||Asymptotic Normality of and Normal Approximation to Interference Power in Wireless Passive Sensor Networks
||(Heewon Seo) ; (Jin Kyung Park) ; (Cheon Won Choi)
|| Wireless passive sensor network; Interference power; Asymptotic normality; Normal approximation; Berry-Esseen bound; Test for normality
||A wireless passive sensor network is distinguished from ordinary wireless sensor networks by radio frequency (RF) sources that radiate RF waves and supply energy to sensor nodes. Against theoretical expectations, such a network suffers from a scarcity of energy, which compels to employ a contending-type medium access control (MAC) scheme. Consequently, a collision may take place among the packets sent by some sensor nodes. Also, the interference power brought by the colliding packets may hinder a sink node from identifying any packet.
Apparently, the interference power highly influences the performance of a wireless passive sensor network. Thus, it is essential to appropriately describe the interference power to evaluate the performance. In this paper, we characterize the interference power, occurring in a wireless passive sensor network, as a sum of random variables governed by log-normal distributions, which are mutually independent but are not necessarily identical. Then, we prove the asymptotic normality of the interference power and, in pursuit of tractability rather than accuracy, we propose a normal approximation to the interference power brought by a finite number of sensor nodes. To investigate the accuracy of the proposed normal approximation, we take the Kolmogorov-Smirnov distance and present an exact expression of the Berry-Esseen bound associated with the interference power.
Also, to explore the acceptability of the normal approximation, we employ three well-known statistical tests for normality. Comparative studies of Berry-Esseen bounds reveal that the normal approximation to the interference power is moderately accurate. Furthermore, hypothesis testing for normality shows that the normal approximation is acceptable even in the case that the interference power is incurred by a relatively small number of packets (or, equivalently, sensor nodes) in a wireless passive sensor network.