Low-rank approximation-based distributed node-specific signal estimation in a fully-connected wireless sensor network

In this paper, we consider the problem of distributed estimation of node-specific signals in a fully-connected wireless sensor network with multi-sensor nodes. The estimation relies on a data-driven design of a spatial filter, referred to as the generalized eigenvalue decomposition (GEVD)-based multi-channel Wiener filter (MWF). In non-stationary or low-SNR conditions, this GEVD-based MWF has been demonstrated to be more robust than the original MWF due to an inherent GEVD-based low-rank approximation of the sensor signal correlation matrix. In a centralized realization where a fusion center has access to all the nodes´ sensor signal observations, the network-wide sensor signal correlation matrix and its low-rank approximation can be directly estimated from the sensor signals. However, in this paper we aim to avoid centralizing the sensor signal observations, in which case this network-wide correlation matrix cannot be estimated. We introduce a distributed algorithm which is able to significantly compress the broadcast signals while still converging to the centralized GEVD-based MWF as if each node would have access to all sensor signal observations.