Recursive Filtering for Complex Networks With Amplify-and-Forward Relays Over Double Time-Correlated Fading Channels

Abstract

In this article, the recursive filtering problem is investigated for a class of complex networks (CNs) incorporating amplify-and-forward (AF) relays and subject to double time-correlated fading channels (TCFCs). To extend the transmission distance, AF relays are deployed between sensors and filters to facilitate the signal transmission process. Both the sensor-to-relay and relay-to-filter channels are modeled as TCFCs, with their fading coefficients governed by distinct dynamical processes. A suitably augmented model is constructed to capture the combined effects of the network state and fading coefficients. Based on this model, a set of recursive filters is designed to ensure an upper bound on the filtering error covariance (FEC), and the corresponding filter gains that minimize this bound are parameterized by solving a set of recursive equations. Furthermore, the filtering performance is rigorously analyzed, and a sufficient condition is provided to guarantee the exponential boundedness of the filtering error in the mean-square sense. Finally, an example is presented to demonstrate the effectiveness of the proposed filtering strategy.