Energy-harvesting recursive filtering for delayed systems with amplify-and-forward relays: Cooperative communication manner

The recursive filtering problem is explored for a class of nonlinear time-delayed systems with amplify-and-forward (AF) relay and energy-harvesting (EH) technology. In order to enhance the signal quality of the remote transmission in wireless communication, the relay under the AF protocol is introduced that posing the merits of low complexity, less energy consumption and fast transmission rate. Meanwhile, to further alleviate the fading and improve the robustness of the signals, the cooperative communication manner is employed, which is different from the commonly encountered two-hop one. In the cooperative communication, the maximal ratio combining (MRC) method is utilized to make sure that the signal-to-noise ratio of the combined output can reach theoretical maximum. In addition, in order to achieve sustainable power supply in harsh environments, the EH sensors and relays are deployed, which can collect energy from external environments with certain probabilities. The aim of this paper is to develop a proper filter so as to reduce the impacts caused by the channel fading and insufficient energy. Furthermore, a minimized upper bound of the filtering error covariance is gained through appropriately designing the filter parameters. Then, the exponential boundedness is analyzed with regard to filtering error. Finally, a numerical example is exhibited to test the validity of the proposed filtering scheme.