Periodic extension phase unwrapping for direction-of-arrival estimation using sparse undersampled arrays: Method and...

To address spatial aliasing and phase ambiguity in broadband direction-of-arrival (DOA) estimation for sparse, spatially undersampled underwater acoustic arrays, this paper presents periodic extension phase unwrapping (PEPU). PEPU first extends the wrapped cross-spectral phase within the physical bound imposed by the interelement-spacing-to-wavelength ratio, thereby constructing a candidate phase space containing the admissible ambiguity orders. It then extracts the dominant phase trajectory from this candidate space using local phase smoothness for initialization and cross-frequency continuity for trajectory selection. By screening candidate trajectories globally rather than linking neighboring points locally, PEPU suppresses isolated low-coherence anomalies caused by multipath propagation or interference nulls and delivers continuous absolute phase for a conventional DOA inversion stage. Results from two sea trials conducted in the South China Sea indicate that the method reduces the influence of anomalous frequency bins associated with multipath propagation, localized coherence collapse, and nonstationary disturbances, thereby improving the stability of broadband phase unwrapping for large-spacing arrays and providing reliable phase input for ambiguity-free DOA estimation.