Direction-of-Arrival Estimation for Distributed Arbitrary Sparse Arrays Exploiting Overlapped Tensor Nuclear Norm

Large-scale array deployment is no longer practicable with sparse linear arrays due to platform limitations, while distributed arrays, providing greater array aperture and higher flexibility, are perfectly suited for this situation. In this article, we design the distributed arbitrary sparse arrays (DASA), whose subarrays are arbitrary sparse linear arrays with holes present in their difference coarrays, and formulate the data fusion model of the DASA structure at the processing center. Based on the aforementioned, a high-precision direction-of-arrival (DOA) estimation algorithm combining overlapped tensor nuclear norm and multiple signal classification (MUSIC) (OTNN-MUSIC) is also proposed for the DASA structure. Specifically, we first employ virtual coarray interpolation to interpolate the virtual co-array signals and perform Toeplitz matrix reconstruction on the interpolated signals. Then, the reconstructed Toeplitz matrices are employed to fuse into the covariance matrix equivalent to the virtual distributed uniform linear arrays, and this covariance matrix is completed by exploiting OTNN. Finally, by directly implementing the MUSIC algorithm on the completed covariance matrix, we can obtain the estimated DOAs. The results of numerical simulations demonstrate that the proposed OTNN-MUSIC algorithm not only possesses the ability of overdetermined and underdetermined estimation but also excellent angular resolution, and that as compared to the existing competing algorithms, the proposed OTNN-MUSIC algorithm generates a higher precision DOA estimation performance. In addition, the experiment results verify that the proposed OTNN-MUSIC algorithm is effective for application in real-world environments.