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We consider the problem of detecting the presence of a complex-valued, possibly improper, but unknown signal, common among two or more sensors (channels) in the presence of spatially independent, unknown, possibly improper and colored, noise. Past work on this problem is limited to signals observed in proper noise. A source of improper noise is in-phase/quadrature-phase imbalance during down-conversion of bandpass noise to baseband. A binary hypothesis testing approach is formulated, and a generalized likelihood ratio test (GLRT) is derived using asymptotic distribution of a frequency-domain sufficient statistic, based on the discrete Fourier transform of an augmented measurement sequence. An asymptotic analytical solution for calculating the test threshold to yield a desired false alarm rate is provided. The performance of the GLRT is analyzed by deriving an approximate asymptotic distribution of the GLRT statistic under a sequence of local alternative hypotheses. These results (GLRT and test threshold calculation) are then modified to address two special cases: detection of improper signals in proper noise and detection of proper signals in proper noise. Simulation examples are presented in support of the proposed approaches.
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