  In this letter, an intelligent reflecting surface (IRS) enhanced full-duplex
MIMO two-way communication system is studied. The system sum rate is maximized
through jointly optimizing the source precoders and the IRS phase shift matrix.
Adopting the idea of Arimoto-Blahut algorithm, the non-convex optimization
problem is decoupled into three sub-problems, which are solved alternatingly.
All the sub-problems can be solved efficiently with closed-form solutions. In
addition, practical IRS assumptions, e.g., discrete phase shift levels, are
also considered. Numerical results verify the convergence and performance of
the proposed scheme.
