Hardware Impairments Aware Transceiver Design for Full-Duplex Amplify-and-Forward MIMO Relaying

In this paper, we consider a full-duplex (FD) and amplify-and-forward (AF) relay with multiple antennas, where hardware impairments of the FD relay are taken into account. Due to the inter-dependence of the transmit relay power and the residual self-interference in an FD-AF relay, we observe a distortion loop that degrades the system performance when relay dynamic range is not high. In this paper, we analyze the relay function, and an optimization problem is formulated to maximize the signal to distortion-plus-noise ratio under relay and source transmit power constraints. Due to the problem complexity, we propose a gradient-projection-based (GP) algorithm to obtain an optimal solution. Moreover, a non-alternating sub-optimal solution is proposed by assuming a rank-1 relay amplification matrix, and separating the design of the relay process into multiple stages (MuStR1). The proposed MuStR1 method is then enhanced by introducing an alternating update over the optimization variables, denoted as AltMuStR1 algorithm. Numerical simulations show that compared to GP, the proposed (Alt)MuStR1 algorithms significantly reduce the required computational complexity at the expense of a slight performance degradation. Moreover, as the hardware impairments increase, or for a system with a high transmit power, the impact of applying a distortion-aware design is significant.