DePattern: A Search-Free DOA Estimation Algorithm with High Precision for Coprime Arrays

Direction of arrival (DOA) estimation using coprime linear arrays has garnered significant attention thanks to its low design complexity and exceptional performance, yet the failure to satisfy the half-wavelength assumption introduces a phase ambiguity problem that remains insufficiently analyzed in existing literature. In this paper, we introduce the concept of root-MUSIC match pattern (RMMP) to visualize the DOA estimation challenges associated with coprime arrays, enabling a more intuitive analysis of the various phase ambiguities through geometric analysis. The term “DePattern" refers to the algorithms and analyses developed based on the RMMP framework. Leveraging RMMP, we propose a search-free DOA estimation algorithm that avoids angle search and anti-ambiguity search while thoroughly resolves the ambiguity problem inherent in coprime arrays. The algorithm further constructs a minimum mean square error (MMSE) estimator and implements adaptive calculation of the estimator weights. This adaptive weighting allows the proposed algorithm to optimize the estimation performance while maintaining computational efficiency. Furthermore, the MMSE estimator also provides convenience for subsequent performance analysis. Simulation results validate the theoretical analysis and demonstrate the effectiveness of the proposed anti-phase ambiguity algorithm. Compared to existing methods, the proposed algorithm achieves estimation accuracy comparable to full-array-based algorithms while maintaining the low computational complexity at the level of the subarray-based algorithm.