Abstract
In this paper, we aim to find the global optimal resource allocation for ultra-reliable and low-latency communications (URLLC), where the blocklength of channel codes is short. The achievable rate in the short blocklength regime is neither convex nor concave in bandwidth and transmit power. Thus, a non-convex constraint is inevitable in optimizing resource allocation for URLLC. We first consider a general resource allocation problem with constraints on the transmission delay and decoding error probability, and prove that a global optimal solution can be found in a convex subset of the original feasible region. Then, we illustrate how to find the global optimal solution for an example problem, where the energy efficiency (EE) is maximized by optimizing antenna configuration, bandwidth allocation, and power control under the latency and reliability constraints. To improve the battery life of devices and EE of communication systems, both uplink and downlink resources are optimized. The simulation and numerical results validate the analysis and show that the circuit power is dominated by the total power consumption when the average inter-arrival time between packets is much larger than the required delay bound. Therefore, optimizing antenna configuration and bandwidth allocation without power control leads to minor EE loss.