###### Abstract
These proposed LSTM models outperform the conventional model-solving-based equalizers; nevertheless, the output equalization accuracy does not possess a good robustness to the noise variation, leading to the degradation of learning efficiency. In order to learn more suitable channel features, the convolutional neural network (CNN) can be used for memory sequence prediction from raw channel outputs [20], since a function could be learned that maps a sequence of past observations as the input to an output observation. In [21], an equalization scheme using the CNN was proposed in an orthogonal-frequency-division-multiplexing (OFDM)-based VLC system for direct equalization. In [22], a novel blind algorithm based on the CNN was introduced to jointly perform equalization and soft demapping for M-ary quadrature amplitude modulation (M-QAM). The results showed that the proposed CNN schemes outperform the existing equalization algorithms and can maintain an excellent BER performance in the linear and nonlinear channel. However, for dynamic and deep memory scenarios, it obtains the optimal equalization performance at the cost of computational complexity, because the dimension of the input spatial information increases sharply and the convolution layer has to undertake tremendous computational pressure, resulting in the increase of network complexity [23]. In order to shrink the network complexity, a specific architecture combination was proposed to distribute the learning task [24; 25]. However, the original input data hardly experienced effective transformation, resulting in a large amount of time cost in the training process to extract the implicit features contained in the samples. Hence, the trade-off among computational complexity, training times, robustness, and generalization is one of the critical challenges and should be further developed in practical VLC applications. Besides, it is also necessary to consider how to consolidate the virgin data into alternate forms by changing the value, structure, or format so that the data may be easily parsed by the machine. In this paper, inspired by the approaches in [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25], the channel impairment compensation is formulated as a spatial memory pattern prediction problem, and an efficient impairment compensation scheme in terms of a model-driven-based CNN-LSTM is proposed to undo the memory nonlinearity of VLC. The underlying idea is that the Volterra structure is applied to pre-emphasize the original sequence and the appropriate pattern is formed as the spatial input accordingly. Then, a hybrid CNN and LSTM neural network is elaborately designed to learn the implicit feature of nonlinearity and predict the memory sequence directly, which can speed up the convergence process and improve the equalization accuracy. The main contribution of this work can be summarized as follows:  
* The structure information of the Volterra model is involved in the proposed DL equalizer to pre-emphasize the virgin data, which is favorable for the memory feature learning. Therefore, it can relax the learning pressure and reduce the structural complexity and training time. * Based on the traditional model-solving procedure, the channel impairment compensation is formulated as a spatial memory pattern prediction problem, and the proposed DL model is ingeniously used to achieve the accurate prediction. * Both the memory nonlinearity of the LED and the dispersive effect of the optical channel in a VLC system are simultaneously considered during the training stage. * The proposed scheme can still provide an excellent BER performance under the mismatched conditions of training and testing, showing a good robustness. Numerical simulations in terms of the learning and generalization show that the proposed scheme is able to predict the original transmitted signal and compensate the impairments with high accuracy and resolution.