Downlink Spectrum Allocation for In-Band and Out-Band Wireless Backhauling of Full-Duplex Small Cells

In-band full-duplex (IBFD) backhauling is a potential technique for wireless backhauling of small cells that allows the use of same spectrum for the backhaul and access links of the small cell base stations (SBSs) concurrently, however, at the expense of backhaul interference and self-interference (SI). This paper investigates the problem of optimal access/backhaul spectrum allocation considering IBFD backhauling, out-of-band full-duplex (OBFD) backhauling (in which the access and backhaul transmissions take place on different spectrum), and the SBSs with the provisioning for hybrid IBFD/OBFD backhauling. We first formulate a problem to maximize the minimum achievable rate (i.e., minimum of the rates in the backhaul link and the access link) at the SBSs in a hybrid IBFD/OBFD setting. The solution of the centralized spectrum allocation problem, which serves as a benchmark for any sub-optimal solution, is provided by transforming the original problem into an epigraph form. As a special case of the formulated problem, we derive closed-form optimal solutions for the access/backhaul spectrum allocation of OBFD backhauling as well as IBFD backhauling. We then propose and comparatively analyze the performance of two distributed backhaul spectrum allocation schemes, namely, maximum received signal power (max-RSP) and minimum received signal power (min-RSP) schemes. For these schemes, we theoretically derive the number of allocated backhaul channels, minimum rate coverage probability, and average achievable rate of each SBS given its distance from the centralized wireless backhaul hub (WBH) for both IBFD and OBFD backhauling. Numerical results reveal that the optimal spectrum allocation rules can significantly vary for IBFD and OBFD backhauling. Optimal OBFD backhauling favors more backhaul spectrum for SBSs located far-away from the WBH. With IBFD backhauling, spectrum allocation for SBSs strongly depends on SI. With the reduction in SI, the optimal backhaul spectrum increases/decreases for nearby/farther SBSs. Simulation results comparing the optimal solution with the distributed spectrum allocation solutions based on max-RSP and min-RSP schemes are also presented.