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Improved GPR-Based CSI Acquisition via Spatial-Correlation Kernel

Syed Luqman Shah, Nurul Huda Mahmood, Italo Atzeni

TL;DR

This work tackles the problem of accurate CSI acquisition under reduced pilot overhead in MIMO systems. It introduces a Spatial-correlation (SC) kernel for Gaussian process regression that encodes the channel's second-order statistics, yielding a closed-form, MMSE-optimal posterior mean without assuming Gaussian channel distributions and without hyperparameter learning. Numerical results show that SC-GPR achieves lower NMSE and better spectral efficiency than learning-based GPR and LS/MMSE across separable and non-separable covariance models, even with up to 75% pilot reduction, while maintaining calibrated uncertainty and reduced computational burden. The approach thus offers a physics-/geometry-aware, uncertainty-aware, and scalable solution for efficient CSI estimation in next-generation wireless systems.

Abstract

Accurate channel estimation with low pilot overhead and computational complexity is key to efficiently utilizing multi-antenna wireless systems. Motivated by the evolution from purely statistical descriptions toward physics- and geometry-aware propagation models, this work focuses on incorporating channel information into a Gaussian process regression (GPR) framework for improving the channel estimation accuracy. In this work, we propose a GPR-based channel estimation framework along with a novel Spatial-correlation (SC) kernel that explicitly captures the channel's second-order statistics. We derive a closed-form expression of the proposed SC-based GPR estimator and prove that its posterior mean is optimal in terms of minimum mean-square error (MMSE) under the same second-order statistics, without requiring the underlying channel distribution to be Gaussian. Our analysis reveals that, with up to 50% pilot overhead reduction, the proposed method achieves the lowest normalized mean-square error, the highest empirical 95% credible-interval coverage, and superior preservation of spectral efficiency compared to benchmark estimators, while maintaining lower computational complexity than the conventional MMSE estimator.

Improved GPR-Based CSI Acquisition via Spatial-Correlation Kernel

TL;DR

This work tackles the problem of accurate CSI acquisition under reduced pilot overhead in MIMO systems. It introduces a Spatial-correlation (SC) kernel for Gaussian process regression that encodes the channel's second-order statistics, yielding a closed-form, MMSE-optimal posterior mean without assuming Gaussian channel distributions and without hyperparameter learning. Numerical results show that SC-GPR achieves lower NMSE and better spectral efficiency than learning-based GPR and LS/MMSE across separable and non-separable covariance models, even with up to 75% pilot reduction, while maintaining calibrated uncertainty and reduced computational burden. The approach thus offers a physics-/geometry-aware, uncertainty-aware, and scalable solution for efficient CSI estimation in next-generation wireless systems.

Abstract

Accurate channel estimation with low pilot overhead and computational complexity is key to efficiently utilizing multi-antenna wireless systems. Motivated by the evolution from purely statistical descriptions toward physics- and geometry-aware propagation models, this work focuses on incorporating channel information into a Gaussian process regression (GPR) framework for improving the channel estimation accuracy. In this work, we propose a GPR-based channel estimation framework along with a novel Spatial-correlation (SC) kernel that explicitly captures the channel's second-order statistics. We derive a closed-form expression of the proposed SC-based GPR estimator and prove that its posterior mean is optimal in terms of minimum mean-square error (MMSE) under the same second-order statistics, without requiring the underlying channel distribution to be Gaussian. Our analysis reveals that, with up to 50% pilot overhead reduction, the proposed method achieves the lowest normalized mean-square error, the highest empirical 95% credible-interval coverage, and superior preservation of spectral efficiency compared to benchmark estimators, while maintaining lower computational complexity than the conventional MMSE estimator.
Paper Structure (9 sections, 2 theorems, 4 equations, 3 figures, 4 tables)

This paper contains 9 sections, 2 theorems, 4 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. The Proposed GPR With the SC Kernel
  4. Numerical Evaluation
  5. Prediction Error and Posterior $95\%$ Credible Ellipses
  6. Uncertainty Calibration ($95\%$ coverage)
  7. Spectral Efficiency
  8. Discussion
  9. Conclusions

Key Result

Proposition 1

Let $\mathbf{R}_{\textnormal{H}}$ be Hermitian PSD. For any finite set $\{\mathbf{z}_m\}_{m=1}^M\subset\mathcal{G}$, the Gram matrix with entries $[k_{\textrm{SC}}(\mathbf{z}_m,\mathbf{z}_{m'})]_{m,m'}$ is Hermitian PSD.

Figures (3)

  • Figure 1: Each scatter plot shows $\mathrm{Re}(\epsilon_{ij})$ versus $\mathrm{Im}(\epsilon_{ij})$ per complex channel entry with the empirical posterior $95\%$ credible ellipse; smaller, more isotropic ellipses indicate lower error variance and weaker residual correlation.
  • Figure 2: SE versus SNR comparing the proposed SC-GPR with reduced overheads against ground-truth and LS/MMSE baselines.
  • Figure 3: SE versus SNR comparing SC-GPR with distance-based kernels under $50\%$ pilot savings and LS/MMSE under full pilots.

Theorems & Definitions (2)

  • Proposition 1: Positive semidefiniteness of $k_{\textrm{SC}}$
  • Proposition 2: Posterior mean equals MMSE