Consensus-Based Distributed Least-Mean Square Algorithm Using Wireless Ad Hoc Networks

We deal with online estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). A fully distributed least-mean square (D-LMS) type of algorithm is presented, which offers simplicity and flexibility whilst solely requiring single-hop communications among sensors. The algorithm entails the minimization of a pertinent cost function by resorting to: (i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and, (ii) stochastic approximation ideas to cope with the unavailability of statistical information. First-order convergence analysis is provided whereas mean-square sense (mss) convergence is corroborated via simulations, even in the presence of additive reception noise.