Distributed Adaptive Estimation of Node-Specific Signals in Wireless Sensor Networks With a Tree Topology

We present a distributed adaptive node-specific signal estimation (DANSE) algorithm that operates in a wireless sensor network with a tree topology. The algorithm extends the DANSE algorithm for fully connected sensor networks, as described in previous work. It is argued why a tree topology is the natural choice if the network is not fully connected. If the node-specific desired signals share a common latent signal subspace, it is shown that the distributed algorithm converges to the same linear MMSE solutions as obtained with the centralized version of the algorithm. The computational load is then shared between the different nodes in the network, and nodes exchange only linear combinations of their sensor signal observations and data received from their neighbors. Despite the low connectivity of the network and the multi-hop signal paths, the algorithm is fully scalable in terms of communication bandwidth and computational power. Two different cases are considered concerning the communication protocol between the nodes: point-to-point transmission and local broadcasting. The former assumes that there is a reserved communication link between node-pairs, whereas with the latter, nodes communicate the same data to all of their neighbors simultaneously. The convergence properties of the algorithm are demonstrated by means of numerical examples.