Power-efficient topology control for static wireless networks with switched beam directional antennas

Topology control problems are associated with assignment of power levels to nodes of a wireless network so that the resulting graph topology satisfies certain properties. In this paper we consider the problem of power-efficient topology control with switched beam directional antennas taking into account their non-uniform radiation pattern within the beamwidth. Previous work in the area have all assumed a uniform gain model with these antennas which renders antenna orientation insignificant as a parameter in topology control algorithms. We present algorithms that take into account a model of non-uniform gain with the objectives of minimizing the total power and maximum power to keep the network connected. We consider two cases: one where the antenna orientation is assumed given and another where the antenna orientation needs to be derived as well. For the first case, we present optimal and approximation algorithms for constructing power-efficient topologies. For the second case, we prove the problem to be NP-complete and present heuristic solutions along with approximation bounds. Through comparison of the two cases by simulation, significant reductions are shown in the maximum as well as total power required to keep the network connected for the second case, thus demonstrating the benefits of using antenna orientation as parameter in topology construction.