## 3 Channel Estimation in Different Frequency Bands  
In the 5G wireless communications, as the low frequency band is utilized fully, the target is shifted to the higher frequency bands with higher bandwidth. MmWave technology is considered to be an effective solution to the problem of spectrum resource shortage, and THz with higher spectrum will also become an important direction for the future beyond 5G (B5G) and 6G wireless communication systems. Although the communication in high frequency bands can solve the problem of spectrum resource shortage, due to its small wavelength characteristics, it will produce serious path loss, resulting in small coverage of mmWave. RIS can improve the coverage of its communication at a lower cost. As shown in Figure 1, the mmWave frequency bands is 30-300 GHz, and its wavelength is only 1-10 mm. The THz has the frequency of 300 GHz-10 THz and it has a much shorter wavelength. The higher frequency band reaches the visible light band, which is 395-750 THz. RIS not only extends wireless coverage, but also plays a role in improving communication quality and expanding communication capacity. However, the optimization of both beamforming and reflection coefficient matrix of RIS transceivers cannot be achieved without accurate CSI; it is crucial to use efficient, low-overhead, and low-complexity channel estimation methods. Due to the difference in frequency bands and hardware architecture, the chosen estimation method will be different. The method chosen will also vary in different system settings such as single input single output (SISO), multiple input single output (MISO), single input multiple output (SIMO), and MIMO. In the following, we outline the advantages and disadvantages of different channel estimation methods in the high and low frequency bands, discuss representative work and present the basic principles. In this discussion, since the channel estimation for BS-user equipment (UE) can often be obtained using common channel estimation methods to obtain CSI or directly propagate blocked, only the channel reflected through the RIS is discussed. As shown in Figure 2, we considered an uplink MIMO system model. Assume that the BS is equipped with \(M=M_{\rm h}\times M_{\rm v}\) antennas uniform planar array (UPA), where \(M_{\rm h}\) is the number of antennas in the horizontal direction and \(M_{\rm v}\) is the number of antennas in the vertical direction. The RIS is equipped with \(N=N_{\rm h}\times N_{\rm v}\) reflecting elements UPA, where \(N_{\rm h}\) and \(N_{\rm v}\) are the number of reflecting elements in the horizontal and vertical directions, respectively. In this communication system, there are \(K\) single antenna users. The channel from the RIS to the BS can be denoted by \(\mathbf{H}\in\mathbb{C}^{M\times N}\), and the channel from the \(k\)th (\(k\in K\)) user to the RIS can be denoted by \(\mathbf{h}_{k}\in\mathbb{C}^{N\times 1}\). The reflection matrix of the RIS element can be denoted by \(\mathbf{\phi}=[\beta_{1}\mathrm{e}^{\mathrm{i}\alpha_{1}},\beta_{2}\mathrm{e}^{ \mathrm{i}\alpha_{2}},\cdots,\beta_{N}\mathrm{e}^{\mathrm{i}\alpha_{N}}]^{ \mathrm{T}}\in\mathbb{C}^{N\times 1}\), where \(\beta_{n}\) and \(\alpha_{n}(n=1,2,\cdots,N)\) denote the reflection amplitude and phase of the \(n\)th RIS reflector, respectively [22; 23; 24]. As shown in Figure 2, assuming that user \(k\) sends the pilot symbol \(x_{k,t}\) at time slot \(t(t\in T)\), the received signal \(\mathbf{y}_{k,t}\) at BS can be expressed as:  
\[\mathbf{y}_{k,t}=\mathbf{h}_{\rm d,k}x_{k,t}+\mathbf{H}\mathrm{diag}(\mathbf{\phi})\mathbf{h}_{k}x _{k,t}+\mathbf{n}_{k,t} \tag{1}\]  
where \(\mathbf{n}_{k,t}\) represents additive white Gaussian noise (AWGN), assuming \(\mathbf{n}_{k,t}\sim\mathcal{CN}(0,\sigma^{2}I_{M})\), and \(\sigma^{2}\) is the noise power. \(\mathbf{h}_{\rm d,k}\) is the direct channel between the BS and user \(k\). This paper assumes that the direct channel is blocked; therefore, \(\mathbf{h}_{\rm d,k}=\mathbf{0}\).