  We propose an optimal MMSE precoding technique using quantized signals with
constant envelope. Unlike the existing MMSE design that relies on 1-bit
resolution, the proposed approach employs uniform phase quantization and the
bounding step in the branch-and-bound method is different in terms of
considering the most restrictive relaxation of the nonconvex problem, which is
then utilized for a suboptimal design also. Moreover, unlike prior studies, we
propose three different soft detection methods and an iterative detection and
decoding scheme that allow the utilization of channel coding in conjunction
with low-resolution precoding. Besides an exact approach for computing the
extrinsic information, we propose two approximations with reduced computational
complexity. Numerical simulations show that utilizing the MMSE criterion
instead of the established maximum-minimum distance to the decision threshold
yields a lower bit-error-rate in many scenarios. Furthermore, when using the
MMSE criterion, a smaller number of bound evaluations in the branch-and-bound
method is required for low and medium SNR. Finally, results based on an LDPC
block code indicate that the receive processing schemes yield a lower
bit-error-rate compared to the conventional design.
