利用有效相位模式计算任意阵列MUSIC谱的快速算法

针对任意阵列MUSIC谱的快速计算问题，提出了一种利用模式空间中有效相位模式(EPM)计算MUSIC谱的快速算法。利用空间谱计算时不同方向各阵元的空间相移因子构成一组新的方向向量，由于各方向向量与噪声子空间中特征向量的乘法计算具有循环卷积特性，从而可以利用DFT实现MUSIC谱函数的计算。新的方向向量可以等效为对相应的虚拟连续圆阵采样的结果，根据圆阵能激发的有效相位模式数远小于MUSIC谱的点数的事实，利用DFT计算MUSIC谱时只需要使用有效的相位模式参与计算，从而使计算量大幅度减小。根据方向向量的过采样特性，通过对方向向量进行抽取，利用抽取后的序列计算有效相位模式，进一步较小了计算量。通过仿真实验验证了提出算法的有效性。 

A Fast Algorithm for Music Spectrum Using Effective Phase Modes of Arbitrary Array

For the fast computation problem of MUSIC spectrum, a fast algorithm using effective phase modes in mode space of arbitrary array is proposed. During the computation process of spatial spectrum in different directions, phase shift factor of each element can form a series of new direction vectors. With certain transformation, the multiplication operation between the new direction vectors and eigenvectors in noise subspace has the characteristics of cyclic convolution, MUSIC spectrum can be realized by discrete Fourier transform (DFT). The new direction vectors are equivalent to sampling results of virtual continuous cycle array. According to the fact that the number of the effective phase modes excited by circular array is far fewer than MUSIC spectrum point, the computational complexity can be obviously decreased by using effective phase modes in the process of MUSIC spectrum computation through DFT. For the over sampling characteristics of direction vectors, effective phase modes can be obtained by the sequences after extraction of direction vectors, which can further reduce computational complexity. The simulation result verifies that the proposed algorithm is valid.