  In this paper we address the linear precoding and decoding design problem for
a bidirectional orthogonal frequencydivision multiplexing (OFDM) communication
system, between two multiple-input multiple-output (MIMO) full-duplex (FD)
nodes. The effects of hardware distortion as well as the channel state
information error are taken into account. In the first step, we transform the
available time-domain characterization of the hardware distortions for FD MIMO
transceivers to the frequency domain, via a linear Fourier transformation. As a
result, the explicit impact of hardware inaccuracies on the residual
selfinterference (RSI) and inter-carrier leakage (ICL) is formulated in
relation to the intended transmit/received signals. Afterwards, linear
precoding and decoding designs are proposed to enhance the system performance
following the minimum-mean-squarederror (MMSE) and sum rate maximization
strategies, assuming the availability of perfect or erroneous CSI. The proposed
designs are based on the application of alternating optimization over the
system parameters, leading to a necessary convergence. Numerical results
indicate that the application of a distortionaware design is essential for a
system with a high hardware distortion, or for a system with a low thermal
noise variance.
