Reconfigurable intelligent surface-assisted AFDM for high-mobility communications

To overcome the large Doppler shift in high-mobility communications, affine frequency division multiplexing (AFDM) has recently emerged as a promising alternative to orthogonal frequency division multiplexing (OFDM). By employing the discrete affine Fourier transform, AFDM effectively mitigates time–frequency doubly selective fading and outperforms OFDM in high-Doppler scenarios. Meanwhile, reconfigurable intelligent surfaces (RIS) have also gained attention as a transformative technology for enhancing communication performance under mobility. To further improve the bit error rate (BER) performance, we propose an RIS-assisted AFDM system tailored for high-mobility settings. We first derive the input–output relations of the system in both the time and discrete affine Fourier domains. Next, the system is extended to a multiple-input multiple-output model. Then, we present an RIS phase-shift design method to maximize the signal-to-noise ratio at the receiver. Finally, we evaluate the influence of critical system parameters such as the number of RIS units, phase optimization methods, channel conditions, and antenna configurations on the system's performance in doubly dispersive channels. Simulation results demonstrate that the proposed optimization method yields a substantial improvement in BER performance over random phase optimization. Furthermore, the proposed RIS-assisted AFDM system achieves significantly lower BER compared to both RIS-OFDM and conventional AFDM systems in doubly dispersive channels.