# The Deep Deterministic Policy Gradient Algorithm Based on RIS Technology in a Coal Mine Tunnel
## 2 System Model  
### Coal Mine Channel Modeling and Reflection Characterization Analysis  
Compared with the indoor space on the ground, the wireless channel in the mine exhibits unique propagation characteristics due to its narrow and closed structure and significant multipath effect. In this closed environment, signals undergo multiple reflections and attenuations between tunnel walls, making the propagation path more complex and uncertain. To thoroughly analyze these characteristics and optimize signal coverage and communication quality, this paper selects a rectangular tunnel with a simple structure and good geometric characteristics as the research model to facilitate the accurate construction of a channel propagation model. In this model, a Cartesian coordinate system is established at the center of the rectangular tunnel section, assuming that the tunnel width is \(2a\) and the height is \(2b\). The relative permittivity of the side walls, top, and bottom is \(\varepsilon_{r}\). As shown in Figure 1, Figure 1a shows the structure of the rectangular straight tunnel model assisted by the coal mine RIS. Figure 1b shows the system model under the corresponding two-dimensional perspective. In addition, it is also worth noting that this paper only investigates the Non-Line of Sight (NLoS) propagation system characteristics and does not consider the effect of Line of Sight (LoS) on the system due to the complex long-distance propagation in the confined space. The model consists of a Base Station (BS) with \(M\) antennas, a RIS with \(N\) intelligent reflection units, and \(K\) single-antenna users (User Equipment, UE). The RIS is deployed on tunnel walls or the surface of large equipment and devices within the environment. By dynamically adjusting the phase shift and amplitude of the RIS reflective element, the propagation direction of the reflected signal can be precisely controlled, thereby constructing an alternative reflection path to bypass obstacles in the tunnel. This enables RIS to effectively redirect signals to users that are originally in an NLoS state, overcoming the limitations of direct signal transmission. It is assumed that the BS-RIS and RIS-UE channels are frequency-flat fading, and all the wireless channels remain unchanged in each transmission block. \(\mathbf{H}_{nm}\in\mathbb{C}^{N\times M}\) represents the channel from the BS to the RIS and \(\mathbf{H}_{rn}\in\mathbb{C}^{N\times K}\) represents the channel from the RIS to the user. The cascaded channel of the system (BS-RIS-UE) can be expressed as follows [30]:  
\[\mathbf{H}=\mathbf{H}_{nm}^{H}\Phi\mathbf{H}_{nn} \tag{1}\]  
\[\mathbf{\Phi}=diag(\phi_{1},\phi_{2},\cdots,\phi_{N})\] \[= \begin{bmatrix}\beta(\theta_{1})e^{i\theta_{1}}&0&\cdots&0\\ 0&\beta(\theta_{2})e^{i\theta_{2}}&\cdots&0\\ \vdots&\vdots&&\vdots\\ 0&0&\cdots&\beta(\theta_{N})e^{i\theta_{N}}\end{bmatrix} _{N\times N} \tag{2}\]  
where \(\phi_{n}=\beta(\theta_{n})e^{i\theta_{n}}\),\(\theta_{n}\in[0,2\pi)\) is the phase shift change caused by the \(n\)th reflection element of the RIS, and \(\beta(\theta_{n})\) is an amplitude function based on the phase shift \(\theta_{n}\), which reflects the amplitude change of the signal reflected from the RIS. \(\beta(\theta_{n})\) and \(\theta_{n}\) satisfy the following relationship:  
\[\beta(\theta_{n})=(1-\beta_{\text{min}})f(\theta_{n})+\beta_{\text{min}} \tag{3}\]  
Figure 1: (**a**) RIS-assisted coal mine communication system; (**b**) RIS-assisted coal mine communication system from a two-dimensional perspective. where \(\beta_{\text{min}}\in[0,1]\) represents the minimum amplitude of the reflection coefficient.