New Insights Into the MVDR Beamformer in Room Acoustics

The minimum variance distortionless response (MVDR) beamformer, also known as Capon´s beamformer, is widely studied in the area of speech enhancement. The MVDR beamformer can be used for both speech dereverberation and noise reduction. This paper provides new insights into the MVDR beamformer. Specifically, the local and global behavior of the MVDR beamformer is analyzed and novel forms of the MVDR filter are derived and discussed. In earlier works it was observed that there is a tradeoff between the amount of speech dereverberation and noise reduction when the MVDR beamformer is used. Here, the tradeoff between speech dereverberation and noise reduction is analyzed thoroughly. The local and global behavior, as well as the tradeoff, is analyzed for different noise fields such as, for example, a mixture of coherent and non-coherent noise fields, entirely non-coherent noise fields and diffuse noise fields. 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 sacrificed 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 supports the theoretical analysis and demonstrates the tradeoff between speech dereverberation and noise reduction. When desiring both speech dereverberation and noise reduction, the results also demonstrate that the amount of noise reduction that is sacrificed decreases when the number of microphones increases.