A gridless direction-of-arrival (DOA) estimation method to improve the estimation accuracy and resolution in nonuniform noise is proposed in this paper. This algorithm adopts the structure of minimum-redundancy linear array (MRA) and can be composed of two stages. In the first stage, by minimizing the rank of the covariance matrix of the true signal, the covariance matrix that filters out nonuniform noise is obtained, and then a gridless residual energy constraint scheme is designed to reconstruct the signal covariance matrix of the Hermitian Toeplitz structure. Finally, the unknown DOAs can be determined from the recovered covariance matrix, and the number of sources can be acquired as a byproduct. The proposed algorithm can be regarded as a gridless version method based on sparsity. Simulation results indicate that the proposed method has higher estimation accuracy and resolution compared with existing algorithms.

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Basis mismatch challenges the conventional direction‐of‐arrival estimation constrained by sparse representation, especially in the case of massive antennas limited to a single snapshot. In this letter, we develop a real‐valued gridless direction‐of‐arrival estimation method to improve angular precision in the aforementioned circumstances. A new data model is first established through real‐valued transformation and then estimate the large low‐rank matrix with nuclear norm minimization. A fast iterative algorithm is designed to recover the underlying matrix faithfully and efficiently by the alternating direction method of multipliers. Numerical examples validate the performance improvement of the proposed method in the massive uniform linear array. This work also shows the potential to apply in measured data of the millimeter‐wave multiple‐input multiple‐output system.

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