On Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems

2024-04-08

AI Summary

Channel estimation in one-bit quantized massive MIMO systems suffers from severe accuracy degradation due to coarse quantization. Method: Breaking the limitations of conventional Bussgang linear approximation, this work establishes the first rigorous minimum mean-square error (MMSE) channel estimation framework grounded in orthant probabilities of multivariate normal distributions. It integrates Bussgang decomposition, statistical channel modeling, and asymptotic analysis to enable efficient MMSE computation. Contribution/Results: Theoretically, we derive necessary and sufficient conditions for the optimality of the Bussgang-linear MMSE (BLMMSE) estimator and obtain a closed-form, analytically tractable MMSE estimator in the high-dimensional regime—revealing the fundamental gap between linear approximation and global optimality. Experiments under typical massive MIMO configurations demonstrate substantial estimation error reduction. Moreover, we explicitly characterize the applicability boundary of BLMMSE and quantify its performance loss as a function of channel correlation structure and pilot design.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Intelligent Robots: State Estimation
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory, the MMSE channel estimator has not been fully investigated in this context due to its general non-linearity and computational complexity. Instead, the typically suboptimal Bussgang linear MMSE (BLMMSE) estimator has been widely adopted. In this work, we develop a new framework to compute the MMSE channel estimator that hinges on computation of the orthant probability of the multivariate normal distribution. Based on this framework, we determine a necessary and sufficient condition for the BLMMSE channel estimator to be optimal and equivalent to the MMSE estimator. Under the assumption of specific channel correlation or pilot symbols, we further utilize the framework to derive analytical expressions for the MMSE channel estimator that are particularly convenient for computation when certain system dimensions become large, thereby enabling a comparison between the BLMMSE and MMSE channel estimators in these cases.

Problem

• One-bit Quantization
• Massive MIMO
• Channel Prediction

Innovation

• MMSE Estimation
• BLMMSE Comparison
• Massive One-bit Quantized MIMO