Hierarchical beamforming for large one-dimensional wireless networks

We consider a wireless network with a large number of source-destination pairs distributed over a line. Under line-of-sight propagation, this network has only one degree of freedom for communication. At high SNR, this one degree of freedom can be readily achieved by multi-hop relaying between nodes. At low SNR, however, the performance is determined by the power transfer in the network. We show that none of the existing architectures can achieve optimal capacity scaling. We develop a digital hierarchical beamforming architecture and show that it is scaling optimal. This result reveals a new regime for large wireless networks, where beamforming techniques are needed to achieve capacity.