## 3 The Proposed Scheme
### System Architecture  
The diagram of the proposed DL-NPE for OFDM-based VLC system is shown in Figure 3. Compared with the conventional OFDM receiver in Figure 1, the DL-NPE replaces the traditional module, i.e., channel estimation and the constellation de-mapping, and employs two subnets, i.e., \(\mathcal{S}1\) and \(\mathcal{S}2\), for channel impairment compensation and symbol detection, respectively. Note that the network \(\mathcal{S}1\) is composed by the cascaded sub-layer block including dense layer and activation function. As for \(\mathcal{S}2\), it is made up by a cascaded sub-layer block containing dense layer, a normalization layer, and an activation function. In addition, different amounts of neurons can be used in different dense layers for both \(\mathcal{S}1\) and \(\mathcal{S}2\). Furthermore, the proposed scheme incorporates the traditional solution of the channel estimation and symbol detection algorithm into the system architecture. After CP removal, FFT calculation, and symmetric data removal, the time domain receiving \(\mathbf{y}\) is transformed into the frequency domain \(\mathbf{Y}\). Since \(\mathbf{Y}\) is the complex symbol and cannot be directly used for the NN input, the real and imaginary parts of \(\mathbf{Y}\) should be split first and reformatted in a new symbol \(\mathbf{Y}\in\mathbb{R}^{\mathcal{M}}\), where \(\mathcal{M}=2(N-1)\). In order to improve the convergence rate and the generalization ability of the DL-NPE, the min-max normalization is utilized to pretreat the \(\mathbf{Y}\), shown as follows:  
\[\overset{-}{\mathbf{Y}}=\frac{\overset{-}{\mathbf{Y}}-\min\left(\overset{-}{ \mathbf{Y}}\right)}{\max\left(\overset{-}{\mathbf{Y}}\right)-\min\left( \overset{-}{\mathbf{Y}}\right)}. \tag{10}\]  
During the training phase, the pilots are deployed in the first OFDM block within one frame of training set, and the remaining are used for the transmitted data. Based on  
Figure 3: Diagram of the proposed DL-NPE scheme for the OFDM-based VLC receiver. this mapping, the distorted pilots \(\mathbf{Y}_{p}\) and useful data \(\mathbf{Y}_{d}\) can be easily extracted from \(\mathbf{Y}\). Instead of using a DNN to estimate the original data straightforwardly ([PERSON] et al., 2018), the \(\mathbf{Y}_{p}\) and \(\mathbf{X}_{p}\) are first fed into the \(\mathcal{S}1\) network for noise reduction and roughly estimating the channel state information. Assume that \(\mathcal{S}1\) employs \(\mathcal{L}_{1}\) layers in FC-DNN. As for the first dense layer, let \(\mathcal{D}_{1}^{\mathcal{S}1}\) denote the number of neurons and \(\mathbf{t}_{1}^{\mathcal{S}1}\in\mathbb{R}^{\mathcal{M}}\) be the layer input. Then, the corresponding output can be expressed as follows:  
\[\mathbf{h}_{1}^{\mathcal{S}1}=\mathbf{W}_{1}^{\mathcal{S}1}\mathbf{t}_{1}^{ \mathcal{S}1}+\mathbf{b}_{1}^{\mathcal{S}1}, \tag{11}\]  
where \(\mathbf{W}_{1}^{\mathcal{S}1}\in\mathbb{R}^{\mathcal{D}_{1}^{\mathcal{S}1} \times\mathcal{M}}\) and \(\mathbf{b}_{1}^{\mathcal{S}1}\in\mathbb{R}^{\mathcal{D}_{1}^{\mathcal{S}1}}\) are the weight matrix and bias vector, respectively. Then, \(\mathbf{h}_{1}^{\mathcal{S}1}\) is fed into the activation function to improve the expression ability of \(\mathcal{S}1\) to the true CIR. Note that the _Relu_ function \(\rho_{RL}(\cdot)\) is employed as the activation function for most layers. However, beyond that, the linear activation function is deployed in the last layer due to the main goal of \(\mathcal{S}1\) being to learn the true CIR from the pilot symbols. In addition, the neuron number of the last layer should be set as \(\mathcal{M}\) so that the dimension of final output of \(\mathcal{S}1\) can keep consistent with that of the pilot. After an efficient learning, the estimated CIR \(\hat{\mathbf{h}}\) can be obtained at the output of \(\mathcal{S}1\).