Abstract-Wireless sensor networks are often deployed over a large area of interest and therefore the quality of the sensor signals may vary significantly across the different sensors. In this case, it is useful to have a measure for the importance or the so-called 'utility' of each sensor, e.g., for sensor subset selection, resource allocation or topology selection. In this paper, we consider the efficient calculation of sensor utility measures for four different signal estimation or beamforming algorithms in an adaptive context. We use the definition of sensor utility as the increase in cost (e.g., mean-squared error) when the sensor is removed from the estimation procedure. Since each possible sensor removal corresponds to a new estimation problem (involving less sensors), calculating the sensor utilities would require a continuous updating of K different signal estimators (where K is the number of sensors), increasing computational complexity and memory usage by a factor K. However, we derive formulas to efficiently calculate all sensor utilities with hardly any increase in memory usage and computational complexity compared to the signal estimation algorithm already in place.

a b s t r a c tA wireless sensor network (WSN) is considered where each node estimates a number of node-specific desired signals by means of the distributed adaptive node-specific signal estimation (DANSE) algorithm. It is assumed that the topology of the WSN is constructed based on one of the two approaches, either a top-down approach where the WSN is composed of heterogeneous nodes, or a bottom-up approach where the nodes are not necessarily heterogeneous. In the top-down approach, nodes with the largest energy budgets are designated as cluster heads and the remaining nodes form clusters around these nodes. In the bottom-up approach, an ad hoc WSN is partitioned into a set of smaller substructures consisting of non-overlapping cliques that are arranged in a tree topology. These two approaches are shown to be conceptually equivalent, in that the same building blocks constitute both envisaged topologies, and the functionality of the DANSE algorithm is extended to such topologies. In using the DANSE algorithm in such topologies, the WSN converges to the same solution as if all nodes had access to all of the sensor signal observations, and provides faster convergence when compared to DANSE in a single tree topology with only a slight increase in per-node energy usage.

A topology-independent distributed adaptive nodespecific signal estimation (TI-DANSE) algorithm is presented where each node of a wireless sensor network (WSN) is tasked with estimating a node-specific desired signal. To reduce the amount of data exchange, each node applies a linear compression to its sensors signal observations, and only transmits the compressed observations to its neighbors. The TI-DANSE algorithm is shown to converge to the same optimal node-specific signal estimates as if each node were to transmit its raw (uncompressed) sensor signal observations to every other node in the WSN. The TI-DANSE algorithm is first introduced in a fully connected WSN and then shown, in fact, to have the same convergence properties in any topology. When implemented in other topologies, the nodes rely on an in-network summation of the transmitted compressed observations that can be accomplished by various means. We propose a method for this in-network summation via a data-driven signal flow that takes place on a tree, where the topology of the tree may change in each iteration. This makes the algorithm less sensitive to link failures and applicable to WSNs with dynamic topologies. Index Terms-Distributed signal estimation, wireless sensor networks, Wiener filtering, ad-hoc topologies I. INTRODUCTIONW IRELESS sensor networks (WSNs) typically consist of a set of sensor nodes, that are deployed throughout a sensing environment to detect or estimate a signal or parameter

A general binaural noise reduction system is considered that employs the multi-channel Wiener filter with partial noise estimation (MWF⌘) allowing for an explicit trade-off between noise reduction and binaural noise cue preservation. In this paper, it is assumed that along with the general binaural system, a remote microphone signal with a high input signalto-noise ratio (SNR) is available for inclusion in the MWF⌘. The use of this remote microphone signal with a high input SNR allows for a simultaneous increase in both noise reduction performance and preservation of the binaural noise cues. To further increase the performance, a modification to the partial noise estimation (PNE) variable, ⌘, is proposed which relies on exploiting the aforementioned trade-off by either constraining the output SNR or binaural noise cues to the same level before and after the addition of the remote microphone signal. The validity of the theoretical results are supplemented via simulations using a binaural setup with a single speech and noise source.

A wireless sensor network is envisaged that performs signal estimation by means of the distributed adaptive nodespecific 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.