Abstract
We address the two-dimensional direction-of-arrival (2-D DOA) estimation problem for L-shaped uniform linear array (ULA) using two kinds of approaches represented by the subspace-like method and the sparse reconstruction method. Particular interest emphasizes on exploiting the generalized conjugate symmetry property of L-shaped ULA to maximize the virtual array aperture for two kinds of approaches. The subspace-like method develops the rotational invariance property of the full virtual received data model by introducing two azimuths and two elevation selection matrices. As a consequence, the problem to estimate azimuths represented by an eigenvalue matrix can be first solved by applying the eigenvalue decomposition (EVD) to a known nonsingular matrix, and the angles pairing is automatically implemented via the associate eigenvector. For the sparse reconstruction method, first, we give a lemma to verify that the received data model is equivalent to its dictionary-based sparse representation under certain mild conditions, and the uniqueness of solutions is guaranteed by assuming azimuth and elevation indices to lie on different rows and columns of sparse signal cross-correlation matrix; we then derive two kinds of data models to reconstruct sparse 2-D DOA via M-FOCUSS with and without compressive sensing (CS) involvements; finally, the numerical simulations validate the proposed approaches outperform the existing methods at a low or moderate complexity cost.
Highlights
We address the two-dimensional direction-of-arrival (2-D DOA) estimation problem for L-shaped uniform linear array (ULA) using two kinds of approaches represented by the subspace-like method and the sparse reconstruction method
For the sparse reconstruction method, first, we give a lemma to verify that the received data model is equivalent to its dictionary-based sparse representation under certain mild conditions, and the uniqueness of solutions is guaranteed by assuming azimuth and elevation indices to lie on different rows and columns of sparse signal cross-correlation matrix; we derive two kinds of data models to reconstruct sparse 2-D DOA via M-FOCUSS with and without compressive sensing (CS) involvements; the numerical simulations validate the proposed approaches outperform the existing methods at a low or moderate complexity cost
Researchers developed numerous methods for estimation of 2-D DOA based on L-shaped ULAs [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. ese methods are roughly categorized into two classes: one class is to decouple L-shaped ULA into two separate ULAs, where azimuths and elevations are estimated independently, and the additional 2-D DOA pairing procedure is needed. e other class developed the Vandermonde structure of steering matrix with automatic angles pairing, such as JSVD [18], 2-D MUSIC [20], 2-D PM, 2-D ESPRIT, and their variants [23, 25], of tensor techniques, such as PARAFAC [26], CS-PARAFAC [27], and the tensor-based PARAFAC [8]
Summary
For the sparse reconstruction method, first, we give a lemma to verify that the received data model is equivalent to its dictionary-based sparse representation under certain mild conditions, and the uniqueness of solutions is guaranteed by assuming azimuth and elevation indices to lie on different rows and columns of sparse signal cross-correlation matrix; we derive two kinds of data models to reconstruct sparse 2-D DOA via M-FOCUSS with and without compressive sensing (CS) involvements; the numerical simulations validate the proposed approaches outperform the existing methods at a low or moderate complexity cost. In order to achieve good estimation performance with automatic angles pairing at the cost of a low or moderate complexity, the conjugate symmetry property of L-shaped ULA is introduced to enlarge virtual array aperture [12]. In order to demodulate the sparse 2-D DOA, the 2-D MMVs (two-dimensional multiple measurement vectors) are converted into one 1-D MMV and K 1-D SMV (one-dimensional single measurement vector) problems, respectively; the CS-based sparse reconstruction methods are developed in this paper
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