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In this paper, we consider the distributed target detection problem in Gaussian clutter with unknown covariance matrix. By exploiting the persymmetry of the covariance matrix, an adaptive detector is proposed according to the two-step design method. The probabilities of detection and false alarm of the proposed detector are derived in closed form, which are verified through Monte Carlo simulations. The expression for the probability of false alarm reveals that the proposed detector bears constant false alarm rate against the covariance matrix. Numerical examples illustrate that the proposed detector outperforms its counterparts, especially in the limited training data environment.