Fast 2-D Direction of Arrival Estimation Using Two-Stage Gridless Compressive Sensing

In this study, we propose and demonstrate a two-dimensional direction of arrival estimation method based on gridless compressive sensing (CS). The method is based on a gridless covariance fitting technique to alleviate the well-known grid mismatch problem of compressive sensing. Classical methods of gridless compressive sensing are limited to 1-D arrays, while extensions to multidimensional arrays are computationally demanding. To overcome these limitations, we introduce a two-stage solution with an angle-pairing matching pursuit algorithm, which enables 2-D arrays with lower computational complexity. We validate the method via numerical experiments on a cross-shaped generic array, then we compare the results with those of widely used methods such as MUSIC and beamforming.