Telescopic beamforming for large wireless networks

We consider a wireless network with n users distributed over a square area A = n. Under line-of-sight propagation, this network has Θ(√n) degrees of freedom. At high SNR, these degrees 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 beamforming architecture where signals are relayed by coherent combining over multiple clusters. The key ingredient is an analysis of the beamforming gain achievable between two clusters of nodes under the line-of-sight propagation model. This result reveals a new regime for large two-dimensional wireless networks, where beamforming techniques are needed to achieve capacity.