  This paper derives the analytical solution of a novel distributed
node-specific block-diagonal linearly constrained minimum variance beamformer
from the centralized linearly constrained minimum variance (LCMV) beamformer
when considering that the noise covariance matrix is block-diagonal. To further
reduce the computational complexity of the proposed beamformer, the
ShermanMorrison-Woodbury formula is introduced to compute the inversion of
noise sample covariance matrix. By doing so, the exchanged signals can be
computed with lower dimensions between nodes, where the optimal LCMV beamformer
is still available at each node as if each node is to transmit its all raw
sensor signal observations. The proposed beamformer is fully distributable
without imposing restrictions on the underlying network topology or scaling
computational complexity, i.e., there is no increase in the per-node complexity
when new nodes are added to the networks. Compared with state-of-the-art
distributed node-specific algorithms that are often time-recursive, the
proposed beamformer exactly solves the LCMV beamformer optimally frame by
frame, which has much lower computational complexity and is more robust to
acoustic transfer function estimation error and voice activity detector error.
Numerous experimental results are presented to validate the effectiveness of
the proposed beamformer.
