The problem of detecting subspace signals in the presence of subspace interference and Gaussian noise is examined by using multiple observations collected from multiple range cells, bands, and/or coherent processing intervals. We exploit persymmetry to propose one-step and two-step detectors, according to the criterion of generalized likelihood ratio test (GLRT). Both the proposed detectors exhibit constant false alarm rate properties against the noise covariance matrix. Moreover, the statistical characterizations of the proposed one-step detector are obtained. We derive exact expressions for the probability of false alarm (PFA) of the proposed one-step detector in six cases where the signal subspace dimension is no more than 4 or the number of observations is no more than 2. In other cases, we derive an approximate expression for the PFA of the proposed one-step detector. Numerical examples illustrate that the proposed detectors outperform their counterparts, especially when the number of training data is small. In addition, the proposed one-step GLRT detector generally has better detection performance than the two-step detector.

通过使用从多个测距单元，频带和/或相干处理间隔收集的多个观测值，检查了在存在子空间干扰和高斯噪声的情况下检测子空间信号的问题。根据广义似然比检验（GLRT）的准则，我们利用不对称性提出了一步和两步检测器。两种提出的检测器均针对噪声协方差矩阵展现出恒定的误报率属性。此外，获得了所提出的一步检测器的统计特征。在信号子空间维数不超过4或观察次数不超过2的六种情况下，我们得出了拟议的一步检测器的误报概率（PFA）的精确表达式。在其他情况下，我们导出了所提出的一步检测器的PFA的近似表达式。数值算例表明，所提出的探测器性能优于同类探测器，特别是在训练数据数量较少的情况下。另外，所提出的一步GLRT检测器通常具有比两步检测器更好的检测性能。