基于谱分解的降阶求根MUSIC算法

求根多重信号分类(Root-MUSIC)算法以多项式求根代替谱峰搜索，降低了波达方向(DOA)估计的计算量，但当阵元数较大时，其计算量依然很大。为进一步降低计算量，该文提出一种降阶Root-MUSIC(RD-Root-MUSIC)算法。该算法基于谱分解将Root-MUSIC多项式的阶次降低一半，再根据矩阵特征多项式与求根多项式的关系构造友阵，采用Arnoldi迭代计算得到友阵的L个大特征值(L为信号数)并估计DOA。仿真结果表明，RD-Root-MUSIC估计精度与Root-MUSIC相近，但其在大阵元下具有比Root-MUSIC更低的计算量。

Reduced-dimension Root-MUSIC Algorithm Based on Spectral Factorization

The Root MUltiple SIgnal Classification (Root-MUSIC) algorithm uses polynomial rooting instead of spectral search to reduce the computational complexity of Direction-Of-Arrival (DOA) estimation. However, when large numbers of sensors are exploited, this algorithm is still time-consuming. To further reduce the complexity, a novel Reduced-Dimension Root-MUSIC (RD-Root-MUSIC) algorithm based on spectral factorization is proposed, in which the dimension of polynomial involved in the rooting step is efficiently reduced to half. A companion matrix whose eigenvalues correspond to the roots of the reduced-dimension polynomial is further constructed, and the Arnoldi iteration is finally used to calculate only the L largest eigenvalues containing DOA information, where L is the number of signals. Simulation results show that RD-Root-MUSIC has a similar performance with much lower complexity as compared to Root-MUSIC.