In this paper, power control problem for full-duplex communications in two-tier femtocell networks is studied, where femtocells share the same frequency with macrocell uplink. In order to be more practical, the channel uncertainty in the real communication environment is considered, and described as probability constraints. To reduce the cross-tier and co-tier interferences among users and achieve the tradeoff of better quality of service(QoS) requirement and lower power consumption, a hierarchical game framework to allocate power is formulated. According to different design objectives, marginal utility and the symbol error rate (SER) are guaranteed in uplink, and transmission rate and delay are guaranteed in downlink. The utility of both uplink and downlink users are maximized. The Lagrangian method and sub-gradient method are used to solve the optimization problem and determine the optimal solution, respectively. A power iteration algorithm to achieve game equilibrium is provided. The simulation results show that the proposed algorithm behaves better performance in aspect of convergence, robustness and QoS provisioning.

Introduction

In recent years, the exponential growth of smart phones and mobile services has led to an increasing demand for high data rate access, and traditional cellular networks are no longer enough to meet people’s needs [1]. In order to effectively utilize the spectrum resources, increase the scope of indoor coverage, reduce operators’ huge infrastructure investment and increase the quality of service (QoS) of users, a femtocell technology has been proposed [2,3]. At the same time, full duplex(FD) communication technology can be combined with femtocell. FD communication technology can send and receive information simultaneously on the same channel. Compared with half duplex communication, full duplex communication has a lot of advantages. For example, it can double the throughput of the system in theory, while the feedback delay and end to end delay are reduced, and the access mode is flexible [4–۶]. Without detailed network planning, the co-channel deployment of femtocells and macrocell would cause serious interference among neighboring femtocells and/or between femtocells and macrocell. Therefore, how to manage interference and ensure the quality of service of users has become an important technological challenge. In [7,8] and [9], some interference management schemes are designed to reduce the co-tier and cross-tier interference in a cellular network. In [10] and [11], with the aid of the means for integrating the channel detection technology into the FBSs, the femtocell can dynamically utilize the spectrum resources authorized to the macrocell by detecting the surrounding communication environment, so that the inter-tier interference can be effectively suppressed.