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2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Bu, Yinyan Yu, Jiajie Pal, Piya Department of ECE University of California La Jolla San Diego United States

ISBN: (纸本)9798350368741

Sparse linear arrays (SLAs) have gained significant attention for automotive radar due to their enhanced aperture and angular resolution. A promising approach to Direction-of-Arrival (DOA) estimation with only a single temporal snapshot and SLAs is to interpolate the missing measurements by solving a low-rank Hankel matrix completion problem. Sampling geometry plays an important role in matrix completion, and random sampling techniques primarily provide non-uniform recovery guarantees, which can be undesirable. Using the unique geometry of nested-type SLAs, we formulate the Hankel matrix completion problem as a non-convex prediction problem which utilizes the latent structures of a low-rank Hankel matrix in order to reduce the number of unknowns. It also provides uniform recovery guarantees (provably in the absence of noise). Our approach can be interpreted as a self-supervised Untrained Neural Network (UNN) which utilizes the inner uniform linear array (ULA) of a nested array to perform prediction, and the outer array to curb error propagation. Our work establishes the first connection between array interpolation and untrained machine learning paradigms. © 2025 IEEE.

关键词： array interpolation Direction-of-arrival Estimation Matrix Completion Sparse Linear array Untrained Networks

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array interpolation and DOA MSE reduction

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2005年第12期53卷 4464-4471页

作者： Hyberg, P Jansson, M Ottersten, B FOI Swedish Def Res Agcy SE-17290 Stockholm Sweden KTH Royal Inst Technol Dept Signals Sensors & Syst SE-10044 Stockholm Sweden

interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. In an earlier companion paper [21], a first-order condition for zero DOA bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias-minimizing theory is now extended to minimize not only bias, but also to consider finite sample effects due to noise and reduce the DOA mean-square error (MSE). An analytical first-order expression for mapped DOA MSE is derived, and a design algorithm for the transformation matrix that minimizes this MSE is proposed. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator criterion function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE,improvements in relevant scenarios, but also a more robust preprocessing for low signal-to-noise ratios (SNRs) as compared with the pure bias-minimizing design developed in the previous paper.

关键词： array interpolation array mapping array preprocessing bias reduction direction-of-arrival (DOA) mean-square-error (MSE) reduction

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array interpolation and bias reduction

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2004年第10期52卷 2711-2720页

作者： Hyberg, P Jansson, M Ottersten, B Swedish Def Res Agcy FOI Stockholm Sweden Royal Inst Technol KTH Dept Signals Sensors & Syst Stockholm Sweden

interpolation (mapping) of data from a given antenna array onto the output of a virtual array of more suitable configuration is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. Conditions for preserving DOA error variance under such mappings have been derived by several authors. However, in many cases, such as omnidirectional signal surveillance over multiple octaves, systematic mapping errors will dominate over noise effects and cause significant bias in the DOA estimates. To prevent mapping errors from unduly affecting the DOA estimates, this paper uses a geometrical interpretation of a Taylor series expansion of the DOA estimator criterion function to derive an alternative design of the mapping matrix. Verifying simulations show significant bias reduction in the DOA estimates compared with previous designs. The key feature of the proposed design is that it takes into account the orthogonality between the manifold mapping errors and certain gradients of the estimator criterion function. With the new design, mapping of narrowband signals between dissimilar array geometries over wide sectors and large frequency ranges becomes feasible.

关键词： array interpolation array mapping array preprocessing bias reduction

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array interpolation for improved SAR imaging

Array interpolation for improved SAR imaging

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Conference on Radar Processing, Technology, and Applications III

作者： Barthelemy, AC Willett, PK Northrop Grumman Norden Syst Inc Norwalk CT 06856 USA

ISBN: (纸本)0819429171

Synthetic Aperture Radar utilizes the motion of the platform on which it is mounted to realize a virtual array antenna. The illumination of a specific patch of ground and the sampling of the radar returns over time and space result in a non-uniform collection space. Motion compensation corrects for certain platform motions, but still may result in a polar collection space with non-uniformly spaced samples. To employ the fast Fourier transform to form an image from this phase history data, the polar raster data must be resampled onto a rectangular grid bq means of polar reformatting. However, non-uniformity errors present in the polar grid will propagate to the rectangular grid, and result in SAR image defocusing. This paper describes a technique that may be used to interpolate the non-uniformly collected radar samples to a uniform polar space, thereby improving the efficacy of the polar-to-rectangular resampling process. This work presents new ideas for polar grid design by demonstrating that certain virtual grids are better for interpolation than others. A measure of the relative interpolation error is established. The step-by-step approach of polar grid interpolation is explained.

关键词： Synthetic Aperture Radar motion compensation array interpolation polar reformatting

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Transmit array interpolation for DOA Estimation via Tensor Decomposition in 2-D MIMO Radar

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第19期65卷 5225-5239页

作者： Cao, Ming-Yang Vorobyov, Sergiy A. Hassanien, Aboulnasr Aalto Univ Dept Signal Proc & Acoust Espoo 02150 Finland Harbin Inst Technol Dept Elect & Informat Engn Harbin 15001 Heilongjiang Peoples R China Wright State Univ Dept Elect Engn Dayton OH 45431 USA

In this paper, we propose a two-dimensional joint transmit array interpolation and beamspace design for planar array mono-static multiple-input-multiple-output radar for direction-of-arrival (DOA) estimation via tensor modeling. Our underlying idea is to map the transmit array to a desired array and suppress the transmit power outside the spatial sector of interest. In doing so, the signal-to-noise ratio is improved at the receive array. Then, we fold the received data along each dimension into a tensorial structure and apply tensor-basedmethods to obtain DOA estimates. In addition, we derive a closed-form expression for DOA estimation bias caused by interpolation errors and argue for using a specially designed look-up table to compensate for the bias. The corresponding Cramer-Rao bound (CRB) is also derived. Simulation results are provided to show the performance of the proposed method and compare its performance to CRB.

关键词： 2D MIMO radar array interpolation direction-of-arrival estimation tensor decomposition

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Robust Nonlinear array interpolation for Direction of Arrival Estimation of Highly Correlated Signals

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SIGNAL PROCESSING 2018年 144卷 19-28页

作者： Marinho, Marco A. M. Antreich, Felix Caizzone, Stefano da Costa, Joao Paulo C. L. Vinel, Alexey de Freitas, Edison Pignaton Univ Brasilia UnB Dept Elect Engn ENE Brasilia DF Brazil Halmstad Univ Sch Informat Technol Halmstad Sweden Fed Univ Ceara UFC Dept Teleinformat Engn Fortaleza Ceara Brazil German Aerosp Ctr DLR Inst Commun & Nav Wessling Germany Fed Univ Rio Grande Sul UFRGS Informat Inst Porto Alegre RS Brazil

Important signal processing techniques need that the response of the different elements of a sensor array have specific characteristics. For physical systems this often is not achievable as the array elements' responses are affected by mutual coupling or other effects. In such cases, it is necessary to apply array interpolation to allow the application of ESPRIT, Forward Backward Averaging (FBA), and Spatial Smoothing (SPS). array interpolation provides a model or transformation between the true and a desired array response. If the true response of the array becomes more distorted with respect to the desired one or the considered region of the field of view of the array increases, nonlinear approaches become necessary. This work presents two novel methods for sector discretization. An Unscented Transform (UT) based method and a principal component analysis (PCA) based method are discussed. Additionally, two novel nonlinear interpolation methods are developed based on the nonlinear regression schemes Multivariate Adaptive Regression Splines (MARS) and Generalized Regression Neural Networks (GRNNs). These schemes are extended and applied to the array interpolation problem. The performance of the proposed methods is examined using simulated and measured array responses of a physical system used for research on mutual coupling in antenna arrays. (C) 2017 The Author(s). Published by Elsevier B.V.

关键词： array interpolation array mapping Antenna arrays Direction of arrival estimation

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Robust array interpolation using second-order cone programming

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IEEE SIGNAL PROCESSING LETTERS 2002年第1期9卷 8-11页

作者： Pesavento, M Gershman, AB Luo, ZQ McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4K1 Canada

We study Friedlander's array interpolation technique, whose main shortcoming in multisource scenarios is that it does not provide sufficient robustness against sources arriving outside specified interpolation sectors. In this letter, we develop a new robust interpolation approach by minimizing the interpolation error inside the sectors of interest while setting multiple "stopband" constraints outside these sectors to prevent performance degradation effects caused by out-of-sector sources. Computationally efficient convex formulations of the robust interpolation matrix design problem using second-order cone programming are derived.

关键词： array interpolation direction finding second-order cone programming

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Off-Grid Direction-of-Arrival Estimation Using Coprime array interpolation

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IEEE SIGNAL PROCESSING LETTERS 2018年第11期25卷 1710-1714页

作者： Zhou, Chengwei Gu, Yujie Shi, Zhiguo Zhang, Yimin D. Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Temple Univ Dept Elect & Comp Engn Philadelphia PA 19122 USA

In this letter, we propose a coprime array interpolation approach to provide an off-grid direction-of-arrival (DOA) estimation. Through array interpolation, a uniform linear array (ULA) with the same aperture is generated from the deterministic non-uniform coprime array. Taking the observed correlations calculated from the signals received at the coprime array, a gridless convex optimization problem is formulated to recover all the rows and columns of the unknown correlation matrix entries corresponding to the interpolated sensors. The optimized Hermitian positive semidefinite Toeplitz matrix functions as the covariance matrix of the interpolated ULA, which enables to resolve off-grid sources. Simulation results demonstrate that the proposed array interpolation-based DOA estimation algorithm achieves improved performance as compared to existing coarray-based DOA estimation algorithms in terms of the number of achievable degrees-of-freedom and estimation accuracy.

关键词： array interpolation coprime array direction-of-arrival estimation matrix recovery off-grid

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A note on most favorable array geometries for DOA estimation and array interpolation

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IEEE SIGNAL PROCESSING LETTERS 1997年第8期4卷 232-235页

作者： Gershman, AB Bohme, JF Signal Theory Group Department of Electrical Engineering Ruhr University of Bochum Bochum Germany

Given an n-element linear array with the fixed positions x(1) and x(n) of the leftmost and rightmost array sensors, it is shown that the stochastic Cramer-Rao bound (CRB) and MUSIC performance depend on positions of the remaining n-2 sensors within the interval [x(1), x(n)]. The asymptotic performance of interpolated array approach shows similar dependence. The most favorable geometries are unrealizable for q < n-1 because the array sensors tend to form q+1 point clusters, where q is the number of sources. An interesting consequence of these facts is that for certain realizable nonuniform linear array (NULA) geometries, interpolated root-MUSIC with virtual uniform linear array (ULA) of the length x(n)-x(1) has better asymptotic performance than conventional root-MUSIC applied to the real ULA of the same length.

关键词： array interpolation DOA estimation root-MUSIC

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A SIGNAL ADAPTIVE array interpolation APPROACH WITH REDUCED TRANSFORMATION BIAS FOR DOA ESTIMATION OF HIGHLY CORRELATED SIGNALS

A SIGNAL ADAPTIVE ARRAY INTERPOLATION APPROACH WITH REDUCED ...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Marinho, Marco A. M. Antreich, Felix da Costa, Joao Paulo C. L. Nossek, Josef A. German Aerosp Ctr DLR Inst Commun & Nav D-82234 Wessling Germany

ISBN: (纸本)9781479928934

Sensor arrays with Vandermonde or centro-hermitian responses cannot always be constructed. However, such array response structure can be achieved by means of a mapping which transforms the real array response to an array response with the desired properties by applying array interpolation algorithms. In this work a low-complexity, multi-sector, signal adaptive array interpolation approach that achieves low transformation bias in the presence of highly correlated signals is presented. Estimation of Signal Parameters via Rotational Invariance (ESPRIT) algorithm with Forward Backward Average (FBA) and Spatial Smoothing (SPS) as well as model order estimation is applied after array interpolation in conjunction with the Vandermonde Invariance Transformation (VIT) to obtain precise high resolution estimates in closed form. A set of numerical simulations show that the proposed approach provides precise estimates for arbitrary array responses in highly correlated signal signal environments.

关键词： array interpolation array Mapping Antenna arrays Vandermonde Invariance Transformation

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