HARQ Optimization for Real-Time Remote Estimation in Wireless Networked Control

This paper analyzes wireless network control for remote estimation of linear time-invariant (LTI) dynamical systems under various Hybrid Automatic Repeat Request (HARQ) based packet retransmission schemes. In conventional HARQ, packet reliability increases gradually with additional packets; however, each retransmission maximally increases the Age of Information (AoI). A slight increase in AoI can cause severe degradation in mean squared error (MSE) performance. We optimize standard HARQ schemes by allowing partial retransmissions to increase the packet reliability gradually and limit the AoI growth. In incremental redundancy HARQ (IR-HARQ), we utilize a shorter time for retransmission, which improves the MSE performance by enabling the early arrival of fresh status updates. In Chase combining HARQ (CC-HARQ), since packet length remains fixed, we propose sending retransmission for an old update and new updates in a single time slot using non-orthogonal signaling. Non-orthogonal retransmissions increase the packet reliability without delaying the fresh updates. Using the Markov decision process formulation, we find the optimal policies of the proposed HARQ based schemes to optimize the MSE performance. We provide static and dynamic policy optimization techniques to improve the MSE performance. The simulation results show that the proposed schemes achieve better long-term average and packet-level MSE performance.