Abstract: In this paper, we derive the joint probability density functions for the instantaneous Stokes vectors of Gaussian randomly-polarized waves, according to which we derive the polarimetric detectors based on Stokes vectors, whose detection performance is then analyzed. We derive the analytical expressions for detection and false alarm probabilities of the detectors, based on which we obtain the detectors’ performance curves for target detection in clutter with different polarization degrees. Detectors based on Stokes vectors and Jones vectors are then comparatively studied. An analytical expression of the performance variance is deduced for the case of large number of pulses, and it is proved that the detector based on Stokes vectors is the optimal polarimetric detector for noncoherent radars with orthogonally-polarized reception channels.