  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, which is a
candidate solution in 5G and beyond, 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 scenario and aim to
minimize total power spent by designing beamformers. We consider the case where
perfect channel state information is not available in the CP. The original
problem includes discontinuous terms with many constraints. We propose a novel
method which transforms the problem into a smooth constraint-free form and a
solution is found by the gradient descent approach. As a comparison, we
consider the optimal method solving an extensive number of convex sub-problems,
a known heuristic search algorithm and some sparse solution techniques.
Heuristic search methods find a solution by solving a subset of all possible
convex sub-problems. Sparse techniques apply some norm approximation
($\ell_0/\ell_1, \ell_0/\ell_2$) or convex approximation to make the objective
function more tractable. We also derive a theoretical performance bound in
order to observe how far the proposed method performs off the optimal method
when running the optimal method is prohibitive due to computational complexity.
Detailed simulations show that the performance of the proposed method is close
to the optimal one, and it outperforms other methods analyzed.
