###### Abstract  
In photon-counting underwater optical wireless communication (UOWC), the recovery of the time slot synchronous clock is extremely important, and it is the basis of symbol synchronization and frame synchronization. We have previously proposed a time slot synchronous clock extraction method based on single photon pulse counting, but the accuracy needs to be further improved. Deep learning is very effective for feature extraction; synchronous information is already implicit in the discrete single photon pulse signal output by single photon avalanche diode (SPAD), which is used as a communication receiver. Aiming at this characteristic, a method of time slot synchronous clock recovery for photon-counting UOWC based on deep learning is proposed in this paper. Based on the establishment of the underwater channel model and SPAD receiver model, the Monte Carlo method is used to generate discrete single photon pulse sequences carrying synchronous information, which are used as training data. Two neural network models based on regression problem and classification problem are  
of 2.70 Gbps. [PERSON] et al. realized a UOWC distance of over 20 m at a high data rate of up to 1.5 Gbps by using a 450 nm LD [15]. In [16], the authors proposed a UOWC system based on a convolutional neural network (CNN) demodulator and analyzed the BER performance of the system. [PERSON] et al. experimentally demonstrated the performance of CNN-based signal decoders in UOWC systems [17]. In [18; 19], the authors used a CNN combiner for feature analysis and combination, and a CNN demodulator to recover the transmitted information. Although a high sensitivity avalanche photon diode (APD) has been used as the receiver detector in the above articles and the communication rate is up to Gbps, the transmission distance is limited to tens of meters. Improving the transmission distance of UOWC from tens to hundreds of meters is a challenging task. In recent years, in order to realize long-distance UOWC, some researchers have used a single photon avalanche diode (SPAD) to detect an optical signal at the receiving end. Compared with APD, SPAD is more sensitive and can detect a single photon as the photon-counting receiver. In 2016, through simulation analysis, [PERSON] et al. found that SPAD-based UOWC is feasible when it transmits more than 100 m in clean ocean and 300 m in pure sea water [20]. In [21], a synchronization method based on photon-counting UOWC was proposed, which achieved a communication distance of more than 100 m with a symbol error rate (SER) of \(10^{-4}\). In [22], UOWC with a communication distance of 46 m based on a multi-pixel photon counter (MPPC) detector was realized. UOWC with a communication distance of 21 m and a data rate of 312.03 Mbps based on MPPC was achieved in [23]. In [24], [PERSON] et al. realized UOWC with a communication distance of 1000 m and a data rate of 10 bps based on photon-counting detectors. In [25], the author proposed a multiple light emitting diode (LED) chips parallel transmission scheme for UOWC based on SPAD, and proved that the system can significantly improve the BER performance. In [26], a real-time, high-speed UPCC system was designed and experimentally validated based on SPAD. A novel deep learning-aided signal detection scheme for an SPAD-based UOWC system was proposed in [27]. In [28], [PERSON] et al. proposed a deep learning based signal detection system for channel estimation and increases in transmission distance. In [29], a novel fully connected deep neural network (FC-DNN)-based receiver was proposed and experimentally demonstrated in a UOWC system. All the above literatures use SPAD as the receiver detector, and all have realized relatively long-distance UOWC, but none of them have specified how to realize synchronization and recover data from the received discrete single photon pulse. Clock recovery is the basis of data recovery, including three-level synchronous clock recovery for time slots, symbols and frames.