旁瓣约束下期望主瓣幅度响应迭代波束设计  

Iterative beam pattern synthesis with mainlobe magnitude approximation under sidelobe response constraints

作　　者：王文侠 鄢社锋[1,2] WANG Wenxia;YAN Shefeng(Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190;University of Chinese Academy of Sciences,Beijing 100190)

机构地区：[1]中国科学院声学研究所,北京100190 [2]中国科学院大学,北京100049

出　　处：《声学学报》2022年第5期568-578,共11页Acta Acustica

基　　金：国家自然科学基金项目(61725106,62192711)资助。

摘　　要：研究了旁瓣约束下的期望主瓣幅度逼近问题,其包含双边绝对值不等式结构,为非凸波束设计问题。针对传统的多约束优化算法难以处理非凸结构,提出了两种迭代算法。一种对原优化问题作局域线性近似,将非凸约束转换为仿射约束,进而迭代局部二阶锥规划问题求解原问题。另一种通过引入辅助变量构建增广拉格朗日函数,将加权向量与各约束解耦合,交替迭代求解关于原变量、主瓣辅助变量与旁瓣辅助变量的三个子优化问题以给出初始非凸问题的解。针对子优化问题,通过灵活运用拉格朗日乘子技术构建了低复杂度求解方案。采用仿真和实测阵列流形验证设计效果,结果表明,所提两种迭代算法可实现主瓣幅度逼近,合成平顶波束图,且对阵型无依赖性。交替迭代法耗时显著低于迭代二阶锥规划法。The synthesis of mainlobe magnitude under sidelobe constraint is studied,which is a non-convex beampattern optimization problem including bilateral absolute value inequality.In view of the difficulty of traditional multi-constraint optimization algorithms to deal with non-convex structures,two iterative algorithms are proposed.One is to take a linear approximation to the original optimization problem,convert the non-convex constraint into an affine constraint,and then iterate the local second-order cone programming problem to solve the original problem.The other is to construct an augmented Lagrangian function by introducing auxiliary variables.The weighting vector is decoupled from constraints,and three optimization sub-problems about the original variables,mainlobe auxiliary variables and sidelobe auxiliary variables are solved alternately to obtain the solution of the initial non-convex problem.On the optimization sub-problems,low complexity solutions are constructed by flexible use of the Lagrange multiplier method.The complexity analysis of the two iterative algorithms is provided.The proposed algorithms are verified by both simulated and measured array manifold.The results show that both the two iterative algorithms can achieve the mainlobe magnitude approximation and synthesize the flat top beampattern,and have no dependence on the array manifold.The time consumption of the alternating iteration method is significantly lower than that of the iterative second-order cone programming method.

关 键 词：二阶锥规划 主瓣 波束设计 辅助变量 增广拉格朗日函数 拉格朗日乘子 多约束优化 交替迭代法 

分 类 号：TB56[交通运输工程—水声工程] TN911.7[理学—物理]