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To Retransmit or Not: Real-Time Remote Estimation in Wireless Networked Control

Kang Huang, Wanchun Liu, Yonghui Li, Branka Vucetic

TL;DR

A hybrid automatic repeat request (HARQ)-based real-time remote estimation framework for linear time-invariant (LTI) dynamic systems and proves the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system and minimizes the mean-squared error (MSE).

Abstract

Real-time remote estimation is critical for mission-critical applications including industrial automation, smart grid, and the tactile Internet. In this paper, we propose a hybrid automatic repeat request (HARQ)-based real-time remote estimation framework for linear time-invariant (LTI) dynamic systems. Considering the estimation quality of such a system, there is a fundamental tradeoff between the reliability and freshness of the sensor's measurement transmission. When a failed transmission occurs, the sensor can either retransmit the previous old measurement such that the receiver can obtain a more reliable old measurement, or transmit a new but less reliable measurement. To design the optimal decision, we formulate a new problem to optimize the sensor's online decision policy, i.e., to retransmit or not, depending on both the current estimation quality of the remote estimator and the current number of retransmissions of the sensor, so as to minimize the long-term remote estimation mean-squared error (MSE). This problem is non-trivial. In particular, it is not clear what the condition is in terms of the communication channel quality and the LTI system parameters, to ensure that the long-term estimation MSE can be bounded. We give a sufficient condition of the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system and minimizes the MSE. Also, we prove that the optimal policy has a switching structure, and derive a low-complexity suboptimal policy. Our numerical results show that the proposed optimal policy notably improves the performance of the remote estimation system compared to the conventional non-HARQ policy.

To Retransmit or Not: Real-Time Remote Estimation in Wireless Networked Control

TL;DR

A hybrid automatic repeat request (HARQ)-based real-time remote estimation framework for linear time-invariant (LTI) dynamic systems and proves the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system and minimizes the mean-squared error (MSE).

Abstract

Real-time remote estimation is critical for mission-critical applications including industrial automation, smart grid, and the tactile Internet. In this paper, we propose a hybrid automatic repeat request (HARQ)-based real-time remote estimation framework for linear time-invariant (LTI) dynamic systems. Considering the estimation quality of such a system, there is a fundamental tradeoff between the reliability and freshness of the sensor's measurement transmission. When a failed transmission occurs, the sensor can either retransmit the previous old measurement such that the receiver can obtain a more reliable old measurement, or transmit a new but less reliable measurement. To design the optimal decision, we formulate a new problem to optimize the sensor's online decision policy, i.e., to retransmit or not, depending on both the current estimation quality of the remote estimator and the current number of retransmissions of the sensor, so as to minimize the long-term remote estimation mean-squared error (MSE). This problem is non-trivial. In particular, it is not clear what the condition is in terms of the communication channel quality and the LTI system parameters, to ensure that the long-term estimation MSE can be bounded. We give a sufficient condition of the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system and minimizes the MSE. Also, we prove that the optimal policy has a switching structure, and derive a low-complexity suboptimal policy. Our numerical results show that the proposed optimal policy notably improves the performance of the remote estimation system compared to the conventional non-HARQ policy.

Paper Structure

This paper contains 13 sections, 3 theorems, 27 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Dynamic Process Modeling
  4. State Estimation at the Smart Sensor
  5. Communication and Remote Estimation
  6. HARQ-Based Remote Estimation
  7. Performance-Optimal Policy
  8. MDP Formulation
  9. Structural Property of the Optimal Policy
  10. Suboptimal Policy
  11. Delay-Optimal Policy: A Benchmark
  12. Numerical Results
  13. Conclusions

Key Result

Theorem 1

There exists a stationary and deterministic optimal policy $\pi^*$ of problem problem in the state space $\mathbb{S}$, if the following condition holds:

Figures (4)

  • Figure 1: Proposed remote estimation system with HARQ, where $x_k\triangleq \left[x_{k,1},x_{k,2}\right]^T$ is the two-dimensional state vector of the dynamic process.
  • Figure 2: An illustration of the sensor's transmission process. The solid circles denote the raw measurement sampling time, the up arrows are the starting points of new transmissions (i.e., only these (pre-filtered) measurements will be sent to the receiver), solid/dashed blocks are new/re-transmission packets, and $\checkmark$/$\times$ denotes a successful/failed detection at the receiver.
  • Figure 3: An illustration of different policies with different $h$, where 'o' and '$\cdot$' denote $a =0$ and $a=1$, respectively.
  • Figure 4: Average MSE with different policies, $h = 0.5$

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Remark 2
  • Proposition 1