## 3 Channel Estimation in Different Frequency Bands
### Channel Estimation for RIS Systems in Low Frequency Bands
#### 3.2.1 Channel Estimation for Fully-Passive RIS
Deep learning methods have received much attention in recent years and can be applied to channel estimation to achieve better performance. [PERSON] et al. [63] proposed a three-stage DNN framework, which can achieve better performance without relying on high pilot overhead and accurate channel statistics. Compared with the OMP method, this method can reduce the pilot overhead by approximately 50%. A cascaded channel estimation scheme based on dual-structured OMP (DS-OMP) was proposed in [64] by exploiting dual structural sparsity of inter-user angular cascade channels. In RIS-assisted wireless communication systems, not all devices are active at the same time, and assigning potential devices to pilot sequences as well would lead to excessive overhead. [PERSON] et al. [65] proposed an unsourced random access (URA) scheme and proposed a rank one decomposition-based message recovery and channel estimation method for RIS-assisted URAs. Both channel estimation and signal recovery alone require a lot of training and computation; therefore, [PERSON]. [66; 67] proposed joint channel estimation and signal recovery methods that were able to cost lower complexity. **Massive MIMO systems:** The larger number of antennas can make channel estimation more difficult to achieve. To complete the channel estimation, [PERSON] et al. [68] proposed a two-stage cascaded channel estimation method. In the first stage, a BiG AMP algorithm with sparse matrix decomposition was used. In the second stage, a matrix-completed Riemannian streamlined gradient algorithm was used to accomplish accurate channel estimation. The size of sparsity affects matrix decomposition and completion. The deep learning approach is further utilized. [PERSON] et al. [69] brought the results of channel recovery into the residual network to reduce the errors caused by grid mismatch. In order to improve the accuracy of the OMP algorithm, a residual structure-based OMP (RS-OMP) network was proposed. Then, a straightforward network (SN) structure was proposed instead of the OMP algorithm. **Wideband systems:** [PERSON] et al. [70] designed a novel phase-shifted channel estimation model for RIS-OFDM systems that satisfies the unit-mode constraint. With the same pilot overhead, this method improves gain by 14 dB over the ON/OFF method. [PERSON] et al. [71] proposed a method using RIS grouping in SISO systems. Both methods provide accurate channel estimation results and a reduction in training overhead. [PERSON] et al. [72] extrapolated the partial RIS elements to the complete channel by closing them and obtaining partial channel information. Using the compression idea, the extrapolation problem was transformed into a problem of recovering the channel parameters. The complete channel was reconstructed using the sparse Bayesian learning (SBL) framework finally. This method can reduce the pilot overhead while ensuring the accuracy. SNR is improved by 12 dB gain compared with the LS method. In OFDM systems, the carrier frequency offset problem is encountered. [PERSON] et al. [73] proposed a joint carrier frequency offset (CFO) and channel impulse response (CIR) estimation method to solve this problem. The method improved the channel estimation accuracy under OFDM systems. This method can improve performance gains up to 30 times compared with the benchmark scheme.