  We consider a heterogeneous cellular network with densely underlaid small
cell access points (SAPs). Wireless backhaul provides the data connection from
the core network to SAPs. To serve as many SAPs and their corresponding users
as possible with guaranteed data rates, admission control of SAPs needs to be
performed in wireless backhaul. Such a problem involves joint design of
transmit beamformers, power control, and selection of SAPs. In order to tackle
such a difficult problem, we apply $\ell_1$-relaxation and propose an iterative
algorithm for the $\ell_1$-relaxed problem. The selection of SAPs is made based
on the outputs of the iterative algorithm. This algorithm is fast and enjoys
low complexity for small-to-medium sized systems. However, its solution depends
on the actual channel state information, and resuming the algorithm for each
new channel realization may be unrealistic for large systems. Therefore, we
make use of random matrix theory and also propose an iterative algorithm for
large systems. Such a large system iterative algorithm produces asymptotically
optimum solution for the $\ell_1$-relaxed problem, which only requires
large-scale channel coefficients irrespective of the actual channel
realization. Near optimum results are achieved by our proposed algorithms in
simulations.
