Two-Dimensional Direction Finding via Sequential Sparse Representations

The problem of two-dimensional direction finding is approached by using a multi-layer L-shaped array. The proposed method is based on two sequential sparse representations, fulfilling respectively the estimation of elevation angles, and azimuth angles. For the estimation of elevation angles, the weighted sub-array smoothing technique for perfect data decorrelation is used to produce a covariance vector suitable for exact sparse representation, related only to the elevation angles. The estimates of elevation angles are then obtained by sparse restoration associated with this elevation angle dependent covariance vector. The estimates of elevation angles are further incorporated with weighted sub-array smoothing to yield a second covariance vector for precise sparse representation related to both elevation angles,and azimuth angles. The estimates of azimuth angles, automatically paired with the estimates of elevation angles, are finally obtained by sparse restoration associated with this latter elevation-azimuth angle related covariance vector. Simulation results are included to illustrate the performance of the proposed method.