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We investigate the unicast problem for ad-hoc networks in the plane usingMIMO techniques. In particular, we use the multi-node beamforming gain andpresent a self-synchronizing algorithm for the necessary carrier phasesynchronization. First, we consider $n$ nodes in a grid where the transmissionpower per node is restricted to reach the neighboring node. We extend the ideaof multi-hop routing and relay the message by multiple nodes attaining jointbeamforming gain with higher reception range. In each round, the message isrepeated by relay nodes at dedicated positions after a fixed waiting period.Such simple algorithms can send a message from any node to any other node intime $\mathcal{O}(\log \log n - \log \lambda)$ and with asymptotical energy$\mathcal{O}(\sqrt{n})$, the same energy an optimal multi-hop routing strategyneeds using short hops between source and target. Here, $\lambda$ denotes thewavelength of the carrier. For $\lambda \in \Theta(1)$ we prove a tight lowertime bound of $\Omega(\log \log n)$. Then, we consider $n$ randomly distributednodes in a square of area $n$ and we show for a transmission range of$\Theta(\sqrt{\log n})$ and for a wavelength of $\lambda =\Omega(\log^{-1/2}n)$ that the unicast problem can be solved in$\mathcal{O}(\log \log n)$ rounds as well. The corresponding transmissionenergy increases to $\mathcal{O}(\sqrt{n} \log n)$. Finally, we presentsimulation results visualizing the nature of our algorithms.

Ad-Hoc Network Unicast in Time O(log log n) using Beamforming