Achievable Rate Analysis and Power Optimization for Cell-Free Massive MIMO URLLC Systems Over Aging and Correlated Channels

In this paper, we consider the cell-free massive multiple-input multiple-output (MIMO) system for supporting ultra-reliable and low-latency communication (URLLC) transmission, where a large number of access points (APs) serve a small number of users in the short packet regime. Assuming channel aging and channel spatial correlation, we derive the closed-form expression of the downlink achievable rate with the normalized conjugate beamforming (NCB). Under the goal of maximizing the minimum user rate, we formulate a max-min power optimization problem with a power constraint at each AP. However, it is challenging to solve this problem because the objective function is a complicated function of power coefficients. To tackle this difficulty, we use a path-following method to approximate the objective function to a logarithmic function and transform the polynomial constraint into a monomial. Thus, we can iteratively solve the original problem by reformulating it as a series of geometric programming problems. Numerical results verify the tightness of the closed-form expression for the downlink achievable rate in the short packet regime. Both channel aging and channel spatial correlation significantly degrade the system performance of CF massive MIMO URLLC systems. Moreover, Using NCB and the proposed max-min power allocation can effectively alleviate this impairment and improve the system performance.