Distributed signal subspace estimation based on local generalized eigenvector matrix inversion

Many array-processing algorithms or applications require the estimation of a target signal subspace, e.g., for source localization or for signal enhancement. In wireless sensor networks, the straightforward estimation of a network-wide signal subspace would require a centralization of all the sensor signals to compute network-wide covariance matrices. In this paper, we present a distributed algorithm for network-wide signal subspace estimation in which such data centralization is avoided. The algorithm relies on a generalized eigenvalue decomposition (GEVD), which allows to estimate a target signal subspace in spatially correlated noise. We show that the network-wide signal subspace can be found from the inversion of the matrices containing the generalized eigenvectors of a pair of reduced-dimension sensor signal covariance matrices at each node. The resulting distributed algorithm reduces the per-node communication and computational cost, while converging to the centralized solution. Numerical simulations reveal a faster convergence speed compared to a previously proposed algorithm.