5G/B5G networks are expected to deliver huge traffic and support various use cases with diverse requirements. With the increasing demand for network capacity, a cost-effective and flexible RAN is urgently needed to provide customized services for users. On this basis, advanced flexible RAN architectures with functional splits are introduced. In this paper, we study the slice-centric fine-grained functional split and resource allocation problem in flexible RAN. We first formulate a multi-objective problem to jointly optimize the functional split selection, processing, and transmission resource allocation for slices, aiming at maximizing the functional split gain while satisfying slices' requirements. Since a multi-objective problem may have multiple Pareto optimal solutions and is difficult to solve, we mathematically analyze and transform the problem into an equivalent parametric convex problem. Then, we propose an upper bound algorithm and a dual based resource allocation algorithm to find the solution for the optimization problem. Theoretical analysis and simulation results show that the proposed algorithms can effectively solve the functional split gain maximization problem and obtain a trade-off between processing and transmission resource gain. In addition, the proposed algorithms also outperform other benchmark approaches in terms of resource saving and flexibility.
