## 4 Channel Estimation Based on Deep Learning for RIS-Aided Communication Systems
### Application of Deep Learning in Channel Estimation for RIS-Aided MU Systems  
MU communication systems serve a vital role in modern wireless communications, which improve the spectrum efficiency by enabling multiple users to share the same spectrum resource simultaneously. By adjusting its surface units, RIS can modulate the reflective properties of signals to optimize channel conditions, thereby enhancing the system performance. However, accurately estimating the channels in RIS-aided MU systems presents a new challenge. Utilizing the powerful learning capability of deep learning to address this issue is a hot trend in current research. In 2021, [PERSON] et al. [92] innovatively proposed a DNN based on the deep image prior (DIP) in channel estimation for RIS-aided MU SIMO-OFDM systems. This network is untrained and can optimize its parameters in real time. In this scheme, the LS algorithm first estimates the effective channel, which is then denoised using the untrained DNN. After denoising, the channel utilizes the information from the DFT-based reflection pattern matrix to obtain the CSI of the direct and cascade channels. In simulations, the untrained DNN exhibits a superior NMSE performance over the conventional methods (LS and MMSE), while it has low complexity because no pre-training is required. Moreover, it can maintain high accuracy in the case of hardware impairments and adjust flexibly to various scenarios and channel settings. In 2022, [PERSON] et al. [93] modelled channel estimation for RIS-aided MU communication (MUC) systems as a noise reduction problem and developed a flexible deep residual learning (DReL)-based channel estimation framework. They derived an MMSE estimator based on a deep residual network (DRN) using Bayesian theory under the MMSE criterion within this framework. In addition, they introduced a CNN-based DRN (CDRN) designed to recover the noisy channel matrix. The network features a CNN denoising module with an element-by-element subtraction structure. This design enables it to simultaneously extract the spatial properties of the noisy channel matrix and the additive characteristics of the noise. Experimental results demonstrate that this framework does not require additional sensing devices in the RIS. Furthermore, its NMSE performance closely approximates the optimal MMSE estimator, which requires deriving from the cascade channel's prior probability density function. In RIS-aided MU MIMO-OFDM systems, the cascaded channel has high dimensionality and complex statistical properties. These factors make it challenging to achieve the ideal MMSE algorithm with the best performance. In [94], [PERSON] et al. applied the concept of image super-resolution and developed an SRDnNet, which combines the properties of SRCNN and DnCNN to obtain accurate CSI. The central idea of SRDnNet is to regard the estimated channel of pilot positions as a low-resolution image. It uses the enhanced SRCNN to extract input features, learns the appropriate interpolation method, and generates a coarsely estimated channel matrix. After that, the DnCNN performs denoising to recover the channel coefficients from the noisy channel matrix. Compared to the ChannelNet [57], the SRDnNet can receive rawer inputs and requires just one division operation between the received and transmitted pilots, leading to decreased computational and time consumption. Without prior information on the direct and cascaded channels, the SRDnNet outperforms the conventional LS, MMSE algorithms, and the ChannelNet, with NMSE gains exceeding 10 dB. In 2023, [PERSON] et al. [95] proposed a DCSaNet based on dilated convolution and self-attention to enhance the channel estimation accuracy of RIS-aided MUC systems. This network uses dilated convolutional blocks to enlarge the receptive field and optimize feature extraction. Additionally, it employs self-attention blocks to enable the system to concentrate on critical channel features.