  High-resolution fully digital transceivers are infeasible at millimeter-wave
(mmWave) due to their increased power consumption, cost, and hardware
complexity. The use of low-resolution converters is one possible solution to
realize fully digital architectures at mmWave. In this paper, we consider a
setting in which a fully digital base station with constant envelope quantized
(CEQ) digital-to-analog converters on each radio frequency chain communicates
with multiple single antenna users with individual
signal-to-quantization-plus-interference-plus-noise ratio (SQINR) constraints
over frequency selective channels. We first establish uplink downlink duality
for the system with CEQ hardware constraints and OFDM-based transmission
considered in this paper. Based on the uplink downlink duality principle, we
present a solution to the multi-user multi-carrier beamforming and power
allocation problem that maximizes the minimum SQINR over all users and
sub-carriers. We then present a per sub-carrier version of the originally
proposed solution that decouples all sub-carriers of the OFDM waveform
resulting in smaller sub-problems that can be solved in a parallel manner. Our
numerical results based on 3GPP channel models generated from Quadriga
demonstrate improvements in terms of ergodic sum rate and ergodic minimum rate
over state-of-the-art linear solutions. We also show improved performance over
non-linear solutions in terms of the coded bit error rate with the increased
flexibility of assigning individual user SQINRs built into the proposed
framework.
