MAXVAR-Based Distributed Correlation Estimation in a Wireless Sensor Network

The performance of most array signal processing tasks relies on the presence of correlation between sensor signals. In a wireless sensor network, where sensor nodes are spread out over a relatively large area, it is useful to identify nodes observing similar sensor signals and hence common phenomenons, for example to partition the network according to the observed latent signals and corresponding correlation structure. This can be achieved via the so-called MAXVAR formulation of generalized canonical correlation analysis, which finds a low-dimensional subspace that highlights correlated signal components between multiple nodes' observed signal subspaces. The classical procedure for computing the solutions of MAXVAR consists in performing a generalized eigenvalue decomposition after collecting all the sensors' signals at a fusion center. However, this typically incurs high communication and computational costs. In this paper, we describe a low communication and computational cost distributed algorithm that computes the solutions of MAXVAR without aggregating the nodes' observations at a central location. We show how a subset of those solutions can be used locally by each node to estimate the global correlation structure across all nodes in the network, thereby allowing any node to evaluate the presence of correlated signals at any other node, even if no direct link is shared. We prove the convergence of the algorithm and validate our method for estimating the correlation structure via simulations.