2-D DOA estimation based on augmented structured Nyquist correlation reconstruction for L-shaped nested array

In this paper, a two-dimensional (2-D) direction-of-arrival (DOA) estimation algorithm based on augmented structured Nyquist correlation reconstruction (ASNCR) is proposed for the L-shaped nested array (LsNA). Specifically, the Nyquist spatial filling method is first introduced to generate the equivalent filled array, followed by utilizing compressed sampling to build the correlation between the covariance matrix in the physical array domain and the equivalent one. Then, the augmented structured correlation matrix reconstruction problem based on nuclear norm minus Frobenius norm (NMF) is established by combining the estimation error of the covariance matrix and structural information in the physical array domain to resolve the noise-free covariance matrix, which in turn yields the estimated azimuth angles. Finally, by joining the cross-correlation matrix (CCM) and the estimated azimuth angles, the estimated elevation angles are obtained. In particular, the automatic pairing of 2-D angles of the source signals can be achieved by this algorithm. The results of numerical simulations show that the ASNCR algorithm possesses the capability of underdetermined DOA estimation. Furthermore, compared to existing competing algorithms, the ASNCR algorithm achieves more favorable performance.