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, and we prove such an algorithm converges locally. Furthermore, 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 the random matrix theory and also propose an iterative algorithm for large systems. Such a large-system iterative algorithm can produce the 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.
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