广义镜象变换及其在信号特征分析中的应用

本文首先介绍了镜象变换及其性质,并将其推广到复数空间中去,引出了广义镜象变换。广义镜象变换保留着镜象变换的主要特性。然后利用广义镜象变换提出了一种信号特征分析的新算法,即广义镜象变换-QR算法。它包括两大步骤:(1)利用广义镜象变换将Hermite阵化为实对称三对角阵。(2)利用带位移的QR方法求实对称三对角阵的特征值。文中给出了上述算法的详细流程。该算法具有收敛速度快和数值稳定的优点。我们将上述方法用于噪声中信号个数的估计问题,给出了Monte-Carlo模拟结果,验证了所述算法的有效性。在模拟实验中,假定天线阵为均匀线性阵,信号源为两个独立的等功率源,目标模型为Swerling Ⅱ,噪声为空间白色的和高斯的。干扰协方差阵由参考噪声样本估计得到。

Generalized Householder Transform and Its Application in Signal Eigenanalysis

Householder transform (HT) is a vector mapping which is an effective approach to simplify matrices. In this pape after briefly describing the HT and its properties, we extend it to the complex case and define the generalized householder transform (GHT). Major properties of the HT remain in the GHT. A new algorithm of signal eigenanalysis based on the GHT and the QR method, i.e. Householder-QR algorithm is presented. It consists of two steps. (1) transform a Hermitian matrix into a real symmetrical triple diagonal matrix by the GHT, and (2) find the eigenvalues of a real symmetrical triple diagonal matrix by the QR method with shift. The detailed flow chart of the new algorithm is listed in the paper. This algorithm is fast convergent and numerically robust.We applied the above new algorithm to estimating the number of targets in spatial noise. Monte-Carlo simulation has demonstrated the effectiveness of the proposed algorithm. In the simulation, the array is uniform and linear, two uncorrelated targets were of equal power, the fluctuating model of Swerling I is assumed, and the interference is spatially white and Gaussian. An estimate of the covariance matrix of the interference is obtained from reference noise samples. The simulation results are given graphically.