This paper proposes a new approach for finding the conditionally optimal solution (the classifier with minimum error probability) for the classification problem where the observations are from the multivariate normal distribution. The optimal Bayes classifier does not exist when the covariance matrix is unknown for this problem. However, this paper proposes a classifier based on the constant false alarm rate (CFAR) and invariance property. The proposed classifier is optimal conditionally as it has the minimum error probability in a subset of solutions. This approach has an analogy to hypothesis testing problems where uniformly most powerful invariant (UMPI) and uniformly most powerful unbiased (UMPU) detectors are used instead of the non-existing optimal UMP detector. Furthermore, this paper investigates using the proposed classifier for modulation classification as an application in signal processing.

本文提出了一种新方法，该方法可以找到针对观测问题来自多元正态分布的分类问题的条件最优解（具有最小错误概率的分类器）。当此问题的协方差矩阵未知时，最佳贝叶斯分类器不存在。然而，本文提出了一种基于恒定误报率（CFAR）和不变性的分类器。所提出的分类器是有条件的最佳选择，因为它在解决方案子集中具有最小的错误概率。这种方法类似于假设检验问题，其中使用一致的最有效不变性（UMPI）和一致的最有效无偏（UMPU）检测器代替不存在的最佳UMP检测器。此外，