Robust downlink beamforming in multi-group multicasting using trace bounds on the covariance mismatches

We consider the problem of worst-case robust beamforming for multi-group multicasting network with erroneous channel state information (CSI). In previous beamforming techniques robustness is ensured for all mismatch matrices of bounded Frobenius norm. In contrast, we present an alternative method of bounding the channel uncertainties, where we only limit the trace of the mismatch matrices. This approach leads to a problem formulation of reduced complexity as compared to the previous methods. Our goal is to minimize the total transmitted power subject to the worst-case user quality-of service (QoS) constraints. Lagrange duality is used to obtain a simple reformulation of the worst-case beamforming problem. The resulting non-convex problem can then be converted into a convex form using semidefinite relaxation (SDR) that can be solved efficiently using interior point methods. The resulting problem is a linear second-order cone programming (SOCP) problem as opposed to the quadratic SOCP problems in the previous robust approaches. Simulation results also show that the proposed method offers a significantly improved performance in terms of transmitted power.