A low complexity method for wideband direction finding based on sparse representation is proposed, which combines the rotational signal subspace (RSS) with weighted subspace fitting (WSF) to improve the performance of...
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ISBN:
(纸本)9781467388238
A low complexity method for wideband direction finding based on sparse representation is proposed, which combines the rotational signal subspace (RSS) with weighted subspace fitting (WSF) to improve the performance of DOA estimation. Exploiting the result of the focusing operation, the covariance matrix at the focusing frequency can be obtained and used as the data for sparse recovery to get wideband DOA estimates. The WSF is employed to reduce the sensitivity to the noise and the regularization parameter is given by the asymptotic distribution of the WSF criterion. Simulations are provided to prove the efficiency and performance of the proposed method.
We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the...
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ISBN:
(纸本)9789082797039
We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the direct (rather involved) Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, we follow Paulraj and Kailath's classical approach in exploiting the special (Toeplitz) structure of the observed covariance. However, we offer a substantial improvement over Paulraj and Kailath's Least Squares (LS) estimate by using asymptotic approximations in order to obtain simple, (quasi-)linear Weighted LS (WLS) estimates of the sensors' gains and phases offsets with asymptotically optimal weighting. As we show in simulation experiments, our WLS estimates exhibit near-optimal performance, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors, w.r.t. the corresponding ordinary LS estimates. We also briefly explain how the methodology derived in this work may be utilized in order to obtain (by certain modifications) the asymptotically optimal ML estimates w.r.t. the raw data via a (quasi)-linear WLS estimate.
Objective. In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in whic...
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Objective. In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain. Approach. It defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.
A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matr...
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A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matrix has to be (i) Positive Definite, (ii) Hermitian, (iii) Toeplitz, and (iv) its noise-subspace eigen-values have to be equal. Existing coarray autocorrelation matrix estimates satisfy a subset of the above conditions. In this work, we propose an optimization framework which offers a novel estimate satisfying all four conditions: we propose to iteratively solve a sequence of distinct structure-optimization problems and show that, upon convergence, we provably obtain a single estimate satisfying (i)-(iv). Numerical studies illustrate that the proposed estimate outperforms standard counterparts, both in autocorrelation matrix estimation error and Direction-of-Arrival estimation. (C) 2021 Published by Elsevier B.V.
Signal parameter estimation from measurements on a sensorarray is an important problem in many engineering applications. Recently, there has been a large interest in parametric methods in the literature. An important...
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Signal parameter estimation from measurements on a sensorarray is an important problem in many engineering applications. Recently, there has been a large interest in parametric methods in the literature. An important assumption in essentially all of these methods is that the spatial correlation structure of the background noise (i.e., the correlation from sensor to sensor) is known to within a multiplicative scalar. In practice, this is often achieved by measuring the array соvariance when no signals are present. This results unavoidably in errors in the noise model. In this paper, the effect of such model errors on parametric methods are examined. The methods in question are the deterministic and stochastic maximum likelihood methods, and the so-called weighted subspace fitting technique. First-order expressions for the mean square etror (MSE) of the parameter estimates are derived. The spatial noise correlation structures that lead to maximum performance loss are identified under different assumptions. In case of high signal to noise ratio (SNR), it is found that the MSE can be increased by a factor m , where m is the number of sensors in the array, as compared to spatially white noise. Simple expressions comparing the asymptotic (for large amounts of data) bias, resulting from a small noise covariance perturbation, with the asymptotic standard deviation are derived. Numerical examples are included to illustrate the obtained results.
We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. W...
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We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. We separate the contributions to the MSE into a bias part caused by modelling errors and a variance part caused by finite (yet large) sample effects. The bias is simply evaluated by comparing the limiting estimate (corresponding to an infinite number of snapshots) with the true DOA’s (which are known to the analyzer). To simplify the variance derivation we assume that the snapshots are complex i.i.d. Gaussian vectors and that the largest eigenvalues of their covariance matrix are distinct; but, otherwise, make none of the assumptions commonly used in previous analyses; in particular we do not constrain the snapshots to satisfy any model equation. The theoretical results obtained are illustrated by means of numerical examples using various modelling errors.
The direction of arrival (DOA) estimation problem is formulated in a compressive sensing (CS) framework, and an extended array aperture is presented to increase the number of degrees of freedom of the array. The ordin...
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The direction of arrival (DOA) estimation problem is formulated in a compressive sensing (CS) framework, and an extended array aperture is presented to increase the number of degrees of freedom of the array. The ordinary least square adaptable least absolute shrinkage and selection operator (OLS A-LASSO) is applied for the first time for DOA estimation. Furthermore, a new LASSO algorithm, the minimum variance distortionless response (MVDR) A-LASSO, which solves the DOA problem in the CS framework, is presented. The proposed algorithm does not depend on the singular value decomposition nor on the orthogonality of the signal and the noise subspaces. Hence, the DOA estimation can be done without a priori knowledge of the number of sources. The proposed algorithm can estimate up to ((M2 2) /2 + M 1) /2 sources using M sensors without any constraints or assumptions about the nature of the signal sources. Furthermore, the proposed algorithm exhibits performance that is superior compared to that of the classical DOA estimation methods, especially for low signal to noise ratios (SNR), spatially-closed sources and coherent scenarios.
We present the asymptotic performance analysis of the interpolated root-MUSIC and manifold separation (MS) techniques for direction-of-arrival (DOA) estimation in arbitrary non-uniform sensorarrays. Our analysis take...
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We present the asymptotic performance analysis of the interpolated root-MUSIC and manifold separation (MS) techniques for direction-of-arrival (DOA) estimation in arbitrary non-uniform sensorarrays. Our analysis takes into account both the effects of a limited number of snapshots and manifold approximation errors.
The problem of estimating the regularization parameter for source localization in sparse-regularization framework is considered in this paper. We employ the distribution about every entry of the square of the Frobeniu...
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ISBN:
(纸本)9781424484447
The problem of estimating the regularization parameter for source localization in sparse-regularization framework is considered in this paper. We employ the distribution about every entry of the square of the Frobenius norm of noise to obtain a larger and more appropriate regularization parameter. The paper analyzes the reason that we can not simply set it equal to the square of the Frobenius norm of noise and presents the estimation in two practical cases: one works without taking singular value decomposition (SVD) of sensor outputs;the other works after that pretreatment for large data quantity. The simulation results demonstrate that the proposed method has many advantages, including enhancing resolution, effectively suppressing spurious peaks, improving robustness to noise, as well as increasing the number of resolvable sources.
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