A Mathematical Framework of Optimal Number of Clusters in 3D Noise-Prone WSN Environment

In this paper an analytical model of the optimal number of clusters and the corresponding optimal probability are derived for different types of 3D WSN settings utilizing singlehop homogeneous LEACH protocol. Three types of 3D network configurations are analyzed. These include cube, cylinder and sphere network configurations. Energy analysis of these network configurations is done in noise-prone communication environment. The noise is modelled utilizing the probability of reception p
_r
. A small value of p
_r
indicates more packets are dropped, which is a sign of large noise. It was shown through analysis and simulation that optimal number of clusters, optimal probability and energy consumption are affected by the geometry of the 3D WSN, noise, and transmission amplification model used.