A dual-input coarse-to-fine residual correction network for underwater acoustic OFDM channel estimation in doubly selective channels

Abstract

In doubly selective underwater acoustic channels, time-varying multipath and Doppler spread destroy the orthogonality among orthogonal frequency division multiplexing (OFDM) subcarriers. As a result, the least squares (LS) estimates at pilot positions are affected by noise, inter-carrier interference (ICI), and spectral distortion. To address this problem, this paper proposes a dual-input coarse-to-fine residual correction network for underwater acoustic OFDM channel estimation in doubly selective channels, named Dual-Input Residual Correction Network (DIRCNet). The proposed method takes the LS estimates at pilot positions and the received frequency-domain signal as joint inputs. The pilot-position LS estimates supply amplitude and phase references after normalization by the known symbols, and the received frequency-domain signal captures signal variations over the complete subcarrier grid. In the network structure, DIRCNet first recovers an initial channel profile through the pilot LS coarse estimation branch. Then, the received signal branch extracts auxiliary time-frequency features. Feature-level late fusion and a residual refinement backbone then predict the correction term relative to the coarse estimate, yielding a coarse-to-fine channel estimation process. Experiments are conducted on the Bellhop-SSML time-varying simulated channel and the WATERMARK NOF1 and KAU1 measured-replay channels, with file-level five-fold cross-validation adopted for the WATERMARK experiments. The proposed method is evaluated in terms of normalized mean square error, bit error rate, model complexity, and robustness to residual carrier frequency offset. The results show that DIRCNet maintains relatively stable channel estimation and demodulation performance on both the simulated channel and the WATERMARK measured-replay channels, and achieves better NMSE and BER performance than conventional methods and multiple single-input and dual-input deep-learning baselines under most test conditions. The residual CFO experiment shows that DIRCNet maintains good robustness over the tested frequency-offset range, while the ablation study further verifies the effectiveness of the received-signal branch, feature-level late fusion, and the residual refinement structure.