Joint block length and pilot length optimization for URLLC in the finite block length regime

In this paper, we maximize the system throughput of a point-to-point ultra-reliable low-latency communications (URLLC) system by jointly optimizing its block length and pilot length under the constraints of latency and block error probability. A finite block length (FBL) is adopted to enable low transmission latency. We prove that the throughput is approximately concave with respect to pilot length, given a block length, and that there exists a unique optimal block length in terms of throughput, with a given pilot length. Closed-form expressions are derived for the near-optimal pilot length with a given block length, as well as the asymptotic block error probability with respect to both block length and pilot length. A low-complexity iterative algorithm is proposed for joint optimization of block length and pilot length, which converges within only 1-3 iterations. Simulation results show that the proposed joint optimization scheme achieves a near-optimal throughput performance of an FBL URLLC system, with a much lower complexity than exhaustive search. It also significantly outperforms the previous approaches that considered either block length optimization or pilot length optimization only.