Underdetermined DOA Estimation Using Arbitrary Planar Arrays via Coarray Manifold Separation

Conventional direction-of-arrival (DOA) estimation algorithms like MUSIC only allow localization of fewer number of sources than the number of physical sensors. In this paper, underdetermined azimuth localization (localizing more sources than the number of sensors) using arbitrary planar arrays has been proposed, using only second-order statistics of the received data. To achieve this, we utilize the difference coarray of the actual array and express the elements of the array covariance matrix as the signal received by the virtual sensors of the coarray. We explore the structure and geometry of the difference coarray of an $N$-element planar array and show that the coarray can provide an increased degree-of-freedom (DOF) of $\mathcal {O}(N^{2})$ which enables underdetermined localization. Then, we extend the manifold separation (MS) technique to the coarray to express the coarray steering matrix in terms of a Vandermonde structured matrix by designing a signal independent coarray characteristic matrix. As the signal model of a coarray is a single snapshot model, the Vandermonde structure enables us to perform a spatial smoothing type operation to restore the rank of the coarray covariance matrix. This allows us to propose a novel subspace-based algorithm, which we call the coarrayMS-MUSIC, to perform underdetermined source localization using arbitrary planar arrays. We have also introduced the polynomial rooting version of our algorithm called the coarrayMS-rootMUSIC. Finally, we have conducted extensive numerical simulations to verify the effectiveness and usefulness of the proposed methods.

I. Introduction

Direction-of-arrival (DOA) estimation is an important area of research in array signal processing and finds application in areas such as radar, sonar, wireless communication, acoustic beamforming, robot audition, source tracking [1]–[4] etc. DOA estimation algorithms are also used to enhance the spatial awareness of vehicles and to localize targets for drones and other aerial vehicles [5], [6]. Conventional subspace-based source localization algorithms like MUSIC [7], [8] allow localization of only sources using an -element sensor array. Recently, however, underdetermined DOA estimation using non-uniform linear arrays (NULAs) has become an active area of research [9]–[18] in the field of multi-channel signal processing. Using the increased degrees-of-freedom (DOF) of the difference coarray of the NULAs, new techniques have been developed that are theoretically capable of localizing sources with only sensors. For NULAs that have holes in their difference coarrays, various coarray interpolation techniques have been proposed [19]–[21] to enhance the DOF of such arrays. But, these techniques are applicable only to NULAs and as such provide a coverage of only in the azimuth direction.