Massive multiple-input multiple-output (MIMO) systems employing one-bit digital-to-analog converters offer a hardware-efficient solution for wireless communications. However, the one-bit constraint poses significant challenges for precoding design, as it transforms the problem into a discrete and nonconvex optimization task. In this paper, we investigate a widely adopted convex-relaxation-then-quantization approach for nonlinear symbol-level one-bit precoding. Specifically, we first solve a convex relaxation of the discrete minimum mean square error precoding problem, and then quantize the solution to satisfy the one-bit constraint. Focusing on a real-valued system with an independently and identically distributed (i.i.d.) Gaussian channel, we develop a novel analytical framework based on approximate message passing (AMP) to characterize the high dimensional asymptotic performance of the considered scheme. The key technical ingredient is an auxiliary AMP iteration that dedicatedly incorporates the nonlinear quantization function into the state evolution analysis. With the proposed framework, we derive a closed-form expression for the symbol error probability (SEP) at the receiver side in the large-system limit, which provides a quantitative characterization of how model and system parameters affect the SEP performance. Our empirical results suggest that the l(infinity)(2) regularizer, when paired with an optimally chosen regularization parameter, achieves optimal SEP performance within a broad class of convex regularization functions. As a first step towards a theoretical justification, we prove the optimality of the l(infinity)(2) regularizer within the mixed l(infinity)(2) -l(2)(2) regularization functions.

Publication:

IEEE TRANSACTIONS ON INFORMATION THEORY

http://dx.doi.org/10.1109/TIT.2026.3682569

Author:

Wu, Zheyu

Imperial Coll London, Dept Elect & Elect Engn, London SW7 2AZ, England

Email address:zheyu.wu@imperial.ac.uk

Clerckx, Bruno

Imperial Coll London, Dept Elect & Elect Engn, London SW7 2AZ, England

Email address:b.clerckx@imperial.ac.uk

Ma, Junjie(corresponding author)

Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Email address:majunjie@lsec.cc.ac.cn

Liu, Ya-Feng

Beijing Univ Posts & Telecommun, Sch Math Sci, Minist Educ, Key Lab Math & Informat Networks, Beijing 102206, Peoples R China

Email address:yafengliu@bupt.edu.cn