Enhanced DOA Estimation Through Coprime Planar Coarray Interpolation via Alternating Projection

Coprime Planar arrays are a class of non-uniform planar arrays that can utilize their difference coarray and the higher degrees of freedom (DOF) associated with the virtual coarray to perform enhanced direction of arrival (DOA) estimation in both the azimuth and elevation direction. However, coprime planar arrays do not have a contiguous uniform coarray and the absent virtual sensors in the coarray are referred to as holes. These holes prevent the utilization of the extra DOF provided by the coarray when using conventional array processing techniques. In this correspondence, we present a coarray interpolation technique that fills the holes of the coarray without needing extra physical sensors using an alternating projection algorithm. We first introduce an efficient technique to enhance the rank of the coarray auto-correlation matrix (ACM), which is a rank one matrix, using its two-fold Toeplitz structure and then propose to interpolate the holes of the coarray as a matrix completion problem resulting in a generalized 2D coarray interpolation method. Our method utilizes the properties of the coarray ACM to alternately project the incomplete coarray ACM into different sets of matrices until the final complete coarray ACM with the interpolated holes is obtained. The interpolated coarray ACM is then used to perform 2D-DOA estimation. Simulation results show the effectiveness of the proposed method.