Low-Overhead CSI Prediction via Gaussian Process Regression -- Part~I: Data-Driven Spatial Interpolation (2510.25390v1)

Abstract: Accurate channel state information (CSI) is critical for current and next-generation multi-antenna systems. Yet conventional pilot-based estimators incur prohibitive overhead as antenna counts grow. In this paper, we address this challenge by developing a novel framework based on Gaussian process regression (GPR) that predicts full CSI from only a few observed entries, thereby reducing pilot overhead. The correlation between data points in GPR is defined by the covariance function, known as kernels. In the proposed GPR-based CSI estimation framework, we incorporate three kernels, i.e., radial basis function, Mat\'ern, and rational quadratic, to model smooth and multi-scale spatial correlations derived from the antenna array geometry. The proposed approach is evaluated across Kronecker and Weichselberger channel models with three distinct pilot probing schemes. Results show that the proposed GPR with 50% pilot saving achieves the lowest prediction error, the highest empirical 95% credible-interval coverage, and the best preservation of mutual information relative to benchmarks. This enables up to 50% pilot reduction while preserving over 92% of the link capacity.