Off-Grid Sparse Bayesian Learning for Direct Localization of Cyclostationary Sources With Adaptive Grid Refinement

Abstract

The growing number of emitters and interferences in 5G and beyond, coupled with limited array resources, poses significant challenges to high-precision passive localization. This paper addresses the off-grid direct position determination problem for cyclostationary signals in the presence of interference. We propose a sparse Bayesian learning framework that integrates cyclic cross-correlation processing with sparse array augmentation. The method constructs enhanced pseudo-snapshots by vectorizing cyclic correlation matrices and averaging entries associated with repeated difference lags, effectively expanding the virtual array aperture. An adaptive grid refinement strategy dynamically adjusts grid resolution through multi-resolution candidate generation and Newton-based optimization, while off-grid offsets are optimized via closed-form updates derived from a second-order Taylor expansion of the array manifold. A two-stage refinement procedure then corrects cyclic cross-correlation mismatch by reconstructing and subtracting off-diagonal interference terms, leading to a purified signal model for high-accuracy estimation. Extensive simulations across overdetermined and underdetermined scenarios demonstrate that the proposed algorithm achieves superior positioning accuracy and robustness, effectively mitigating grid bias and interference while outperforming state-of-the-art counterparts.