Chapter 9 The MVDR Beamformer for Speech Enhancement Emanuƒ el A.P. Habets, Jacob Benesty, Sharon Gannot, and Israel Cohen Abstract The minimum variance distortionless response (MVDR) beamformer is widely studied in the area of speech enhancement and can be used for both speech dereverberation and noise reduction 1 . This chapter summarizes some new insights into the MVDR beamformer. SpeciØcally, the local and global behaviour of the MVDR beamformer is analysed, diÆerent forms of the MVDR beamformer and relations between the MVDR and other optimal beamformers are discussed. In addition, the tradeoÆ between dereverberation and noise reduction is analysed. This analysis is done for a mixture of coherent and non-coherent noise Øelds and entirely non-coherent noise Øelds. It is shown that maximum noise reduction is achieved when the MVDR beamformer is used for noise reduction only. The amount of noise reduction that is sacriØced when complete dereverberation is required depends on the direct-to-reverberation ratio of the acoustic impulse response between the source and the reference microphone. The performance evaluation demonstrates the tradeoÆ between dereverberation and noise reduction. Emanuƒ el A.P. Habets Imperial College London, United Kingdom, e-mail: e.habets@imperial.ac.uk Jacob Benesty INRS-EMT, University of Quebec, Quebec, Canada, e-mail: benesty@emt.inrs.ca Sharon Gannot Bar-Ilan University, Israel, e-mail: gannot@eng.biu.ac.il Israel Cohen Technion{Israel Institute of Technology, Israel, e-mail: icohen@ee.technion.ac.il 1 This work was supported by the Israel Science Foundation under Grant 1085/05. 197