Achieving Energy-Efficient Uplink URLLC with MIMO-Aided Grant-Free Access

The optimal design of the energy-efficient multiple-input multiple-output (MIMO) aided uplink ultra-reliable low-latency communications (URLLC) system is an important but unsolved problem. For such a system, we propose a novel absorbing-Markov-chain-based analysis framework to shed light on the puzzling relationship between the delay and reliability, as well as to quantify the system energy efficiency. We derive the transition probabilities of the absorbing Markov chain considering the Rayleigh fading, the channel estimation error, the zero-forcing multi-user-detection (ZF-MUD), the grant-free access, the ACK-enabled retransmissions within the delay bound and the interactions among these technical ingredients. Then, the delay-constrained reliability and the system energy efficiency are derived based on the absorbing Markov chain formulated. Finally, we study the optimal number of user equipments (UEs) and the optimal number of receiving antennas that maximize the system energy efficiency, while satisfying the reliability and latency requirements of URLLC simultaneously. Simulation results demonstrate the accuracy of our theoretical analysis and the effectiveness of massive MIMO in supporting large-scale URLLC systems.