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Robust Source-Relay Beamforming for Full-Duplex Relay Networks with Energy Harvesting

A full-duplex multiple-input multiple-output (MIMO) power splitting based relay system with channel uncertainty is considered in this paper. Full-duplex mode allows the relay to harvest energy and forward wireless information simultaneously from the same radio frequency (RF) signal. With the consideration of imperfect channel state information (CSI), the self-interference cannot be suppressed completely at relay node. Hence, a robust beamforming problem is formulated to minimum total mean squared error (MSE) of the network while guaranteeing the power constraints and zero forcing constraint. Such a problem is a non-convex optimization problem and is converted into three subproblems by alternating optimizationmethod. The joint robust source-relay beamforming design is then proposed based on the optimization guaranteed semidefinite relaxation algorithm. To be specific, a closed-form expression for the beamforming matrix at the source node is derived as a low-complexity scheme. Numerical results demonstrate that the proposed beamforming algorithms reduce the MSE and provide great robustness against channel uncertainties.