  This paper investigates the robust design of symbol-level precoding (SLP) for
multiuser multiple-input multiple-output (MIMO) downlink transmission with
imperfect channel state information (CSI) caused by channel aging. By utilizing
the a posteriori channel model based on the widely adopted jointly correlated
channel model, the imperfect CSI is modeled as the statistical CSI
incorporating the channel mean and channel variance information with spatial
correlation. With the signal model in the presence of channel aging, we
formulate the signal-to-noise-plus-interference ratio (SINR) balancing and
minimum mean square error (MMSE) problems for robust SLP design. The former
targets to maximize the minimum SINR across users, while the latter minimizes
the mean square error between the received signal and the target constellation
point. When it comes to massive MIMO scenarios, the increment in the number of
antennas poses a computational complexity challenge, limiting the deployment of
SLP schemes. To address such a challenge, we simplify the objective function of
the SINR balancing problem and further derive a closed-form SLP scheme.
Besides, by approximating the matrix involved in the computation, we modify the
proposed algorithm and develop an MMSE-based SLP scheme with lower computation
complexity. Simulation results confirm the superiority of the proposed schemes
over the state-of-the-art SLP schemes.
