Direction-of-arrival (DOA) estimation refers to the process of retrieving the direction information of several electromagnetic waves/sources from the outputs of a number of receiving antennas that form a sensor array. DOA estimation is a major problem in array signal processing and has wide applications in radar, sonar, wireless communications, etc. With the development of sparse representation and compressed sensing, the last decade has witnessed a tremendous advance in this research topic. The purpose of this article is to provide an overview of these sparse methods for DOA estimation, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm. Several future research directions are also discussed.

Sparse methods for direction-of-arrival estimation

This article presents a survey of recent research on sparsity-driven synthetic aperture radar (SAR) imaging. In particular, it reviews 1) the analysis and synthesis-based sparse signal representation formulations for SAR image formation together with the associated imaging results, 2) sparsity-based methods for wide-angle SAR imaging and anisotropy characterization, 3) sparsity-based methods for joint imaging and autofocusing from data with phase errors, 4) techniques for exploiting sparsity for SAR imaging of scenes containing moving objects, and 5) recent work on compressed sensing (CS)-based analysis and design of SAR sensing missions.

/pdf/sparsity-driven-synthetic-aperture-radar-imaging-5a4zcvv5rb.pdf

Sparsity-Driven Synthetic Aperture Radar Imaging: Reconstruction, autofocusing, moving targets, and compressed sensing

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.

pdf/sparse-signal-estimation-by-maximally-sparse-convex-4xc39hiol5.pdf

Sparse Signal Estimation by Maximally Sparse Convex Optimization

This paper provides principles and applications of the sparse microwave imaging theory and technology. Synthetic aperture radar (SAR) is an important method of modern remote sensing. During decades microwave imaging technology has achieved remarkable progress in the system performance of microwave imaging technology, and at the same time encountered increasing complexity in system implementation. The sparse microwave imaging introduces the sparse signal processing theory to radar imaging to obtain new theory, new system and new methodology of microwave imaging. Based on classical SAR imaging model and fundamental theories of sparse signal processing, we can derive the model of sparse microwave imaging, which is a sparse measurement and recovery problem and can be solved with various algorithms. There exist several fundamental points that must be considered in the efforts of applying sparse signal processing to radar imaging, including sparse representation, measurement matrix construction, unambiguity reconstruction and performance evaluation. Based on these considerations, the sparse signal processing could be successfully applied to radar imaging, and achieve benefits in several aspects, including improvement of image quality, reduction of data amount for sparse scene and enhancement of system performance. The sparse signal processing has also been applied in several specific radar imaging applications.

Sparse microwave imaging: Principles and applications

Recently, millimeter-wave 3D holography techniques employing a scanning 1D multiple input multiple output (MIMO) array have shown several superiorities for short-range applications than traditional single input single output ones. However, current imaging algorithms for this emerging regime are not satisfied, either too slow as a back projection manner is used or of poor quality since several steps of approximations are introduced. In this paper, two fast fully focused imaging algorithms are developed towards fixing these drawbacks. Both algorithms are based on the assumption that the receivers are evenly distributed. The first algorithm further hypothesizes that the transmitters are also evenly located, while the second algorithm needs looser restrictions that the transmitters can be arbitrarily positioned. The frequency domain expressions of the modified Kirchhoff method are also derived and used to promote the precision of the proposed algorithms. In addition, several implementation issues, including resolution, sampling criteria, and computational complexity are discussed. Finally, both simulation and experimental results validate the effectiveness of the proposed methods on reconstruction quality and computational efficiency.

Novel Efficient 3D Short-Range Imaging Algorithms for a Scanning 1D-MIMO Array

Through waveform diversity, multiple-input multiple-output (MIMO) radar can provide higher resolution, improved sensitivity, and increased parameter identifiability compared to more traditional phased-array radar schemes. Existing methods for target estimation, however, often fail to provide accurate MIMO angle-range-Doppler images when there are only a few data snapshots available. Sparse signal recovery algorithms, including many l1-norm based approaches, can offer improved estimation in that case. In this paper, we present a regularized minimization approach to sparse signal recovery. Sparse learning via iterative minimization (SLIM) follows an lq-norm constraint (for 0 <; q ≤ 1), and can thus be used to provide more accurate estimates compared to the l1-norm based approaches. We herein compare SLIM, through imaging examples and examination of computational complexity, to several well-known sparse methods, including the widely used CoSaMP approach. We show that SLIM provides superior performance for sparse MIMO radar imaging applications at a low computational cost. Furthermore, we will show that the user parameter q can be automatically determined by incorporating the Bayesian information criterion.

Sparse Learning via Iterative Minimization With Application to MIMO Radar Imaging

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Sparse Learning via Iterative Minimization With Application to MIMO Radar Imaging