  Intelligent reflecting surface (IRS) is an emerging technology that is able
to reconfigure the wireless channel via tunable passive signal reflection and
thereby enhance the spectral and energy efficiency of wireless networks
cost-effectively. In this paper, we study an IRS-aided multiuser multiple-input
single-output (MISO) wireless system and adopt the two-timescale (TTS)
transmission to reduce the signal processing complexity and channel training
overhead as compared to the existing schemes based on the instantaneous channel
state information (I-CSI), and at the same time, exploit the multiuser channel
diversity in transmission scheduling. Specifically, the long-term passive
beamforming is designed based on the statistical CSI (S-CSI) of all links,
while the short-term active beamforming is designed to cater to the I-CSI of
all users' reconfigured channels with optimized IRS phase shifts. We aim to
minimize the average transmit power at the access point (AP), subject to the
users' individual quality of service (QoS) constraints. The formulated
stochastic optimization problem is non-convex and difficult to solve since the
long-term and short-term design variables are complicatedly coupled in the QoS
constraints. To tackle this problem, we propose an efficient algorithm, called
the primal-dual decomposition based TTS joint active and passive beamforming
(PDD-TJAPB), where the original problem is decomposed into a long-term problem
and a family of short-term problems, and the deep unfolding technique is
employed to extract gradient information from the short-term problems to
construct a convex surrogate problem for the long-term problem. The proposed
algorithm is proved to converge to a stationary solution of the original
problem almost surely. Simulation results are presented which demonstrate the
advantages and effectiveness of the proposed algorithm as compared to benchmark
schemes.
