Distributed GEVD-based signal subspace estimation in a fully-connected wireless sensor network

In this paper, we present a distributed algorithm for network-wide signal subspace estimation in a fully-connected wireless sensor network with multi-sensor nodes. We consider scenarios where the noise field is spatially correlated between the nodes. Therefore, rather than an eigenvalue decomposition (EVD-) based approach, we apply a generalized EVD (GEVD-) based approach which allows to directly incorporate the (estimated) noise covariance. Furthermore, the GEVD is also immune to unknown per-channel scalings. We first use a distributed algorithm to estimate the principal generalized eigenvectors (GEVCs) of a pair of network-wide sensor signal covariance matrices, without explicitly constructing these matrices, as this would inherently require data centralization. We then apply a transformation at each node to extract the actual signal subspace estimate from the principal GEVCs. The resulting distributed algorithm can reduce the per-node communication and computational cost. We demonstrate the effectiveness of the algorithm by means of numerical simulations.