# Symbol-level precoding is symbol-perturbed ZF when energy Efficiency is sought

## TL;DR

This paper uncovers a hidden equivalence between symbol-level precoding and zero-forcing beamforming with symbol perturbations under energy efficiency considerations, providing new insights and a SEP-constrained design for QAM.

## Contribution

It reveals that SLP is equivalent to a perturbed ZF scheme under energy minimization, and introduces a SEP-constrained SLP design for QAM.

## Key findings

- SLP is equivalent to a perturbed ZF scheme under energy minimization.
- New insights into SLP and linear beamforming connection.
- Developed a SEP-constrained SLP design for QAM.

## Abstract

This paper considers symbol-level precoding (SLP) for multiuser multiple-input single-output (MISO) downlink. SLP is a nonlinear precoding scheme that utilizes symbol constellation structures. It has been shown that SLP can outperform the popular linear beamforming scheme. In this work we reveal a hidden connection between SLP and linear beamforming. We show that under an energy minimization design, SLP is equivalent to a zero-forcing (ZF) beamforming scheme with perturbations on symbols. This identity gives new insights and they are discussed in the paper. As a side contribution, this work also develops a symbol error probability (SEP)-constrained SLP design formulation under quadrature amplitude modulation (QAM) constellations.