  This paper analyzes wireless network control for remote estimation of linear
time-invariant dynamical systems under various Hybrid Automatic Repeat Request
(HARQ) packet retransmission schemes. In conventional HARQ, packet reliability
increases gradually with additional packets; however, each retransmission
maximally increases the Age of Information and causes severe degradation in
estimation 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, we optimize
the retransmission time to enable the early arrival of the next status updates.
In Chase combining HARQ, since packet length remains fixed, we allow
retransmission and new updates in a single time slot using non-orthogonal
signaling. Non-orthogonal retransmissions increase packet reliability without
delaying the fresh updates. We formulate bi-objective optimization with the
proposed variance of the MSE-based cost function and standard long-term average
MSE cost function to guarantee short-term performance stability. Using the
Markov decision process formulation, we find the optimal static and dynamic
policies under the proposed HARQ schemes to improve MSE performance further.
The simulation results show that the proposed HARQ-based policies are more
robust and achieve significantly better and more stable MSE performance than
standard HARQ-based policies.
