This paper considers the unavailability of complete channel state information (CSI) in ultra-dense cloud radio access networks (C-RANs). The user-centric cluster is adopted to reduce the computational complexity, while the incomplete CSI is considered to reduce the heavy channel training overhead, where only large-scale inter-cluster CSI is available. Channel estimation for intra-cluster CSI is also considered, where we formulate a joint pilot allocation and user equipment (UE) selection problem to maximize the number of admitted UEs with fixed number of pilots. A novel pilot allocation algorithm is proposed by considering the multi-UE pilot interference. Then, we consider robust beam-vector optimization problem subject to UEs data rate requirements and fronthaul capacity constraints, where the channel estimation error and incomplete inter-cluster CSI are considered. The exact data rate is difficult to obtain in closed form, and instead we conservatively replace it with its lower-bound. The resulting problem is non-convex, combinatorial, and even infeasible. A practical algorithm, based on UE selection, successive convex approximation (SCA) and semi-definite relaxation approach, is proposed to solve this problem with guaranteed convergence. We strictly prove that semidefinite relaxation is tight with probability 1. Finally, extensive simulation results are presented to show the fast convergence of our proposed algorithm and demonstrate its superiority over the existing algorithms.
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