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The knowledge of the target speech presence probability in a mixture of signals captured by a speech communication system is of paramount importance in several applications including reliable noise reduction algorithms. In this correspondence, we establish a new expression for speech presence probability when an array of microphones with an arbitrary geometry is used. Our study is based on the assumption of the Gaussian statistical model for all signals and involves the noise and noisy data statistics only. In comparison with the single-channel case, the new proposed multichannel approach can significantly increase the detection accuracy. In particular, when the additive noise is spatially coherent, perfect speech presence detection is theoretically possible, while when the noise is spatially white, a coherent summation of speech components is performed to allow for enhanced speech presence probability …