小训练样本数下多通道雷达信号检测方法研究

Signal detection with low sample support is a difficult problem often encountered in multichannel radar systems. Conventional methods to solve this difficulty are usually assuming that a priori knowledge about the noise covariance matrix is available. However, this knowledge may be difficult to be accurately obtained in practice. Moreover, when the knowledge is inaccurate, the conventional detectors will suffer considerable performance loss. In this project we will investigate many kinds of problems for multichannel radar signal detection with low sample support, use the signal structure information to design effective detectors which do not depend on the prior knowledge about the noise covariance matrix. For subspace signal detection with low sample support, we adopt the scheme of “signal integration before detection” to devise detectors; for detection problem in interference with low sample support, we employ the scheme of “interference cancellation before detection” to devise detectors; for the problem of generalized direction detection with low sample support, we use the scheme of “generating virtual training data before detection” to devise detectors. Moreover, we will investigate the statistical performance of the proposed detectors and derive their analytical probabilities of detection. In addition, after all the problems above are solved, we will compare the detection performance of the proposed approaches with the conventional ones in the case of sufficient training data, and obtain useful conclusions. The research achievements can provide significantly theoretical and technical supports for multichannel signal detection with low sample support.

小训练样本数下的信号检测是多通道雷达系统所面临的难题之一。为解决该问题，通常的做法是假设预先获得噪声协方差矩阵的部分先验信息。然而，在实际应用中往往很难准确获得该先验信息，而且当先验信息不准确时，检测器可能遭受严重的性能损失。本项目拟研究小训练样本数下多通道雷达信号检测的多种问题，充分利用信号的结构信息，探索不依赖噪声协方差矩阵先验知识的解决途径。针对子空间信号检测问题，拟采用“先信号积累、后检测”的策略进行检测器设计；针对存在干扰时的检测问题，拟采用“先干扰抑制、后检测”的策略进行检测器设计；针对广义方向检测问题，拟采用“先数据变换产生虚拟训练样本、后检测”的策略进行检测器设计；并分析各检测器的统计性能。在解决上述问题之后，拟进一步比较所提检测方法与常规方法在训练样本充足时的区别与联系，得出有益结论。该项目研究成果对训练样本不足时的多通道信号检测具有重要的理论意义和应用价值。

本项目围绕小训练样本数下多通道雷达信号检测问题，开展了多方面的研究工作：（1）针对子空间信号检测问题，采用“先信号积累、后检测”的策略提出了有效的检测器并得到了统计特性；基于杂波加噪声协方差矩阵斜对称的性质，提出了小训练样本数下适用于点目标及扩展目标的自适应检测器并得到了统计特性；利用降秩技术构造了适用于小训练样本的有效降秩子空间检测器；基于先验知识，提出了适用于复合高斯非均匀环境的小训练样本检测器；基于子空间正交投影思想，提出了小训练样本数下适用于运动目标的检测器。（2）针对存在干扰时的检测问题，采用“先干扰抑制、后检测”的策略提出了适用于小训练样本环境下的检测器。此外，基于稀疏贝叶斯思想，提出了小训练样本下一种抑制灵巧干扰的有效方法。（3）针对广义方向检测问题，基于广义似然比准则，提出了适用于部分均匀环境中的有效检测器。在完成上述既定的研究内容基础上，本项目进一步拓展了研究范围，取得了多项研究成果，包括：无需训练样本的MIMO雷达目标检测、小样本数下基于稀疏恢复的机载雷达杂波抑制、小样本数下基于协方差矩阵斜对称的信干噪比分析、训练样本充足下均匀及部分均匀环境中存在信号失配的扩展目标检测、存在干扰时的子空间目标检测及统计性能分析、子空间信号失配下自适应检测器的统计性能分析、结构非均匀环境中的子空间信号检测、干扰条件下部分均匀环境中的方向检测、基于盲源分离的雷达抗干扰问题，等。在基金资助下发表及录用SCI论文41篇、EI论文6篇、中文核心论文1篇，申请国家发明专利7项。研究成果对多通道信号检测，尤其是小训练样本情况下的信号检测具有重要的理论意义和应用价值，为我国相控阵雷达及MIMO雷达目标探测能力提升提供了一定的理论支撑。