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.