A Two-Stage Transformer Framework for Sparse-Array Direction-of-Arrival Estimation via Correlation Vector Recovery

Accurate direction-of-arrival (DOA) estimation with high resolution is fundamental to many array sensing applications. In practice, however, sparse arrays with missing sensors and snapshot-limited observations often lead to incomplete and noisy second-order statistics, which substantially degrades the performance of conventional eigendecomposition-based estimators. In this paper, we propose a two-stage Transformer framework for sparse-array DOA estimation that explicitly separates correlation recovery from angle inference. The first stage operates in the correlation domain and learns to reconstruct a clean and complete correlation vector from partially observed measurements using masking-aware tokenization and global-context modeling. The recovered representation can be further converted into a structured covariance matrix, providing an interpretable interface to classical signal processing back-ends. Based on the recovered features, the second stage adopts a Transformer regressor to directly predict multi-source DOAs. Extensive simulations on a large-scale dataset with SNRs from -5 to 10 dB and various snapshot numbers demonstrate that the proposed method delivers robust accuracy and improved stability in low-SNR and snapshot-limited regimes, while maintaining competitive performance at higher SNRs. Additional evaluations with an ESPRIT back-end further confirm that the recovery-based covariance yields more reliable DOA estimation than conventional difference-coarray processing, with particularly evident gains under challenging noise conditions.