# Active RIS-Assisted Uplink NOMA with MADDPG for Remote State Estimation in Wireless Sensor Networks
## 1 Introduction
MADDPG is particularly suitable for this problem setting because it explicitly models the interactions among agents and handles decentralized control in partially observable environments. In our scenario, each sensor acts as an agent, making decisions based only on its local state, such as channel gain and estimation covariance. This naturally forms a Dec-POMDP (Decentralized Partially Observable Markov Decision Process), to which MADDPG is well suited. It enables coordinated learning during centralized training while maintaining independent execution, supports hybrid discrete-continuous action spaces, and offers scalability in large sensor networks with dynamic channel conditions. The main contributions of this paper are summarized as follows:  
1. Joint Integration of an Active RIS and MADDPG: We propose a joint optimization framework that integrates an active RIS and MADDPG-based decentralized learning for uplink WSNs. This design improves the estimation accuracy, reduces the power consumption, and enhances the system's adaptability. 2. Real-Time Estimation via Kalman Filtering: The proposed method incorporates Kalman filtering (KF) to enable real-time state tracking, which improves the estimation robustness under varying network conditions. 3. Decentralized Resource Allocation: We formulate a novel decentralized resource allocation problem that jointly considers sensor grouping, power control, and active RIS beamforming to minimize the RSE error--an optimization objective rarely addressed in existing works. Each sensor acts as an independent agent and makes decisions based on its local state in a Dec-POMDP setting. The MADDPG framework is employed to enable scalable and coordinated learning among agents. While our method is built upon an established RL architecture, it is tailored to a unique estimation-driven optimization task in WSNs. We also acknowledge the absence of a formal theoretical convergence analysis and highlight this as a direction for future investigation. 4. Performance Gains Verified by Simulations: Simulation results show significant improvements in the RSE error reduction and system reliability compared to those under conventional and single-agent approaches, confirming the practicality of the proposed framework. The remainder of this paper is organized as follows: Section 2 details the local sensor state estimation and the uplink NOMA transmission model with an active RIS, including the derivation of the RSE error metrics and the outage probability model. Section 3 introduces the MADDPG-based decentralized algorithm, elaborating on the joint optimization framework that integrates sensor grouping, power allocation, and active RIS beamforming, as well as incorporating KF or enhanced real-time state estimation. Section 4 presents the simulation experiments, performance comparisons with benchmark algorithms, and a comprehensive analysis of the results demonstrating improvements in the RSE accuracy and network reliability. Finally, Section 5 concludes this paper by summarizing the key findings and potential directions for future research. Notations: \(\mathbb{R}\) denotes the set of real numbers. \(\mathbb{C}\) represents the set of complex numbers. The symbol \((\cdot)^{\mathrm{T}}\) denotes the transpose operation, and the superscript \((\cdot)^{-1}\) indicates the matrix inverse. The notation \(\mathbb{P}[\cdot]\) refers to probability and \(\mathbb{E}[\cdot]\) to expectation. \(\mathrm{Tr}(\cdot)\) represents the trace operator of a matrix. A bold symbol (e.g., **P**) is used to denote vectors or matrices, with lowercase bold letters representing vectors and uppercase bold letters representing matrices. Non-bold symbols (e.g., \(p\)) indicate scalar quantities such as real-valued parameters or constants.