In this paper, we deal with the problem of adaptive detection of point-like targets in Gaussian disturbance with unknown but persymmetric structured covariance matrix induced by a symmetric antenna geometry. In particular, at the design stage we modify the noise-only hypothesis assuming the presence of a fictitious signal orthogonal to the nominal one. The performance assessment, conducted by Monte Carlo simulation, has shown that the proposed receiver can significantly outperform its unstructured counterpart and guarantee enhanced rejection performance of unwanted signals.