# Learning Approach for Angle Estimation Based on Characteristics of Phase Drift
## 4 Performance Evaluation
### Analysis of Experiment Results
#### 4.3.2 Computation Cost Evaluations  
To determine the most suitable model architecture for angle estimation, we conducted extensive experiments comparing different neural network structures, including both recurrent-based models (LSTM, GRU) and Transformer-based models. Our experimental results demonstrate that GRUs provided the best balance between accuracy and computational efficiency, making them the most suitable choice for real-time angle estimation in resource-constrained environments. Compared to LSTM, which required 311,617 parameters with a validation MAE of 0.0513, the GRU model achieved a lower MAE of 0.031 with fewer parameters (250,689), making it a more efficient alternative. Figure 12: Error analysis by angle for the GRU layer model. Unlike LSTM, which consists of three gates (forget, input, and output), GRU uses only two gates (reset and update), reducing computational complexity. This structural difference allows GRU to perform faster training and inference while maintaining comparable accuracy. Additionally, the Transformer model, while lightweight (35,565 parameters), exhibited higher MAE (1.3103), indicating poorer accuracy in angle estimation. While Transformer-based models are highly effective in capturing long-range dependencies, they may not be the optimal choice for AoA estimation. Unlike natural language processing tasks where attention-based mechanisms excel, AoA estimation relies heavily on local temporal dependencies in phase drift signals. Recurrent-based models, such as GRU, are inherently more suited for such tasks, as they efficiently capture sequential patterns over time. Simplified gated recurrent unit (SGRU) [44] and LightGRU [45] are variants of the GRU designed to reduce computational complexity. SGRU simplifies certain computations of the original GRU, maintaining its advantages while offering faster computation due to a more lightweight design. LightGRU, on the other hand, adopts an even more streamlined structure to facilitate efficient operation in resource-constrained environments such as embedded systems. This model aims to minimize computational cost without compromising GRU's performance. The key differences between these models and the original GRU lie in their architecture. SGRU reduces the number of computations by merging or removing specific parameters and gates, which results in faster operations. LightGRU goes further by reducing the parameter count or simplifying computational processes, making it particularly suitable for embedded systems. Therefore, we also applied both the SGRU and LightGRU to our experiments to evaluate their performance in enhancing angle prediction accuracy compared to traditional GRU. In Figure 13, the SGRU layer model's error distribution by angle shows more variability compared to the GRU layer model shown in Figure 12. The standard deviation is significantly larger in multiple angular regions, particularly around \(\pm 75^{\circ},\pm 25^{\circ}\), and near \(0^{\circ}\). Additionally, the variance, represented by the blue line, shows multiple spikes throughout the angle spectrum. This suggests that the SGRU layer model's performance is less stable overall, with more pronounced prediction errors at various angles. One potential reason for this behavior is the impact of multipath reflections in the indoor environment. The experimental setup includes multiple desks, chairs, walls, and a whiteboard, which can cause signal reflections and diffractions, introducing phase distortions at specific angles. Notably, the regions around \(\pm 75^{\circ}\) and \(\pm 25^{\circ}\) are more exposed to these environmental structures, likely increasing signal interference effects. Since the same dataset was used for training all models, the higher variability observed in SGRU indicates that it is more sensitive to such variations compared to GRU and LightGRU.