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

In this article, we consider the cell-free massive multiple-input-multiple-output (MIMO) system for supporting ultrareliable 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.