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Based on a diversely polarized antenna, we address the problems of adaptive detection and performance enhancement in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor. The matched subspace detector and adaptive subspace detector are employed to handle the detection problem for the cases of known and unknown noise covariance matrix structure, respectively. The performance of the two detectors is evaluated in terms of their probabilities of false alarm and detection. In particular, a waveform design algorithm to enhance the detection performance of the two detectors is proposed. A numerical analysis is presented to demonstrate the potential performance improvement obtained with this algorithm.