Alternating projections gridless covariance-based estimation for DOA

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

Extension of Co-Prime Arrays Based on the Fourth-Order Difference Co-Array Concept

An effective sparse array extension method for maximizing the number of consecutive lags in the fourth-order difference co-array is proposed, leading to a novel enhanced sparse array structure based on co-prime arrays (CPAs) with significantly increased number of degrees of freedom (DOFs). One method to exploit the increased DOFs based on nonstationary signals is also proposed, with simulation results provided to demonstrate the effectiveness of the proposed structure

Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review

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

Extension of Nested Arrays with the Fourth-Order Difference Co-Array Enhancement

To reach a higher number of degrees of freedom by exploiting the fourth-order difference co-array concept, an effective structure extension based on two-level nested arrays is proposed. It increases the number of consecutive lags in the fourth-order difference coarray, and a virtual uniform linear array (ULA) with more sensors and a larger aperture is then generated from the proposed structure, leading to a much higher number of distinguishable sources with a higher accuracy. Compressive sensing based approach is applied for direction-of-arrival (DOA) estimation by vectorizing the fourthorder cumulant matrix of the array, assuming non-Gaussian impinging signals

Wideband DOA Estimation with Frequency Decomposition via a Unified GS-WSpSF Framework

A unified group sparsity based framework for wideband sparse spectrum fitting (GS-WSpSF) is proposed for wideband direction-of-arrival (DOA) estimation, which is capable of handling both uncorrelated and correlated sources. Then, by making four different assumptions on a priori knowledge about the sources, four variants under the proposed framework are formulated as solutions to the underdetermined DOA estimation problem without the need of employing sparse arrays. As verified by simulations, improved estimation performance can be achieved by the wideband methods compared with narrowband ones, and adopting more a priori information leads to better performance in terms of resolution capacity and estimation accuracy

Statistical Nested Sensor Array Signal Processing

Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N − 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing. This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed. First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources. Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue. We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods

An Expanding and Shift Scheme for Constructing Fourth-Order Difference Co-Arrays

An expanding and shift (EAS) scheme for efficient fourth-order difference co-array construction is proposed. It consists of two sparse sub-arrays, where one of them is modified and shifted according to the analysis provided. The number of consecutive lags of the proposed structure at the fourth order is consistently larger than two previously proposed methods. Two effective construction examples are provided with the second sparse sub-array chosen to be a two-level nested array, as such a choice can increase the number of consecutive lags further. Simulations are performed to show the improved performance by the proposed method in comparison with existing structures

Performance Improvement for Wideband DOA estimation with White Noise Reduction Based on Uniform Linear Arrays

A method is proposed for reducing the effect of white noise in wide- band uniform linear arrays via a combination of a judiciously de- signed transformation followed by highpass filters. The reduced noise level leads to a higher signal to noise ratio for the system, which can have a significant effect on the performance of various direction of arrival (DOA) estimation methods. As a representative example, the compressive sensing-based wideband DOA estimation method is employed here to demonstrate the improved estimation performance, this is confirmed by simulation results