Minimize Average PAoI for Grant-Free Random Access Scheme in Cell-Free Massive MIMO

In this letter, we minimize the average peak age of information (PAoI) for a grant-free random access scheme in cell-free massive multiple-input multiple-output (MIMO) system. Leveraging the established dual-disk model, the probability of successful access is derived using stochastic geometry. A closed-form expression of the PAoI is then obtained, enabling exploration of its dependence on key design parameters. By jointly optimizing access control parameters and pilot length, we formulate the problem of minimizing the average PAoI. To efficiently solve this optimization problem, the simulated annealing (SA) algorithm is employed. Finally, simulation results are provided to validate the theoretical analysis and demonstrate the effectiveness of the proposed approach.