  The increased power consumption of high-resolution data converters at higher
carrier frequencies and larger bandwidths is becoming a bottleneck for
communication systems. In this paper, we consider a fully digital base station
equipped with 1-bit analog-to-digital (in uplink) and digital-to-analog (in
downlink) converters on each radio frequency chain. The base station
communicates with multiple single antenna users with individual SINR
constraints. We first establish the uplink downlink duality principle under
1-bit hardware constraints under an uncorrelated quantization noise assumption.
We then present a linear solution to the multi-user downlink beamforming
problem based on the uplink downlink duality principle. The proposed solution
takes into account the hardware constraints and jointly optimizes the downlink
beamformers and the power allocated to each user. Optimized dithering obtained
by adding dummy users to the true system users ensures that the uncorrelated
quantization noise assumption is true under realistic settings. Detailed
simulations carried out using 3GPP channel models generated from Quadriga show
that our proposed solution outperforms state of the art solutions in terms of
the ergodic sum and minimum rate especially when the number of users is large.
We also demonstrate that the proposed solution significantly reduces the
performance gap from non-linear solutions in terms of the uncoded bit error
rate at a fraction of the computational complexity.
