Min-Max Decoding Error Probability Oriented Beamforming for Downlink Multiuser URLLC Systems

In this paper, we focus on the decoding error probability based beamforming design for a downlink multi-antenna multiuser ultra reliable and low-latency communication (URLLC) system. We first optimize the transmit beamformer to minimize the maximum finite blocklength (FBL) decoding error probability under block fading channels, which turns out to be a complicated nonconvex problem with a non-closed-form objective function. A successive convex approximation (SCA)-based algorithm is developed to determine a high-quality solution. Moreover, in order to reduce the computational complexity of the proposed algorithm, we perform the downlink beamforming optimization by solving a simpler virtual uplink problem. The complexity of the resultant solution only scales linearly with the number of transmit antennas. Furthermore, a special case with quasi-static channels is investigated, where the proposed SCA and the uplink-downlink duality based solutions for the block fading channel can be simplified in a non-trivial manner. Simulation results verify the performance superiorities of the proposed algorithms in the context of short packet communication. In particular, the proposed designs outperform conventional regularized zero-forcing (RZF) and max-min signal-to-interference-plus-noise ratio (SINR) beamforming by evident gains in terms of the FBL decoding error probability.