## 2 System Model and CSI Collection
### CSI Model  
Unlike wired channels, wireless channels may face a series of attenuation processes during signal transmission, such as large-scale fading, shadowing, multipath effects, and distortion. CSI is used to describe the state attributes of a communication link. It can reflect the attenuation of signals in the transmission link. Mathematically, it corresponds to the value of each element in the channel gain matrix \(\mathbf{H}\), such as distance attenuation, environmental attenuation, and signal scattering information. By using channel state information, communication systems can adaptively adjust relevant transmission and reception processes to adapt to the time-domain dynamics of the channel. CSI information can also guide the adjustment process of multi-antenna communication systems to improve the overall performance of the system. The signal reception process of a wireless fading channel can be modeled as follows:  
\[\mathbf{y}=\mathrm{H}\mathbf{x}+\mathbf{w}, \tag{1}\]  
where \(\mathbf{y}\) denotes the received signal vector, \(\mathbf{w}\sim N(0,\sigma_{w}^{2}\,\mathbf{I}_{\mathbf{n}})\) is the additive Gaussian white noise vector, and \(\mathbf{x}=[x_{1},\ldots,x_{M}]\) represents the transmitted signal vector. Considering the characteristics of the normal distribution, the channel coefficient matrix \(\mathbf{H}=diag\{h_{1},\dots,h_{N}\}\) also follows the same logarithmic normal distribution. Without a loss of generality, the probability density function of \(h\) can be expressed as follows [25; 26]:  
\[p_{h}(h)=\frac{1}{\sqrt{2\pi}\,\sigma_{h}\,h}\exp[-\frac{\left(\ln h-\mu_{h} \right)^{2}}{2\,\sigma_{h}^{2}}]. \tag{2}\]  
\(\sigma_{h}^{2}\) and \(\mu_{h}\) correspond to the variance and mean of \(\ln h\), respectively, and \(\ln h\) follows a Gaussian distribution. We standardize \(h\), i.e., \(E[h]=1\), where \(E[. ]\) represents the expectation calculation to ensure that the average power of the wireless signal is constant. Thus, the probability density function of \(h\) can be further expressed as follows:  
\[p_{h}(h)=\frac{1}{\sqrt{2\pi}\,\sigma_{h}\,h}\exp[-\frac{\left(\ln h+\sigma_{h }^{2}\,/2\right)^{2}}{2\,\sigma_{h}^{2}}]. \tag{3}\]  
For the symbol detection process of the receiver, a simple and low complexity linear detector minimum mean square error (MMSE) is usually used for processing to achieve channel estimation and equalization, which can be represented as follows:  
\[\mathbf{\hat{x}}=\underset{x\in X}{\arg\min}\left\|\mathbf{y}-\mathbf{\hat{H} x}\right\|_{2}^{2}, \tag{4}\]  
where \(\mathbf{\hat{H}}\) represents the estimated value of the channel state information, and \(\left\|.\right\|_{2}\) represents the binomial operation. According to references [27; 28], it can be assumed that each constituent element in \(\mathbf{\hat{H}}\) follows a Gaussian distribution; then, we have \(\mathbf{\hat{H}}\sim N(\mathbf{H},\sigma_{h}^{2}\,\mathbf{I_{n}})\). From the above derivation, it can be seen that the channel state information can be calculated by referring to the estimation process of the channel. The complex sequence corresponding to CSI values can be extracted as follows:  
\[\mathbf{Y}\in\mathbb{C}^{N_{sa}\times N_{tx}\times N_{tx}\times N_{rx}}, \tag{5}\]  
where \(N_{sa}\) represents the number of sampled network packets, \(N_{sc}\) represents the number of subcarriers, and \(N_{tx}\) and \(N_{rx}\) represent the number of transmitted and received antennas, respectively. It is worth noting that the CSI information of wireless channels has two unique properties. On the one hand, the interchangeability of channel status indicates that the channel state information detected by the transmitting and receiving ends at the same time is nearly the same. On the other hand, there is negligible spatial correlation; that is, when the distance between the channel transmitting and receiving ends is more than half a wavelength, the detected CSI information is not correlated with the information of the transmitting and receiving ends.