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

Mingjie Shao, Wei-Kun Chen, Cheng-Yang Yu, Ya-Feng Liu, Wing-Kin Ma

TL;DR

This work tackles the challenging one-bit MIMO detection problem by establishing its NP-hardness and delivering a globally optimal solution method via a tailored MILP reformulation with delayed constraint generation integrated into a branch-and-bound framework. To address the amplitude loss inherent to one-bit quantization, it introduces an amplitude retrieval (AR) formulation with simpler objective functions and develops an efficient ABB-based first-order algorithm (with homotopy) to solve it. Through extensive simulations, the authors show that the global ML detector (gML) offers superior BER, while the AR-based approaches, particularly AR-L1-ABB, achieve competitive BER at substantially reduced runtime, and can serve as practical benchmarks and fast detectors for large-scale one-bit MIMO systems. The proposed methods advance practical detection in coarse-quantized massive MIMO and provide valuable trade-offs between performance and complexity for next-generation wireless systems.

Abstract

As communication systems advance towards the future 6G era, the incorporation of large-scale antenna arrays in base stations (BSs) presents challenges such as increased hardware costs and energy consumption. To address these issues, the use of one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) has gained significant attentions. This paper focuses on one-bit multiple-input multiple-output (MIMO) detection in an uplink multiuser transmission scenario where the BS employs one-bit ADCs. One-bit quantization retains only the sign information and loses the amplitude information, which poses a unique challenge in the corresponding detection problem. The maximum-likelihood (ML) formulation of one-bit MIMO detection has a challenging likelihood function that hinders the application of many high-performance detectors developed for classic MIMO detection (under high-resolution ADCs). While many approximate methods for the ML detection problem have been studied, it lacks an efficient global algorithm. This paper fills this gap by proposing an efficient branch-and-bound algorithm, which is guaranteed to find the global solution of the one-bit ML MIMO detection problem. Additionally, a new amplitude retrieval (AR) detection approach is developed, incorporating explicit amplitude variables into the problem formulation. The AR approach yields simpler objective functions that enable the development of efficient algorithms offering both global and approximate solutions. The paper also contributes to the computational complexity analysis of both ML and AR detection problems. Extensive simulations are conducted to demonstrate the effectiveness and efficiency of the proposed formulations and algorithms.

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

TL;DR

This work tackles the challenging one-bit MIMO detection problem by establishing its NP-hardness and delivering a globally optimal solution method via a tailored MILP reformulation with delayed constraint generation integrated into a branch-and-bound framework. To address the amplitude loss inherent to one-bit quantization, it introduces an amplitude retrieval (AR) formulation with simpler objective functions and develops an efficient ABB-based first-order algorithm (with homotopy) to solve it. Through extensive simulations, the authors show that the global ML detector (gML) offers superior BER, while the AR-based approaches, particularly AR-L1-ABB, achieve competitive BER at substantially reduced runtime, and can serve as practical benchmarks and fast detectors for large-scale one-bit MIMO systems. The proposed methods advance practical detection in coarse-quantized massive MIMO and provide valuable trade-offs between performance and complexity for next-generation wireless systems.

Abstract

As communication systems advance towards the future 6G era, the incorporation of large-scale antenna arrays in base stations (BSs) presents challenges such as increased hardware costs and energy consumption. To address these issues, the use of one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) has gained significant attentions. This paper focuses on one-bit multiple-input multiple-output (MIMO) detection in an uplink multiuser transmission scenario where the BS employs one-bit ADCs. One-bit quantization retains only the sign information and loses the amplitude information, which poses a unique challenge in the corresponding detection problem. The maximum-likelihood (ML) formulation of one-bit MIMO detection has a challenging likelihood function that hinders the application of many high-performance detectors developed for classic MIMO detection (under high-resolution ADCs). While many approximate methods for the ML detection problem have been studied, it lacks an efficient global algorithm. This paper fills this gap by proposing an efficient branch-and-bound algorithm, which is guaranteed to find the global solution of the one-bit ML MIMO detection problem. Additionally, a new amplitude retrieval (AR) detection approach is developed, incorporating explicit amplitude variables into the problem formulation. The AR approach yields simpler objective functions that enable the development of efficient algorithms offering both global and approximate solutions. The paper also contributes to the computational complexity analysis of both ML and AR detection problems. Extensive simulations are conducted to demonstrate the effectiveness and efficiency of the proposed formulations and algorithms.
Paper Structure (23 sections, 3 theorems, 46 equations, 5 figures, 3 algorithms)

This paper contains 23 sections, 3 theorems, 46 equations, 5 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Our Contributions
  4. Organization and Notations
  5. One-Bit ML MIMO Detection
  6. Signal Model
  7. ML Detection
  8. An Efficient Global Algorithm
  9. Complexity Analysis
  10. An Efficient Global Algorithm
  11. An MILP Reformulation
  12. A Delayed Constraint Generation Framework
  13. An Efficient Branch-and-Bound Algorithm
  14. Subproblems and Their LP Relaxations
  15. Proposed Algorithm
  16. ...and 8 more sections

Key Result

Theorem 1

The one-bit ML MIMO detection problem eq:ML is NP-hard.

Figures (5)

  • Figure 1: The ratio between the total number of $i$ with ${\bm b}_i^{\top} {\bm x}<0$ and $M$.
  • Figure 2: BER performance of all compared approaches under different problem sizes.
  • Figure 3: Runtime performance of all compared approaches with varying problem sizes.
  • Figure 4: The ratio $|\mathcal{S}|/|\mathcal{C}|$ when gML converges.
  • Figure 5: Runtime performance of all compared algorithms with varying SNRs.

Theorems & Definitions (3)

  • Theorem 1
  • Lemma 1
  • Theorem 2