Channel estimation based on dual frequency domain Transformer in time–frequency doubly-selective fading underwater acoustic channels

Abstract

In underwater acoustic (UWA) channels with time–frequency doubly-selective fading, the performance of traditional channel estimation algorithms is seriously degraded. To solve this problem, this paper proposes a dual frequency-domain Transformer Channel Estimation (DFTCE) based model for UWA-orthogonal frequency division multiplexing (UWA-OFDM) systems. The model uses two parallel CNNs to extract UWA channel features from the channel response at the pilot and the frequency-domain received signal, respectively, and then inputs the channel features into the Transformer for channel estimation. In the extraction of channel features from the channel response at the pilot, this study comprehensively accounts for the influence of both channel features and noise. Utilizing the carrier frequency interval of the pilot, a high-frequency feature extraction module is devised to extract high-frequency channel features while eliminating low-frequency noise components. In the extraction of channel features from the frequency-domain received signal, a global feature extraction module is developed, considering distinct subcarrier frequency ranges to capture nuanced features of the overall channel variations at different time instances. Furthermore, a multi-head attention mechanism is utilized to concentrate on variations among subcarriers. This helps alleviate the influence of channel noise and Inter-Carrier Interference (ICI), consequently enhancing the performance of channel estimation. Simulation experiments conducted using the UWA channel dataset WATERMARK reveal that the proposed method demonstrates a performance improvement of 2 dB-3 dB compared to the linear minimum mean square error (LMMSE) algorithm in an UWA environment with significant Doppler effect.