# Active RIS-Assisted Uplink NOMA with MADDPG for Remote State Estimation in Wireless Sensor Networks
## 4 Simulation Results  
Based on the above discussion, we divide the computational complexity of applying the MADDPG algorithm to solving Problem 2 into three components:  
* The critic network (centralized training): During the centralized training phase, the critic network evaluates the global state-action pairs involving all \(N\) agents. Suppose that the maximum number of episodes is denoted as \(E^{\max}\), and each agent requires a complexity of \(\mathcal{O}(1)\) for a single update: the overall complexity becomes \(\mathcal{O}(E^{\max}N)\). * The actor network (decentralized execution): In the decentralized execution phase, each agent independently selects actions using its actor network. Since each agent makes decisions independently with the complexity \(\mathcal{O}(1)\) per episode, the total complexity for all episodes is \(\mathcal{O}(E^{\max})\). Therefore, the total computational complexity of the MADDPG algorithm is represented as  
\[\mathcal{O}(E^{\max}N+E^{\max})=\mathcal{O}(E^{\max}N) \tag{27}\]  
Moreover, we critically analyze the overhead costs compared to those of the baseline models. Specifically, compared to the centralized DDPG method--which incurs a complexity of approximately \(\mathcal{O}(E^{\max}N^{2})\) due to the joint optimization of the actions over all agents--MADDPG significantly reduces the complexity by decentralizing the actor network computations, compared to that of the standard reinforcement learning methods. Figure 3 compares our proposed MADDPG algorithm with active RIS assistance against three baseline approaches: MADDPG with a passive RIS, DDPG with an active RIS, and MADDPG without RIS assistance. The results demonstrate substantial reductions in the performance errors provided by the active RIS. Specifically, the MADDPG algorithm with active RIS assistance achieves an 88% reduction in error compared to that with a passive RIS and a 200% reduction compared to that with no RIS assistance. Additionally, the active RIS within the MADDPG framework surpasses active-RIS-assisted DDPG by approximately 87% in its error reduction. These results clearly highlight the superior performance of the MADDPG algorithm with the active RIS, underscoring the potential of the active RIS to optimize WSNs. To enhance the clarity further, we have specified in the figure captions that the horizontal axis denotes the iteration steps and the vertical axis corresponds to the normalized estimation errors, both of which are dimensionless quantities. Figure 4 illustrates the impact of the number of reflection elements on the sensor's RSE error. It can be observed that increasing the number of elements to 128 results in substantial error reductions of 32%, 78%, and 120% when compared to configurations with 32, 16, and 8 elements, respectively. This performance gain is attributed to the improved signal reflection and enhanced spatial diversity enabled by more reflection elements. These results demonstrate that a higher number of elements significantly enhances the sensing accuracy, thereby playing a crucial role in reducing the estimation error. Figure 5 presents the convergence behavior of the RSE error under different maximum power constraints (10 dBm, 15 dBm, and 20 dBm). While the general convergence trends are visually similar, higher power constraints clearly lead to faster convergence and a lower steady-state RSE error. This is because larger transmission power budgets improve the  
To investigate the system-level trade-offs further, Figure 6 presents the convergence behavior of the proposed algorithm under different sensor-to-channel configurations (e.g., two sensors with six channels, three sensors with four channels, and four sensors with three channels). It can be observed that as the number of sensors increases under limited channel resources, the RSE error grows due to heightened interference and limited degrees of freedom for resource allocation. This validates the system's sensitivity to the sensor density and available spectrum.