  It is known that data rates in standard cellular networks are limited due to
inter-cell interference. An effective solution of 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 idea where 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.
