Beamforming Design in Short-Packet Transmission for URLLC in Cell-Free Massive MIMO System

Low latency, high reliability, and high data rate are three performance indicators of Ultra-reliable and low latency communication (URLLC) systems, but they are not able to be met simultaneously. Based on the determined latency and reliability requirements, this paper investigates the problem of the weighted sum rate (WSR) in cell-free massive multi-input multi-output (MIMO) system with multiple access points (APs). User-centric access point selection is considered to further reduce the computational complexity for AP used with acceptable performance loss. The transmitting beamforming is designed to mitigate inter-user interference so as to maximize the WSR under the backhaul and transmitting power constraints. Since the proposed problem is non-convex, two algorithms are proposed to solve the problem under the general SINR regime and the high SINR regime, respectively. For the former, we first approximate the objective function with the difference of convex (DC) programming and reformulate the problem into a semi-definite relaxation (SDR) form. Afterward, auxiliary variables are introduced in accordance with the successive convex approximation (SCA) method to further transform the nonconvex problem into a convex one. In the end, the sub-optimal WSR is obtained by iteratively solving a final convex problem. For the latter, the well-known WMMSE method is applied to address the WSR problem. Numerical results demonstrate the efficiency of our proposed algorithm, e.g., the maximum performance gain of the proposed algorithm is about 25% compared to the classical MMSE method. And the user-centric approach achieves 8 times computational complexity reduction with 4% performance loss.