Statistically Robust Beamforming Optimization for Multi-Antenna Full-Duplex DF Relaying

This paper studies robust beamforming optimization for full-duplex (FD) multi-antenna decode-and-forward (DF) relaying subject to stochastic channel state information (CSI) errors. By exploiting the statistics of CSI errors, we jointly optimize the receive and transmit beamformers of the FD relay to maximize the system achievable rate. Firstly, we prove that the original optimization problem can be equivalently transformed into a solvable convex feasibility check problem with second-order cone (SOC) constraints, whose globally optimal solution can be obtained in polynomial time. In order to reduce the computational complexity of the optimal beamforming, we further advocate a semi-closed form solution which achieves near-optimal performance. Afterwards, concerning a special case with spatially uncorrelated CSI errors, we develop a closed-form relay beamforming solution which reveals the optimality of the maximum ratio combining/maximum ratio transmission (MRC/MRT) strategy. Simulations are conducted to validate the effectiveness of the proposed robust FD relay beamforming designs.