  We study the beamforming optimization for an intelligent reflecting surface
(IRS)-aided full-duplex (FD) communication system in this letter. Specifically,
we maximize the sum rate of bi-directional transmissions by jointly optimizing
the transmit beamforming and the beamforming of the IRS reflection. A fast
converging alternating algorithm is developed to tackle this problem. In each
iteration of the proposed algorithm, the solutions to the transmit beamforming
and the IRS reflect beamforming are obtained in a semi-closed form and a closed
form, respectively. Compared to an existing method based on the Arimoto-Blahut
algorithm, the proposed method achieves almost the same performance while
enjoying much faster convergence and lower computational complexity.
