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We exploit persymmetric structures to design a generalized likelihood ratio test for detecting subspace signals in homogeneous Gaussian clutter with unknown covariance matrix. The subspace model is employed to account for mismatches in the target steering vector. An exact but finite-sum expression for the probability of false alarm of the proposed detector is derived, which is verified using Monte Carlo simulations. This expression is irrelevant to the clutter covariance matrix, indicating that the proposed detector exhibits a constant false alarm rate property against the clutter covariance matrix. Numerical examples show that the proposed detector has strong robustness to the target steering vector mismatch.
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