Optimal transmission range for cluster-based wireless sensor networks with mixed communication modes

Prolonging the network lifetime is one of the most important designing objectives in wireless sensor networks (WSN). We consider a heterogeneous cluster-based WSN, which consists of two types of nodes: powerful cluster-heads and basic sensor nodes. All the nodes are randomly deployed in a specific area. To better balance the energy dissipation, we use a simple mixed communication modes where the sensor nodes can communicate with cluster-heads in either single-hop or multi-hop mode. Given the initial energy of the basic sensor nodes, we derive the optimal communication range and identify the optimal mixed communication mode to maximize the WSN´s lifetime through optimizations. Moreover, we also extend our model from 2-D space to 3-D space