IEEEIt is known that data rates in standard cellular networks are limited due to inter-cell interference. An effective solution to this problem is to use the multi-cell cooperation idea. In Cloud Radio Access Network (C-RAN), which is a candidate solution in 5G and future communication networks, cooperation is applied by means of central processors (CPs) connected to simple remote radio heads with finite capacity fronthaul links. In this study, we consider a downlink C-RAN with a wireless fronthaul and aim to minimize total power spent by jointly designing beamformers for fronthaul and access links. We consider the case where perfect channel state information is not available in the CP. We first derive a novel theoretical performance bound for the problem defined. Then we propose four algorithms with different complexities to show the tightness of the bound. The first two algorithms apply successive convex optimizations with semi-definite relaxation ideas where the other two are adapted from well-known beamforming design methods. The detailed simulations under realistic channel conditions show that as the complexity of the algorithm increases, the corresponding performance becomes closer to the bound.