  In this paper we propose a new binaural beamforming technique which can be
seen as a relaxation of the linearly constrained minimum variance (LCMV)
framework. The proposed method can achieve simultaneous noise reduction and
exact binaural cue preservation of the target source, similar to the binaural
minimum variance distortionless response (BMVDR) method. However, unlike BMVDR,
the proposed method is also able to preserve the binaural cues of multiple
interferers to a certain predefined accuracy. Specifically, it is able to
control the trade-off between noise reduction and binaural cue preservation of
the interferers by using a separate trade-off parameter per interferer.
Moreover, we provide a robust way of selecting these trade-off parameters in
such a way that the preservation accuracy for the binaural cues of the
interferers is always better than the corresponding ones of the BMVDR. The
relaxation of the constraints in the proposed method achieves approximate
binaural cue preservation of more interferers than other previously presented
LCMV-based binaural beamforming methods that use strict equality constraints.
