Crosscorrelation and DOA Estimation for L-Shaped Array via Decoupled Atomic Norm Minimization

A novel two-phase method for two-dimensional (2D) direction-of-arrival (DOA) estimation with L-shaped array based on decoupled atomic norm minimization (DANM) is proposed in this paper. In the first phase, given the sample crosscorrelation matrix, the gridless DANM technique considering the noise and finite snapshots effects is employed to exploit the structure and sparse properties of the crosscorrelation matrix. The resulting DANM-based algorithm not only enables the crosscorrelation matrix reconstruction (CCMR) but also reconstructs the covariance matrix of the L-shaped array. Hence, sequentially, in the second phase, the conventional 2D DOA estimators for the L-shaped array can be adopted for the angle estimation. With appropriate 2D DOA estimators, the resulting proposed algorithms can not only achieve better performance but also detect more source number, compared with conventional crosscorrelation-based DOA estimators. Moreover, the proposed method, termed CCMR-DANM, not only has blind characteristic that it does not require the prior information of source numbers but also is more efficient than the existing CCMR-based counterparts. Numerical simulations demonstrate the effectiveness and outperformance of the proposed method.