Efficient DOA Estimation Method for Extended-Aperture Moving Coprime Arrays Based on ANM-ADMM

Coprime arrays achieve a larger virtual array aperture with the same number of physical elements through their difference co-array. However, the improvement in degrees of freedom (DOF) is still limited by the physical array. Additionally, many existing algorithms require significant computational resources to find optimal solutions, which makes them unsuitable for large-scale array direction of arrival (DOA) estimation. To effectively tackle these challenges, we present an efficient DOA estimation method for extended-aperture moving coprime arrays based on the atomic norm minimization-alternating direction method of multipliers (ANM-ADMM). First, we establish a general framework for the motion model of coprime and analyze the relationship between array motion intervals and the resulting additional holes in the co-array. To fully exploit the information from the received signals, we develop an ANM-based method to complete the missing entries in the virtual array, thereby recovering its covariance matrix. To alleviate the computational burden typically associated with traditional ANM approaches, we introduce an ADMM-based algorithm that decomposes the optimization problem into iterative subproblems, significantly enhancing computational efficiency. Simulation results demonstrate that the proposed method enables a larger array aperture with fewer physical elements by synthesizing extended apertures through array motion, considerably enhancing DOF and DOA estimation accuracy. Notably, efficient DOA estimation is achieved even when the array motion exceeds multiple wavelengths. For an array with 4 physical elements, the proposed method achieves a theoretical DOF of 44 through 4 motion steps. When SNR exceeds 5 dB, the RMSE of DOA estimation for 25 targets is below 0.1.