Robust Beamforming and Phase Shift Design for IRS-Enhanced Multi-User MISO Downlink Communication

Intelligent reflecting surface (IRS), with a large number of reflective elements, is a promising technology to achieve both spectrum and energy efficient wireless communication. The IRS can reflect the incident electromagnetic wave passively and steer it to the desirable way before reaching the intended receiver by adjusting the phase shift on the reflective elements. In order to better improve communication quality, the beamforming vector at the base station (BS) and the phase shift induced by the IRS should be jointly designed carefully. However, thus far, previous works on IRS have assumed that the channel state information (CSI) is perfectly known at the BS, which is not available in the practical systems. In this paper, we study an IRS-enhanced multi-user multiple-input single-output (MISO) downlink communication system assuming imperfect CSI. An optimization problem is formulated to jointly optimize the beamforming vector at the BS and the phase shift at the IRS such that the total transmit power is minimized under the individual outage probability constraints. An algorithm based on alternating optimization (AO) and semi-definite relaxation (SDR) is proposed to solve this challenging non-convex problem. Finally, numerical results have validated the effectiveness of the proposed algorithm.