## 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  
In a fully passive RIS-assisted low frequency system, channel estimation can be accomplished for the cascaded channel. In addition, the obtained CSI is sufficient to accomplish setting the optimal phase to achieve maximum transmission efficiency. The methods applied will be varied for different system settings, we will present the channel estimation methods for different system settings in the following. **MISO systems:** [PERSON] et al. [53] first proposed the ON/OFF channel estimation method. This method accomplishes channel estimation by sequentially turning on the RIS element. Since the cascaded channels are only estimated one by one, the estimated variance of each element is equal to 2. To reduce the variance, a minimum variance unbiased (MVU) estimator was proposed in [54]. This method can be \(T\) (training periods) times more accurate than the ON/OFF method of estimation. However, it required large pilot overhead. To further reduce the pilot overhead, different approaches were proposed in [55; 56]. [PERSON] et al. [55] proposed a rank-one matrix factorization (MF) approach. AM and gradient descent methods were then used to find the approximate optimal solution. An iterative expectation maximization (EM) algorithm for semi-blind channel estimation was proposed in [56]. The method first transforms the channel estimation problem into a maximum likelihood estimation problem by initializing the semi-blind channel estimation with pilots and solving it using EM. This method can reduce the pilot overhead by 85% compared with the benchmark solution. [PERSON] et al. [57] proposed an linear minimum mean square error (LMMSE) based channel estimation method that further utilized CNN to approximate the optimal solution. Both denoising CNN (DnCNN) and fast and flexible denoising network (FFDNet) were considered in this paper. Improved MSE performance of DnCNN and FFDNet-based  
Figure 4: Channel estimation for RIS systems in low frequency bands. channel estimators as channels become more highly correlated. This method offered high performance and relatively low implementation complexity. **MIMO systems:** The increased number of users and antennas can make channel estimation more challenging. In [58], a three-stage channel estimation method was proposed considering the redundancy among channels without any assumption of sparsity and low rank. The channel matrix of a typical user directly to the BS and the channel matrix reflected by the RIS were estimated in the first two stages, respectively. Finally, the channel estimation for other users was completed using the strong correlation between other users and that user. This can reduce the pilot overhead and save estimation time in MIMO systems. [PERSON] et al. [59] used the quasi static property of BS-RIS to perform channel estimation at the time scale. Small-scale channel estimation was performed between UE and RIS, which can reduce the pilot overhead significantly. Although this method reduces pilot overhead, performance is worse than MVU. This property is used in later channel estimation methods frequently. A normally open training protocol was proposed in [60] and utilized a common link structure to reduce the pilot overhead. This method offers a performance gain of approximately 15 dB compared with the ON/OFF method. To reduce the training overhead, [PERSON] et al. [61] proposed the anchor-assisted approach, which assisted RIS in channel estimation by setting anchor points. While achieving the same performance as the baseline solution, this method reduces the number of training symbols by approximately 50. The tensor modeling approach is also applicable to channel estimation. [PERSON] et al. [62] proposed channel estimation method relying on parallel factor (PARAFAC) of received signal tensor modeling. This method dealt with the non-ideal case, when there is phase perturbation and when the receiver does not know the RIS phase shift.