  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.
