Transmit Beamformer Design for Multiuser MISO URLLC Systems: An FBL Decoding Error Probability Minimization Solution

In this article, we study the transmit beamformer design to minimize the weighted sum finite blocklength (FBL) decoding error probability for a downlink multiuser multiple-input–single-output (MISO) ultrareliable and low-latency communication (URLLC) system. Since the Gaussian Q-function in the design objective does not admit a closed form, the considered problem is challenging to solve. In order to handle the complicated problem, we first obtain its reformulation via a tight Gaussian Q-function approximation, which is then solved via the majorization–minimization (MM) technique tailored for the reformulated problem. Moreover, in order to further reduce the computational complexity, we first obtain the optimal structure of the transmit beamformer for the original problem, based on which we establish a neural network solution that avoids solving convex problems. Furthermore, we also investigate the extension to the statistically robust beamforming design with the imperfect channel state information (CSI). The simulation results verify the clear performance advantages of the proposed solutions over several state-of-the-art schemes as well as widely used beamforming schemes such as regularized zero-forcing (RZF) precoding in terms of the FBL decoding error probability. Moreover, the low-complexity solutions can effectively approach the proposed MM-based algorithms with much reduced computational costs.