  Robust transceiver design against unresolvable system uncertainties is of
crucial importance for reliable communication. For instance, full-duplex
communication suffers from such uncertainties when canceling the
self-interference, since the residual self-interference (RSI) remains
uncanceled due to imperfect channel knowledge. We consider a MIMO multi-hop
system, where the source, the relay and the destination are equipped with
multiple antennas. We allow multi-stream beamforming granted by MIMO technique,
without restricting the transmissions to single streaming. The relay can
operate in either half-duplex or full-duplex mode, and it changes the mode
depending on the RSI strength. Furthermore, the relay is assumed to perform a
decode-and-forward (DF) strategy. We investigate a robust transceiver design
problem, which maximizes the throughput rate of the worst-case RSI under RSI
channel uncertainty bound constraint. The problem turns out to be a non-convex
optimization problem. We propose an efficient algorithm to obtain a local
optimal solution iteratively. Eventually, we obtain insights on the optimal
antenna allocation at the relay input-frontend and output-frontend, for relay
reception and transmission, respectively. Interestingly, with less number of
antennas at the source than that at the destination, more number of antennas
should be used at the relay input-frontend than the relay output-frontend.
