A game theoretic approach to the power control in D2D communications underlay cellular networks

In this paper the problem of uplink power control in Device to Device communications underlaying a cellular network is addressed. The time and frequency resources of the network are organized into resource blocks according to 3^rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) Advanced specifications. The users of the network can communicate through their serving base station or directly with each other. Irrespective of their mode of communication they may share and compete for the same resource blocks. We model this kind of interaction between the users through a non- cooperative power control game where various and different users´ Quality of Service (QoS) requirements are taken into account. We prove the existence of its Nash Equilibrium point in terms of uplink transmission power and a fast heuristic distributed and iterative algorithm is proposed to obtain the game´s Nash equilibrium point. Finally, the operational effectiveness of the proposed approach is evaluated through modeling and simulation while its superiority against other power control frameworks in device to device underlay cellular networks in the literature, is illustrated.