Cooperative beamforming in ad-hoc networks with sublinear transmission power

The efficiency of routing algorithms in ad-hoc networks is measured by delay, throughput, and energy. Here, we focus on routing algorithms optimizing energy consumption while providing small routing delay. For this, we exploit the sender beamforming gain in the line-of-sight path-loss model, where multiple nodes (each with a single antenna) cooperate for beamforming and the routing algorithms provide distributed self-synchronization. While direct point-to-point communication over distance d in the line-of-sight model needs transmission power Θ(d²), and multi-hop power needs power Θ(d) and delay Θ(d), we can reduce the power to Θ(√d) or Θ(log d) depending on the geometry. We present three algorithms with different trade-offs. The first algorithm is designed for grid nodes in the plane and has a point-to-point delay of Θ(log d) and overall power consumption of Θ(√d). The second algorithm for the same geometry decreases the delay to Θ(1 over ε log log d) with power Θ((√d)^1+ε) for ε > 0. The third algorithm requires a three-dimensional grid network and achieves a delay of Θ(log d) and reduces the energy needed by all nodes to Θ(log d).