# Indoor Localization Using 6G Time-Domain Feature and Deep Learning
## 4 Numerical Results  
Figure 5 is the layout of the environment. A typical laboratory with 22 m \(\times\) 10 m \(\times\) 3 m is simulated to test the positioning algorithm. CIR data from terahertz sensors is collected to extract the fingerprint. The dataset includes data from 289 receiving antennas, 3 transmitters, and 1024 frequency points, spanning a frequency range from 120 GHz to 130.23 GHz, with a frequency resolution of 0.01 GHz. The half-wave dipoles are used for transmitting and receiving antennas. The maximum number of reflections is set to 5, and the number of diffractions is 1. The CIR data are measured 200 times per receiver, with data from 289 receiving antennas, resulting in a significant dataset for training the model. The CIR features are extracted, normalized, and reshaped for model convergence. A database of pre-collected signals is created across the environment to generate fingerprint data. The fingerprint data includes the first path amplitude, time of arrival of the first path, channel impulse response power, root mean square delay spread, and RSSI from CIR. These features are normalized to standardize the input, thereby improving model training. There are three metal bookcases, with a height of 2 m, and seven desks with a height of 0.7 m in the laboratory. Three transmitters, of 1 m tall, located at Tx1(10, 1) m, Tx2(0.5, 5.5) m and Tx3(10.5, 10) m are used to transmit the signal. 289 receivers, all 1 m in height, are uniformly distributed from (1, 1) m to (9, 9) m as shown in Figure 5. The Adam optimizer is  
Figure 4: Spatial local attention block (SLAB). Figure 5: Laboratory layout. The green triangles denote transmitters. * denotes receivers. used for training, including 200 epochs with a mini-batch size of 128, and an initial learning rate of 0.002. The training is conducted on a GPU. L2 regularization and gradient clipping are employed to improve performance. This paper primarily focuses on the time-domain to assess the accuracy of position prediction models for indoor positioning systems. The errors in predicted positions are typically computed as the Euclidean distance between the predicted and actual positions at each time point. The overall positioning error across all data points can be represented by the Root Mean Square Error (RMSE), which is calculated as follows:  
\[RMSE=\sqrt{\frac{1}{N}\frac{N}{i=1}^{N}\bigg{(}\left(x_{i}^{true}-x_{i}^{pred} \right)^{2}+\left(y_{i}^{true}-y_{i}^{pred}\right)^{2}\bigg{)}} \tag{3}\]  
where \(N\) denotes the total number of data points. \(x_{i}^{pred}\) and \(y_{i}^{pred}\) are the predicted x- and y-coordinates of the i-th data point. \(x_{i}^{true}\) and \(y_{i}^{true}\) are the true x- and y-coordinates of the i-th data point. The RMSE provides a more intuitive understanding of the error, with units equivalent to those of the original data (e.g., meters), making it suitable for real-world applications. Lower RMSE values indicate better accuracy, and the RMSE is particularly useful for understanding how well the model generalizes its predictions. In this section, we analyze the numerical results obtained from four different models under various noise conditions. The four models include the ResNet, ResNet with CLAB, ResNet with SLAB, and ResNet with CLAB and SLAB. The evaluation is based on RMSE, which measures the positioning accuracy of each model. The networks are trained with 10% noise. Figure 6 shows the RMSE performance under different noise levels. Table 1 provides a summary of the results for different noise levels. As shown, the ResNet with CLAB model outperforms ResNet in all noise scenarios, demonstrating its ability to improve feature selection. For a 10% noise level, RMSE is reduced from 0.0969 m to 0.0752 m, achieving a 22.4% improvement. However, the performance gain varies more significantly with different noise levels.