Transmit power distribution of wireless ad-hoc networks with topology control

Topology control and routing protocols are used by designers of wireless packet data networks to lower the node degree, simplify routing and lower the nodes' energy consumption, while preserving strong connectivity. We assume a popular fading channel model and study the impact of several topology control schemes on the transmit power of nodes randomly distributed over a large area according to a Poisson point process, where each node controls the pattern of its one-hop neighbors by independently adjusting its transmit power. We provide the distribution of the transmit power of individual nodes under several different topology control algorithms, allowing designers to estimate the life time of battery energized devices, and the implications. of choosing the nodes' peak transmit power. We also allow easy comparisons between several different topology control algorithms with respect to the nodes' power consumption.