  Symbol-level precoding (SLP), which converts the harmful multi-user
interference (MUI) into beneficial signals, can significantly improve
symbol-error-rate (SER) performance in multi-user communication systems. While
enjoying symbolic gain, however, the complicated non-linear symbol-by-symbol
precoder design suffers high computational complexity exponential with the
number of users, which is unaffordable in realistic systems. In this paper, we
propose a novel low-complexity grouped SLP (G-SLP) approach and develop
efficient design algorithms for typical max-min fairness and power minimization
problems. In particular, after dividing all users into several groups, the
precoders for each group are separately designed on a symbol-by-symbol basis by
only utilizing the symbol information of the users in that group, in which the
intra-group MUI is exploited using the concept of constructive interference
(CI) and the inter-group MUI is also effectively suppressed. In order to
further reduce the computational complexity, we utilize the Lagrangian dual,
Karush-Kuhn-Tucker (KKT) conditions and the majorization-minimization (MM)
method to transform the resulting problems into more tractable forms, and
develop efficient algorithms for obtaining closed-form solutions to them.
Extensive simulation results illustrate that the proposed G-SLP strategy and
design algorithms dramatically reduce the computational complexity without
causing significant performance loss compared with the traditional SLP schemes.
