  Full-Duplex (FD) Amplify-and-Forward (AF) Multiple-Input Multiple-Output
(MIMO) relaying has been the focus of several recent studies, due to the
potential for achieving a higher spectral efficiency and lower latency,
together with inherent processing simplicity. However, when the impact of
hardware distortions are considered, such relays suffer from a
distortion-amplification loop, due to the inter-dependent nature of the relay
transmit signal covariance and the residual self-interference covariance. The
aforementioned behavior leads to a significant performance degradation for a
system with a low or medium hardware accuracy. In this work, we analyse the
relay transfer function as well as the Mean Squared-Error (MSE) performance of
an FD-AF MIMO relaying communication, under the impact of collective sources of
additive and multiplicative transmit and receive impairments. Building on the
performed analysis, an optimization problem is devised to minimize the
communication MSE and solved by employing the recently proposed Penalty Dual
Decomposition (PDD) framework. The proposed solution converges to a stationary
point of the original problem via a sequence of convex quadratic programs
(CQP)s, thereby enjoying an acceptable arithmatic complexity as the problem
dimensions grow large. Numerical simulations verify the significance of the
proposed distortion-aware design and analysis, compared to the common
simplified approaches, as the hardware accuracy degrades.
