  We study multi-user massive multiple-input single-output (MISO) systems and
focus on downlink transmission, where the base station (BS) employs a large
antenna array with low-cost 1-bit digital-to-analog converters (DACs). The
direct combination of existing beamforming schemes with 1-bit DACs is shown to
lead to an error floor at medium-to-high SNR regime, due to the coarse
quantization of the DACs with limited precision. In this paper, based on the
constructive interference we consider both a quantized linear beamforming
scheme where we analytically obtain the optimal beamforming matrix, and a
non-linear mapping scheme where we directly design the transmit signal vector.
Due to the 1-bit quantization, the formulated optimization for the non-linear
mapping scheme is shown to be non-convex. To solve this problem, the non-convex
constraints of the 1-bit DACs are firstly relaxed, followed by an element-wise
normalization to satisfy the 1-bit DAC transmission. We further propose a
low-complexity symbol scaling scheme that consists of three stages, in which
the quantized transmit signal on each antenna element is selected sequentially.
Numerical results show that the proposed symbol scaling scheme achieves a
comparable performance to the optimization-based non-linear mapping approach,
while its corresponding complexity is negligible compared to that of the
non-linear scheme.
