# Asymptotic Analysis of Nonlinear One-Bit Precoding in Massive MIMO Systems via Approximate Message Passing

arXiv: https://arxiv.org/abs/2509.13955 · HTML: https://mlsanity.com/paper/2509.13955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Error bounds, quadratic growth, and linear convergence of proximal methods](https://mlsanity.com/paper/1602.06661/) (2016)
- [A unifying tutorial on Approximate Message Passing](https://mlsanity.com/paper/2105.02180/) (2021)
- [Approximate Message Passing algorithms for rotationally invariant matrices](https://mlsanity.com/paper/2008.11892/) (2020)
- [What Will 5G Be?](https://mlsanity.com/paper/1405.2957/) (2014)
- [A Survey of Recent Advances in Optimization Methods for Wireless Communications](https://mlsanity.com/paper/2401.12025/) (2024)
- [The Asymptotic Distribution of the MLE in High-dimensional Logistic Models: Arbitrary Covariance](https://mlsanity.com/paper/2001.09351/) (2020)
- [Massive MIMO 1-Bit DAC Transmission: A Low-Complexity Symbol Scaling Approach](https://mlsanity.com/paper/1709.08278/) (2017)
- [A Framework for One-Bit and Constant-Envelope Precoding over Multiuser Massive MISO Channels](https://mlsanity.com/paper/1810.03159/) (2018)
- [Symbol Error Rate Performance of Box-relaxation Decoders in Massive MIMO](https://mlsanity.com/paper/1711.11215/) (2017)
- [Unifying AMP Algorithms for Rotationally-Invariant Models](https://mlsanity.com/paper/2412.01574/) (2024)
- [Interference Exploitation 1-Bit Massive MIMO Precoding: A Partial Branch-and-Bound Solution with Near-Optimal Performance](https://mlsanity.com/paper/1908.03678/) (2019)
- [Efficient CI-Based One-Bit Precoding for Multiuser Downlink Massive MIMO Systems with PSK Modulation](https://mlsanity.com/paper/2110.11628/) (2021)
- [Sharp Analysis of RLS-based Digital Precoder with Limited PAPR in Massive MIMO](https://mlsanity.com/paper/2205.12077/) (2022)
- [Asymptotic SEP Analysis and Optimization of Linear-Quantized Precoding in Massive MIMO Systems](https://mlsanity.com/paper/2307.06714/) (2023)
- [Multi-user Downlink Beamforming using Uplink Downlink Duality with 1-bit Converters for Flat Fading Channels](https://mlsanity.com/paper/2206.14427/) (2022)
- [Asymptotic Analysis of One-bit Quantized Box-Constrained Precoding in Large-Scale Multi-User Systems](https://mlsanity.com/paper/2502.02953/) (2025)

## Abstract (arXiv)

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_∞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_∞2 regularizer within the mixed ℓ_∞2-ℓ22 regularization functions.