GEVD-Based Low-Rank Approximation for Distributed Adaptive Node-Specific Signal Estimation in Wireless Sensor Networks

Abstract

In this paper, we address the problem of distributed adaptive estimation of node-specific signals for signal enhancement or noise reduction in wireless sensor networks with multisensor nodes. The estimation is performed by a multi-channel Wiener filter (MWF) in which a low-rank approximation based on a generalized eigenvalue decomposition (GEVD) is incorporated. In non-stationary or low-SNR conditions, this GEVDbased MWF has been demonstrated to be more robust than the original MWF. In a centralized realization where a fusion center has access to all the nodes' sensor signal observations, the network-wide sensor signal correlation matrices and the low-rank approximation can be directly estimated and used to compute the network-wide GEVD-based MWF. However, in this paper we aim to avoid centralizing the sensor signal observations, in which case the network-wide sensor signal correlation matrices cannot be estimated. To this end, we start from the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm, and include GEVD-based low-rank approximations in the per-node local computations. Remarkably, the new algorithm is able to significantly compress the signal observations transmitted between the nodes, while still converging to the network-wide GEVD-based MWF as if each node would have access to all sensor signal observations, even though the lowrank approximations are applied locally at each node. We provide a theoretical convergence analysis, which shows that the algorithm converges to the network-wide GEVD-based MWF under conditions that are less strict than in the original DANSE algorithm. The convergence and performance of the algorithm are further investigated via numerical simulations.

Adaptive Quantization for Multichannel Wiener Filter-Based Speech Enhancement in Wireless Acoustic Sensor Networks

“…These issues arise often in high frequencies, where the desired speech component may have very low power. To improve robustness in low SNR and nonstationary conditions, an implementation based on the generalized eigenvalue decomposition (GEVD) can be employed [17,18].…”

Multi-task wireless acoustic sensor network for node-specific speech enhancement and DOA estimation

“…Moreover, in low-SNR conditions,Rss may even lose its positive semi-definiteness, leading to suboptimal or even unstable filters [28]. A GEVD-based rank-1 approximation ofRss can be alternatively incorporated in the MWF solution (3) to increase the estimation performance in such cases (more discussion in [25], [28]). …”

“…• If all nodes were MWF nodes, i.e., if K = K MWF , one could run the GEVD-based distributed adaptive node-specific signal estimation (DANSE) algorithm [25], in which all nodes sequentially perform the following operations (compare to (2), (7)). …”

“…In all of the three aforementioned algorithms (i.e., [25], [33], [20]), the fusion rule is updated in a similar fashion, i.e., the updating node q updates fq by replacing it with the first Mq rows of wq, i.e.,…”

“…Based on the multi-channel Wiener filter (MWF), a distributed algorithm was derived to obtain the centralized linear minimum mean square error estimates of the node-specific desired signals in binaural hearing aids [21] or in wireless networks with a fully-connected topology [22], a tree topology [23] and combinations thereof [24]. To run all these algorithms over networks that operate under non-stationary and low-SNR conditions, in [25] the estimation of each node-specific desired signal is performed by a MWF in which a low-rank approximation based on a generalized eigenvalue decomposition (GEVD) is incorporated. Moreover, the authors in [26] derived a distributed algorithm under which the estimation of the node-specific signals is undertaken through two different but coupled blind minimum variance distortionless response (MVDR) beamformers.…”