  In this paper, we investigate an intelligent reflecting surface (IRS)
assisted multi-user multiple-input multiple-output (MIMO) full-duplex (FD)
system. We jointly optimize the active beamforming matrices at the access point
(AP) and uplink users, and the passive beamforming matrix at the IRS to
maximize the weighted sum-rate of the system. Since it is practically difficult
to acquire the channel state information (CSI) for IRS-related links due to its
passive operation and large number of elements, we conceive a mixed-timescale
beamforming scheme. Specifically, the high-dimensional passive beamforming
matrix at the IRS is updated based on the channel statistics while the active
beamforming matrices are optimized relied on the low-dimensional real-time
effective CSI at each time slot. We propose an efficient stochastic successive
convex approximation (SSCA)-based algorithm for jointly designing the active
and passive beamforming matrices. Moreover, due to the high computational
complexity caused by the matrix inversion computation in the SSCA-based
optimization algorithm, we further develop a deep-unfolding neural network (NN)
to address this issue. The proposed deep-unfolding NN maintains the structure
of the SSCA-based algorithm but introduces a novel non-linear activation
function and some learnable parameters induced by the first-order Taylor
expansion to approximate the matrix inversion. In addition, we develop a
black-box NN as a benchmark. Simulation results show that the proposed
mixed-timescale algorithm outperforms the existing single-timescale algorithm
and the proposed deep-unfolding NN approaches the performance of the SSCA-based
algorithm with much reduced computational complexity when deployed online.
