We consider multi-user massive multiple-input single-output systems (MU-MISO) for downlink with QAM constellation. Massive MISO systems is a key technique for many users in future wireless systems. The base station (BS) employs 1-bit digital-to-analog converters (DACs) for low cost and low quantization power consumption. In this systems, Non-linearity precoding method is big issue for this systems due to 1-bit DAC. We first construct a feasibility condition that guarantee the transmit vector make a noiseless received signal is placed in own decision region in QAM constellation. For the robustness at a noise, We set up a optimization propblem to a mixed integer linear programming (MILP). We propose efficient 1-bit precoding method based on the problem. Via simulation results, we demonstrate the proposed structure is feasible and robust at noise. Also, The proposed method show better performance and complexity gain than existing 1-bit precoding with QAM constellations.
