Connectivity Trade-offs in 3D Wireless Sensor Networks Using Directional Antennae

We consider a 3D antenna orientation problem for maintaining connectivity of a wireless network in 3D space using only directional antennae. Sensors are located at points in 3D space and are equipped with directional antennae. The strong connectivity antenna orientation problem is concerned with deciding whether or not for given solid angle Ω and range r it is possible to orient the antennae so as to ensure that the sensor network resulting from the induced transmissions is strongly connected. In this paper we 1) present an algorithm ensuring optimal antenna range for the case when Ω ≥ 18π/5, 2) show that determining whether or not there exists a strong orientation of directional sensors of solid angle Ω <; π -ε having optimal range is NP-complete, for any ε >; 0, and 3) provide an algorithm for approximating the antennae range so as to ensure strong connectivity of the resulting graph, provided the solid angle of the antennae is 2π ≤ Ω <; 18π/5· In addition, we study the effect of replacing omnidirectional antennae with directional antennae on the hop stretch factor of the resulting network of directional antennae and present some simulation results on the variation of hop stretch factor with different network sizes and solid angles of directional antennae. This is the first paper concerning the strong connectivity antennae orientation problem in 3D space.