Real-Time Remote Estimation with Hybrid ARQ in Wireless Networked Control

TL;DR

This paper proposes a hybrid automatic repeat request (HARQ)-based real-time remote estimation framework for linear time-invariant (LTI) dynamic systems, and derives a sufficient condition of the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system and minimizes the MSE.

Abstract

Real-time remote estimation is critical for mission-critical applications including industrial automation, smart grid and 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. We formulate a new problem to optimize the sensor's online transmission control policy for static and Markov fading channels, which depends 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 challenging to derive the condition in terms of the communication channel quality and the LTI system parameters, to ensure a bounded long-term estimation MSE. We derive an elegant 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 accordingly derive a low-complexity suboptimal policy. Numerical results show that the proposed optimal policy significantly improves the performance of the remote estimation system compared to the conventional non-HARQ policy.

Figures (11)

• Figure 1: Proposed remote estimation system with HARQ, where $\mathbf{x}_k\triangleq \left[x_{k,1},x_{k,2}\right]^T$ is the two-dimensional state vector of the dynamic process, and $\hat{\mathbf{x}}^s \triangleq \left[\hat{x}^s_{k,1},\hat{x}^s_{k,1}\right]^T$.
• Figure 2: The switching structure of the optimal policy in the state space $\mathbb{S}$.
• Figure 3: Illustration of the state space and state transitions in the high SNR scenario, where $\theta = 4$.
• Figure 4: The stability regions in terms of $\Lambda_1$ and $\Lambda_2$ with $\rho^2(\mathbf{A})=1.1,\ 2,\ 3$ and $5$, respectively.
• Figure 5: Illustration of the state space and state transitions of the optimal transmission control policy in the high SNR scenario, where the channel is a $2$-state Markov channel, $\theta_1 = 4$ and $\theta_2=3$.

Theorems & Definitions (18)

• Remark 1
• Theorem 1
• proof
• Remark 2
• Theorem 2
• proof
• Remark 3
• Proposition 1
• Proposition 2
• Theorem 3