Improved GPR-Based CSI Acquisition via Spatial-Correlation Kernel

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.