The problem of detecting rank-one signals is considered in the presence of subspace interference and Gaussian noise with unknown covariance matrix. A generalized likelihood ratio test (GLRT) detector has already been designed for this detection problem. In this correspondence, we provide analytical performance analysis for the GLRT detector in the mismatched case where the nominal target steering vector is not aligned with the true one. All theoretical results are confirmed using Monte Carlo techniques. It is revealed that the detector bears a constant false alarm rate property against the noise covariance matrix. The expressions derived for the probabilities of false alarm and detection can greatly facilitate the threshold setting and performance evaluations. Numerical examples indicate that the GLRT is sensitive to steering vector mismatches.

中文翻译：

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子空间干扰加高斯噪声中秩一信号检测的解析性能

在存在子空间干扰和协方差矩阵未知的高斯噪声的情况下考虑秩一信号的检测问题。已经针对该检测问题设计了广义似然比测试 (GLRT) 检测器。在这种对应关系中，我们为 GLRT 检测器在标称目标导向向量与真实导向向量不匹配的不匹配情况下提供分析性能分析。所有理论结果均使用蒙特卡罗技术进行确认。结果表明，检测器对噪声协方差矩阵具有恒定的误报率特性。为虚警和检测概率导出的表达式可以极大地促进阈值设置和性能评估。数值例子表明 GLRT 对导向矢量不匹配很敏感。