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In this paper, we establish a generalized noise reduction scheme, called the spatially pre-processed speech distortion weighted multi-channel Wiener filter (SP-SDW-MWF), that encompasses the generalized sidelobe canceller (GSC) and a recently developed multichannel Wiener filtering technique (MWF) as extreme cases. In addition, the scheme allows for in-between solutions such as the speech distortion regularized GSC (SDR-GSC). The SDR-GSC adds robustness against signal model errors to the GSC by taking speech distortion explicitly into account in the design criterion of the adaptive stage. Compared to the widely studied GSC with quadratic inequality constraint (QIC-GSC), the SDR-GSC achieves better noise reduction for small model errors, while guaranteeing robustness against large model errors. In addition, the extra filtering of the speech reference signal in the SP-SDW-MWF further improves the …