期3卷 74-84页

作者： Liu, Z. M. Huang, Z. T. Zhou, Y. Y. Natl Univ Def Technol China Dept Elect Sci & Engn Changsha 410073 Hunan Peoples R China

The effect of mutual coupling in antenna elements heavily deteriorates the performance of existing array-based bearing-finding methods. Such a bias of music in uniform and general linear arrays is analytically studied and an explicit expression of a relationship between this bias and the effect of mutual coupling together with the direction of the incident source is given. The biases of different arrays are also compared to provide a reference when choosing the right array under the considerable effect of mutual coupling.

关键词： array signal processing covariance matrix uniform linear antenna array covariance matrices antenna element mutual coupling Antenna theory music algorithm bias analysis Signal processing and detection multiple signal classification array-based bearing-finding method electromagnetic coupling Algebra direction-of-arrival estimation antenna theory Antenna arrays linear antenna arrays signal classification

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music算法用于低信噪比下的包络分析

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声学技术 2005年第Z1期24卷 61-62页

作者：王庆福杜栓平机州应用声学研究所海洋声学国家重点实验室杭州310012 机州应用声学研究所海洋声学国家重点实验室杭州310012

　　1引言　　可将水卢目标螺旋桨噪卢建模为一个受窄带调制的宽带随机过程[1],其窄带调制信号(又称包络信号)是本文的分析对象.在声纳信号处理中把通过对接收的宽带信号进行解调(常采用平方律解调)以计算低频解调谱的算法称为DEMON(De... 详细信息

　　1引言　　可将水卢目标螺旋桨噪卢建模为一个受窄带调制的宽带随机过程[1],其窄带调制信号(又称包络信号)是本文的分析对象.在声纳信号处理中把通过对接收的宽带信号进行解调(常采用平方律解调)以计算低频解调谱的算法称为DEMON(Detection of Envelope Modulation On Noise)分析,解调后的低频时域信号称为包络信号,其功率谱称为DEMON谱(又称包络谱).实际情况下,我们所期望的包络信号可能会淹没在噪声中而无法检测出来. 　　……

关键词：算法低信噪比包络分析 music algorithm 包络信号解调谱声纳信号处理宽带随机过程窄带时域信号宽带信号分析对象调制信号低频平方律螺旋桨功率谱包络谱噪声目标

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music for single-snapshot spectral estimation: Stability and super-resolution

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2016年第1期40卷 33-67页

作者： Liao, Wenjing Fannjiang, Albert Stat & Appl Math Sci Inst Durham NC USA Duke Univ Dept Math Durham NC 27706 USA Univ Calif Davis Dept Math Davis CA 95616 USA

This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The single-snapshot measurement data are turned into a Hankel data matrix which admits the Vandermonde decomposition and is suitable for the music algorithm. The music algorithm amounts to finding the null space (the noise space) of the adjoint of the Hankel matrix, forming the noise-space correlation function and identifying the s smallest local minima of the noise-space correlation as the frequency set. In the noise-free case exact reconstruction is guaranteed for any arbitrary set of frequencies as long as the number of measurement data is at least twice the number of distinct frequencies to be recovered. In the presence of noise the stability analysis shows that the perturbation of the noise-space correlation is proportional to the spectral norm of the noise matrix as long as the latter is smaller than the smallest (nonzero) singular value of the noiseless Hankel data matrix. Under the assumption that the true frequencies are separated by at least twice the Rayleigh Length (RL), the stability of the noise-space correlation is proved by means of novel discrete Ingham inequalities which provide bounds on the largest and smallest nonzero singular values of the noiseless Hankel data matrix. The numerical performance of music is tested in comparison with other algorithms such as BLO-OMP and SDP (TV-min). While BLO-OMP is the stablest algorithm for frequencies separated above 4 RL, music becomes the best performing one for frequencies separated between 2 RL and 3 RL. Also, music is more efficient than other methods. music truly shines when the frequency separation drops to 1 RL or below when all other methods fail. Indeed, the resolution length of music decreases to zero as noise decreases to zero as a power law with an exponent smaller than an upper bound established by Donoho. (C) 2014 Elsevier Inc. All rights reserved.

关键词： music algorithm Single-snapshot spectral estimation Stability Super-resolution Discrete Ingham inequalities

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music-type electromagnetic imaging of a collection of small three-dimensional inclusions

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2007年第2期29卷 674-709页

作者： Ammari, Habib Iakovleva, Ekaterina Lesselier, Dominique Perrusson, Gaele CNRS UMR 7641 Ctr Math Appl F-91128 Palaiseau France Ecole Polytech F-91128 Palaiseau France UPS CNRS SUPELEC Lab Signaux & SystDept Rech Electromagnetisme F-91192 Gif Sur Yvette France

In this paper we consider the localization of a collection of small, three-dimensional bounded homogeneous inclusions via time-harmonic electromagnetic means, typically using arrays of electric or magnetic dipole transmitters and receivers with given polarization(s) at some distance from the collection, possibly also lying in the far field. The inclusions, somewhat apart or closely spaced, are buried within a homogeneous medium, and are of arbitrary contrast of permittivity, conductivity, and permeability vis-a-vis this embedding medium. The problem is formulated as an inverse scattering problem for the full Maxwell equations and it involves a robust asymptotic modeling of the multistatic response matrix. No specific application is studied at this stage, but characterization of obstacles in subsoils, nondestructive evaluation of man-made structures, and medical imaging are primary felds of application envisaged. The proposed approach uses a music ( multiple signal classification)-type algorithm, and it yields fast numbering, accurate localization, and estimates of the electromagnetic and geometric parameters ( polarization tensors) of the inclusions. The mathematical machinery is detailed. rst, some specific attention being given to triaxial ellipsoidal inclusions and degenerate spherical shapes ( for the latter known results are retrieved). Then, the viability of this algorithm - which would be easily extended to planarly layered environments by introduction of their Green's functions - is documented by a variety of numerical results from synthetic, noiseless, and severely noisy field data.

关键词： electromagnetic inclusions Maxwell's equations imaging inverse problems music algorithm

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music-type imaging of perfectly conducting cracks in limited-view inverse scattering problems

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APPLIED MATHEMATICS AND COMPUTATION 2014年 240卷 273-280页

作者： Joh, Young-Deuk Kwon, Young Mi Park, Won-Kwang Kookmin Univ Dept Math Seoul 136702 South Korea

Although standard MUltiple Signal Classification (music) algorithm has been considered a promising non-iterative imaging technique for cracks, its application is restricted to the full-view inverse scattering problems. Many experimental results revealed that music can be applied to the imaging of perfectly conducting cracks with small length in limited-view inverse scattering problem. On the other hand, music is not applicable for imaging of extended cracks in limited-view problems but the reason behind this restricted application has not been theoretically investigated. This gave an impetus for this study to attempt to identify the structure of music-type algorithm that appears in the limited-view inverse scattering problems by establishing a relationship between music and Bessel functions of integer order of the first kind. Some numerical experiments are illustrated to support the identified structure of music. (C) 2014 Elsevier Inc. All rights reserved.

关键词： music algorithm Perfectly conducting cracks Limited-view inverse scattering Bessel functions Numerical experiments

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