基于信息几何理论的信号检测方法

Signal Detection Method Based on Information Geometry Theory

信息几何理论将统计推断问题转换为几何问题进行处理,从而能够从几何的角度分析进行统计推断。以高斯噪声下的信号检测为研究对象,给出了基于信息几何理论的信号检测所需的理论基础,分析了测地线距离与检测器性能之间的关系。分别以简单假设和复合假设两种情况,分析了两种距离检测器的性能,并与Neyman-Pearson检测器和广义似然比检测器进行了对比。计算机分析结果表明,测地线长度和方向共同决定了检测性能,且距离检测器性能与似然比检测器性能相当。

Based on the information geometry theory, the statistical inference can be transformed into the geometry problem, and hence, can be realized from a geometric perspective. In this paper, we consider the signal detection in Gaussian noise, and provide the fundamentals necessary for signal detection based on the information geometry theory. The relationship between the geodesic distance and the detection perform- ance is analyzed. The two distance detectors are analyzed for simple hypothesis and compound hypothesis re- spectively. The computer analysis results indicate that the detection performance is determined by the geo- desic distance and orientation, and the detection performance of the distance detector is comparative to the likelihood ratio detector.