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In this work, we consider spectrum sensing of Gaussian signals with structured covariance matrices. We show that the optimal detector based on the probability distribution of the sample covariance matrix is equivalent to the optimal detector based on the raw data, if the covariance matrices are known. However, the covariance matrices are unknown in general. Therefore, we propose to estimate the unknown parameters using covariance matching estimation techniques (COMET). We also derive the optimal detector based on a Gaussian approximation of the sample covariance matrix, and show that this is closely connected to COMET.