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Distributed Network Utility Maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, the authors shall investigate the convergence behavior and tracking errors of the iterative Primal-Dual Scaled Gradient Algorithm (PDSGA) with Dynamic Scaling Matrices (DSC) for solving distributive NUM problems under time-varying fading channels.
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