On the application of the LCMV beamformer to speech enhancement

In theory the linearly constrained minimum variance (LCMV) beamformer can achieve perfect dereverberation and noise cancellation when the acoustic transfer functions (ATFs) between all sources (including interferences) and the microphones are known. However, blind estimation of the ATFs remains a difficult task. In this paper the noise reduction of the LCMV beamformer is analyzed and compared with the noise reduction of the minimum variance distortionless response (MVDR) beamformer. In addition, it is shown that the constraint of the LCMV can be modified such that we only require relative transfer functions rather than ATFs to achieve perfect cancellation of coherent interferences. Finally, we evaluate the noise reduction performance achieved by the LCMV and MVDR beamformers for two coherent sources: one desired and one undesired.