Antenna Orientation and Range Assignment Algorithms in Directional WSNs

Abstract

Consider a set S of nodes in the plane such that the unit-disk graph G(S) spanning all nodes is connected. Each node in S is equipped with a directional antenna with beam-width θ = π/2. The objective of the directional antenna orientation (AO) problem concerning symmetric connectivity is to determine an orientation of the antennas with a minimum transmission power range r = O(1) such that the induced symmetric communication graph is connected. Another related problem is the AO and power assignment (AOPA) problem whose objective is to assign each node u ∈ S an orientation of its antenna as well as a range r(u) such that the induced symmetric communication graph is connected and the total power assigned Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u∈S</sub> r(u) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sup> is minimized, where β ≥ 1 is the distance-power gradient (typically 2 ≤ β ≤ 5). In this paper, we study both problems by first proving that they are NP-hard. We then propose two algorithms for the AO problem that orient the antennas to yield a symmetric connected communication graph where the transmission power ranges are bounded by 9 and 7, respectively, which are currently the best results for this problem. We also propose constant-factor approximation algorithms for the AOPA problem where our constants are smaller than Aschner et al's. Finally, we study the performance of our algorithms through simulations.