Worst case fair beamforming for multiple multicast groups in multicell networks

The design problem associated with robust downlink beamforming in multicast, multigroup, multicell wireless systems is addressed. The channel state information (CSI) of users is assumed to be imperfect and the uncertainty of CSI is modelled using the Frobenius norm. The objective is to optimise the signal-to-interference-plus-noise ratio over all users with a constraint on the maximum total transmitted power. This was achieved through a robust solution using the successive convex approximation (SCA) method. The beamforming problem is treated as a bi-convex problem, which is solved using the iterate-alternative convex technique. Here, the CSI uncertainty is addressed using a convex package through the non-monotone spectral projected gradient method and the beamforming vector is extracted using the SCA method. Also, the authors offer the required condition to extract the beamform vector using the SCA method through a suboptimal solution that always addressed before using different beamforming methods. Their simulation results examine all proposed system parameters in order to show convergence and feasibility of the solution. They also compare the solution with a suboptimal solution and the quality of service method for imperfect CSI in downlink beamforming. Numerical results show that the robust solution achieves the best power efficiency for practical solutions.