Transmit Power Distribution of Wireless Ad Hoc Networks with Topology Control

We study the impact of several topology control schemes on the transmit power of nodes in a wireless packet data network, where the nodes are randomly distributed over a large area according to a Poisson point process, and the propagation channels are subject to fading. Topology control has been proposed as a technique to improve the performance of multi-hop networks, e.g. ad hoc networks and sensor networks. It amounts to adjusting the transmit power of each node independently so as to optimize certain performance measures, such as throughput, connectivity, lifespan of networks of battery-powered nodes, simplifying the routing algorithms, etc. Many such algorithms use the pattern of immediate neighbors observed by each node as the basis for power adjustment. Most published research on topology control is based on a simplistic radio propagation model, where the area covered by a transmitter is a perfect disk centered at the transmitter. Similarly, the self interference of the network, if considered, is caused only by transmitters located inside such a disk centered at the receiver. With this propagation model, the statistical properties of the communication range are easily derived from the desired number of one-hop neighbors (assuming that the latter is known, and is the only criterion to be satisfied). It is not always trivial to derive the resulting statistical properties of the node transmit power when a certain pattern of neighbors is desired in a fading environment. However, this is the information required when the lifespan of a network of battery-powered devices is of interest. In this paper we calculate the statistical properties of the nodes' transmit power in networks produced by several topology control algorithms, when the propagation channels are subject to fading.