Max-Min Fairness in IRS-Aided Multi-Cell MISO Systems With Joint Transmit and Reflective Beamforming

This paper investigates an intelligent reflecting surface (IRS)-aided multi-cell multiple-input single-output (MISO) network with a set of multi-antenna base stations (BSs) each communicating with multiple single-antenna users, 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 vectors at the BSs and the reflective beamforming vector (with both reflecting phases and amplitudes) 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 constraints at the BSs and the reflection constraints at the IRS. To solve the non-convex min-weighted-SINR maximization problem, we first present an exact-alternating-optimization approach to optimize the transmit and reflective beamforming vectors in an alternating manner, in which the transmit and reflective beamforming optimization subproblems are solved exactly in each iteration by using the techniques of second-order-cone program (SOCP) and semi-definite relaxation (SDR), respectively. However, the exact-alternating-optimization approach 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 approach, in which the transmit and reflective beamforming optimization subproblems are solved inexactly in each iteration based on the principle of successive convex approximation (SCA). In addition, to further reduce the computational complexity, we propose a low-complexity inexact-alternating-optimization design, in which the reflective beamforming optimization subproblem is solved more inexactly. Via numerical results, it is shown that the proposed three designs achieve significantly increased min-weighted-SINR values, as compared with benchmark schemes without the IRS or with random reflective beamforming. It is also shown that the inexact-alternating-optimization design outperforms the exact-alternating-optimization one in terms of both the achieved min-weighted-SINR value and the computational complexity, while the low-complexity inexact-alternating-optimization design has much lower computational complexity with slightly compromised performance. Furthermore, we show that our proposed design can be applied to the scenario with unit-amplitude reflection constraints, with a negligible performance loss.