Snapshot-similarity-guided sparse unfolding transformer for accurate DOA estimation

Most direction-of-arrival (DOA) estimation algorithms require sufficient snapshots of data, and suffer severe performance degradation when the number of snapshots is extremely limited. Instead of constructing input data with several snapshots as traditional methods do, this work considers the inter-snapshot similarity and constructs a deep-unfolding model, which takes few pieces of single-snapshot data and predicts an equal number of results simultaneously. Such a design more efficiently utilizes the information from few snapshots. Specifically, few-snapshot DOA estimation is approached as a sparse dictionary-learning problem regularized by l1-norm and inter-snapshot similarity function, and a deep-unfolding transformer architecture called Snapshot-similarity-guided Sparse Unfolding Transformer (SSUT) is proposed to solve the problem. The deep-unfolding self-attention layer optimizes the inter-snapshot similarity, and the deep-unfolded approximate message passing (DAMP) layer minimizes the sparse regularized energy function. Such a network simultaneously considers two physical mechanisms (sparsity and inter-snapshot similarity) as prior knowledge, which enables better DOA estimation results with few snapshots. Extensive numerical simulations verify the superior performance of the proposed SSUT algorithm and data efficiency with few snapshots, limited signal-to-noise (SNR) level and multiple targets. Experiment on SWellEx-96 dataset further demonstrates the practicability of SSUT.