Persymmetric detection of subspace signals based on multiple observations in the presence of subspace interference

Abstract

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.