基于实数多项式的根值最小范数算法.pdf

优先出版 计 算 机 应 用 研 究 第33 卷 基于实数多项式的根值最小范数算法* 1, 2 1, 2 1, 2 1, 2 张爱丽 ，刘团宁 ，孙茂泽 ，王婧娟 (1 ．河南师范大学 计算机与信息工程学院，河南 新乡 453007 ；2 ．“智慧商务与物联网技术”河南省工程实验室，河 南 新乡 453007) 摘 要：在根值最小范数算法中须对复数多项式求根，计算量较大。针对此问题，提出了一种基于实数多项式的根值最 小范数算法，该算法适用于均匀线性阵列。首先通过保角变换将分布在复平面单位圆的变量映射到实数轴的[-1,1]范围 内，其能够将算法中的复数多项式转换为实数多项式；其次对该实数多项式求根，并从中选出[-1,1]范围内的根值；最 后将筛选出的根值代入信号频谱函数中，根据频谱函数的值选择出最优的波达方向估值。理论分析说明本文算法比根值 最小范数算法的时间复杂度低；仿真实验表明，与根值最小范数相比，在信号和噪声不相关时，本文算法的均方根误差 略小，在信号和噪声相关时，随着信噪比的增加，本文算法的均方根误差逐渐变小。 关键词：最小范数；线性阵列；波达方向估计；实数多项式；保角变换 中图分类号：TN911.23 Root minimum norm algorithm based on real polynomial Zhang Aili1, 2, Liu Tuanning1, 2, Sun Maoze1, 2, Wang Jingjuan1, 2 (1. College of Computer Information Engineering, Henan Normal University, Xinxiang Henan 453007, China; 2. Engineering Lab of Henan Province for Intelligence Business Internet of Things, Xinxiang Henan 453007, China) Abstract: The root minimum norm algorithm must solve roots of the complex polynomial, but it requires a large amount of calculations. Aiming at solving this problem, this paper proposed a root minimum norm algorithm based on real polynomial, which is suitable for uniform linear array. Firstly, the authors used conformal transformation to transform variables of distributed on the complex plane unit circle into the real line range of [-1, 1]. Thus, the complex polynomial of root minimum norm algorithm became real polynomial. Secondly, from the real polynomial, the roots of the algorithm can be solved, and those within the range of [-1, 1] were feasible