A sparse blocking matrix for multiple constraints GSC beamformer

Modern high performance speech processing applications incorporate large microphone arrays. Complicated scenarios comprising multiple sources, motivate the use of the linearly constrained minimum variance (LCMV) beamformer (BF) and specifically its efficient generalized sidelobe canceler (GSC) implementation. The complexity of applying the GSC is dominated by the blocking matrix (BM). A common approach for constructing the BM is to use a projection matrix to the null-subspace of the constraints. The latter BM is denoted as the eigen-space BM, and requires M
²
complex multiplications, where M is the number of microphones. In the current contribution, a novel systematic scheme for constructing a multiple constraints sparse BM is presented. The sparsity of the proposed BM substantially reduces the complexity to K × (M - K) complex multiplications, where K is the number of constraints. A theoretical analysis of the signal leakage and of the blocking ability of the proposed sparse BM and of the eigen-space BM is derived. It is proven analytically, and tested for narrowband signals and for speech signals, that the blocking abilities of the sparse and of the eigen-space BMs are equivalent.