Distributed Combined Acoustic Echo Cancellation and Noise Reduction in Wireless Acoustic Sensor and Actuator Networks

The paper presents distributed algorithms for combined acoustic echo cancellation (AEC) and noise reduction (NR) in a wireless acoustic sensor and actuator network (WASAN) where each node may have multiple microphones and multiple loudspeakers, and where the desired signal is a speech signal. A centralized integrated AEC and NR algorithm, i.e., multichannel Wiener filter (MWF), is used as starting point where echo signals are viewed as background noise signals and loudspeaker signals are used as additional input signals to the algorithm. By including prior knowledge (PK), namely that the loudspeaker signals do not contain any desired signal component, an alternative centralized cascade algorithm (PK-MWF) is obtained with an AEC stage first followed by an MWF-based NR stage which has a lower computational complexity. Distributed algorithms can then be obtained from the MWF and PK-MWF algorithm, i.e., the generalized eigenvalue decomposition (GEVD)-based distributed adaptive node-specific signal estimation (DANSE) and PK-GEVD-DANSE algorithm, respectively. In the former, each node performs a reduced dimensional integrated AEC and NR algorithm and broadcasts only 1 fused signal (instead of all its signals) to the other nodes. In the PK-GEVD-DANSE algorithm, each node performs a reduced dimensional cascade AEC and NR algorithm and broadcasts only 2 fused signals (instead of all its signals) to the other nodes. The distributed algorithms achieve the same performance, upon convergence, as the corresponding centralized integrated (MWF) and centralized cascade (PK-MWF) algorithm. It is observed, however, that the communication cost in the PK-GEVD-DANSE algorithm can also be reduced, where each node then broadcasts only 1 fused signal (instead of 2 signals) to the other nodes. The resulting algorithm, referred to as the pruned PK-GEVD-DANSE (pPK-GEVD-DANSE) algorithm, then effectively combines the lowest possible communication cost (as low as in the GEVD-DANSE algorithm) with a lowest possible computational complexity in each node (further reduced from the PK-GEVD-DANSE computational complexity), within the class of algorithms considered in this paper.