  The availability of very wide spectrum in millimeter wave bands combined with
large antenna arrays and ultra dense networks raises two basic questions: What
is the true value of overly abundant degrees of freedom and how can networks be
designed to fully exploit them? This paper determines the capacity scaling of
large cellular networks as a function of bandwidth, area, number of antennas
and base station density. It is found that the network capacity has a
fundamental bandwidth scaling limit, beyond which the network becomes
power-limited. An infrastructure multi-hop protocol achieves the optimal
network capacity scaling for all network parameters. In contrast, current
protocols that use only single-hop direct transmissions can not achieve the
capacity scaling in wideband regimes except in the special case when the
density of base stations is taken to impractical extremes. This finding
suggests that multi-hop communication will be important to fully realize the
potential of next-generation cellular networks. Dedicated relays, if
sufficiently dense, can also perform this task, relieving user nodes from the
battery drain of cooperation. On the other hand, more sophisticated strategies
such as hierarchical cooperation, that are essential for achieving capacity
scaling in ad hoc networks, are unnecessary in the cellular context.
