  Multi-cell coordinated beamforming (MCBF), where multiple base stations (BSs)
collaborate with each other in the beamforming design for mitigating the
inter-cell interference, has been a subject drawing great attention recently.
Most MCBF designs assume perfect channel state information (CSI) of mobile
stations (MSs); however CSI errors are inevitable at the BSs in practice.
Assuming elliptically bounded CSI errors, this paper studies the robust MCBF
design problem that minimizes the weighted sum power of BSs subject to
worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the
MSs. Our goal is to devise a distributed optimization method that can obtain
the worst-case robust beamforming solutions in a decentralized fashion, with
only local CSI used at each BS and little backhaul signaling for message
exchange between BSs. However, the considered problem is difficult to handle
even in the centralized form. We first propose an efficient approximation
method in the centralized form, based on the semidefinite relaxation (SDR)
technique. To obtain the robust beamforming solution in a decentralized
fashion, we further propose a distributed robust MCBF algorithm, using a
distributed convex optimization technique known as alternating direction method
of multipliers (ADMM). We analytically show the convergence of the proposed
distributed robust MCBF algorithm to the optimal centralized solution and its
better bandwidth efficiency in backhaul signaling over the existing dual
decomposition based algorithms. Simulation results are presented to examine the
effectiveness of the proposed SDR method and the distributed robust MCBF
algorithm.
