  {Robust transceiver design against unresolvable system uncertainties is of
crucial importance for reliable communication. We consider a MIMO multi-hop
system, where the source, the relay, and the destination are equipped with
multiple antennas. Further, an intelligent reconfigurable surface (IRS) is
established to cancel the RSI as much as possible. The considered
decode-and-forward (DF) hybrid relay can operate in either half-duplex or
full-duplex mode, and the mode changes adaptively depending on the RSI
strength. We investigate a robust transceiver design problem, which maximizes
the throughput rate corresponding to the worst-case RSI under a
self-interference channel uncertainty bound constraint. To the best of our
knowledge, this is the first work that uses the IRS for RSI cancellation in
MIMO full-duplex DF relay systems. The yielded problem turns out to be a
non-convex optimization problem, where the non-convex objective is optimized
over the cone of semidefinite matrices. We propose a closed-from lower bound
for the IRS worst case RSI cancellation. Eventually, we show an important
result that, for the worst case scenario, IRS can be helpful only if the number
of IRS elements are at least as large as the size of the interference channel.
Moreover, a novel method based on majorization theory is proposed to find the
best response of the transmitters and relay against worst case RSI.
Furthermore, we propose a multi-level water-filling algorithm to obtain a
locally optimal solution iteratively. Finally, we obtain insights on the
optimal antenna allocation at the relay input-frontend and output-frontend, for
relay reception and transmission, respectively.
