采用二阶锥规划和压缩感知的方向图综合算法

Pattern synthesis algorithm using second-order cone programming and compressed sensing theory

常规自适应方向图综合在求解最优权值向量时需经过复杂的广义矩阵求逆运算,计算过程繁琐,占用存储空间大。针对这一问题,提出一种采用二阶锥规划与压缩感知理论的改进自适应方向图综合算法。改进的算法将传统算法中的误差性能函数通过数学变换转换成标准二阶锥规划形式快速求解,同时应用压缩感知理论将大规模阵列权值稀疏化处理,从而得到最优天线阵列权值向量并减少训练时间。仿真结果表明,采用二阶锥规划与压缩感知的改进算法在大规模阵列天线方向图综合时求解速度快、运算精度高,且在应用压缩感知后形成的方向图有较低旁瓣,干扰方向零陷深,接近满阵时的波束性能。

In order to solve some problems such as the generalized inverse of a complex matrix consumes a lot of memory space in the conventional adaptive pattern synthesis methods,this paper proposed an improved adaptive pattern synthesis algorithm based on second-order cone programming（ SOCP） and compressed sensing（ CS） theory. First,the improved algorithm converted the error performance function of traditional algorithm into a standard second-order cone programming. Then,it used the compressed sensing theory in large array weights sparse processing,so as to obtain the optimal weight vector of the antenna array. The simulation results show that the improved algorithm based on SOCP and CS has faster computing speed in large-scale array antenna pattern synthesis and high computing accuracy. And the obtained pattern has better performance,lowest side lobe level and the deepest nulling steering through the application of compressed sensing.