# One-Bit MIMO Detection: From Global Maximum-Likelihood Detector to Amplitude Retrieval Approach

**Authors:** Mingjie Shao, Wei-Kun Chen, Cheng-Yang Yu, Ya-Feng Liu, Wing-Kin Ma  
**arXiv:** [2407.11079](https://arxiv.org/abs/2407.11079)  
**Date:** 2024-07-13  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2407.11079v2/

## Key points

- Integration of large-scale antenna arrays in base stations (BSs) introduces challenges such as escalating hardware costs and energy consumption
- Growing interest in utilizing one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) to mitigate issues
- One-bit quantization presents a unique hurdle by retaining only sign information while discarding amplitude details
- Maximum-likelihood (ML) formulation for one-bit MIMO detection poses a challenge due to complex likelihood function, hindering high-performance detectors designed for traditional MIMO setups with high-resolution ADCs
- Introduction of an innovative branch-and-bound algorithm to find the global solution for the one-bit ML MIMO detection problem
- Development of a novel amplitude retrieval (AR) detection approach by incorporating explicit amplitude variables into the problem formulation
- Analysis of computational complexity of both ML and AR detection problems
- Extensive simulations demonstrate effectiveness and efficiency of proposed formulations and algorithms in optimizing communication systems for future advancements

## Summary

In the rapidly evolving landscape of communication systems moving towards the future 6G era, the integration of large-scale antenna arrays in base stations (BSs) has introduced challenges such as escalating hardware costs and energy consumption. To mitigate these issues, there has been a growing interest in utilizing one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs). This paper delves into the realm of one-bit multiple-input multiple-output (MIMO) detection within an uplink multiuser transmission scenario where the BS is equipped with one-bit ADCs. One-bit quantization presents a unique hurdle in the detection problem at hand by retaining only sign information while discarding amplitude details. The maximum-likelihood (ML) formulation for one-bit MIMO detection poses a formidable challenge due to its complex likelihood function, impeding the application of high-performance detectors designed for traditional MIMO setups with high-resolution ADCs. While various approximate methods have been explored to tackle this problem, there remains a gap in efficient global algorithms. To bridge this gap, this paper introduces an innovative branch-and-bound algorithm that guarantees finding the global solution for the one-bit ML MIMO detection problem. Additionally, a novel amplitude retrieval (AR) detection approach is developed by incorporating explicit amplitude variables into the problem formulation. The AR approach simplifies objective functions and enables the development of efficient algorithms that offer both global and approximate solutions. Furthermore, this paper contributes to analyzing the computational complexity of both ML and AR detection problems. Through extensive simulations, it demonstrates the effectiveness and efficiency of the proposed formulations and algorithms. By addressing key challenges in one-bit MIMO detection and offering novel solutions backed by rigorous analysis and simulations, this research significantly advances our understanding of optimizing communication systems for future advancements in technology.