Symmetric connectivity in WSNs equipped with multiple directional antennas

This paper concerns wireless sensor networks (WSNs) of which each node is equipped with k ≥ 1 directional antennas having beam-width θ ∈ (0, 2π). The sum ϕ k of the beam-widths of the k antennas of each node is in (0, 2π). Each node is initially assigned a transmission range 1 that yields a connected unit disk graph spanning all nodes. The objective of the Antenna Orientation (AO) problem concerning symmetric connectivity is to compute an orientation of the antennas and to find a minimum transmission power range r = O(1) such that the induced symmetric communication graph (SCG) is connected. In this paper, we study the AO problem assuming that each node has two antennas (k = 2) each of which has beam-width θ = π/3 or π/4. We propose two approximation algorithms that orient the antennas to yield symmetric connected communication graphs (SCCGs) where the transmission power ranges are bounded by 4 and 5 when θ = π/3 and π/4, respectively. These bounds are the first results for this problem. We also study the performance of our algorithms through simulation.