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Joint Mode Selection and Spectrum Partitioning for Device-to-Device Communication: A Dynamic Stackelberg Game

Device-to-device (D2D) communication technology is a promising add-on component for future wireless networks to provide local area services with increased spectrum efficiency and improved user experience. Three modes (i.e., cellular mode, reuse mode, and dedicated mode) can be used for D2D communication. A potential D2D user equipment (UE) can select a communication mode and dynamically adapt the mode selection according to the performance and the cost. This is referred to as the user-controlled mode selection problem. Also, a base station (BS) needs to reserve a spectrum band for the dedicated mode of operation, which we refer to as spectrum partitioning. The optimal spectrum partitioning needs to consider the utility of the BS that depends on the distribution of the users' mode selection, which, in turn, is governed by the spectrum partitioning. To jointly address the problems of spectrum partitioning and user-controlled mode selection (which are cyclically dependent on each other), we propose a dynamic Stackelberg game framework in which the BS and the potential D2D UEs act as the leader and the followers, respectively. Specifically, the adaptive mode selection of potential D2D UEs is formulated as a follower evolutionary game, and an evolutionary stable strategy is considered to be the solution. The dynamic control of spectrum partitioning by the BS is formulated as a leader optimal control problem. We also extend the formulation by considering information delays in control and state. Numerical analysis is performed to evaluate the effectiveness of the proposed framework, which shows that although the mode selection is performed in a distributed and user-controlled manner, the dynamic spectrum partitioning can be viewed as an effective incentive mechanism to drive the user distribution close to the optimal one.