In this paper, we investigate the theoretical aspects of the nonuniform node distribution strategy in wireless sensor networks, which aims to avoid the energy hole around the sink. We find that in a circular sensor network with a nonuniform node distribution and constant data reporting, the unbalanced energy depletion among the nodes in the whole network is unavoidable. This is because although all the inner, nodes have used up their energy simultaneously, the outmost part of the network may still have energy left. In spite of this fact, a suboptimal energy efficiency among the inner parts of the network is possible if the number of nodes increases with geometric proportion from the outer parts to the inner ones. In our proposed nonuniform node distribution strategy, the ratio between the node densities of the adjacent (i+1)th corona and the ith corona is equal to (2i-1)/q(2i+1), where q is the geometric proportion mentioned above. We also present a routing algorithm with this node distribution strategy. Simulation experiments demonstrate that when the network lifetime has ended, the nodes in the inner parts of the network achieve nearly balanced energy depletion, and only less than 10% of the total energy is wasted.
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