101 research outputs found

    Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review

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    Direction of arrival (DOA) estimation from the perspective of sparse signal representation has attracted tremendous attention in past years, where the underlying spatial sparsity reconstruction problem is linked to the compressive sensing (CS) framework. Although this is an area with ongoing intensive research and new methods and results are reported regularly, it is time to have a review about the basic approaches and methods for CS-based DOA estimation, in particular for the underdetermined case. We start from the basic time-domain CSbased formulation for narrowband arrays and then move to the case for recently developed methods for sparse arrays based on the co-array concept. After introducing two specifically designed structures (the two-level nested array and the co-prime array) for optimizing the virtual sensors corresponding to the difference coarray, this CS-based DOA estimation approach is extended to the wideband case by employing the group sparsity concept, where a much larger physical aperture can be achieved by allowing a larger unit inter-element spacing and therefore leading to further improved performance. Finally, a specifically designed ULA structure with associated CS-based underdetermined DOA estimation is presented to exploit the difference co-array concept in the spatio-spectral domain, leading to a significant increase in DOFs. Representative simulation results for typical narrowband and wideband scenarios are provided to demonstrate their performance

    Alternating projections gridless covariance-based estimation for DOA

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    We present a gridless sparse iterative covariance-based estimation method based on alternating projections for direction-of-arrival (DOA) estimation. The gridless DOA estimation is formulated in the reconstruction of Toeplitz-structured low rank matrix, and is solved efficiently with alternating projections. The method improves resolution by achieving sparsity, deals with single-snapshot data and coherent arrivals, and, with co-prime arrays, estimates more DOAs than the number of sensors. We evaluate the proposed method using simulation results focusing on co-prime arrays.Comment: 5 pages, accepted by (ICASSP 2021) 2021 IEEE International Conference on Acoustics, Speech, and Signal Processin

    Low complexity DOA estimation for wideband off-grid sources based on re-focused compressive sensing with dynamic dictionary

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    Under the compressive sensing (CS) framework, a novel focusing based direction of arrival (DOA) estimation method is first proposed for wideband off-grid sources, and by avoiding the application of group sparsity (GS) across frequencies of interest, significant complexity reduction is achieved with its computational complexity close to that of solving a single frequency based direction finding problem. To further improve the performance by alleviating both the off-grid approximation errors and the focusing errors which are even worse for the off-grid case, a dynamic dictionary based re-focused off-grid DOA estimation method is developed with the number of extremely sparse grids involved in estimation refined to the number of detected sources, and thus the complexity is still very low due to the limited increased complexity introduced by iterations, while improved performance can be achieved compared with those fixed dictionary based off-grid methods

    Discrete and Continuous Sparse Recovery Methods and Their Applications

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    Low dimensional signal processing has drawn an increasingly broad amount of attention in the past decade, because prior information about a low-dimensional space can be exploited to aid in the recovery of the signal of interest. Among all the different forms of low di- mensionality, in this dissertation we focus on the synthesis and analysis models of sparse recovery. This dissertation comprises two major topics. For the first topic, we discuss the synthesis model of sparse recovery and consider the dictionary mismatches in the model. We further introduce a continuous sparse recovery to eliminate the existing off-grid mismatches for DOA estimation. In the second topic, we focus on the analysis model, with an emphasis on efficient algorithms and performance analysis. In considering the sparse recovery method with structured dictionary mismatches for the synthesis model, we exploit the joint sparsity between the mismatch parameters and original sparse signal. We demonstrate that by exploiting this information, we can obtain a robust reconstruction under mild conditions on the sensing matrix. This model is very useful for radar and passive array applications. We propose several efficient algorithms to solve the joint sparse recovery problem. Using numerical examples, we demonstrate that our proposed algorithms outperform several methods in the literature. We further extend the mismatch model to a continuous sparse model, using the mathematical theory of super resolution. Statistical analysis shows the robustness of the proposed algorithm. A number-detection algorithm is also proposed for the co-prime arrays. By using numerical examples, we show that continuous sparse recovery further improves the DOA estimation accuracy, over both the joint sparse method and also MUSIC with spatial smoothing. In the second topic, we visit the corresponding analysis model of sparse recovery. Instead of assuming a sparse decomposition of the original signal, the analysis model focuses on the existence of a linear transformation which can make the original signal sparse. In this work we use a monotone version of the fast iterative shrinkage- thresholding algorithm (MFISTA) to yield efficient algorithms to solve the sparse recovery. We examine two widely used relaxation techniques, namely smoothing and decomposition, to relax the optimization. We show that although these two techniques are equivalent in their objective functions, the smoothing technique converges faster than the decomposition technique. We also compute the performance guarantee for the analysis model when a LASSO type of reconstruction is performed. By using numerical examples, we are able to show that the proposed algorithm is more efficient than other state of the art algorithms

    Statistical Performance Analysis of Sparse Linear Arrays

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    Direction-of-arrival (DOA) estimation remains an important topic in array signal processing. With uniform linear arrays (ULAs), traditional subspace-based methods can resolve only up to M-1 sources using M sensors. On the other hand, by exploiting their so-called difference coarray model, sparse linear arrays, such as co-prime and nested arrays, can resolve up to O(M^2) sources using only O(M) sensors. Various new sparse linear array geometries were proposed and many direction-finding algorithms were developed based on sparse linear arrays. However, the statistical performance of such arrays has not been analytically conducted. In this dissertation, we (i) study the asymptotic performance of the MUtiple SIgnal Classification (MUSIC) algorithm utilizing sparse linear arrays, (ii) derive and analyze performance bounds for sparse linear arrays, and (iii) investigate the robustness of sparse linear arrays in the presence of array imperfections. Based on our analytical results, we also propose robust direction-finding algorithms for use when data are missing. We begin by analyzing the performance of two commonly used coarray-based MUSIC direction estimators. Because the coarray model is used, classical derivations no longer apply. By using an alternative eigenvector perturbation analysis approach, we derive a closed-form expression of the asymptotic mean-squared error (MSE) of both estimators. Our expression is computationally efficient compared with the alternative of Monte Carlo simulations. Using this expression, we show that when the source number exceeds the sensor number, the MSE remains strictly positive as the signal-to-noise ratio (SNR) approaches infinity. This finding theoretically explains the unusual saturation behavior of coarray-based MUSIC estimators that had been observed in previous studies. We next derive and analyze the Cramér-Rao bound (CRB) for general sparse linear arrays under the assumption that the sources are uncorrelated. We show that, unlike the classical stochastic CRB, our CRB is applicable even if there are more sources than the number of sensors. We also show that, in such a case, this CRB remains strictly positive definite as the SNR approaches infinity. This unusual behavior imposes a strict lower bound on the variance of unbiased DOA estimators in the underdetermined case. We establish the connection between our CRB and the classical stochastic CRB and show that they are asymptotically equal when the sources are uncorrelated and the SNR is sufficiently high. We investigate the behavior of our CRB for co-prime and nested arrays with a large number of sensors, characterizing the trade-off between the number of spatial samples and the number of temporal samples. Our analytical results on the CRB will benefit future research on optimal sparse array designs. We further analyze the performance of sparse linear arrays by considering sensor location errors. We first introduce the deterministic error model. Based on this model, we derive a closed-form expression of the asymptotic MSE of a commonly used coarray-based MUSIC estimator, the spatial-smoothing based MUSIC (SS-MUSIC). We show that deterministic sensor location errors introduce a constant estimation bias that cannot be mitigated by only increasing the SNR. Our analytical expression also provides a sensitivity measure against sensor location errors for sparse linear arrays. We next extend our derivations to the stochastic error model and analyze the Gaussian case. We also derive the CRB for joint estimation of DOA parameters and deterministic sensor location errors. We show that this CRB is applicable even if there are more sources than the number of sensors. Lastly, we develop robust DOA estimators for cases with missing data. By exploiting the difference coarray structure, we introduce three algorithms to construct an augmented covariance matrix with enhanced degrees of freedom. By applying MUSIC to this augmented covariance matrix, we are able to resolve more sources than sensors. Our method utilizes information from all snapshots and shows improved estimation performance over traditional DOA estimators

    Maximizing the Number of Spatial Nulls with Minimum Sensors

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    In this paper, we attempt to unify two array processing frameworks viz, Acoustic Vector Sensor (AVS) and two level nested array to enhance the Degrees of Freedom (DoF) significantly beyond the limit that is attained by a Uniform Linear Hydrophone Array (ULA) with specified number of sensors. The major focus is to design a line array architecture which provides high resolution unambiguous bearing estimation with increased number of spatial nulls to mitigate the multiple interferences in a deep ocean scenario. AVS can provide more information about the propagating acoustic field intensity vector by simultaneously measuring the acoustic pressure along with tri-axial particle velocity components. In this work, we have developed Nested AVS array (NAVS) ocean data model to demonstrate the performance enhancement. Conventional and MVDR spatial filters are used as the response function to evaluate the performance of the proposed architecture. Simulation results show significant improvement in performance viz, increase of DoF, and localization of more number of acoustic sources and high resolution bearing estimation with reduced side lobe level

    Sparse Automotive MIMO Radar for Super-Resolution Single Snapshot DOA Estimation With Mutual Coupling

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    A novel sparse automotive multiple-input multiple-output (MIMO) radar configuration is proposed for low-complexity super-resolution single snapshot direction-of-arrival (DOA) estimation. The physical antenna effects are incorporated in the signal model via open-circuited embedded-element patterns (EEPs) and coupling matrices. The transmit (TX) and receive (RX) array are each divided into two uniform sparse sub-arrays with different inter-element spacings to generate two MIMO sets. Since the corresponding virtual arrays (VAs) of both MIMO sets are uniform, the well-known spatial smoothing (SS) algorithm is applied to suppress the temporal correlation among sources. Afterwards, the co-prime array principle between two spatially smoothed VAs is deployed to avoid DOA ambiguities. A performance comparison between the sparse and conventional MIMO radars with the same number of TX and RX channels confirms a spatial resolution enhancement. Meanwhile, the DOA estimation error due to the mutual coupling (MC) is less pronounced in the proposed sparse architecture since antennas in both TX and RX arrays are spaced larger than half wavelength apart
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