In many acoustic applications, the extraction of only one desired source signal from a mixture of signals is required. We propose a novel method to perform this extraction in the overdetermined case where more sensors than sources are available. We apply Blind Signal Processing techniques in a structure that is similar to a Generalized Sidelobe Canceller (GSC). In a GSC the upper branch reproduces the desired source signal with a beamformer while the lower branch reduces the contribution of both noise and interferers. In this work the upper branch is used to extract the desired source from a noisy mixture of all sources and the lower branch is solely used to perform noise reduction. Therefore, the underlying optimization problem is essentially different from the conventional GSC. We validate our method by means of a computer simulation.