  In this paper, we consider symbol-level precoding (SLP) in channel-coded
multiuser multi-input single-output (MISO) systems. It is observed that the
received SLP signals do not always follow Gaussian distribution, rendering the
conventional soft demodulation with the Gaussian assumption unsuitable for the
coded SLP systems. It, therefore, calls for novel soft demodulator designs for
non-Gaussian distributed SLP signals with accurate log-likelihood ratio (LLR)
calculation. To this end, we first investigate the non-Gaussian characteristics
of both phase-shift keying (PSK) and quadrature amplitude modulation (QAM)
received signals with existing SLP schemes and categorize the signals into two
distinct types. The first type exhibits an approximate-Gaussian distribution
with the outliers extending along the constructive interference region (CIR).
In contrast, the second type follows some distribution that significantly
deviates from the Gaussian distribution. To obtain accurate LLR, we propose the
modified Gaussian soft demodulator and Gaussian mixture model (GMM) soft
demodulators to deal with two types of signals respectively. Subsequently, to
further reduce the computational complexity and pilot overhead, we put forward
a novel neural soft demodulator, named pilot feature extraction network (PFEN),
leveraging the transformer mechanism in deep learning. Simulation results show
that the proposed soft demodulators dramatically improve the throughput of
existing SLPs for both PSK and QAM transmission in coded systems.
