Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantification of Errors of the Performance Estimators in the Linear-Quantized Precoding Models for Massive MIMO Systems

Jie Zhang, Huifu Xu

TL;DR

The paper addresses quantized linear-precoding in massive MIMO with low-resolution DACs and quantifies how finite-dimensional SINR and SEP deviate from asymptotic predictions. It introduces three models—original, statistically equivalent, and asymptotic—and derives stability bounds linking finite-system performance to asymptotic limits using Ky Fan distance and random matrix theory. The work yields explicit convergence guarantees for received signals and for the SINR/SEP metrics, and provides a framework for relating finite-dimensional optimization to its asymptotic counterpart. These results offer practical design guidance for robust precoding under hardware constraints in large-scale MIMO deployments.

Abstract

Massive MIMO (Multiple-Input Multiple-Output) is a key enabler for 5G and future wireless systems, boosting channel capacity, energy efficiency, and spectral efficiency. However, high power consumption and hardware costs of Digital-to-Analog Converters (DACs) in massive MIMO create practical challenges. To mitigate these, recent work proposes low-resolution DACs-restricting transmitted signals to finite voltage levels-to cut power and costs. This requires studying quantized precoding: signals are processed via a linear precoding matrix, then quantized by DACs. In this paper, we explore the linear-quantized precoding model and its statistically or asymptotically equivalent variants. We derive error bounds for two key metrics:Signal-to-Interference-plus-Noise Ratio (SINR) and Symbol Error Probability (SEP), based on the linear-quantized model and its equivalent counterparts. We also formulate and analyze the SINR maximization problem in both asymptotic and finite-dimensional scenarios. Our analysis shows that as system dimensions scale, finite-dimensional problem solutions/values converge to their asymptotic equivalents-underscoring the practical value of asymptotic insights with stability guarantees. These findings theoretically support robust precoding design under hardware constraints, enabling efficient massive MIMO implementation with low-resolution DACs. Beyond validating asymptotic predictions in finite regimes, our framework offers practical optimization guidelines for real-world systems, linking theory and applications.

Quantification of Errors of the Performance Estimators in the Linear-Quantized Precoding Models for Massive MIMO Systems

TL;DR

The paper addresses quantized linear-precoding in massive MIMO with low-resolution DACs and quantifies how finite-dimensional SINR and SEP deviate from asymptotic predictions. It introduces three models—original, statistically equivalent, and asymptotic—and derives stability bounds linking finite-system performance to asymptotic limits using Ky Fan distance and random matrix theory. The work yields explicit convergence guarantees for received signals and for the SINR/SEP metrics, and provides a framework for relating finite-dimensional optimization to its asymptotic counterpart. These results offer practical design guidance for robust precoding under hardware constraints in large-scale MIMO deployments.

Abstract

Massive MIMO (Multiple-Input Multiple-Output) is a key enabler for 5G and future wireless systems, boosting channel capacity, energy efficiency, and spectral efficiency. However, high power consumption and hardware costs of Digital-to-Analog Converters (DACs) in massive MIMO create practical challenges. To mitigate these, recent work proposes low-resolution DACs-restricting transmitted signals to finite voltage levels-to cut power and costs. This requires studying quantized precoding: signals are processed via a linear precoding matrix, then quantized by DACs. In this paper, we explore the linear-quantized precoding model and its statistically or asymptotically equivalent variants. We derive error bounds for two key metrics:Signal-to-Interference-plus-Noise Ratio (SINR) and Symbol Error Probability (SEP), based on the linear-quantized model and its equivalent counterparts. We also formulate and analyze the SINR maximization problem in both asymptotic and finite-dimensional scenarios. Our analysis shows that as system dimensions scale, finite-dimensional problem solutions/values converge to their asymptotic equivalents-underscoring the practical value of asymptotic insights with stability guarantees. These findings theoretically support robust precoding design under hardware constraints, enabling efficient massive MIMO implementation with low-resolution DACs. Beyond validating asymptotic predictions in finite regimes, our framework offers practical optimization guidelines for real-world systems, linking theory and applications.

Paper Structure

This paper contains 22 sections, 45 theorems, 477 equations.

Table of Contents

  1. Introduction
  2. System operation models and performance metrics
  3. The original system operation model
  4. A statistically equivalent model
  5. An asymptotic version of the model
  6. SINR and SEP
  7. Quantifying the effect of model change on SEP and SINR
  8. Quantifying the asymptotic error of SEP
  9. Quantification of the impact on SINR
  10. Concluding remarks
  11. Appendix
  12. Preliminaries of set convergence
  13. Lipschitz continuity of the cdf of a Gaussian distribution
  14. Some basic inequalities in deviation
  15. Bernstein's inequality
  16. ...and 7 more sections

Key Result

Proposition 2.1

When $N \geq 3$ and $K \geq 3$, the distribution of $(\mathbf{y}, \mathbf{s})$ in the original model (eq:y-precoding-eta-q) is the same as that of $(\hat{\mathbf{y}}, \mathbf{s})$ specified by eq:haty-stat-equiv-model.

Theorems & Definitions (92)

  • Proposition 2.1
  • Proposition 2.2
  • Definition 2.1
  • Proposition 2.3
  • Lemma 3.1
  • proof
  • Remark 3.1
  • Theorem 3.1: Discrepancy between $\widehat{\text{SEP}}_k(\beta)$ and $\overline{\text{SEP}}(\beta)$
  • proof
  • Theorem 3.2: Discrepancy between $\widehat{\text{SINR}}_k$ and $\overline{\text{SINR}}$
  • ...and 82 more