Robust Beamforming Design With Finite Blocklength for URLLC

Ultra-reliable and low-latency communications (URLLC) are essential for mission-critical applications, such as telemedicine, automatic drive, etc. In the design of URLLC, the robustness of multi-user beamforming transmission scheme is critical and challenging. To this end, we consider a robust beamforming design in the finite blocklength regime for a multi-user multi-antenna downlink system in the case of imperfect channel state information at the transmitter. A transmission power minimization problem is formulated to optimize the beamforming vectors under the premise of guaranteeing the requirements on transmission latency, reliability and the target user rates, which is non-convex. To solve it, we first reformulate the problem into a tractable form by using the convexity and concavity of asymptotic capacity in the finite blocklength regime, then adopt S-Procedure to convert the infinite constraints into finite ones. Finally, the Gaussian randomization method and the penalty function method are utilized to generate a feasible solution to the original optimization problem and to provide a good rank-one approximation, respectively. The simulation results confirm the robustness and effectiveness of the beamforming design.