Forward Sort-and-Gather Alignment Network for Joint Source Count and Multi-Source DOA Estimation

Wenjie Wang

doi:10.3390/electronics15194485

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Forward Sort-and-Gather Alignment Network for Joint Source Count and Multi-Source DOA Estimation

2026-10-01

Wenjie Wang

Lei Liu *

DOI：10.3390/electronics15194485

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Abstract

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Direction-of-arrival (DOA) estimation remains difficult when the source count is unknown, the signal-to-noise ratio (SNR) is low, or several sources are closely spaced. This paper proposes the Forward Sort-and-Gather Alignment Network (FSA-Net) for joint source count classification and continuous multi-source DOA estimation. A three-channel representation of the sample covariance matrix, normalized by a common Frobenius norm, is processed by a shared feature extractor with angle, slot existence, and source count heads. During the forward pass, the predicted angles are sorted, and the same permutation is applied to the existence logits. This operation preserves cross-branch correspondence without combinatorial assignment at inference. Adjacent-gap loss further constrains the relative geometry of neighboring sources. A single model handles mixed K = 1, 2, and 3 cases without prior knowledge of K. In Monte Carlo simulations with a uniform linear array and mutually uncorrelated narrowband sources, FSA-Net achieves sub-degree localization RMSE for all three source counts over the tested SNR range from −15 to 15 dB under the oracle K, localization protocol, while the independently evaluated source count accuracy exceeds 99% overall. The method also maintains favorable joint localization performance under the evaluated low-SNR and closely spaced source conditions. Controlled ablations show that permutation-consistent sort-and-gather alignment provides the largest improvement among the investigated components.

Keywords:

direction-of-arrival estimation

multi-source localization

source count estimation

deep learning