Overlap-Summation-Based Pulse Shaping Transceiver for Affine Frequency Division Multiplexing

Abstract

Affine frequency division multiplexing (AFDM) has recently emerged as a promising waveform for doubly-selective channels. A direct-windowing-based pulse shaping transceiver (PS-AFDM) was proposed to suppress the Doppler sidelobes, thus improving the accuracy of channel estimation. We observe that, when the path delays and Doppler shifts are randomly distributed, the legacy PS-AFDM scheme significantly increases the condition number of the effective channel matrix. The resulting ill-conditioning degrades the numerical stability of channel equalization in noise and consequently increases the BER. To address this issue, this letter applies the existing weighted overlap-summation (WOLA) transceiver to AFDM and proposes a novel channel-aware (CA) receive shaping window design, which simultaneously achieves accurate channel estimation and robust equalization performance, at the cost of additional prefix overhead and receive-window calculation. The resulting scheme is termed CAWOLA-AFDM. Compared with the legacy WOLA scheme, which employs a fixed receive window, the proposed CAWOLA design exploits the channel estimates of slowly varying power gains and Doppler shifts to design a channel-tailored receive shaping window in closed form, thereby further enhancing channel-estimation accuracy while maintaining the channel condition number when a Nyquist prototype window is adopted. The proposed CAWOLA receive-window design aims to produce an effective AFDM channel with more compact support in the DAFT domain. The source code for the simulations is provided at https://github.com/SANIS-HITSZ/Waveform_AFDM.

arXiv commentAccepted for publication in SCIENCE CHINA Information Sciences (Sci. China. Inf. Sci.), 2026, DOI: 10.1360/s11432-026-5192-6. The appendices A to C mentioned in the latest arXiv version can be viewed in the SUPPLEMENTARY FILE after its official publication in SCIS journal, or in the previous arXiv versions