Information theoretic upper bound on the capacity of wireless backhaul networks

We derive an information theoretic upper bound on the capacity of a wireless backhaul network modeled as a classical random extended network, except that we assume the number of antennas at each base station (BS) also scales up as an arbitrary function of network size. The antenna scaling is justified because of the increasing maturity of higher transmission frequencies which enables us to pack large number of antennas in small form factors. The main technical arguments are based on the generalization of geometric exponential stripping technique of [1] to channel matrices with complex-valued channel gains. An important consequence of our result is a lower bound on the number of antennas per BS required for network scalability.