Real-Time Wireless Control with Non-orthogonal HARQ

In this paper, we design Non-orthogonal multi-access (NOMA) inspired Hybrid Automatic Repeat Request (HARQ) techniques for real-time remote estimation of a linear time-invariant (LTI) system. Standard HARQ improves the quality of status updates of a process with retransmission while losing a fresh status update during retransmission intervals. We propose dynamic non-orthogonal HARQ (DN-HARQ), which schedules retransmitting old updates and freshly generated status updates using non-orthogonal packet combining with appropriate power-sharing fraction $\alpha$. We design policy optimization problems targeting minimizing the average and packet-level estimation mean square error (MSE). We transform complex optimization problems using Markov decision process (MDP) framework and obtain the optimal policies with simple numerical techniques. By fixing $\alpha$ in all time slots in DN-HARQ, a low complexity static non-orthogonal HARQ (SN-HARQ) is obtained. We also obtain optimal policies under NOMA-HARQ when two distinct LTI processes are required to schedule simultaneously. The simulation results show significant performance gains of the proposed scheme over standard HARQ.