Research on optimal number of Cluster Head per round in wireless sensor network

Wireless sensor network (WSN) has attracted many research. It is an obstracle that node has limited supplication of energy which limites developments of WSN. To tackle the strict limitation of energy supplication in large scale WSN, hierarchical structure of WSN is proposed by seperating WSN into many jointed cluster with a Cluster Head (CH) in each clusters. Hierarchical structure is a useful mechanism used to prolong lifetime of WSN. It is a critical problem that how many clusters should be separated. Suitable cluster number will prolong the lifetime of WSN and reduce energy dissipated in Cluster Head (CH) selection per round. Considering the character of communication scope of node in cluster, there exist areas of redundant place between jointed clusters. To give a precise number of CH, we use efficient coverage instead of full coverage of cluster to calculate the optimal number of CH per round, according to characters of one and two order partial derivative functions.