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For hearing-impaired listeners, it is required not only to enhance the target speech by suppressing ambient noises, but also to preserve the binaural cues of important directional sources, such that a complete spatial awareness of the acoustic scene is obtained. It was shown that the binaural minimum variance distortionless response (BMVDR) filter enables a joint enhancement and binaural cue preservation of the target source. By adding more linear constraints associated with the acoustic transfer functions of noise sources to BMVDR, the binaural linearly constrained minimum variance (BLCMV) filter is obtained, which can further preserve the spatial cues of interfering sources at the cost of sacrificing the noise reduction performance. Both BMVDR and BLCMV beamformers enforce a hard decision on the spatial awareness. In this paper, we therefore propose a generalization for BMVDR and BLCMV, namely …