基于加权特征投影的信源数估计方法

Estimation method of the number of sources based on weighted eigenspace projection

摘要:

考虑到色噪声或低快条件下噪声特征值发散，导致基于特征分解的信源数估计方法得到的信号判据值和噪声判据值区分不明显，提出了一种基于加权特征投影的信源数估计方法。首先，为了使该方法可适用于低信噪比条件，对阵列接收数据的协方差矩阵进行降噪处理，并利用降噪后协方差矩阵所有特征值和特征向量构造了一个用来区分信号和噪声的加权空间矩阵；然后，将降噪后的协方差矩阵在该加权空间矩阵上投影，从而增大了信号判据值与噪声判据值的差异；最后，结合幂函数的缩放性构建了判决函数，进而实现信源数估计。通过理论分析和实验验证，该方法不仅适用于白噪声和色噪声条件，而且在低快拍和低信噪比条件下优势明显，尤其是在信源数较多时效果鲁棒。

Abstract:

Under the condition of colored noise or low speed, the noise eigenvalues will be diverted, which lead to no significant difference between the signal standard value obtained by the eigen-decomposition-based signal source number estimation method and the noise standard value. Therefore, a method of estimating the number of sources based on weighted eigenspace projection is proposed. First, in order to make the method suitable for low signal-to-noise ratio conditions, the covariance matrix of the data received by the array is denoised, and all eigenvalues and eigenvectors of the denoised covariance matrix are used to construct a noise weighted space matrix. The denoised covariance matrix is projected onto the weighted space matrix to increase the difference between the signal standard value and the noise standard value. Finally, the number of sources is estimated by combining the scalability of the power function to construct decisions. After theoretical analysis and experimental verification, this method is not only suitable for white noise and color noise conditions, but also has obvious advantages under low snapshot and low signal-to-noise ratio conditions, especially when there are more information sources.