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We propose a new detector to test the presence of a radar signal with unknown parameters in unknown variance additive white Gaussian noise. Uniformly most powerful invariant (UMPI) tests and unitary filter banks are combined in a new detector. This problem does not fit the linear model due to the unknown Doppler frequency. It is found that the UMPI test does not exist for such a problem. In our detector, we apply an appropriate linear transformation, which is a unitary filter bank, to the concerned radar signal and the problem is converted to the canonical form. Since the UMPI test does exist for the canonical form, then we derive an optimal invariant test for our problem.