A Local-Global Feature Extraction Self-Supervision Network for Gridless DOA Estimation With Arbitrary Sparse Arrays

In this work, we consider the challenging gridless direction-of-arrival (DOA) estimation problem with arbitrary sparse arrays. By utilizing the feature relationship between the received array signals and the gridless sparse recovery method, a local-global feature extraction self-supervision network (LGFS-Net) is proposed to achieve gridless sparse recovery without labels. The proposed network consists of a local-global feature extraction module and a complex atomic norm minimization (ANM) self-supervision module. The feature extraction module models the relationship of array elements to recover the missing data corresponding to the holes of the virtual array by learning the local and global features between the received data of different array elements. The complex ANM self-supervision module is embedded in the ANM problem, which realizes gridless Toeplitz matrix recovery and ensures the complex data structure in each network layer by complex singular value decomposition (SVD), positive semidefinite constraints (PSD), and ANM loss. By training the network using the received data of an arbitrary sparse array and constructing a self-supervised loss function that does not require labels, the network exhibits excellent performance when there are holes in the virtual array, and its signal recovery and parameter estimation performance is similar to the case of uniform linear arrays and better than traditional gridless recovery methods, as demonstrated by computer simulations.