Wake-up Control with Kernel Density Estimation for Top-k Query in Wireless Sensor Networks

This paper aims to improve the efficiency of wake-up control for top-
$k$
query in wireless sensor networks (WSNs) by introducing a function to estimate the data distribution of sensors. In order to minimize the wasteful wake-up of nodes outside the top-
$k$
set, the sink gradually enlarges the search region of data from the highest value by employing countdown content-based wake-up (CDCoWu). In this case, the step size to enlarge the search region plays an important role: a larger step causes many nodes to simultaneously wake up, which leads to severe congestion, while a smaller step leads to the failed wake-up trial with no replies. In this paper, in order for the sink to appropriately select the step size, we introduce kernel density estimation into wake-up control, by which the sink first estimates the probability density function (PDF) of data owned by sensor nodes. The efficiency of CDCoWu can be improved with more accurate estimation on PDF, which, however, requires larger estimation cost. In this paper, we analyze the trade off between the accuracy of estimation and efficiency of CDCoWu, and investigate whether the overall efficiency in terms of energy consumption and delay can be improved by the proposed wake-up control with density estimation. Our numerical results show that the proposed wake-up control achieves better energy effi-ciency and data collection delay than the conventional CDCoWu employing a fixed step size.