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IEEE Workshop on Statistical Signal processing (SSP)

作者： Vo, Ba Ngu Vo, Ba Tuong Curtin Univ Dept Elect & Comp Engn Perth WA Australia

ISBN: (纸本)9781479949755

A new unified mathematical framework for sensor array processing is proposed. The proposed framework combines Bayesian estimation with stochastic geometry to accommodate prior information, uncertainty in array parameters, and unknown and stochastically time-varying number of nonstationary sources. A system model for a common signal setting is constructed to demonstrate the proposed framework.

关键词： sensor array processing Bayesian estimation random sets

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Self-Calibration of Acoustic Scalar and Vector sensor arrays

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IEEE TRANSACTIONS ON SIGNAL processing 2023年 71卷 61-75页

作者： Ramamohan, Krishnaprasad Nambur Chepuri, Sundeep Prabhakar Comesana, Daniel Fernandez Leus, Geert Microflown NL-6824 BV Arnhem Netherlands Indian Inst Sci Dept Elect Commun Engn Bengaluru 560012 Karnataka India Delft Univ Technol Fac EEMCS NL-2628 CD Delft Netherlands

In this work, we consider the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensor arrays. Unlike many previous iterative approaches, we propose solvers that can be readily used for both linear and non-linear arrays for jointly estimating the sensor gain, phase errors, and the source DOAs. We derive these algorithms for both the conventional element-space and covariance data models. We focus on sparse and regular arrays formed using scalar sensors as well as vector sensors. The developed algorithms are obtained by transforming the underlying non-linear calibration model into a linear model, and subsequently by using convex relaxation techniques to estimate the unknown parameters. We also derive identifiability conditions for the existence of a unique solution to the self-calibration problem. To demonstrate the effectiveness of the developed techniques, numerical experiments, and comparisons to the state-of-the-art methods are provided. Finally, the results from an experiment that was performed in an anechoic chamber using an acoustic vector sensor array are presented to demonstrate the usefulness of the proposed self-calibration techniques.

关键词： Acoustics Measurement uncertainty Acoustic vector sensors direction-of-arrival estimation self-calibration sensor array processing

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Effect of Approximate Planar Wavefront on Far-Field Direction Finding

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IEEE COMMUNICATIONS LETTERS 2022年第3期26卷 657-661页

作者： He, Jin Shu, Ting Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai Key Lab Intelligent Sensing & Recognit Shanghai 200240 Peoples R China

Existing sensor array direction-finding algorithms in the open literature simplify the far-field source wavefront as exactly planar in order to facilitate the algorithmic development. In fact, since the wavefront of a point emitter is necessarily spherical, this planar wavefront assumption should actually be approximate, especially for large-scale arrays. Mismatch between the actual and approximate propagation models would introduce a non-random bias on the performance of the direction-finding algorithms. This non-random bias is inevitable due to the mismatch between the algorithm's presumptions and the data it actually processes. This work derives the mathematical expression of this non-random bias, along with several qualitative analyses. The analysis is carried out using the Taylor-series expansion. Also, the effect of the model mismatch on direction-finding algorithms is evaluated numerically.

关键词： Data models Mathematical models Multiple signal classification Approximation algorithms Numerical models sensor arrays Estimation Direction-finding sensor array processing model mismatch spherical wavefront planar wavefront

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Asymptotically Optimal Blind Calibration of Uniform Linear sensor arrays for Narrowband Gaussian Signals

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IEEE TRANSACTIONS ON SIGNAL processing 2020年 68卷 5322-5333页

作者： Weiss, Amir Yeredor, Arie Weizmann Inst Sci Fac Math & Comp Sci Dept Comp Sci & Appl Math IL-7610001 Rehovot Israel Tel Aviv Univ Fac Engn Sch Elect Engn IL-69978 Tel Aviv Israel

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cramer-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task.

关键词： sensor array processing direction-of-arrival gain estimation phase estimation self calibration weighted least squares maximum likelihood Cramer-Rao lower bound

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Structured autocorrelation matrix estimation for coprime arrays

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SIGNAL processing 2021年 183卷 107987-107987页

作者： Chachlakis, Dimitris G. Markopoulos, Panos P. Rochester Inst Technol Dept Elect & Microelect Engn Rochester NY 14623 USA

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.

关键词： sensor array processing Coprime arrays Coarray Autocorrelation estimation

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Adaptive filtering algorithm for direction-of-arrival (DOA) estimation with small snapshots

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DIGITAL SIGNAL processing 2019年 94卷 84-95页

作者： Liu, Beiyi Gui, Guan Matsushita, Shin-ya Xu, Li Akita Prefectural Univ Dept Intelligent Mechatron Akita 0150055 Japan Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing 210003 Jiangsu Peoples R China

The direction-of-arrival (DOA) estimation problem with a few noisy snapshots can be formulated as a problem of finding a joint sparse representation of multiple measurement vectors (MMV), and some algorithms based on compressive sensing (CS), such as the joint l(0) approximation DOA (JLZA-DOA) and Multiple Snapshot Matching Pursuit Direction of Arrival (MSMPDOA) algorithms, have recently been proposed for solving this problem. Compared with the conventional DOA methods, the CS-based methods can achieve super-resolution by using only small number of snapshots, without the necessity of an accurate initialization, with small sensitivity to the correlation of the source signals. However, these CS-based algorithms usually do not work well in low signal-noise ratio (SNR) environment. In addition, the increased number of sensors in massive multiple-input-multiple-output (MIMO) systems lead to a huge matrix, and the matrix inversion operation in each iteration of the CS-based algorithm results in a relatively high computational cost. The purpose of this paper is to propose a novel adaptive filtering algorithm, i.e., the l(2,0)-least mean square (l(2.0)-LMS) algorithm, which can be viewed as a generalization of the l(0)-LMS algorithm for single measurement vector (SMV) problem. Our proposed algorithm incorporates a mixed norm (l(2)(,0)-norm) to treat the joint sparsity and inherits the robustness against noise and the low complexity of the l(0)-LMS algorithm, and can thus work well for massive MIMO systems. Numerical experiments demonstrate that the proposed algorithm can achieve much better estimation performance with a lower computational cost than the existing ones. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Direction-of-arrival estimation sensor array processing Sparse signal representation Adaptive filter Mixed-norm Massive MIMO system

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Blind Gain and Phase Calibration via Sparse Spectral Methods

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第5期65卷 3097-3123页

作者： Li, Yanjun Lee, Kiryung Bresler, Yoram Univ Illinois Urbana IL 61801 USA Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some cases, sparse structure in the unknown signal alleviates the illposedness of BGPC. Recently, there has been renewed interest in solutions to BGPC with careful analysis of error bounds. In this paper, we formulate BGPC as an eigenvalue/eigenvector problem and propose to solve it via power iteration, or in the sparsity or joint sparsity case, via truncated power iteration. Under certain assumptions, the unknown gains, phases, and the unknown signal can be recovered simultaneously. Numerical experiments show that power iteration algorithms work not only in the regime predicted by our main results, but also in regimes where theoretical analysis is limited. We also show that our power iteration algorithms for BGPC compare favorably with competing algorithms in adversarial conditions, e.g., with noisy measurement or with a bad initial estimate.

关键词： Auto-calibration greedy algorithm inverse rendering multichannel blind deconvolution nonconvex optimization power method SAR autofocus sensor array processing truncated power iteration

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Blind Calibration of sensor arrays for Narrowband Signals with Asymptotically Optimal Weighting 27

Blind Calibration of Sensor Arrays for Narrowband Signals wi...

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27th European Signal processing Conference (EUSIPCO)

作者： Weiss, Amir Yeredor, Arie Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

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.

关键词： sensor array processing gain estimation phase estimation self-calibration weighted least squares

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Anti-jamming DOA Estimation Based on Compressive Sensing via Blocking Matrix 23

Anti-jamming DOA Estimation Based on Compressive Sensing via...

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23rd IEEE International Conference on Digital Signal processing (DSP)

作者： Liu, Beiyi Gui, Guan Matsushita, Shin-ya Xu, Li Akita Prefectural Univ Dept Elect & Informat Syst Akita 0150055 Japan Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing 210003 Jiangsu Peoples R China

ISBN: (纸本)9781538668122;9781538668115

Disturbed by strong jamming, the compressive sensing (CS) based direction-of-arrival (DOA) estimation methods in colocated multiple-input-multiple-output (MIMO) radars are distorted easily. In this paper, a CS based anti-jamming DOA estimation method employing a blocking matrix is proposed. In the new DOA estimation method, the QR decomposition algorithm is used to construct a blocking matrix which is orthogonal to the steering vector of jamming. After the preprocessing with the blocking matrix, the jamming component is removed from the received snapshots. Then, the DOA estimation problem with the blocking matrix is formulated as a CS sparse recovery problem, and CS algorithms are used to solve it. Computer simulations show that the proposed method performs than the traditional methods.

关键词： compressive sensing direction of arrival (DOA) sensor array processing QR decomposition

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Identifiability in Bilinear Inverse Problems With Applications to Subspace or Sparsity-Constrained Blind Gain and Phase Calibration

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第2期63卷 822-842页

作者： Li, Yanjun Lee, Kiryung Bresler, Yoram Univ Illinois Dept Elect & Comp Engn Coordinated Sci Lab Champaign IL 61801 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, the properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some success in practice. However, there are few results on uniqueness in BIPs. For most BIPs, the fundamental question of under what condition the problem admits a unique solution is yet to be answered. For example, blind gain and phase calibration (BGPC) is a structured BIP, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution (MBD). It is interesting to study the uniqueness of such problems. In this paper, we define identifiability of a BIP up to a group of transformations. We derive necessary and sufficient conditions for such identifiability, i.e., the conditions under which the solutions can be uniquely determined up to the transformation group. These conditions take the form of dividing the identifiability of the pair of unknown variables into the individual identifiability of each variable. Although verifying these individual conditions requires problem-specific procedures, this framework is universally applicable to all BIPs. Applying these results to BGPC, we derive sufficient conditions for unique recovery under several scenarios, including subspace, joint sparsity, and sparsity models. For BGPC with joint sparsity or sparsity constraints, we develop a procedure to compute the transformation groups corresponding to inherent ambiguities. We also give necessary conditions in the form of tight lower bounds on sample complexities, and demonstrate the tightness of these bounds by numerical experim

关键词： Ambiguity blind gain and phase calibration equivalence class inverse rendering multichannel blind deconvolution SAR autofocus sensor array processing transformation group uniqueness

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