基于黎曼流形的MIMO雷达目标检测方法

针对样本数少时不能用样本协方差代替统计协方差的问题，提出了一种基于黎曼流形的单基地MIMO ( Multiple-Input Multiple-Output) 雷达目标检测新方法。该方法利用拓普利兹-厄米特正定( THPD: Toeplitz- Hermitian Positive Definite) 矩阵会在信号空间形成黎曼流形的特点，通过burg 递推法分别生成单快拍下接收信 号和噪声的THPD 协方差矩阵，并计算噪声THPD 协方差矩阵的黎曼均值，将其与接收信号THPD 协方差矩阵 之间的黎曼距离作为检测统计量。该方法可增加黎曼流形上接收信号与噪声间的差异性。仿真结果表明， 与传统的基于欧几里得距离的检测方法相比，显著提高了低信噪比和单快拍下的目标检测性能。

Target Detection Method for MIMO Radar Based on Riemannian Manifold

Aiming at the problem that the sample covariance can not replace the statistical covariance when the number of samples is small，a novel target detection method based on Riemannian manifold is proposed for monostatic MIMO( Multiple-Input Multiple-Output) radar． It takes advantage of the fact that the THPD( Toeplitz- Hermitian Positive Definite) matrix can form Riemannian manifold in signal space． The single-snapshot THPD covariance matrices of received signals and noises are respectively generated through the burg algorithm，and the Riemannian mean of the noise THPD covariance matrices is calculated． The Riemannian distance between the THPD covariance matrices of received signal and noise is taken as the detection statistic． The method can increase the dissimilarity between the received signal and noise on the Riemannian manifold． The simulation results indicate that compared to the traditional method which uses the Euclidean distance，the proposed method can significantly improve the target detection performance under low SNR ( Signal-to-Noise Ratio) and singlesnapshot．