基于协方差矩阵加权的阵列波束优化方法

针对目前二阶统计量加权波束形成存在的能量波束输出有负值和高旁瓣问题,提出了基于协方差矩阵加权的,适用于任意阵结构和阵元指向性传感器阵列的三种优化波束形成方法.一种是设计波束以最小加权均方误差逼近期望波束方法;另一种是旁瓣约束高增益协方差矩阵加权波束形成;第三种是主瓣约束条件下最低旁瓣协方差矩阵加权波束形成.这三种波束优化问题都可以转化为二阶锥约束优化形式,应用已有内点方法求出加权矩阵的数值解.计算机仿真和实验数据处理表明,它们均克服了高旁瓣和波束输出有负值的缺点,获得了不同约束条件下的最佳协方差矩阵加权波束.

Beampattern Optimization for Sensor Arrays Based on Covariance Matrix Weighting

Three optimal beamforming methods for sensor arrays of arbitrary geometry and element directivity were developed. The first one minimizes the square errors between the design beam and the desired beam while keeping unity output in the look direction. This method can design the beam according to the desired beam response. The second approach maximizes the array gain while keeping mainlobe direction and contolling the maximum sidelobe level. The third method minimizes the sidelobe level while keeping unity output in the look direction. These three methods can all overcome the two questions of second statistical weighted beamforming methods,which are the higher sidelobe and negative values in the beam patterns. They are converted to a convex form as the so called second-order cone programming and easily solved using well-developed interior-point methods. Results of computer simulation and lake-experiment for a circular array show superior performance of the proposed methods developed compared to the existing optimal beamforming methods.