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 closedform 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. Fronthaul Links BBU Pool BBU BBU BBU UE 1 RRH 1 RRH 2 UE 2 UE 3 UE 4 UE 5 UE 6 RRH 3 RRH 4 RRH 5 RRH 6 RRH 7 RRH 8 RRH 9 BBU Fig. 1. Illustration of a UD-CRAN with nine RRHs and six UEs, i.e., I = 9, K = 6. To reduce the complexity, each UE is served by the RRHs within the dashed circle centered around the UE. achieving a high system throughput [1]. In UDNs, the average distance between small BSs and users can be dramatically reduced, which can translate into improved link reliability. However, since all small BSs reuse the same frequency, the users are also exposed to severe inter-cell interference, which is a severe performance limiting factor. Hence, the interference should be judiciously managed in order to reap the potential benefits of UDNs. As a result, the cloud radio access network (CRAN) concept has been recently proposed as a promising network architecture [2]. In CRAN, all the signal processing tasks are performed at the BBU pool, and all the conventional small BSs are replaced by low-cost low-power RRHs, which are only responsible for simple transmission/reception functions. The RRHs are connected to the BBU pool through the fronthaul links to support the centralized signal processing. Hence, the interference in the network can be effectively mitigated by employing the coordinated multipoint (CoMP) technique.Furthermore, due to their low-complexity functionalities, the mobile operator can densely deploy the RRHs at a low capital cost. Hence, the CRAN architecture is an ideal platform for supporting UDNs. Th...