## 4 Signal Processing Algorithms for RIS Channel Estimation
### Composition-Based Algorithms for RIS Channel Estimation
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Ref.** & **Year** &
\begin{tabular}{c} **Antenna/RIS** \\ **Architecture** \\ \end{tabular} & **Channel Model** & **Performance Analysis of Deep Learning Model** \\ \hline [PERSON] et al. [28] & 2022 & MISO/Passive RIS & Time-varying Channel & Designed a two-part network of the proposed time interpolation and space extrapolation to improve estimation accuracy and robustness \\ [PERSON] et al. [36] & 2022 & MIMO/Passive RIS & Static channel & Designed the GAN-CBD, CBDNet, and MRDNet to get better generalization and fitting ability \\ [PERSON] et al. [57] & 2021 & MISO/Passive RIS & Static channel & Designed a denoising CNN to reduced computational complexity and improved estimation accuracy \\ [PERSON] et al. [63] & 2021 & MIMO/Semi-passive RIS & Static channel & Designed a three-stage training strategy RNN to reduced pilot overhead and improved estimation accuracy \\ [PERSON] et al. [104] & 2020 & MIMO/Passive RIS & Static channel & Designed a CNN network to improved channel estimation accuracy \\ [PERSON] et al. [105] & 2022 & MIMO/Passive RIS & Static channel & Used a learning-based CNN to reduced computational complexity and improved channel estimation accuracy (when the the number of pilots was more than 120, \(e_{\text{NMSE}}\) \textless{} 0.2) \\ [PERSON] et al. [107] & 2021 & MIMO/Passive RIS & Static channel & Used a graph attention network to enhanced system robustness and reduced pilot overhead \\ [PERSON] et al. [106] & 2022 & MIMO/Passive RIS & Static channel & Designed the deep residual network and CNN network to improved estimation accuracy and reduced reflective elements by 70\% compared with LMMSE (\(e_{\text{NMSE}}\) = \(-\)8 dB) \\ [PERSON] et al. [108] & 2021 & MISO/Passive RIS & Static channel & Designed a channel extrapolation network to improved estimation accuracy and enhanced network generalization \\ [PERSON] et al. [109] & 2020 & MIMO/Passive RIS & Time-varying channels & Used a deep reinforcement learning network to increased system capacity and suppressed interference \\ [PERSON] et al. [110] & 2023 & MIMO/Passive RIS & Static channel & Designed a double deep learning network to reduced computational complexity \\ [PERSON] et al. [111] & 2022 & MISO/Passive RIS & Time-varying channel & Designed a sparse-connected LSTM network to improved estimation accuracy, reduced time delay and pilot overhead \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Deep learning-based algorithms comparison for RIS channel estimation. **AMP-deep learning:** Conventional CS algorithms AMP algorithm can reduce the pilot overhead substantially, but the estimation accuracy is insufficient. [PERSON] et al. [113] proposed a hypernetwork-assisted based learned AMP network with dynamic shrinkage parameters, where the adaptive shrinkage parameters of the network output are used among layers instead of a fixed value, thus improving the estimation accuracy. The core of the conventional approach is in the human perception and modeling of the target problem, as well as proposing a solver to solve the model. Deep learning methods that use parameters to fit the problem can outperform conventional methods in case of good convergence. In most cases, the ability to fit a large number of network parameters is stronger than that of the models constructed using some prior knowledge in conventional methods. As the complexity of the problem increases, the advantage of deep learning becomes more obvious; the conventional solution incorporating deep learning solution has a broad development prospect. The composition-based channel estimation algorithms and performance comparison are described in Table 9. Table 9 describes the methods from three aspects: antenna/RIS architecture, major problem, and performance analysis of deep learning model.