© 2002-2012 IEEE. In this contribution, we investigate a coarsely quantized multi-user multiple-input single-output downlink communication system, where we assume 1-bit digital-to-analog converters at the base station antennas. First, we analyze the achievable sum rate lower-bound using the Bussgang decomposition under new assumptions. In the presence of the non-linear quantization, our analysis indicates the potential merit of reconsidering traditional signal processing techniques in coarsely quantized systems, i.e., reconsidering transmit covariance matrices whose rank is equal to the rank of the channel. Furthermore, in the latter part of this paper, we propose a linear precoder design that achieves the predicted increase in performance compared with a state-of-the-art linear precoder design. Moreover, our linear signal processing algorithm allows for higher order modulation schemes to be employed.