###### Abstract  
Since visible-light communication (VLC) has become an increasingly promising candidate for 6G, the field of underwater visible-light communication (UVLC) has also garnered significant attention. However, the impairments introduced by practical systems and the time-varying underwater channels always limit the performance of underwater visible-light communication. In this paper, we propose and experimentally demonstrate an autoencoder-based geometric shaping model (AEGSM) framework to jointly optimize quadrature amplitude modulation (QAM) signals at the symbol-wise and bit-wise levels for underwater visible-light communication. Unlike traditional geometric shaping (GS) methods, which only give theoretically optimal shaping solutions, our framework can always obtain the globally optimal shaping scheme for a specific channel condition or different application scenarios. In our AEGSM framework, an autoencoder is used to find the optimal shaping scheme at the symbol-wise level and a revised pairwise optimization (RPO) algorithm is applied to achieve bit-wise optimization. In a real UVLC system, 2.05 Gbps transmission is achieved under the hard decision-forward error correction (HD-FEC) threshold of \(3.8\times 10^{-3}\) by employing the autoencoder-based 8 QAM (AE-8 QAM) optimized by the AEGSM, which is 103 Mbps faster than the Norm-8 QAM. The AE-8 QAM also shows its resistance to nonlinearity and enables the UVLC system to operate within a larger dynamic range of driving voltages. The results substantiate the potential and practicality of the proposed AEGSM framework in the realm of underwater visible-light communication. underwater visible-light communication; geometric shaping; autoencoder; pairwise optimization; quadrature amplitude modulation 202310809  
divergence angle of LD is relatively small, so strict alignment is required in LD-based visible-light communication systems [9]. Therefore, LED-based underwater VLC systems are more suitable for application scenarios involving mobile autonomous underwater vehicles and remotely operated underwater vehicles due to their wide lighting area coverage [10]. However, in the real LED-UVLC system, the modulation bandwidth of LEDs [11; 12] is limited and the optoelectronic device has a nonlinear response, resulting in severe inter-symbol interference (ISI) and nonlinear interference for the transmitted signal [13]. In order to combat the nonlinear effects and limited bandwidth of the system and achieve high-speed information transmission, it is necessary to employ appropriate modulation formats and efficient digital signal processing methods to increase the transmission capacity of the system. In general, spectrum-efficient modulation formats, such as quadrature amplitude modulation-discrete multitone modulation (QAM-DMT) and carrierless amplitude and phase modulation (CAP), are widely used to reach a high transmission data rate [14]. A large-coverage underwater single-input multiple-output VLC system over 1.2 m based on blue LED chips and 2 \(\times\) 2 PIN arrays, using quadrature amplitude modulation-discrete multitone modulation (QAM-DMT), achieved a data transmission rate of 1.8 Gbps [15]. Recently, a transmission rate of 2.85 Gbps was achieved using 64 QAM-carrierless amplitude and phase (CAP) modulation based on the constellation division scheme and blue LED [16]. It is worth noting that the constellation distribution schemes in QAM modulation formats currently used in underwater visible-light communication are mostly fixed and not adaptable, which makes it difficult to achieve an optimal performance for visible-light transmission based on norm QAM modulation under certain channel conditions. The design and optimization of constellations for specific channels is always a challenge. Geometric shaping (GS), probabilistic shaping (PS), and their combination have greatly advanced the development of constellation design [17; 18; 19].