Linear Capacity Scaling in Wireless Networks: Beyond Physical Limits?

We investigate the role of cooperation in wireless networks subject to a spatial degrees of freedom limitation. To address the worst case scenario, we consider a free-space line-of-sight type environment with no scattering and no fading. We identify three qualitatively different operating regimes that are determined by how the area of the network $A$, normalized with respect to the wavelength $\lambda$, compares to the number of users $n$. In networks with $\sqrt{A}/\lambda\leq \sqrt{n}$, the limitation in spatial degrees of freedom does not allow to achieve a capacity scaling better than $\sqrt{n}$ and this performance can be readily achieved by multi-hopping. This result has been recently shown in \cite{FMM09}. However, for networks with $\sqrt{A}/\lambda> \sqrt{n}$, the number of available degrees of freedom is $\min(n, \sqrt{A}/\lambda)$, larger that what can be achieved by multi-hopping. We show that the optimal capacity scaling in this regime is achieved by hierarchical cooperation. In particular, in networks with $\sqrt{A}/\lambda> n$, hierarchical cooperation can achieve linear scaling.