Millimeter wave (mmWave) communication not only provides ultra-high speed radio access but is also ideally suited for efficient and flexible wireless backhauling. Specifically for dense deployments, a mmWave macro base station (MBS) that serves a large number of mmWave micro base stations (µBSs) is much more cost effective than legacy cellular architectures which connect µBSs to the core network through fibers. In addition, µBSs can cooperate with each other by acting as relay nodes. The directional nature of mmWave communication allows for spatial reuse, even in the presence of interference, which can be exploited to optimize mmWave wireless backhaul performance. The optimization opportunistically prioritizes the use of good connections at the MBS and further leverages compact and concurrent transmissions between µ BS. Relays and directional antennas speed up communication, but increase the complexity of the scheduling problem. In this work, we study the mmWave backhaul scheduling problem and derive an MILP formulation for it as well as upper and lower bounds. We prove that the problem is NP-hard and can be approximated, but only if interference is negligible. By means of numerical simulations, we compare theoretical results with heuristics in small system sizes. Results validate the analysis and demonstrate the high performance of our heuristics in realistic cellular settings.

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