Greedy distributed node selection for node-specific signal estimation in wireless sensor networks

• We extend previous techniques to compute single sensor utility to more generalized multi-sensor utilities.
• We define utility bounds in a distributed context which are related to either the increase or decrease in MMSE.
• Nodes use the derived utility bounds to add or remove themselves from the wireless sensor network.

A wireless sensor network is envisaged that performs signal estimation by means of the distributed adaptive node-specific signal estimation (DANSE) algorithm. This wireless sensor network has constraints such that only a subset of the nodes are used for the estimation of a signal. While an optimal node selection strategy is NP-hard due to its combinatorial nature, we propose a greedy procedure that can add or remove nodes in an iterative fashion until the constraints are satisfied based on their utility. With the proposed definition of utility, a centralized algorithm can efficiently compute each nodes's utility at hardly any additional computational cost. Unfortunately, in a distributed scenario this approach becomes intractable. However, by using the convergence and optimality properties of the DANSE algorithm, it is shown that for node removal, each node can efficiently compute a utility upper bound such that the MMSE increase after removal will never exceed this value. In the case of node addition, each node can determine a utility lower bound such that the MMSE decrease will always exceed this value once added. The greedy node selection procedure can then use these upper and lower bounds to facilitate distributed node selection.