This paper investigates a joint beamforming design in a multiuser multiple-input single-output (MISO) communication network aided with an intelligent reflecting surface (IRS) panel. The symbol-level precoding (SLP) is adopted to enhance the system performance by exploiting the multiuser interference (MUI) with consideration of bounded channel uncertainty. The joint beamforming design is formulated into a nonconvex worst-case robust programming to minimize the transmit power subject to single-to-noise ratio (SNR) requirements. To address the challenges due to the constant modulus and the coupling of the beamformers, we first study the single-user case. Specifically, we propose and compare two algorithms based on the semidefinite relaxation (SDR) and alternating optimization (AO) methods, respectively. It turns out that the AO-based algorithm has much lower computational complexity but with almost the same power to the SDR-based algorithm. Then, we apply the AO technique to the multiuser case and thereby develop an algorithm based on the proximal gradient descent (PGD) method. The algorithm can be generalized to the case of finite-resolution IRS and the scenario with direct links from the transmitter to the users. Numerical results show that the SLP can significantly improve the system performance. Meanwhile, 3-bit phase shifters can achieve near-optimal power performance.
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