Distributed adaptive node-specific signal estimation in a wireless sensor network with noisy links.

• Fusion rules for distributed adaptive node-specific signal estimation (DANSE) are not optimal when communication links are noisy in a wireless sensor network. • Fusion rules which take noisy links into account are developed, resulting in new algorithm named N-DANSE. • The strategy to prove convergence of N-DANSE is different from the strategy used for DANSE without noisy links, and includes the latter as a special case. • N-DANSE performs better than DANSE in scenarios with noisy links. • N-DANSE is consistently closer to the optimal performance than DANSE. We consider a distributed signal estimation problem in a wireless sensor network where each node aims to estimate a node-specific desired signal using all sensor signals available in the network. In this setting, the distributed adaptive node-specific signal estimation (DANSE) algorithm is able to learn optimal fusion rules with which the nodes fuse their sensor signals, as the fused signals are then transmitted between the nodes. Under the assumption of transmission without errors, DANSE achieves the performance of centralized estimation. However, noisy communication links introduce errors in these transmitted signals, e.g., due to quantization or communication errors. In this paper we show fusion rules which take additive noise in the transmitted signals into account at almost no increase in computational complexity, resulting in a new algorithm denoted as 'noisy-DANSE' (N-DANSE). As the convergence proof for DANSE cannot be straightforwardly generalized to the case with noisy links, we use a different strategy to prove convergence of N-DANSE, which also proves convergence of DANSE without noisy links as a special case. We validate the convergence of N-DANSE and compare its performance with the original DANSE through numerical simulations, which demonstrate the superiority of N-DANSE over the original DANSE in noisy links scenarios. [ABSTRACT FROM AUTHOR]