Research on convergence performance of distributed synchronization algorithm in WSNs based on node degree distribution

The study of the synchronization problems in wireless sensor networks (WSNs) is increasingly significant, researchers found that the topology of the network has an important impact on the convergence performance of the synchronization in WSNs. In this paper, we find that the WSNs can be described by RGGs, and the convergence rate of distributed synchronization algorithm depends on the second largest eigenvalue of the update matrix based on the RGG topology. Then we study on one of the basic topology properties of a distributed network, node degree distribution. In a certain RGG network model, the relation between node degree distribution and node number, communication radius is explored. What´ s more, this paper gives the mathematical expression of the degree distribution with theoretical derivation. Then the simulations of node degree distribution are taken by changing the communication radius and node density to show that the theoretical derivation and the simulation result correspond. Further we verify the relation between average degree of the network and the second largest eigenvalue.