The node degree for wireless ad hoc networks in shadow fading environments

Node degree has been regarded as one of the important and convenient metrics to measure the connectivity of the wireless ad hoc networks. Many studies concerning node degree are based on the assumption of static connectivity graph on the number of nodes, which can not reflect the mobility characteristics in ad hoc networks. In this paper we investigate three fundamental characteristics of a wireless ad hoc network: its node degree distribution, its average node degree and its maximum node degree experienced by all the nodes during theirs movement. We employ a novel mathematical modeling to derive their analytical expressions in presence of radio channel fading. The results of this paper are useful in the study of connectivity and improving algorithm complexity of incentive protocols. Also, these results are of practical value for researchers in this area, e.g., if they set the parameters in a network-level simulation of a mobile ad hoc network or if they design a wireless sensor network.