  Symbol-level precoding (SLP) has recently emerged as a new paradigm for
physical-layer transmit precoding in multiuser multi-input-multi-output (MIMO)
channels. It exploits the underlying symbol constellation structure, which the
conventional paradigm of linear precoding does not, to enhance symbol-level
performance such as symbol error probability (SEP). It also allows the precoder
to take a more general form than linear precoding. This paper aims to better
understand the relationships between SLP and linear precoding, subsequent
design implications, and further connections beyond the existing SLP scope.
Focused on the quadrature amplitude modulation (QAM) constellations, our study
is built on a basic signal observation, namely, that SLP can be equivalently
represented by a zero-forcing (ZF) linear precoding scheme augmented with some
appropriately chosen symbol-dependent perturbation terms, and that some
extended form of SLP is equivalent to a vector perturbation (VP) nonlinear
precoding scheme augmented with the above-noted perturbation terms. We examine
how insights arising from this perturbed ZF and VP interpretations can be
leveraged to i) substantially simplify the optimization of certain SLP design
criteria, namely, total or peak power minimization subject to SEP quality
guarantees; and ii) draw connections with some existing SLP designs. We also
touch on the analysis side by showing that, under the total power minimization
criterion, the basic ZF scheme is a near-optimal SLP scheme when the QAM order
is very high -- which gives a vital implication that SLP is more useful for
lower-order QAM cases. Numerical results further indicate the merits and
limitations of the different SLP designs derived from the perturbed ZF and VP
interpretations.
