## 1 Introduction
In [34], a DL-based approach is employed to design the multi-colored VLC system, where an unsupervised DL is used to train the end-to-end symbol recovery process including the transceiver pair and a channel layer. The results of the average symbol error probability demonstrate that the learned VLC outperforms existing techniques. A DL framework is proposed in [35] for the design of a binary signaling transceiver in dimmable VLC, where the optical channel layers and binarization techniques are introduced in DL to reflect the physical and discrete nature of the OOK-based VLC systems. In [36], a model-driven DL approach using an autoencoder (AE) network is proposed to mitigate the LED nonlinearity for DCO-OFDM-based VLC systems. The constellation mapping and de-mapping of the transmitted symbols are adaptively acquired and optimized through the DL technique. The results show that the proposed scheme exhibits better BER performance than some existing methods, and it can also further accelerate the training speed. Similar to [36], an end-to-end learning AE network is proposed in [37] to address the high PAPR and the LED nonlinearity problems in asymmetrically clipped (AC) O-OFDM. The results show that the hybrid AE achieves a distinct PAPR reduction and is more robustness to LED nonlinearities. To address real-life application constraints in VLC, the literature [38] considers that the input-dependent noise originated from the shot noise for the sake of generality and propose a VLCnet that uses flicker reducing activation units for error rate decreases. The simulation results show the performance superiority of the proposed VLCnet method in the case of input-independent and -dependent noise. In this paper, inspired by the approaches in [26; 27; 28; 29; 30; 31], we formulate the channel impairment mitigation problem as a learning task and propose a model-driven DL scheme, abbreviated as DL-NPE, for the DCO-OFDM-based VLC system. The underlying idea is that the traditional signal processing blocks in OFDM in terms of channel estimation and the constellation de-mapping module are denoted by two DL networks, respectively. With an efficient learning and performance optimization, the channel characteristics and symbol de-mapping relationship can be learned from the training data, and the proposed DL-NPE can reconstruct the original bit streams directly and accurately. The main contribution of this work can be summarized as follows:  
It considers both the memory nonlinearity of the LED and the multipath optical channel during the training stage. Besides the line-of-sight (LOS) optical link, the non-LOS (NLOS) links are also simultaneously learned by the proposed scheme in the training stage. This is the main difference compared with the work in [29; 30]. 1. The overall network architecture is constructed by imitating the existing communication signal processing algorithm rather than treated as a black box without any expert knowledge. In addition, the initialization input of the network also contains the traditional solution instead of random numbers. 2. The refining layer with the simple _Signum_ function is applied to the network output, which can refine the coarse bit stream and can improve the detection accuracy of the network. 3. The proposed scheme can still provide an excellent equalization performance even under cyclic prefix (CP) removal, which outperforms the traditional equalizers and demonstrates its powerful self-study and robustness ability of the DL approach. In addition, compared with [31], this work has been significantly improved and the system performance is further evaluated. The simulation results show that the overall channel impairment is relieved and that the BER performance is improved by the proposed scheme effectively. The remainder of this paper is organized as follows. In Section 2, an overview of the system model is given and the channel impairments of IM/DD channel are introduced. Section 3 presents the architecture of the proposed DL-NPE.