Iterative Primal-Dual Scaled Gradient Algorithm with Dynamic Scaling Matrices for Solving Distributive NUM over Time-Varying Fading Channels

In this paper, we investigate the convergence behavior of the primal-dual scaled gradient algorithm (PDSGA) for solving distributed network utility maximization problems under time-varying fading channels. Our analysis shows that the proposed PDSGA converges to a limit region rather than a point under FSMC channels. We also show that the asymptotic tracking errors are given by $\mathcal{O}\left(\overline{T}\big/ \overline{N}\right)$, where $\overline{T}$ and $\overline{N}$ are the update interval and the average sojourn time of the FSMC, respectively. Based on these analysis, we derive a distributive solution for determining the scaling matrices based on local CSI at each node. The numerical results show the superior performance of the proposed PDSGA over several baseline schemes.