Incorporating Observation Quality Information into the Incremental LMS Adaptive Networks

Abstract

In this paper we investigate the effect of observation quality information (OQI) on the performance of a special class of adaptive networks known as distributed incremental least-mean square (DILMS) algorithm. To this aim we consider two different cases: (1) a homogeneous environment where all the nodes have the same observation noise variance (ONV) and (2) an inhomogeneous environment, where different nodes have different ONVs. In the first case we show that, for the same steady-state error, the DILMS algorithm has faster convergence rate in comparison with a non-cooperative scheme. In the second case, we first show that regardless of what ONVs are, the steady-state curves of mean-square deviation, excess mean-square error and mean square error (MSE) in each node are monotonically increasing functions of step-size parameter. Then, to use the OQI, we reformulate the parameter estimation as a constrained optimization problem with MSE criterion as the cost function and ONVs as the constraints. Using the Robbins-Monro method to solve the resultant problem, a new algorithm (which we call noise-constrained incremental LMS algorithm) is obtained which has faster convergence rate than the existing incremental LMS algorithm. Simulation results are also provided to clarify the performance of proposed algorithm.