## 2 System Model  
The system framework is shown in Figure 1. This paper considers a point-to-point millimeter-wave MIMO system, adopts the geometric Saleh-Valenzuela channel model, and uses a uniform square planar array (USPA). Because of the symmetrical structure of the precoding system, the hybrid combiner at the receiving end can be designed similarly as the hybrid precoder, so we omit it and focus on the design of precoders. Figure 1: Dynamic sub-connected hybrid precoding structure. Assuming the transmitter with \(\rm{N_{t}}\) antennas sends \(\rm{N_{s}}\) data streams to the receiver with \(\rm{N_{r}}\) receiving antennas, the number of RF chains is \(\rm{N_{rf}^{t}}\), and \(\rm{N_{s}}\leq\rm{N_{rf}^{t}}\leq\rm{N_{t}}\). The baseband signal \(\rm{y}\in\rm{C^{N_{r}\times 1}}\) at the receiver can be written as:  
\[\rm{y}=\rm{HFBx}+\rm{n} \tag{1}\]  
where \(\rm{H}\in\rm{C^{N_{r}\times N_{t}}}\) denotes the millimeter wave channel matrix; \(\rm{F}\in\rm{C^{N_{r}\times N_{s}^{t}}}\) is the analog precoding matrix; \(\rm{B}\in\rm{C^{N_{rf}^{t}\times N_{s}}}\) is the digital precoding matrix, satisfying \(\rm{\|FB\|_{F}^{2}=N_{s}}\); \(\rm{x}\in\rm{C^{N_{s}\times 1}}\) denotes the transmitted signal; \(\rm{n}\in\rm{C^{N_{r}\times 1}}\) denotes noise vector, obeying complex Gaussian distribution with 0-mean and \(\sigma^{2}\rm{I}\)-covariance. The input signal \(\rm{x}\) satisfies \(\rm{E_{x}}(\rm{x}\rm{x}^{H})=P/N_{s}*\rm{I_{N_{s}}}\). \(\rm{I_{N_{s}}}\) is the \(\rm{N_{s}}\)-dimensional unit matrix, and \(\rm{P}\) is the total output power. MmWave propagation has limited spatial selectivity or scattering, and the massive MIMO antenna array increases the correlation between the antennas [8]. Therefore, we adopted the geometric Saleh-Valenzuela channel model in this paper, using a uniform square planar array, and the channel matrix \(\rm{H}\) can be expressed as:  
\[\rm{H}=\sqrt{\frac{{N_{t}}{{N_{r}}}}{{N_{cl}}{N_{\rm{ray}}}}}\sum\limits_{i=1} ^{{N_{cl}}}{\sum\limits_{l=1}^{{N_{ny}}}{\alpha_{il}a_{r}(\Phi_{il}^{r},\theta_ {il}^{r})a_{l}(\Phi_{il}^{t},\theta_{il}^{t})^{H}}} \tag{2}\]  
where \(N_{cl}\) is the number of scattering clusters and \(N_{ray}\) is the number of paths in each cluster; \(\alpha_{il}\) denotes the complex gain of the \(\rm{I}\)-th path of the \(\rm{i}\)-th cluster; \(\phi_{il}^{r}\left(\phi_{il}^{t}\right)\) and \(\theta_{il}^{r}\left(\theta_{il}^{t}\right)\), respectively, denote the horizontal angle of arrival (departure) and the vertical angle of arrival (departure); \(a_{r}\left(\Phi_{il}^{r},\theta_{il}^{t}\right)\) and \(a_{t}\left(\Phi_{il}^{t},\theta_{il}^{t}\right)\) represent the antenna array response vectors at the receiver and the transmitter, respectively, and can be written as:  
\[a_{t}\left(\Phi_{il}^{t},\theta_{il}^{t}\right)=\frac{1}{\sqrt{N_{t}}}\left[ \begin{array}{c}1,e^{jkd\left(m\sin\left(\Phi_{il}^{t}\right)\sin\left(\theta _{il}^{t}\right)+n\cos\left(\theta_{il}^{t}\right)\right)},\ldots,\\ e^{jkd\left(\left(\sqrt{N_{t}}-1\right)\sin\left(\[PERSON]_{il}^{t}\right)\sin\left( \theta_{il}^{t}\right)+\left(\sqrt{N_{t}}-1\right)\cos\left(\theta_{il}^{t} \right)\right)}\end{array} \right]^{T} \tag{3}\]  
\[a_{r}\left(\[PERSON]_{il}^{r},\theta_{il}^{t}\right)=\frac{1}{\sqrt{N_{r}}}\left[ \begin{array}{c}1,e^{jkd\left(m\sin\left(\[PERSON]_{il}^{t}\right)\sin\left( \theta_{il}^{t}\right)+n\cos\left(\theta_{il}^{t}\right)\right)},\ldots,\\ e^{jkd\left(\left(\sqrt{N_{r}}-1\right)\sin\left(\[PERSON]_{il}^{t}\right)\sin \left(\theta_{il}^{t}\right)+\left(\sqrt{N_{r}}-1\right)\cos\left(\theta_{il}^ {t}\right)\right)}\end{array} \right]^{T} \tag{4}\]  
where \(k=2\pi/\lambda\), \(\lambda\) is the wavelength, \(d\) is the antenna spacing, and we set \(d=\lambda/2\). In addition, in the angle domain, the central angle of the cluster is uniformly distributed, and the angle spread of the multipath component in the cluster obeys the Laplace distribution.