# Active RIS-Assisted Uplink NOMA with MADDPG for Remote State Estimation in Wireless Sensor Networks
## 1 Introduction  
With the increasing number of wireless devices and the development of ultra-5G and 6G technologies in industrial Internet of Things (IoT) networks, wireless sensor networks (WSNs) [1], as a key component of IoT systems, face higher demands for low latency, low remote state estimation (RSE) errors, and low system error rates (SERs) [2, 3, 4]. As the number of smart devices grows and large-scale IoT applications proliferate, ensuring the efficiency and reliability of these systems has become a critical issue to address. To enhance spectrum efficiency in WSNs, non-orthogonal multiple access (NOMA) technology has been widely adopted due to its capability to support multiple sensors with the same time-frequency resources through superposition coding and successive interference cancellation [5, 6]. Recent studies have enhanced NOMA further by integrating active reconfigurable intelligent surfaces (RISs) to boost the link reliability and energy efficiency. For instance, the work presented in [7] investigates joint UAV trajectory optimization and active RIS control in NOMA systems, highlighting significant energy efficiency gains. However, this study primarily addressed aerial-terrestrial network scenarios and was not directly applicable to ground-based sensor networks. Both passive and active RIS technologies have been explored extensively for improving NOMA system performance. Recent research, such as that presented in [8], demonstrates passive RISs' effectiveness in reducing the bit error rate (BER) and extending the network coverage. Nevertheless, a passive RIS lacks active amplification capabilities and adaptability under highly dynamic channel conditions. Conversely, an active RIS, as explored in [9], enhances the physical-layer security by providing analytical derivations for the secrecyoutage probability. However, this study does not incorporate critical aspects such as sensor grouping strategies or estimation error optimization. Traditional optimization methods like block coordinate descent (BCD) and successive convex approximation (SCA) have been employed for resource allocation in RIS-assisted NOMA networks. For example, the research by [PERSON] et al. [10] achieves improved system sum rates using BCD-based resource scheduling techniques. Additionally, recent efforts such as [11] have explored low-complexity signal processing schemes, including sparse channel parameter estimation for MIMO-FBMC systems, which are highly relevant to industrial big data communication scenarios. However, these approaches typically focus on the physical layer and do not address joint decision-making strategies or cross-layer coordination for sensor estimation. Moreover, they lack multi-agent coordination mechanisms and considerations for remote state estimation (RSE) error control, which are essential in practical WSN deployments. Meanwhile, reinforcement learning methodologies, including deep reinforcement learning (DRL), deep deterministic policy gradient (DDPG), and multi-agent DDPG (MADDPG), have emerged as effective solutions for dynamic resource allocation. A recent IEEE Transactions study [12] presents an attention-augmented MADDPG framework applied to NOMA-based vehicular mobile edge computing, demonstrating improved convergence rates and predictive accuracy under realistic workload scenarios. Additionally, recent studies such as [13] have employed DRL approaches to jointly optimize the UAV trajectories, transmission power, and RIS phase shifts in RIS-aided UAV-NOMA systems. Nonetheless, these studies have predominantly considered passive RIS configurations and assumed static user grouping, limiting the adaptability in dynamic scenarios. To the best of our knowledge, no existing research has jointly tackled the sensor state estimation error (RSE), sensor grouping, transmission power control, and active RIS beamforming within an uplink NOMA-assisted WSN using a decentralized multi-agent reinforcement learning framework. To this end, we propose a MADDPG-based distributed policy learning approach.