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 relay transceiver is taken into account. Due to the
inter-dependency of the transmit relay power on each antenna and the residual
self-interference in an FD-AF relay, we observe a distortion loop that degrades
the system performance when the relay dynamic range is not high. In this
regard, we analyze the relay function in presence of the hardware inaccuracies
and an optimization problem is formulated to maximize the signal to
distortion-plus-noise ratio (SDNR), 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 nonalternating 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. It is observed that compared to GP, (Alt)MuStR1
algorithms significantly reduce the required computational complexity at the
expense of a slight performance degradation. Finally, the proposed methods are
evaluated under various system conditions, and compared with the methods
available in the current literature. In particular, it is observed that as the
hardware impairments increase, or for a system with a high transmit power, the
impact of applying a distortion-aware design is significant.Comment: Submitted to IEEE Transactions on Wireless Communication
