Game theory for SINR-based power control in device-to-device communications

Abstract

Device-to-Device (D2D) communication underlaying cellular network can improve the spectrum efficiency due to both direct proximity communication and frequency reuse. However, such performance improvement is influenced by the co-channel interference and time varying nature of channels. The purpose of this paper is to study and to investigate both pure and mixed games, using two utility functions game for CUE and DUE, in order to enhance the system spectral efficiency and increase the SINR. Unlike previous works which have dealt with potential and dynamic games etc., we propose in this paper a pure and mixed game. The most important, is that the used game and utility function of each user (CUE and DUE) should be appropriately aligned to the global objective for pure and mixed games and can meet this requirement. To tackle this problem, we first define a pure and mixed strategies non-cooperative games, in order to model the interactions between the cellular and D2D users. Indeed, each kind of users (D2D and Cellular users) is modeled as a rational player, aiming at maximizing its own net utility, while a Quality of Service (QoS), in terms of Signal-to-Interference plus-Noise-Ratio (SINR) threshold, should be satisfied for both D2D and cellular users. Second, for each kind of game: pure and mixed, a closed form of NE amount of power is derived, where existence and uniqueness of the Nash equilibrium (NE) are also investigated. Finally, simulations are conducted to compare the proposed framework of the two kinds of proposed PC mechanisms: centralized and distributed according to the two kinds of users: D2D and cellular users.