This paper deals with subspace detection for range-spread target in non-homogeneous clutter with unknown covariance matrix where structured interference is presented in the received data. Through exploiting the persymmetry of the clutter covariance matrix, we propose two adaptive target detectors, which are referred to as persymmetric subspace Rao to suppress interference and persymmetric subspace Wald to suppress interference (“PS-Rao-I” and “PS-Wald-I”), respectively. The persymmetry-based design brings in the advantage of easy implementation for small training sample support. The signal flow analysis of the two detectors shows that the PS-Rao-I rejects interference and integrates signals successively through separated matrix projection, while the PS-Wald-I jointly achieves interference elimination and signal combination via oblique projection. In addition, both detectors are shown to be constant false alarm rate detectors, significantly improving the detection performance with other competing detectors under the condition of limited training.