## 4 Channel Estimation Based on Deep Learning for RIS-Aided Communication Systems  
RIS is one of the most promising techniques for 6G communications, consisting of numerous passive reflective metamaterial antenna elements that form a plane with low cost, low power consumption, easy deployment, etc. RIS can reconfigure the wireless propagation environment by intelligently adjusting the amplitude and phase to enhance wireless communications' spectrum and energy efficiency [82]. When combined with wireless communication systems, RIS can modify or improve existing communication concepts, thereby assisting in meeting the high standards of 6G communication. Figure 18 shows an example of RIS-aided communication systems. In this setup, the base station (BS) is outfitted with \(M\) antennas and serves \(K\) users, each with a single antenna, and the RIS is outfitted with a total of \(N\) passive reflective elements. Furthermore, the BS adjusts the parameters of the reflective elements through the RIS controller. The direct link between the BS and the users is blocked, making the BS unable to communicate properly with the users. With the deployment of RIS, an additional link between them is established. Let \(\mathbf{h}_{d,k}\in\mathbb{C}^{M\times 1}\) represent the direct channel between the \(k\)th user and the BS, \(\mathbf{h}_{r,k}\in\mathbb{C}^{N\times 1}\) is the channel between the \(k\)th user and the RIS, and \(\mathbf{G}\in\mathbb{C}^{M\times N}\) is the channel between the RIS and the BS. Then, the received signal at BS can be expressed as:  
\[\mathbf{y}=\sum_{k=1}^{K}(\mathbf{h}_{d,k}+\mathbf{G}\mathrm{diag}(\theta) \mathbf{h}_{r,k})u_{k}+\mathbf{v} \tag{12}\]  
where \(\theta=[\theta_{1},\theta_{2},\dots,\theta_{N}]^{\mathrm{T}}\) denotes the reflection vector of the RIS, \(\theta_{n}\) is the reflection coefficient of the \(n\)th reflection element, \(u_{k}\) is the symbol sent by the \(k\)th user, and \(\mathbf{v}\in\mathbb{C}^{M\times 1}\) is the received noise. In particular, \(\theta_{n}\) can be further denoted by \(\theta_{n}=\beta_{n}e^{\phi_{n}}\), with \(\beta_{n}\in[0,1]\) \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**Characteristics**} & \multicolumn{1}{c}{**Data-Driven Approach**} & \multicolumn{1}{c}{**Model-Driven Approach**} \\ \hline \multirow{4}{*}{Advantages} & Self-learning/automatic feature extraction & ✓ & \\ \cline{2-4}  & High accuracy & ✓ (With sufficient training data) & ✓ (When the model is well designed) \\ \cline{2-4}  & Utilization of prior knowledge & & ✓ \\ \cline{2-4}  & Interpretability & & ✓ \\ \hline \multirow{4}{*}{Disadvantages} & Large data requirements & ✓ & \\ \cline{2-4}  & Risk of overfitting & ✓ & \\ \cline{1-1} \cline{2-4}  & High computational complexity & ✓ & \\ \cline{1-1} \cline{2-4}  & Inflexibility & & ✓ \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of the advantages and disadvantages of data-driven and model-driven approaches. and \(\phi_{n}\in[0,2\pi]\) corresponding to the amplitude and phase of the \(n\)th reflection element, respectively. Since passive RIS elements cannot actively transmit and receive signals and perform additional signal processing, \(\mathbf{h}_{r,k}\in\mathbb{C}^{N\times 1}\) and \(\mathbf{G}\in\mathbb{C}^{M\times N}\) cannot be directly estimated. Therefore, it is necessary to estimate the channel between the \(k\)th user and the RIS and between the RIS and the BS as the cascaded channel \(\mathbf{H}_{k}\triangleq\mathbf{G}\mathrm{diag}(\mathbf{h}_{r,k})\in\mathbb{C }^{M\times N}\). In this instance, Equation (12) can be re-expressed as:  
\[\mathbf{y}=\sum_{k=1}^{K}(\mathbf{h}_{d,k}+\mathbf{H}_{k}\theta)u_{k}+\mathbf{v} \tag{13}\]  
It is noteworthy that, in a TDD system, the downlink CSI can be obtained from the uplink channel estimation because of the channel reciprocity [83]. Channel estimation in RIS-aided systems presents more challenges compared to traditional systems. During signal reflection, RIS functions as a passive device without the capability to receive or sample signals.