## 4 Signal Processing Algorithms for RIS Channel Estimation
### Deep Learning-Based Algorithms for RIS Channel Estimation  
Deep learning has been widely used for RIS channel estimation [98; 99]. The learning ability of neural networks can be used to estimate the full channel from the partial pilot channel information [100; 101]; it can also be combined with image processing techniques to imagine the RIS channel information as two images: one corresponding to the real part channel information and one corresponding to the imaginary part channel information. Image processing techniques are more mature, and common interpolation and denoising methods for images are further applied in RIS. The coarse channel information is extracted, preprocessed, and then trained in the network to get the accurate CSI image. The introduction of image processing techniques has opened up a new area worth exploring for CSI [102; 103]. Most of the data processed by the channel estimation are complex numbers, but the existing deep learning library functions do not support the operation of the complex number domain. The general practice is that the data need to be preprocessed before input to the network, and the real and imaginary parts of the complex numbers are extracted and then input to the neural network. Due to there being two kinds of real numbers without mining the phase information of the complex numbers, this preprocessing scheme brings much information loss. The deep learning-based algorithms for RIS channel estimation are presented by different network architectures, which are divided into six main aspects: end to end, CNN, graph attention network (GANet), DNN, recurrent neural network (RNN), and long short-term memory (LSTM). **End to end network:** Existing RIS systems have separate functions for coding and modulation, channel estimation, channel equalisation, decoding and demodulation. Actually, these modules can be also considered as a whole and modelled as an end to end network. The end to end network can further optimise the performance of the system by avoiding the system falling into local optima. Simultaneously, it optimizes the connection weight coefficients of the sender, RIS and receiver to minimize the cross-entropy loss function of the system [100]. **CNN:** [PERSON] et al. [104] designed CNN networks for direct channel and cascade channel estimation, where the users accessed the network directly to estimate their own channels. A large amount of reflective surface channel information was coupled with each other, which were computationally difficult. Compensated learning-based neural network was proposed in [105] to dynamically track the CSI. Due to the powerful adaptive capability of deep learning networks, the estimation process learned the fading channel knowledge directly without the priori knowledge. [PERSON] et al. [105] reduced the number of hidden nodes and introduced an offset learning module to improve the performance in the network. [PERSON] et al. [57] modelled the channel estimation as an image problem, using CNN networks to denoise and approximate the optimal MMSE channel results. [PERSON] et al. [106] developed a deep residual learning (DReL) framework applied to multi-user cascaded RIS channel estimation. The correctness of DReL is verified by applying it to CNN networks using Bayesian estimation theory derivation, avoiding the multi-dimensional integral calculation of MMSE estimation. The accuracy of channel estimation is further improved by exploiting the advantages of CNN and DReL in feature extraction and denoising. **GANet:** [PERSON] et al. [107] used GANet for full duplex wireless communication link channel estimation. The training results are robust under different propagation channels with better performance compared with conventional LS estimation. **DNN:** During the estimation of partially activated RIS element channel coefficients, a three-stage estimation scheme was proposed in [63] for direct channel. Active RIS element cascade channel and inactive RIS element cascade channel was continuously trained to achieve good accuracy. [PERSON] et al.