  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 some 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. 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 of the worstcase RSI under
the self-interference channel uncertainty bound constraint. 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. Without loss of
generality, we simplify the problem to the optimization over multiple scalar
parameters using majorization theory. Furthermore, 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, given a number of antennas at the relay, the robustness improves
if more antennas are allocated to reception than to transmission.
