Gridless 2D DOA estimation for sparse planar arrays via 2-level Toeplitz reconstruction

This paper develops a statistically efficient gridless two-dimensional (2D) direction-of-arrival (DOA) estimation method for sparse planar arrays under the coarray signal model. Our approach is based on the 2-level Toeplitz structure of the augmented covariance matrix and includes two steps. In the first step, to reconstruct the 2-level Toeplitz augmented covariance matrix, we propose a rank-constrained weighted least squares (WLS) method and then design an alternating direction method of multipliers (ADMM) algorithm to implement it. Compared to the conventional coarray-based scheme, the proposed method considers the distribution of the array output and hence has better estimation accuracy. In addition, our augmented covariance matrix reconstruction method is still valid even if there exist holes in the difference coarray. In the second step, we present a gridless algorithm to recover and automatically pair DOAs from the estimate of the 2-level Toeplitz augmented covariance matrix. We theoretically show that the proposed estimator is consistent and its performance can attain the Cramér–Rao bound (CRB) for a large number of snapshots. Numerical results confirm the statistical efficiency of our approach.