  This paper investigates an intelligent reflecting surface (IRS)-aided
multi-cell multiple-input single-output (MISO) system with several
multi-antenna base stations (BSs) each communicating with a single-antenna
user, in which an IRS is dedicatedly deployed for assisting the wireless
transmission and suppressing the inter-cell interference. Under this setup, we
jointly optimize the coordinated transmit beamforming at the BSs and the
reflective beamforming at the IRS, for the purpose of maximizing the minimum
weighted signal-to-interference-plus-noise ratio (SINR) at the users, subject
to the individual maximum transmit power at the BSs and the reflection
constraints at the IRS. To solve the non-convex problem, we first present an
exact-alternating-optimization design to optimize the transmit and reflective
beamforming vectors in an alternating manner, in which the transmit and
reflective beamforming optimization subproblems are solved exactly by using the
technique of semi-definite relaxation (SDR). However, it has high computational
complexity and may lead to compromised performance due to the uncertainty of
randomization in SDR. To avoid these drawbacks, we further propose an
inexact-alternating-optimization design, in which the transmit and reflective
beamforming optimization subproblems are solved inexactly based on the
principle of successive convex approximation (SCA). In addition, to further
reduce the complexity, we propose a low-complexity
inexact-alternating-optimization design, in which the reflective beamforming
optimization subproblem is solved more inexactly. Numerical results show that
the significant performance gains achieved by the proposed three designs
against benchmark schemes. Moreover, the inexact-alternating-optimization
designs outperform the exact-alternating-optimization one in terms of both the
achieved min-weighted-SINR value and the computational complexity.
