基于特征值梯度跃变的半谱搜索DOA估计算法

Half-Spectral Search DOA Estimation Algorithm Based on Eigenvalue Gradient Jump

摘要:

针对传统子空间类波达方向（Direction of Arrival，DOA）估计算法需已知信源数目，以及计算复杂度高的问题，提出一种基于特征值梯度跃变的半谱搜索 DOA 估计算法。该方法首先利用接收信号协方差矩阵及其复共轭构建新矩阵，同时引入扫描源，构造了以扫描角度为变量的全新协方差矩阵，并对构造的协方差矩阵进行特征值分解，利用信号子空间与噪声子空间特征值间的功率差异，构造特征值梯度判别函数； 通过检测该函数极大值点，实现信源数目的自主估计。该方法基于信号与噪声特征值功率强度的差异分界特性，以特征值梯度变化作为判定依据，无需信源数目的先验知识。随后，将估计的信源数目与低复杂度半谱搜索谱函数结合，在降低计算复杂度前提下，有效提升了复杂环境下（如包含对称角、0°入射角）的 DOA 估计精度。数值仿真结果证明了本算法在均匀线阵下具有鲁棒性。

Abstract:

To address the issues that traditional subspace-based direction of arrival（DOA）estimation algorithms require prior knowledge of the number of sources and suffer from high computational complexity，a half-spectral search DOA estimation algorithm based on the gradient jump of eigenvalues is proposed in this paper. The method first constructs a new matrix using the covariance matrix of the received signal and its complex conjugate. Simultaneously，it introduces scanning sources to form a novel covariance matrix with the scanning angle as a variable. Subsequently，eigenvalue decomposition is performed on the constructed covariance matrix. Leveraging the significant power difference between the eigenvalues of the signal subspace and noise subspace，an eigenvalue gradient discrimination function is formulated. The number of signal sources is automatically estimated by detecting the maximum points of this function. Based on the distinct demarcation characteristic between the power intensities of signal and noise eigenvalues，this method takes the gradient variation of eigenvalues as the judgment criterion and does not require prior knowledge of the number of signal sources. Subsequently，by combining the estimated number of signal sources with the low-complexity half-spectral search spectrum function，it effectively improves the DOA estimation accuracy in complex environments.