Distributed Delay and Sum Beamformer for Speech Enhancement via Randomized Gossip

In this paper, we investigate the use of randomized gossip for distributed speech enhancement and present a distributed delay and sum beamformer (DDSB). In a randomly connected wireless acoustic sensor network, the DDSB estimates the desired signal at each node by communicating only with its neighbors. We first provide the asynchronous DDSB (ADDSB) where each pair of neighboring nodes updates its data asynchronously. Then, we introduce an improved general distributed synchronous averaging (IGDSA) algorithm, which can be used in any connected network, and combine that with the DDSB algorithm where multiple node pairs can update their estimates simultaneously. For convergence analysis, we first provide bounds for the worst case averaging time of the ADDSB for the best and worst connected networks, and then we compare the convergence rate of the ADDSB with the original synchronous DDSB (OSDDSB) and the improved synchronous DDSB (ISDDSB) in regular networks. This convergence rate comparison is extended to randomly connected non-regular networks using simulations. The simulation results show that the DDSB using the different updating schemes converges to the optimal estimates of the centralized beamformer and that the proposed IGDSA algorithm converges much faster than the original synchronous communication scheme, in particular for non-regular networks. Moreover, comparisons are performed with several existing distributed speech enhancement methods from literature, assuming that the steering vector is given. In the simulated scenario, the proposed method leads to a slight performance improvement at the expense of a higher communication cost. The presented method is not constrained to a certain network topology (e.g., tree connected or fully connected), while this is the case for many of the reference methods.