认知网络中基于纳什议价解的功率控制方法

本文基于合作博弈论中的纳什议价博弈理论，研究了认知无线电网络中的功率控制问题。提出一种基于信干扰比(Signal-to-Interference plus Noise Ratio, SINR)的效用函数模型，按照纳什定理基于该模型的合作功率控制算法获得的纳什议价解(Nash Bargaining Solution, NBS)可以保证整个系统的帕雷托最优性，同时通过证明纳什议价解实质是比例公平性的一般形式从而保证用户之间的公平性。在主要用户干扰温度限和认知用户的最大传输功率等限制条件下，按照纳什定理把基于NBS的功率控制问题转化为求解多重限制条件下的最优化问题，通过引入拉氏乘子求解该问题有效获得了各个认知用户的传输功率水平，实现SINR门限的要求。仿真结果表明本文算法有较快的收敛速度，同时较非合作算法相比可以有效改善认知用户之间的公平性和系统的整体性能。

Power Control Method Based on Nash Bargaining Solution for Cognitive Radio Networks

The power control method for Cognitive Radio Networks (CRN) is investigated in this paper, which is based on the Nash bargaining cooperative game theory. A utility function based on (Signal-to-Interference plus Noise) SINR is proposed for this model. Based on the Nash Bargaining Solution (NBS) from the cooperative game theory, the power control method not only provides the power level of users that are Pareto optimal from the point of view of the whole system, but also are consistent with the fairness axioms of game theory. Meanwhile, we prove the NBS is essentially a general form of the proportional fairness. Under the constraints from the interference temperature of the primary user and the maximum transmit power of the cognitive users, and according to NBS Nash theorem, we convert the power control problem into the optimization problem with multiple constraints. Through introducing the Lagrange operators, the optimal power levels are obtained, and achieving the SINR threshold requirements are met. The simulation results show that our algorithm has a faster convergence rate, and compared to reference traditional method, our algorithm can effectively improve the understanding between users, the fairness of the cognitive users and the overall performance of the whole system.