  We model the self-interference in a multiple input single output (MISO)
full-duplex two-way channel and evaluate the achievable rate region. We
formulate the boundary of the achievable rate region termed as the Pareto
boundary by a family of coupled, non-convex optimization problems. Our main
contribution is decoupling and reformulating the original non-convex
optimization problems to a family of convex semidefinite programming problems.
For a MISO full-duplex two-way channel, we prove that beamforming is an optimal
transmission strategy which can achieve any point on the Pareto boundary.
Furthermore, we present a closed-form expression for the optimal beamforming
weights. In our numerical examples we quantify gains in the achievable rates of
the proposed beamforming over the zero-forcing beamforming.
