Analysis of incremental LMS adaptive algorithm over wireless sensor networks with delayed-links.

Wireless sensor networks (WSN) are used for many delay-sensitive applications, e.g. military surveillance, emergency response, city management, etc. Therefore, modeling of delay is very important. This paper presents a study of the impact of sensors' sensing delay, process delay and transmission delay in the estimation of the desired unknown parameter in the WSN. Recently proposed wireless sensor networks, in the literature, assume perfect nodes and links, in view of delay. It means that no consideration has been made about the delay in the sensing, processing and, transmission procedures. The proposed method in this paper analyzes the behavior of the distributed incremental estimation algorithm in the presence of delay in wireless sensor networks. Weighted spatio-temporal energy conservation method is used to evaluate the transient and steady state behavior of the wireless sensor networks with delay without putting any restriction on regressor's distribution. The equations that illustrate mean square deviation (MSD), excess mean square error (EMSE) and mean square error (MSE) behavior of individual nodes, are driven. Also, simulations show that overall delay could be calculated to turn off nodes in some iterations without affecting the performance of the distributed estimation algorithm or adding extra latency to the network, which can improve power management strategies by modifying sleep-wake scheduling protocols. Eventually, it is shown that simulation results have a good match with derived theoretical expressions.