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This paper addresses the optimization problem of symbol-level precoding (SLP)in the downlink of a multiuser multiple-input multiple-output (MU-MIMO)wireless system while the precoder's output is subject to partially-knowndistortions. In particular, we assume a linear distortion model with boundedadditive noise. The original signal-to-interference-plus-noise ratio (SINR)-constrained SLP problem minimizing the total transmit power is firstreformulated as a penalized unconstrained problem, which is referred to as therelaxed robust formulation. We then adopt a worst-case design approach toprotect the users' intended symbols and the targeted constructive interferencewith a desired level of confidence. Due to the non-convexity of the relaxedrobust formulation, we propose an iterative algorithm based on the blockcoordinate ascent-descent method. We show through simulation results that theproposed robust design is flexible in the sense that the CI constraints can berelaxed so as to keep a desirable balance between achievable rate and powerconsumption. Remarkably, the new formulation yields more energy-efficientsolutions for appropriate choices of the penalty parameter, compared to theoriginal problem.

A Worst-Case Performance Optimization Based Design Approach to Robust Symbol-Level Precoding for Downlink MU-MIMO