Analysis of compressed distributed adaptive filters

Abstract

In order to estimate an unknown high-dimensional sparse signal in the network, we present a class of compressed distributed adaptive filtering algorithms based on consensus strategies and compressive sensing (CS) method. This class of algorithms is designed to first use the compressed regressor data to obtain an estimate for the compressed unknown signal, then apply some signal reconstruction algorithms to obtain a high-dimensional estimate for the original unknown signal. Here we consider the compressed consensus normalized least mean squares (NLMS) algorithm, and show that even if the traditional non-compressed distributed algorithm cannot fulfill the estimation or tracking task due to the sparsity of the regressors, the compressed algorithm introduced in this paper can be used to estimate the unknown high-dimensional sparse signal under a compressed information condition, which is much weaker than the cooperative information condition used in the existing literature, without such stringent conditions as independence and stationarity for the system signals.