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Multi-Sensor Scheduling for Remote State Estimation over Wireless MIMO Fading Channels with Semantic Over-the-Air Aggregation

Minjie Tang, Photios A. Stavrou, Marios Kountouris

TL;DR

This work addresses remote state estimation over wireless MIMO fading channels with multiple sensors by introducing semantic over-the-air aggregation (SemOTA) and a finite-horizon dynamic programming framework. The authors derive a structured, semantic scheduling policy via a Q-function that adapts to the estimation error covariance and channel state, and they propose a PSD cone decomposition to bound the Q-function for tractable, approximate scheduling. The resulting algorithm balances estimation accuracy and sensor power consumption, achieving significant NMSE improvements and substantial power savings compared with baselines while preserving OTA advantages. Overall, SemOTA offers a practical, energy-efficient solution for real-time remote estimation in large-scale, resource-constrained wireless networks.

Abstract

In this work, we study multi-sensor scheduling for remote state estimation over wireless multiple-input multiple-output (MIMO) fading channels using a novel semantic over-the-air (SemOTA) aggregation approach. We first revisit Kalman filtering with conventional over-the-air (OTA) aggregation and highlight its transmit power limitations. To balance power efficiency and estimation performance, we formulate the scheduling task as a finite-horizon dynamic programming (DP) problem. By analyzing the structure of the optimal Q-function, we show that the resulting scheduling policy exhibits a semantic structure that adapts online to the estimation error covariance and channel variations. To obtain a practical solution, we derive a tractable upper bound on the Q-function via a positive semidefinite (PSD) cone decomposition, which enables an efficient approximate scheduling policy and a low-complexity remote estimation algorithm. Numerical results confirm that the proposed scheme outperforms existing methods in both estimation accuracy and power efficiency.

Multi-Sensor Scheduling for Remote State Estimation over Wireless MIMO Fading Channels with Semantic Over-the-Air Aggregation

TL;DR

This work addresses remote state estimation over wireless MIMO fading channels with multiple sensors by introducing semantic over-the-air aggregation (SemOTA) and a finite-horizon dynamic programming framework. The authors derive a structured, semantic scheduling policy via a Q-function that adapts to the estimation error covariance and channel state, and they propose a PSD cone decomposition to bound the Q-function for tractable, approximate scheduling. The resulting algorithm balances estimation accuracy and sensor power consumption, achieving significant NMSE improvements and substantial power savings compared with baselines while preserving OTA advantages. Overall, SemOTA offers a practical, energy-efficient solution for real-time remote estimation in large-scale, resource-constrained wireless networks.

Abstract

In this work, we study multi-sensor scheduling for remote state estimation over wireless multiple-input multiple-output (MIMO) fading channels using a novel semantic over-the-air (SemOTA) aggregation approach. We first revisit Kalman filtering with conventional over-the-air (OTA) aggregation and highlight its transmit power limitations. To balance power efficiency and estimation performance, we formulate the scheduling task as a finite-horizon dynamic programming (DP) problem. By analyzing the structure of the optimal Q-function, we show that the resulting scheduling policy exhibits a semantic structure that adapts online to the estimation error covariance and channel variations. To obtain a practical solution, we derive a tractable upper bound on the Q-function via a positive semidefinite (PSD) cone decomposition, which enables an efficient approximate scheduling policy and a low-complexity remote estimation algorithm. Numerical results confirm that the proposed scheme outperforms existing methods in both estimation accuracy and power efficiency.
Paper Structure (15 sections, 3 theorems, 23 equations, 2 figures, 1 algorithm)

This paper contains 15 sections, 3 theorems, 23 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Dynamic Plant and Wireless Sensors
  4. Wireless Communication Model
  5. Remote State Estimator
  6. Semantic Over-the-Air Aggregation
  7. Problem Formulation and Optimal Solution
  8. Optimal Solution
  9. Approximate Solution
  10. Numerical Results
  11. State Estimation NMSE versus the Number of Sensors
  12. Power Consumption at Sensors versus Timeslot
  13. Conclusions
  14. Proof of Theorem 1
  15. Proof of Theorem 2

Key Result

Theorem 1

(DP Equation) Let $\mathbf{H}_{k}=\left\{\mathbf{H}_{1,k},...,\mathbf{H}_{M,k} \right\}$ denote the set of channel fading gains at time $k$. For $k = K-1,\ldots, 0$, Problem problem:1 can be optimally solved backward in time using the following DP recursions based on $Q$-functions: where and In the DP recursions given by Equation dp eq, the state consists of the estimation error covariance $\Si

Figures (2)

  • Figure 1: Architecture of a remote state estimation system.
  • Figure 2: Numerical results.

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof