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 < 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
by Franceschetti et al. 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.Comment: 10 pages, 5 figures, in Proc. of IEEE Information Theory and
Applications Workshop, Feb. 201