Optimal distributed minimum-variance beamforming approaches for speech enhancement in wireless acoustic sensor networks

In multiple speaker scenarios, the linearly constrained minimum variance (LCMV) beamformer is a popular microphone array-based speech enhancement technique, as it allows minimizing the noise power while maintaining a set of desired responses towards different speakers. Here, we address the algorithmic challenges arising when applying the LCMV beamformer in wireless acoustic sensor networks (WASNs), which are a next-generation technology for audio acquisition and processing. We review three optimal distributed LCMV-based algorithms, which compute a network-wide LCMV beamformer output at each node without centralizing the microphone signals. Optimality here refers to equivalence to a centralized realization where a single processor has access to all signals. We derive and motivate the algorithms in an accessible top-down framework that reveals their underlying relations. We explain how their differences result from their different design criterion (node-specific versus common constraints sets), and their different priorities for communication bandwidth, computational power, and adaptivity. Furthermore, although originally proposed for a fully connected WASN, we also explain how to extend the reviewed algorithms to the case of a partially connected WASN, which is assumed to be pruned to a tree topology.