A Novel Symbol Level Precoding based AFDM Transmission Framework: Offloading Equalization Burden to Transmitter Side

Abstract

Affine Frequency Division Multiplexing (AFDM) has attracted considerable attention for its robustness to Doppler effects. However, its high receiver-side computational complexity remains a major barrier to practical deployment. To address this, we propose a novel symbol-level precoding (SLP)-based AFDM transmission framework, which shifts the signal processing burden in downlink communications from user side to the base station (BS), enabling direct symbol detection without requiring channel estimation or equalization at the receiver. Specifically, in the uplink phase, we propose a Sparse Bayesian Learning (SBL) based channel estimation algorithm by exploiting the inherent sparsity of affine frequency (AF) domain channels. In particular, the sparse prior is modeled via a hierarchical Laplace distribution, and parameters are iteratively updated using the Expectation-Maximization (EM) algorithm. We also derive the Bayesian Cramer-Rao Bound (BCRB) to characterize the theoretical performance limit. In the downlink phase, the BS employs the SLP technology to design the transmitted waveform based on the estimated uplink channel state information (CSI) and channel reciprocity. The resulting optimization problem is formulated as a second-order cone programming (SOCP) problem, and its dual problem is investigated by Lagrangian function and Karush-Kuhn-Tucker conditions. Simulation results demonstrate that the proposed SBL estimator outperforms traditional orthogonal matching pursuit (OMP) in accuracy and robustness to off-grid effects, while the SLP-based waveform design scheme achieves performance comparable to conventional AFDM receivers while significantly reducing the computational complexity at receiver, validating the practicality of our approach.