###### Abstract  
Orthogonal chirp division multiplexing (OCDM) offers a promising modulation technology for shallow water underwater acoustic (UWA) communication systems due to multipath fading resistance and Doppler resistance. To handle the various channel distortions and interferences, obtaining accurate channel state information is vital for robust and efficient shallow water UWA communication. In recent years, deep learning has attracted widespread attention in the communication field, providing a new way to improve the performance of physical layer communication systems. In this paper, the pilot-based channel estimation is transformed into a matrix completion problem, which is mathematically equivalent to the image super-resolution problem arising in the field of image processing. Simulation results show that the deep learning-based method can improve the channel distortion, outperforming the equalization performed by traditional estimator, the performance of Bit Error Rate is improved by 2.5 dB compared to the MMSE method in OCDM system. At the 7.5 to 20 dB region, it achieves better bit error rate performance than OFDM systems, and the bit error rate is reduced by approximately 53% compared to OFDM when the SNR value is 20, which is very useful in shallow water UWA channels with multipath extension and severe time-varying characteristics. deep learning-based channel estimation; orthogonal chirp division multiplexing; underwater acoustic communication 2024242424624  
used multi-carrier scheme for UWA communication [6]. However, the existence of Doppler frequency shift in the shallow water UWA channel destroys the orthogonality of OFDM subcarriers, which greatly reduces the performance of OFDM in dual-selection channels. This undoubtedly increases the complexity of the OFDM system. Since the autocorrelation function of the Chirp signal offers precise time resolution and is more insensitive to the Doppler shifts [7], it holds a significant advantage in addressing Doppler shifts within the shallow water acoustic channel. The difference between OFDM and orthogonal chirp division multiplexing (OCDM) are as follows: OFDM is based on the Fourier transform, which consists of a set of orthogonal subcarriers that are modulated independently, the subcarrier frequency does not vary with time and is sensitive to Doppler shifts, the orthogonality of subcarriers is disrupted in shallow water acoustic channels, leading to performance degradation. OCDM is based on the Fresnel transform [8], which consists of multiple orthogonal chirp waveforms sharing the same bandwidth and time slot. OCDM signals enhance data transmission reliability by effectively utilizing multipath diversity and exhibiting stronger fading resistance when compared to OFDM signals [9]. Similar to the OFDM communication system, channel estimation is crucial in the UWA-OCDM communication system. OCDM signals will be distorted when passing through a shallow water acoustic channel (SWAC), an accurate channel state information (CSI) is required to compensate the distortion from the channel and to restore the transmission signal. Pilot-based channel estimation is the most widely used method of obtaining CSI, as both data symbols and pilot symbols are sent together for channel estimation. Traditional frequency-domain equalizers used in OCDM include the zero forcing (ZF) equalizer and the minimum mean square error (MMSE) equalizer. Among them, the ZF equalizer does not use prior information and is extremely sensitive to noise; therefore, its performance at low signal-to-noise ratios (SNR) is often unsatisfactory. The MMSE equalizer can effectively balance the noise and compensate the channel, making its performance better than the ZF equalizer [10]. Deep learning, an artificial intelligence technique, excels in addressing complex nonlinear problems and performs well in fields like computer vision and natural language processing [11].