We study the problem of downlink beamforming for the Weighted Sum Rate maximization (WSR) of Multi-User Multiple-Input-Single-Output systems with low-resolution Digital-to-Analog Converters (DACs) in a single-cell setup. The DACs, modeled as quantizers, are performing a nonlinear operation on the signals and are linearized using Bussgang decomposition and a linear approximation of the covariance of quantized signals. For the maximization of the WSR of the linearized system, we propose a gradient-based solution and a lower-complexity heuristic solution, based on the structure of the globally optimal solution. Through numerical simulations, we show that taking quantization into account in the filter design results in significant performance improvement when the number of transmit antennas is comparable to the number of users. When the number of transmit antennas becomes much larger than the number of users, it is found that the heuristic solution achieves near-optimal performance and that a quantization-aware design becomes less important.
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