Distortion-loop-aware amplify-and-forward full-duplex relaying with multiple antennas

In this work we study the behavior of a full-duplex (FD) and amplify-and-forward (AF) relay with multiple antennas, where hardware impairments of the FD transceivers are taken into account. Due to the inter-dependency of the transmit relay power on each antenna and the residual self-interference intensity in an AF-FD relay, we observe a distortion loop which degrades the system performance. An optimization problem is formulated to maximize the end-to-end communication rate, under relay and source transmit power constraints. Due to the resulting problem complexity, we propose a gradient-projection-based algorithm to approach an optimum solution. An iterative relay transmit covariance shaping algorithm is also proposed, following the quadratic approximation of the relay function in each iteration. The aforementioned algorithm provides a convex optimization framework to approach an optimal solution with small number of optimization iterations. The performance of the proposed designs are then compared to a similar setup with a decode-and-forward (DF) process, where the distortion loop effect is eliminated due to decoding, via numerical simulations.