基于博弈论的二次博弈波束成形算法

Twice Game Beamforming Algorithm Based on Game Theory

针对波束成形算法中,用户的信号方向估计值和用户之间的功率分配存在着相互矛盾,本文提出了一种基于博弈论的二次博弈波束成形算法,构建了波束成形博弈算法数学模型,首先在第一次博弈的时候,将波束成形算法中的信号方向和功率分配映射为博弈论数学模型中的"局中人",将其建模为函数的极大极小值求解问题,先求解出信号方向;然后在第二次博弈的时候,将不同用户的功率分配过程描述为一个多用户的博弈过程,设计了功率分配更新算法,通过数学推导论证了纳什平衡点的存在性和唯一性。最后在仿真中,与传统最大信噪比算法进行比较。结果表明该文算法的性能要优于最大信噪比算法,并且讨论了不同参数对该文算法的影响。

There is mutual contradiction between direction estimation of user＇s signal and power allocation among all users in the beamforming algorithm. A twice game beamforming algorithm based on game theory is proposed to deal with it. Beamforming game algorithm mathematics model is constructed. During the first game, direction of signal and power allocation are mapped the game theory as ＂player＂, which are modeled as the problem of maximin function and obtain direction estimation first. Then during the second game, power allocations of different users are described as a multi-user game. Power updated algorithm is designed. The existence and uniqueness of the Nash equilibrium in the twice game beamforming algorithm based on game theory are proved by mathematics derivation. Finally in simulation the proposed algorithm is compared with conventional maximum SNR algorithm. The results show that the proposed algorithm is better than MaxSNR algorithm and the impact of different parameters on the proposed algorithm is discussed.