# High-Speed Surface Property Recognition with a 140 GHz Frequency
## 5 Scenario and Network Analysis  
We described the actual collaborative perception scenario that our experimental setup aims to emulate, as shown in Figure 3. The target surface reflects signals launched by a base station to a terminal (terahertz sensor) on a moving vehicle. The vertical distance between the surface and the vehicle's trajectory is assumed to be 10 m. To avoid the challenges of excessive distances, we focused on a detection range where the incident angle does not exceed 60\({}^{\circ}\). This corresponds to a horizontal span of 17.3 m. With a turntable rotating at an angular speed of 10\({}^{\circ}\)/s, it takes 6 s to traverse a range of 60\({}^{\circ}\). This corresponds to a \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Idx.**} & **Rotational** & \multirow{2}{*}{**Average \#**} & **Query Interval** & **Cumulative** & \multirow{2}{*}{**Counts**} \\  & **Speed (\({}^{\circ}\)/s)** & & **(s)** & **Length** & \\ \hline
1 & 20 & 4 & 0.1 & 55 & 504 \\
2 & 20 & 4 & 0.05 & 85 & 504 \\
3 & 20 & 1 & 0.05 & 85 & 504 \\
4 & 10 & 4 & 0.1 & 110 & 504 \\
5 & 10 & 1 & 0.05 & 170 & 504 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Original Data. vehicular speed of approximately 10 km/h, which is similar to the pace of a pedestrian. For a rotational speed of 20\({}^{\circ}\)/s, the emulated vehicular speed increases to around 20 km/h, which is similar to the speed of a vehicle in low-speed cruising. Using the raw dataset we collected, we have performed a classification task to distinguish between different rough surfaces. The model takes scattering sequence data (\(X\)) from a specific position on a surface as input. Each sequence comprises scattering data captured at different angles, represented as \(X=[x_{0},x_{1},\ldots,x_{N}]\), where \(N\) is the number of sampling points in one sequence. Due to the complexities of real-world high-speed scenarios, it is impractical to assume that the data points adhere to a specific angle-related sequence. Therefore, it is necessary to combine the numerical representations of the sampling points and scattering angles, resulting in the representation \(x_{t}=[\theta_{t},V_{t}]\). The model's output is a probability distribution over different surface categories, expressed as \(Y=[y_{0},y_{1},\ldots,y_{M}]\), where \(M\) is the total number of surface categories. To enhance the execution of sequence tasks, addressing the inherent variability in sequence lengths is crucial; we use a highly stable LSTM model [29], which is a type of recurrent neural network (RNN). LSTM models have unique gated structures that effectively filter and process information, mitigating redundancy in memory storage. This architecture is particularly well-suited for tasks involving lengthy sequences and it also solves the vanishing gradient problem that is prevalent in traditional RNNs. The LSTM architecture has a memory cell (\(m_{t}\)) as well as three key gate mechanisms: the input gate (\(i_{t}\)), the output gate (\(i_{o}\)), and the forget gate (\(i_{f}\)). At each time step, the model updates the states of these gates based on the current input and output from the previous time step. This process determines which pieces of information should be retained, discarded, or produced as output. The variable \(g_{t}\) represents the input information. \[i_{t} =\sigma(W_{i}x_{t}+U_{i}h_{t-1}+b_{i}) \tag{1}\] \[f_{t} =\sigma(W_{f}x_{t}+U_{f}h_{t-1}+b_{f})\] (2) \[o_{t} =\sigma(W_{o}x_{t}+U_{o}h_{t-1}+b_{o})\] (3) \[g_{t} =\phi(W_{g}x_{t}+U_{g}h_{t-1}+b_{t}) \tag{4}\]  
with \(\sigma(. )\) representing a logistic sigmoid function and \(\phi(. )\) representing a hyperbolic tangent function (tanh). Next, the memory cell, \(m_{t}\), is updated based on the input and forget gates. The learnable parameters in these expressions are represented by \(W\), \(U\), and \(b\). \[m_{t}=f_{t}\odot m_{t-1}+i_{t}\odot g_{t} \tag{5}\]  
Here, \(\odot\) denotes element-wise product operation. Finally, the model determines what to output based on the memory and output gates.