Distributed control of wireless ad-hoc networks connectivity incorporating realistic channel models

In this paper, we propose a distributed method to control the connectivity of wireless ad hoc networks taking into account the impairments resulting from the propagation through realistic channel models incorporating fading, noise and packet collision. We illustrate a mechanism to estimate the algebraic connectivity of the expected graph and we show that the method is robust against random packet drops. Then, we show how the algebraic connectivity of the expected graph Laplacian depends on the transmit power of each node. The interesting result is that there exists an optimal power that maximizes the algebraic connectivity, as a tradeoff between the degree of each node and the number of collisions. Finally, we propose a distributed algorithm to evaluate the optimal transmission power that maximizes the network connectivity in the presence of realistic MAC protocols.