Deep unfolded networks have recently been regarded as an essential way to direction of arrival (DOA) estimation due to the fast convergence speed and high interpretability. However, few consider gridless DOA estimation. This paper proposes two deep unfolded gridless DOA estimation networks to resolve the above problem. We first consider the atomic norm-based 1D and decoupled atomic norm-based 2D gridless DOA models solved by the alternating iterative minimization of variables, respectively. Then, the corresponding deep networks are trained offline after constructing the corresponding complete training datasets. At last, the trained networks are applied to realize the 1D DOA and 2D estimation, respectively. Simulation results reveal that the proposed networks can secure higher 1D and 2D DOA estimation performances while maintaining a lower computational expenditure than typical methods.

Providing higher precision Direction of Arrival (DOA) estimation has become a hot topic in the field of array signal processing for parameter estimation in recent years. However, when the physical aperture of the actual array is small, its aperture limitation means that even with super-resolution estimation algorithms, the achievable estimation precision is limited. This paper takes a novel approach by constructing an optimization algorithm using the covariance fitting criterion based on the array output’s covariance matrix to fit and obtain the covariance matrix of a large aperture virtual array, thereby providing high-precision angular resolution through virtual aperture expansion. The covariance fitting expansion analysis and discussion are unfolded for both uniform linear arrays (ULAs) and sparse linear arrays (SLAs) under four different scenarios. Theoretical analysis and simulation experiments demonstrate that these methods can enhance the effective performance of angle estimation, especially in low signal-to-noise ratios (SNRs) and at small angular intervals by fitting virtual extended aperture data.

To tackle the challenges of intractable parameter tuning, significant computational expenditure and imprecise model-driven sparse-based direction of arrival (DOA) estimation with array error (AE), this paper proposes a deep unfolded amplitude-phase error self-calibration network. Firstly, a sparse-based DOA model with an array convex error restriction is established, which gets resolved via an alternating iterative minimization (AIM) algorithm. The algorithm is then unrolled to a deep network known as AE-AIM Network (AE-AIM-Net), where all parameters are optimized through multi-task learning using the constructed complete dataset. The results of the simulation and theoretical analysis suggest that the proposed unfolded network achieves lower computational costs compared to typical sparse recovery methods. Furthermore, it maintains excellent estimation performance even in the presence of array magnitude-phase errors.