Sparse Bayesian Learning based AFDM Channel Estimation Exploiting Hierarchical Laplace Priors

As an emerging waveform suitable for high-speed communication scenarios, the Affine Frequency Division Multiplexing (AFDM) exhibits inherent sparsity of its affine frequency domain channel matrix. Exploiting such sparsity, we investigate the channel estimation in AFDM communication systems with Sparse Bayesian Learning (SBL). The channel estimation problem is first reformulated as a joint sparsifying dictionary learning and sparse signal recovery task. We then introduce an SBL framework by modeling the sparse signal prior using a hierarchical Laplace distribution, with the Expectation-Maximization (EM) algorithm employed to iteratively update the model parameters. Numerical results highlight the superiority of the proposed algorithm compared to conventional orthogonal matching pursuit (OMP) methods in terms of estimation error, and enhanced tolerance to off-grid effects.