## 3 Channel Estimation in Different Frequency Bands
### Channel Estimation for RIS Systems in High Frequency Bands
#### 3.1.1 Channel Estimation for Fully-Passive RIS  
**Single-user:** With passive characteristics of fully-passive RIS, it cannot complete the reception and transmission of the signal. Therefore, the existing channel estimation method is to complete the estimation of the cascaded channel, as shown in Figure 2a. To achieve good reflection characteristics, the channels of BS-RIS and RIS-UE are considered as the overall channel, and the CSI obtained through the cascaded channel is sufficient to complete the phase shift setting of the RIS. The sparsity of mmWave can be exploited to convert the channel estimation problem into a sparse channel recovery problem, which can be solved using a compressive sensing (CS) algorithm. [PERSON] et al. [26] converted the channel estimation problem into a sparse recovery representation of the cascaded channel using the property of Khatri-Rao and Kronecker products. The problem was solved using the orthogonal matching pursuit (OMP) and generalized approximate message passing (GAMP) algorithms. Compared with the least square (LS) method, which requires at least 1024 overheads, the GAMP algorithm in this paper requires only 100 overheads and has an NMSE of 0.04. In channel estimation, excessive training overhead can lead to a reduction in signal efficiency. Therefore, different approaches are proposed in the following literatures. [PERSON] et al. [27] proposed a two-stage beam training and channel estimation method based on fast alternating LS (FALS), which can reduce the complexity. The training overhead can be reduced by recovering the complete channel matrix using the observed partial channel matrix. Compared with the OMP and atomic norm minimization (ANM) algorithms, the method used in this paper can reduce the number of training symbols by about 45% and is second only to the OMP algorithm in terms of complexity. Deep learning methods have attracted much attention in recent years and can be effectively applied to channel estimation. [PERSON] et al. [28] proposed a channel subsampling and a two-part deep neural network (DNN) approach to reduce the training overhead in dynamic time-varying channels. The first part describes the RIS dynamic channel using the neural ordinary differential equation (ODE), and the latter part uses the ODE to modify the structure of the neural network to complete the channel extrapolation. [PERSON] et al. [29] simulated a conventional gradient descent algorithm using a model-driven depth unfolding approach. A computationally intensive training process was performed in the offline phase, and only low-complexity computations are required in the projection phase. The deep learning approach used in this paper reduces the overhead by 25% compared with the LS algorithm. Figure 3: Channel estimation for RIS systems in high frequency bands. **Multi-user:** More pilot overhead and interference among UEs need to be considered in multi-user scenarios; therefore, a more suitable method for channel estimation needs to be found. Since the number of paths in the BS-RIS-UE will be few unlike conventional MIMO mmWave channels where only row sparsity is available, in RIS-assisted mmWave communication systems with row block sparsity, this feature can be exploited to further reduce the training overhead [25]. To reduce training overhead and pilot overhead, [PERSON] et al. [22] used row-column block sparsity on the foundation of [25]. Using this property, a method was proposed to exploit inter-user correlation to achieve joint channel recovery for multiple users. The proposed method reduces the pilot overhead compared with LS, multiple measurement vector (MMV), etc. By projecting and exploiting the scaling relationships among different users, the approach in this paper reduces the overhead by 80% and 60%, respectively, compared with the LS algorithm and MMV. Channel estimation efficiency can be improved by setting up a reasonable transmission protocol. To reduce the pilot overhead, the sparsity, and correlation of mmWave multi-user were exploited in [23; 30].