Persymmetric Subspace GLRT for Signal Detection With Known Waveform Under Steering Vector Uncertainties

This paper investigates signal detection in active sensing systems employing known encoded waveforms in the presence of steering vector mismatch arising from multipath propagation and imperfect calibration. To account for such steering vector uncertainties, a subspace-based signal model is adopted. Furthermore, to enhance detection performance, a symmetrically spaced linear array is employed at the receiver, which induces a persymmetric structure in the received data. By exploiting the persymmetric property, the complex-valued quantities are transformed into real-valued forms, based on which the corresponding generalized likelihood ratio test (GLRT), referred to as the persymmetric subspace GLRT, is developed in the real domain. A closed-form expression for the false alarm probability of the proposed GLRT detector is obtained, demonstrating that it possesses the constant false alarm rate property. Finally, numerical simulation results validate the theoretical analysis and show that the proposed persymmetric subspace GLRT outperforms the conventional subspace GLRT without persymmetry. It is also demonstrated that the proposed persymmetric subspace GLRT detector is robust to the steering vector uncertainties.