Weighted Sum-Rate Outage Probability Constrained Transmission Design for IRS-Enhanced Communication

Intelligent reflection surface (IRS) has been identified as a promising technology for improving the performance of wireless communication systems. This paper focuses on the downlink scenario of an IRS-enhanced multi-user multiple-input single-output system. However, the channel state information (CSI) of the channels associated with IRS is difficult to estimate due to the passive feature of IRS. Meanwhile, the ideal continuous phase shifts of IRS elements are challenging to obtain owing to the hardware imperfection. This paper establishes an optimization model to minimize the base station (BS) transmit power subject to the discrete phase shifts of IRS and the weighted sumrate outage probability, which takes into account the practical statistical CSI error. We first apply the decomposition-based large deviation inequality to safely approximate the weighted sum-rate outage probability since the closed form expression of outage probability is hard to obtain. Then, the alternating optimization framework is introduced to iteratively solve the joint BS and IRS beamforming. In particular, the negative square penalty method is used to solve the non-convex sub-problem, i.e., the IRS passive beamforming. Numerical results demonstrate the effectiveness of the proposed algorithm.