This study considers Rao test and Wald test for adaptive detection based on a diversely polarized antenna (DPA) in partially homogeneous environment. The theoretical expressions for the probability of false alarm and detection are derived, and constant false alarm rate (CFAR) behaviour is remarked on. Furthermore, the monotonicities of detection probability of the two detectors are proved, and a polarization optimization detection algorithm to enhance the detection performance is proposed. The numerical simulations are conducted to attest to the validity of the above theoretical analysis and illustrate the improvement in the detection performance of the proposed optimization algorithm.