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  • Research Article
  • Open Access

Performance Analysis of the Consensus-Based Distributed LMS Algorithm

  • 1,
  • 1 and
  • 1Email author
EURASIP Journal on Advances in Signal Processing20092009:981030

  • Received: 15 May 2009
  • Accepted: 8 October 2009
  • Published:


Low-cost estimation of stationary signals and reduced-complexity tracking of nonstationary processes are well motivated tasks than can be accomplished using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is developed in this paper, in which sensors exchange messages with single-hop neighbors to consent on the network-wide estimates adaptively. The novel approach does not require a Hamiltonian cycle or a special bridge subset of sensors, while communications among sensors are allowed to be noisy. A mean-square error (MSE) performance analysis of D-LMS is conducted in the presence of a time-varying parameter vector, which adheres to a first-order autoregressive model. For sensor observations that are related to the parameter vector of interest via a linear Gaussian model and after adopting simplifying independence assumptions, exact closed-form expressions are derived for the global and sensor-level MSE evolution as well as its steady-state (s.s.) values. Mean and MSE-sense stability of D-LMS are also established. Interestingly, extensive numerical tests demonstrate that for small step-sizes the results accurately extend to the pragmatic setting whereby sensors acquire temporally correlated, not necessarily Gaussian data.


  • Sensor Network
  • Autoregressive Model
  • Hamiltonian Cycle
  • Nonstationary Process
  • Sensor Observation

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Authors’ Affiliations

Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street SE, Minneapolis, MN 55455, USA


© Gonzalo Mateos et al. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.