Abstract
In this paper, we investigate a 6G ultra-dense cellu-lar Internet of Things (IoT) system, where devices transmit time-sensitive sampled data to a base station (BS) with code-domain non-orthogonal multiple access (NOMA) and grant-free random access (GFRA) protocols. Due to the complex interference in the GFRA among a large number of devices and the dynamic changes in the wireless environment, it is a challenging task to find the optimal backoff policy for massive IoT devices with energy constraints. To solve this problem, we first model the optimization problem as a multi-user noncooperative dynamic stochastic game (MUN-DSG) and then transform the MUN-DSG into a mean field game (MFG). By solving the Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations corresponding to the proposed MFG, we numerically derive the optimal backoff delay strategy for all the devices. Numerical results show that the proposed Mean Field-based Dynamic Backoff (MFDB) scheme can adapt to the energy constraints and channel dynamics to minimize the accumulated costs.