A Novel Geometry-Aware GPR-Based Energy-Efficient and Low-Overhead Channel Estimation Scheme

Accurate channel state information (CSI) acquisition under tight pilot and training-energy budgets is crucial for next-generation wireless networks. We reduce pilot overhead and training energy by activating only a subset of transmit antennas during training. This yields sparse and noisy observations of the channel coefficients, casting CSI acquisition as a highly underdetermined Bayesian inverse problem. To solve this problem, we model the wireless channel as a proper complex Gaussian process (GP) over the joint transmit–receive antenna-index lattice and develop a GPR framework that reconstructs the full CSI by extrapolating observed pairs to unobserved ones. The GP prior is specified through a novel array-geometry-based spectral-mixture covariance function (GB-SMCF), which is Hermitian positive-semidefinite. Unlike standard distance-based kernels, the proposed GB-SMCF captures both smooth spatial decay and the oscillatory correlations induced by multipath propagation. The hyperparameters of the GB-SMCF are learned online within each coherence block by maximizing the marginal likelihood of the sparse pilot observations, requiring neither offline training nor prior knowledge of the channel covariance. Numerical results show that the proposed estimator reduces pilot overhead by up to 75% and total training energy by up to 93.75%, while achieving lower normalized mean-square error than the considered baselines. It also yields higher spectral efficiency in the low-to-moderate SNR regime. © 2002 IEEE.