In the direction estimation of noncircular signals, the sensor array can be virtually extended by adding its complex conjugated version. Exploiting the centro-Hermitian of the extended signal vector without specific requirements of array geometry, we present a computationally efficient method for direction estimation based on the multiple signal classification (MUSIC) principle. When the MUSIC-like estimation is formulated in the virtually extended array, the resulting objective function includes the variable of the phase of a noncircular signal as well as the variable of its direction. The minimum of the two-variable function with respect to the phase is shown to be the same as double the smallest eigenvalue of a 2 x 2 matrix involved in it. Accordingly the estimation for directions of arrival is carried out by calculating the minimum eigenvalue, rather than the determinant of the matrix that conventional methods have usually employed. The eigenvalue-based method (EBM) can be efficiently implemented through real number computation utilizing the centro-Hermitian property. Simulation results demonstrate the superiority of EBM over the determinant-based conventional one.

在非圆形信号的方向估计中，可以通过添加其复杂的共轭形式来虚拟扩展传感器阵列。利用扩展的信号矢量的中心-Hermitian，而不需要阵列几何的特殊要求，我们提出了一种基于多信号分类（MUSIC）原理的方向估计算法，该算法十分有效。当在近似扩展的阵列中制定类似MUSIC的估计时，所得目标函数将包括非圆形信号相位的变量以及其方向的变量。相对于相位，二元函数的最小值显示为与其所涉及的2 x 2矩阵的最小特征值的两倍相同。因此，通过计算最小特征值来进行到达方向的估计，而不是常规方法通常使用的矩阵的行列式。基于特征值的方法（EBM）可以通过利用Centro-Hermitian属性进行实数计算而有效地实现。仿真结果证明了EBM优于基于行列式的传统方法。