## 4 Signal Processing Algorithms for RIS Channel Estimation
### Deep Learning-Based Algorithms for RIS Channel Estimation
[36] used residual neural networks for cascaded channel estimation. The online cascade channel estimation was proposed to use the network as a multi-residual dense network. As shown in Figure 5, [PERSON] et al. [108] proposed a deep learning network architecture for RIS channel estimation. To reduce the pilot overhead, a strategy of RIS grouping was used. The grouping assumes that each group of RIS shares the same reflection coefficient, which is not consistent with reality and causes channel interference under a certain degree. [PERSON] et al. [108] designed two deep learning networks. The first network eliminates channel interference when RIS grouping was used, and the second network extrapolated the full channel from a partial channel. To separate the \(\mathbf{A^{\prime}}\) real part from the imaginary part, the network consists of three convolutional layers and multiple residual blocks (RBs) of the same structure. Each RB contains three identical dense blocks (DBs); each DB consists of five convolutional layers. A leaky rectified linear unit (LReLU) was used as the activation function for the first four layers in a DB. The output feature information from the previous layers was used as input to each subsequent convolutional layer, and \(\mathbf{\hat{A}^{\prime}}\) was the output of IENet to improved estimation accuracy for the partial channels. the result learned by the nonlinear transformations, was multiplied by a constant \(\beta\) and then added to the result. CENet was constructed from two convolutional layers and the same RBs. \(\mathbf{\hat{A}}\) was the output of CENet. In turn, all channel information was obtained. **RNN:** Considering the large number of RIS components and the relatively short coherence time, [PERSON] et al. [28] considered a deep learning scheme to infer the full channel from partial channels in the antenna domain. [PERSON] et al. used a RNN network in the time domain to explore the connection among different time blocks. In [109], the deep deterministic policy gradient-based scheme was developed to adapt to the dynamic channel variations to suppress the interference of time-varying channels. Machine learning for channel estimation using reinforcement learning correlation algorithms was not applicable in RIS systems. For the RIS phase shift problem, the data samples associated with the transition from one state to another, and it was difficult to define. In [110], a deep neural network model consisting of two DNNs was proposed which was more effective for a large number of RIS elements. **LSTM:** The work in [111] exploited the dual time-scale channel property, where the BS and RIS channels were static and the channel between the RIS and the user was dynamic. In the subsequent channel estimation process, [PERSON] et al. designed a LSTM based neural network framework for the channel decomposition process and the channel prediction process. [PERSON] et al. changed the connection layer according to the nonlinear mapping relationship between the input and the output, thus reducing the complexity. The specific application scenarios of various network architectures in the process of RIS channel estimation were described above. Suitable networks improve channel estimation performances in unfavorable scenarios such as high-speed time-varying, noisy, etc. The deep learning-based channel estimation algorithms and performance comparison are described in Table 8. Table 8 describes the methods from three aspects: antenna/RIS architecture, channel model, and performance analysis of deep learning model. Figure 5: A deep learning network architecture for RIS channel estimation.