[Paper Review] Channel Estimation for Spatially/Temporally Correlated Massive MIMO Systems with One-Bit ADCs

Hwanjin Kim, Junil Choi|arXiv (Cornell University)|Oct 29, 2019

Advanced MIMO Systems Optimization35 references30 citations

TL;DR

This paper proposes a Kalman filter-based channel estimation technique for massive MIMO systems with one-bit ADCs that exploits both spatial and temporal channel correlations. By applying Bussgang decomposition to linearize one-bit quantization and modeling quantization noise as Gaussian, the method enables successive estimation with significantly improved accuracy over single-shot approaches, validated by numerical results showing reduced NMSE with increasing time slots and negligible performance loss using a low-complexity truncated polynomial expansion approximation.

ABSTRACT

This paper considers the channel estimation problem for massive multiple-input multiple-output (MIMO) systems that use one-bit analog-to-digital converters (ADCs). Previous channel estimation techniques for massive MIMO using one-bit ADCs are all based on single-shot estimation without exploiting the inherent temporal correlation in wireless channels. In this paper, we propose an adaptive channel estimation technique taking the spatial and temporal correlations into account for massive MIMO with one-bit ADCs. We first use the Bussgang decomposition to linearize the one-bit quantized received signals. Then, we adopt the Kalman filter to estimate the spatially and temporally correlated channels. Since the quantization noise is not Gaussian, we assume the effective noise as a Gaussian noise with the same statistics to apply the Kalman filtering. We also implement the truncated polynomial expansion-based low complexity channel estimator with negligible performance loss. Numerical results reveal that the proposed channel estimators can improve the estimation accuracy significantly by using the spatial and temporal correlations of channels.

Motivation & Objective

• Address the lack of temporal correlation exploitation in prior one-bit ADC channel estimation for massive MIMO.
• Develop a successive channel estimation framework that jointly leverages spatial and temporal correlations.
• Reduce computational complexity of Kalman filtering in large-scale systems using truncated polynomial expansion (TPE).
• Improve estimation accuracy beyond single-shot methods by incorporating channel dynamics over time.

Proposed method

• Apply Bussgang decomposition to linearize the non-linear one-bit quantization model, transforming it into a linear model with colored noise.
• Model the effective quantization noise as Gaussian with identical mean and covariance to enable Kalman filtering.
• Implement a Kalman filter-based estimator (KFB) that recursively updates channel state estimates using temporal correlation.
• Introduce a truncated polynomial expansion (TPE) approximation to reduce the complexity of matrix inversion in the Kalman gain computation.
• Use pilot sequences and spatial correlation matrix estimation to initialize the state and covariance matrices.
• Analyze the performance of the TPE-based estimator and derive its minimum NMSE using first-order approximation.

Experimental results

Research questions

• RQ1 Can exploiting temporal correlation in one-bit ADC massive MIMO systems improve channel estimation accuracy beyond single-shot methods?
• RQ2 How does the Kalman filter-based estimator perform under spatially and temporally correlated channels with one-bit quantization?
• RQ3 To what extent can the truncated polynomial expansion (TPE) approximation reduce computational complexity with minimal performance loss?
• RQ4 How does the estimation accuracy evolve over successive time slots when both spatial and temporal correlations are leveraged?
• RQ5 What is the impact of SNR and temporal correlation on the performance of the proposed estimators?

Key findings

• The proposed Kalman filter-based (KFB) estimator achieves significantly lower normalized mean square error (NMSE) than single-shot estimators by exploiting temporal correlation.
• NMSE of the KFB estimator decreases with increasing time slots, demonstrating improved tracking performance over time.
• In high temporal correlation and low SNR regimes, the TPE-based estimator achieves nearly identical performance to the KFB estimator even with low approximation order (L=1).
• With low temporal correlation and high SNR, the TPE-based estimator maintains close performance to KFB when using L=2, showing robustness across diverse conditions.
• The KFB estimator exhibits a saturation effect at high SNR due to one-bit quantization noise, which limits further NMSE improvement.
• Theoretical analysis confirms that the NMSE of the TPE-based estimator also decreases with time slots under moderate assumptions, validating its convergence behavior.