## 1 Introduction  
Compared with the traditional radio frequency (RF) communication, OWC has the advantages of high system capacity, interference immunity, good security, flexibility and fast, and low cost [1]. However, the transmission of optical wireless signals is affected by atmospheric turbulence, atmospheric absorption, scattering, and refraction. It is difficult for the receiver to obtain an accurate signal with the variation in refractive-index structure constant caused by random variation in atmospheric temperature and pressure. The multiband carrier-free amplitude phase (CAP) modulation technique was proposed in [2] to improve the system capacity and frequency band utilization of OWC under the Gamma-Gamma atmospheric turbulence channel. The experimental results demonstrate that the phase shift is well compensated and the inter-symbol interference (ISI) is effectively suppressed using the multi-modulus algorithm (MMA). However, for the purpose of achieving ISI free transmission in digital communication systems, the symbol rate must follow the Nyquist criterion. This limits the further improvement in the spectral efficiency of the OWC system. In 1975, Mazo proved that higher transmission rates could be achieved using FTN technology [3]. However, FTN introduces ISI to achieve spectral efficiency, which increases the difficulty of signal detection. In recent years, studies on FTN mainly focus on model-driven detection algorithms. Detection algorithms, such as the linear detection algorithm based on minimum mean square error estimation (MMSE) [4], zero forcing (ZF), maximum a posteriori algorithm (MAP) [5], and nonlinear detection algorithm, have unsatisfactory performance for FTN signals with a high acceleration factor and the implementation complexity is extremely high. It is interesting that the FTN signal detection algorithm performance based on deep learning (DL) outbalances the traditional model-driven algorithms [6]. In [7], DL is deployed at the transceiver of an FSO system for atmospheric turbulence compensation. This indicates that using DL in OWC can achieve superior performance with lower complexity. In order to eliminate the high complexity of channel estimation caused by the lack of translation invariance of the covariance matrix, [PERSON] et al. employed the MMSE and convolutional neural networks (CNNs) to compensate for this deficiency in [8]. [PERSON] et al. proposed a dual-selective channel fading estimation method based on deep neural networks (DNNs) for channel estimation in [9]. It combines offline training and online learning to achieve high-precision super-resolution channel estimation by DNN. On the other hand, channel equalization technology is often utilized to eliminate the ISI to improve the quality of signal [10; 11]. From the perspective of DL, channel equalization can be regarded as the problem of how to recover the transmitted symbols as accurately as possible from the received symbols. The DL module can be regarded as a \"black box\", which is decoded by the neural network at the receiver, thus realizing the demodulation of the transmitted signal. [PERSON] et al. set up an experimental system of differential FTN precoding visible light communication using CAP modulation in [12]. It optimizes the decoding algorithm by the DL method and verifies the practicability of DL in the FTN-FSO system. As an improvement to RNN, the LSTM network was proposed by [PERSON] and [PERSON] in 1997 and has been utilized in many fields [13]. A convolutional long short-term deep neural network (CLDNN) was introduced in [14], which exploits the complementary nature of CNN and LSTM to combine the architectures of CNN and LSTM into deep neural networks. The authors of [15] proposed an RNN called bi-directional long short-term memory (Bi-LSTM) to characterize the feature of ISI introduced in FTN signaling. Moreover, it describes a \"mismatch SNR\" strategy for building the training dataset that can effectively help to prevent overfitting.