  Uplink and downlink cloud radio access networks are modeled as two-hop K-user
L-relay networks, whereby small base-stations act as relays for end-to-end
communications and are connected to a central processor via orthogonal
fronthaul links of finite capacities. Simplified versions of network
compress-forward (or noisy network coding) and distributed decode-forward are
presented to establish inner bounds on the capacity region for uplink and
downlink communications, that match the respective cutset bounds to within a
finite gap independent of the channel gains and signal to noise ratios. These
approximate capacity regions are then compared with the capacity regions for
networks with no capacity limit on the fronthaul. Although it takes infinite
fronthaul link capacities to achieve these "fronthaul-unlimited" capacity
regions exactly, these capacity regions can be approached approximately with
finite-capacity fronthaul. The total fronthaul link capacities required to
approach the fronthaul-unlimited sum-rates (for uplink and downlink) are
characterized. Based on these results, the capacity scaling law in the large
network size limit is established under certain uplink and downlink network
models, both theoretically and via simulations.
