Performance Analysis of the Consensus-Based Distributed LMS Algorithm
- PDF / 733,834 Bytes
- 19 Pages / 600.05 x 792 pts Page_size
- 106 Downloads / 212 Views
Research Article Performance Analysis of the Consensus-Based Distributed LMS Algorithm Gonzalo Mateos, Ioannis D. Schizas, and Georgios B. Giannakis Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street SE, Minneapolis, MN 55455, USA Correspondence should be addressed to Georgios B. Giannakis, [email protected] Received 15 May 2009; Accepted 8 October 2009 Recommended by Husheng Li 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 DLMS 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. Copyright © 2009 Gonzalo Mateos et al. 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.
1. Introduction The advent of wireless sensor networks (WSNs) has created renewed interest in the field of distributed computing, calling for collaborative solutions that enable low-cost estimation of stationary signals as well as reduced-complexity tracking of nonstationary processes. Different from WSN topologies that include a fusion center (FC), ad hoc ones are devoid of hierarchies and rely on in-network processing to effect agreement among sensors on the estimate of interest. A great body of literature has been amassed in recent years, building-up the field of consensus-based distributed signal processing; the reader is referred to the tutorial in [1] for general results and a vast list of related works. Formidable challenges arise as emergent WSN-based estimation applications demand promptly available, yet accurate local estimates under increasingly restrictive and unpredictable operational constraints. Specifically, often times sensors need to perform estimation in a constantly changing environment without having available a (statistical) model for the underlying
proc
Data Loading...
