Interference-Constrained Pricing for D2D Networks
  The concept of device-to-device (D2D) communications underlaying cellular networks opens up potential benefits for improving system performance but also brings new challenges such as interference management. In this paper, we propose a pricing framework for interference management from the D2D users to the cellular system, where the base station (BS) protects itself (or its serving cellular users) by pricing the crosstier interference caused from the D2D users. A Stackelberg game is formulated to model the interactions between the BS and D2D users. Specifically, the BS sets prices to a maximize its revenue (or any desired utility) subject to an interference temperature constraint. For given prices, the D2D users competitively adapt their power allocation strategies for individual utility maximization. We first analyze the competition among the D2D users by noncooperative game theory and an iterative based distributed power allocation algorithm is proposed. Then, depending on how much network information the BS knows, we develop two optimal algorithms, one for uniform pricing with limited network information and the other for differentiated pricing with global network information. The uniform pricing algorithm can be implemented by a fully distributed manner and requires minimum information exchange between the BS and D2D users, and the differentiated pricing algorithm is partially distributed and requires no iteration between the BS and D2D users. Then a suboptimal differentiated pricing scheme is proposed to reduce complexity and it can be implemented in a fully distributed fashion. Extensive simulations are conducted to verify the proposed framework and algorithms. 
Yuan Liu, Rui Wang, and Zhu Han
cs.IT math.IT