The ultra-dense cloud radio access network (UD-CRAN), in which remote radio heads (RRHs) are densely deployed in the network, is considered. To reduce the channel estimation overhead, we focus on the design of robust transmit beamforming for user-centric frequency division duplex (FDD) UD-CRANs, where only limited channel state information (CSI) is available. Specifically, we conceive a complete procedure for acquiring the CSI that includes two key steps: channel estimation and channel quantization. The phase ambiguity (PA) is also quantized for coherent cooperative transmission. Based on the imperfect CSI, we aim for optimizing the beamforming vectors in order to minimize the total transmit power subject to users' rate requirements and fronthaul capacity constraints. We derive the closed-form expression of the achievable data rate by exploiting the statistical properties of multiple uncertain terms. Then, we propose a low-complexity iterative algorithm for solving this problem based on the successive convex approximation technique. In each iteration, the Lagrange dual decomposition method is employed for obtaining the optimal beamforming vector. Furthermore, a pair of low-complexity user selection algorithms are provided to guarantee the feasibility of the problem. Simulation results confirm the accuracy of our robust algorithm in terms of meeting the rate requirements. Finally, our simulation results verify that using a single bit for quantizing the PA is capable of achieving good performance.