# An Approximate Solution for Symbol-Level Multiuser Precoding Using Support Recovery

## TL;DR

This paper introduces a low-complexity approximate solution for symbol-level multiuser precoding that improves performance over existing methods while maintaining computational efficiency, especially in large systems.

## Contribution

It recasts the precoding problem as a non-negative least squares problem and enhances an existing closed-form scheme using support recovery conditions, resulting in better performance with minimal complexity increase.

## Key findings

- ICF-SLP outperforms CF-SLP in simulations.
- ICF-SLP is comparable to iterative NNLS algorithms with limited iterations.
- The method is computationally efficient and close to optimal in large systems.

## Abstract

In this paper, we propose a low-complexity method to approximately solve the SINR-constrained optimization problem of symbol-level precoding (SLP). First, assuming a generic modulation scheme, the precoding optimization problem is recast as a standard non-negative least squares (NNLS). Then, we improve an existing closed-form SLP (CF-SLP) scheme using the conditions for nearly perfect recovery of the optimal solution support, followed by solving a reduced system of linear equations. We show through simulation results that in comparison with the CF-SLP method, the improved approximate solution of this paper, referred to as ICF-SLP, significantly enhances the performance with a negligible increase in complexity. We also provide comparisons with a fast-converging iterative NNLS algorithm, where it is shown that the ICF-SLP method is comparable in performance to the iterative algorithm with a limited maximum number of iterations. Analytic discussions on the complexities of different methods are provided, verifying the computational efficiency of the proposed method. Our results further indicate that the ICF-SLP scheme performs quite close to the optimal SLP, particularly in the large system regime.