  This paper investigates an intelligent reflecting surface (IRS)-aided
multi-cell multiple-input single-output (MISO) system consisting of 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 received signal-to-interference-plus-noise ratio (SINR) at users,
subject to the individual maximum transmit power constraints at the BSs and the
reflection constraints at the IRS. To solve the difficult non-convex minimum
SINR maximization problem, we propose efficient algorithms based on alternating
optimization, in which the transmit and reflective beamforming vectors are
optimized in an alternating manner. In particular, we use the second-order-cone
programming (SOCP) for optimizing the coordinated transmit beamforming, and
develop two efficient designs for updating the reflective beamforming based on
the techniques of semi-definite relaxation (SDR) and successive convex
approximation (SCA), respectively. Numerical results show that the use of IRS
leads to significantly higher SINR values than benchmark schemes without IRS or
without proper reflective beamforming optimization; while the developed
SCA-based solution outperforms the SDR-based one with lower implementation
complexity.
