Robust MMSE Beamforming for Multiantenna Relay Networks

In this paper, we propose a robust minimum mean square error (MMSE)-based beamforming technique for multi-antenna relay broadcast channels, where a multiantenna base station transmits signal to single antenna users with the help of a multiantenna relay. The signal transmission from the base station to the single antenna users is completed in two time slots, where the relay receives the signal from the base station in the first time slot, and it then forwards the received signal to different users based on amplify and forward (AF) protocol. We propose a robust beamforming technique for a sum-power minimization problem with an imperfect channel state information (CSI) between the relay and the users. This robust scheme is developed based on the worst-case optimization framework and the Nemirovski Lemma by incorporating uncertainties in the CSI. The original optimization problem is divided into three subproblems due to joint nonconvexity in terms of beamforming vectors at the base station, the relay amplification matrix, and receiver coefficients. These subproblems are formulated into a convex optimization framework by exploiting the Nemirovski Lemma, and an iterative algorithm is developed by alternatively optimizing each of them with channel uncertainties. In addition, we provide an optimization framework to evaluate the achievable worst-case mean square error (MSE) of each user for a given set of design parameters. Simulation results are provided to validate the convergence of the proposed algorithm.