  Recently, multi-user multiple input multiple output (MU-MIMO) systems with
low-resolution digital-to-analog converters (DACs) has received considerable
attention, owing to the capability of dramatically reducing the hardware cost.
Besides, it has been shown that the use of low-resolution DACs enable great
reduction in power consumption while maintain the performance loss within
acceptable margin, under the assumption of perfect knowledge of channel state
information (CSI). In this paper, we investigate the precoding problem for the
coarsely quantized MU-MIMO system without such an assumption. The channel
uncertainties are modeled to be a random matrix with finite second-order
statistics. By leveraging a favorable relation between the multi-bit DACs
outputs and the single-bit ones, we first reformulate the original complex
precoding problem into a nonconvex binary optimization problem. Then, using the
S-procedure lemma, the nonconvex problem is recast into a tractable formulation
with convex constraints and finally solved by the semidefinite relaxation (SDR)
method. Compared with existing representative methods, the proposed precoder is
robust to various channel uncertainties and is able to support a MUMIMO system
with higher-order modulations, e.g., 16QAM.
