Prediction-driven Untrained Network for Single-snapshot Sparse Array Interpolation

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.