A Worst-Case Robust Beamforming Design for Multi-Antenna AF Relaying

In this paper, we consider relay precoder optimization for a multi-antenna amplify-and-forward (AF) relaying system using imperfect channel state information (CSI) with either additive or multiplicative deterministic uncertainties. Adopting worst-case robustness, we aim to maximize the worst-case received signal-to-noise ratio (SNR) at the destination subject to the power constraint at the relay. Despite the non-convexity of the design problem, we obtain a closed-form solution and discover that beamforming along the nominal channel direction achieves the best performance with channel uncertainties. Based on the optimal solution, we further analyze the impact of imperfect CSI on the performance of the robust multi-antenna AF relaying system and carry out simulations to verify our analysis.