Sparse linear arrays (SLAs) have gained significant attention for automotive radar due to their enhanced aperture and angular resolution. A promising approach to Direction-of-Arrival (DOA) estimation with only a single temporal snapshot and SLAs is to interpolate the missing measurements by solving a low-rank Hankel matrix completion problem. Sampling geometry plays an important role in matrix completion, and random sampling techniques primarily provide non-uniform recovery guarantees, which can be undesirable. Using the unique geometry of nested-type SLAs, we formulate the Hankel matrix completion problem as a non-convex prediction problem which utilizes the latent structures of a low-rank Hankel matrix in order to reduce the number of unknowns. It also provides uniform recovery guarantees (provably in the absence of noise). Our approach can be interpreted as a self-supervised Untrained Neural Network (UNN) which utilizes the inner uniform linear array (ULA) of a nested array to perform prediction, and the outer array to curb error propagation. Our work establishes the first connection between array interpolation and untrained machine learning paradigms.

We address the challenge of achieving angular super-resolution in multi-antenna radar systems that are widely used for localization, navigation, and automotive perception. A multi-antenna radar achieves very high resolution by computationally creating a large virtual sensing system using very few physical antennas. However, practical constraints imposed by hardware, noise, and a limited number of antennas can impede its performance. Conventional supervised learning models that rely on extensive pre-training with large datasets, often exhibit poor generalization in unseen environments. To overcome these limitations, we propose NEAR, an untrained implicit neural representation (INR) framework that predicts radar responses at unseen locations from sparse measurements, by leveraging latent harmonic structures inherent in radar wave propagation. We establish new theoretical results linking antenna array response to expressive power of INR architectures, and develop a novel physics-informed and latent geometry-aware regularizer. Our approach integrates classical signal representation with modern implicit neural learning, enabling high-resolution radar sensing that is both interpretable and generalizable. Extensive simulations and real-world experiments using radar platforms demonstrate NEAR's effectiveness and its ability to adapt to unseen environments.