The multiple signal classification (MUSIC) algorithm is widely used in direction of arrival (DOA) estimation. Conventional MUSIC-like algorithms suffer from the heavy computational burden imposed by the two-dimensional (2-D) angle search and an exhaustive spectral search. We propose a two-stage unitary spherical harmonics MUSIC (TSU-SHMUSIC) that converts 2-D MUSIC into two new one-dimensional (1-D) MUSICs. The spherical harmonic steering vector is expressed in two forms, the linear weight of a uniform phase vector and the linear weight of a vector constructed by associated Legendre functions. These two expressions are used conjunction with Lagrange multiplier method to obtain two new corresponding search functions for the elevation and azimuth. We exploit the characteristics of real-valued spherical harmonics to construct virtual signals from the mirror directions of signal sources. A new noise subspace is computed from the covariance matrices of the virtual and real signals. We use this noise subspace to reduce the angle search ranges to half of the total angular field of view. The proposed methods have a considerably lower computational complexity than U-SHMUSIC. Numerical simulations demonstrate that the proposed methods provide perform better than the two-stage decoupled approach (TSDA).

多信号分类（MUSIC）算法广泛应用于到达方向（DOA）估计。传统的类似于MUSIC的算法遭受了二维（2-D）角度搜索和穷举频谱搜索带来的沉重计算负担。我们提出了一个两阶段的单一球面谐波MUSIC（TSU-SHMUSIC），它将2-D MUSIC转换为两个新的一维（1-D）MUSIC。球形谐波控制矢量以两种形式表示：均匀相位矢量的线性权重和由相关联的勒让德函数构造的矢量的线性权重。这两个表达式与拉格朗日乘数法结合使用，以获得两个新的对应仰角和方位角搜索函数。我们利用实值球谐函数的特性从信号源的镜像方向构造虚拟信号。从虚拟信号和真实信号的协方差矩阵计算出一个新的噪声子空间。我们使用该噪声子空间将角度搜索范围减小到总视场的一半。所提出的方法具有比U-SHMUSIC低得多的计算复杂度。数值模拟表明，所提出的方法比两阶段解耦方法（TSDA）的性能更好。所提出的方法具有比U-SHMUSIC低得多的计算复杂度。数值模拟表明，所提出的方法比两阶段解耦方法（TSDA）的性能更好。所提出的方法具有比U-SHMUSIC低得多的计算复杂度。数值模拟表明，所提出的方法比两阶段解耦方法（TSDA）的性能更好。