基于线性约束最小方差对角加载的稳健频率不变波束形成算法

Robust frequency invariant beamforming algorithm based on linear constrained minimum variance diagonal loading method

针对实际环境中因麦克风阵列失配误差导致宽带波束形成器性能下降的问题,提出基于线性约束最小方差对角加载的稳健频率不变波束形成算法.该算法首先在线性约束最小方差准则的基础上,结合空间响应偏差函数,并对波束形成器权矢量的二范数施加不等式约束,再通过拉格朗日乘子法和凸优化工具箱CVX(Con Ve X)分别在不等约束条件下求得权矢量的解析解和全局最佳解,以有效解决麦克风的增益、相位和位置等的不确定性造成的失配误差问题,提高频率不变波束器的稳健性.仿真结果表明:采用拉格朗日乘子法求解该算法的最优权矢量所得到的波束形成器对失配误差最不敏感,性能最稳健.

In order to improve the beamforming robustness of microphone array with mismatch errors in actual environment,a robust frequency invariant beamforming algorithm is proposed based on linear constrained minimum variance diagonal loading method.In this proposed algorithm,the spatial response variation function is incorporated with linear constrained minimum variance beamforming algorithm,and the two norm of the weight vector of beamformer is constrainted into inequality,then the analytical solution and global optimal solution for the weight vector can be solved by using Lagrange multiplier method and CVX iterative,which can improve the robustness of frequency invariant beampattern,as well solve the mismatch error caused by uncertainty in microphone gain,phase or position.Simulation results illustrate that Lagrange multiplier method of the proposed algorithm outperform CVX iterative solution in improving the robustness of frequency invariant beamformer.