Chirp Rate Design for AFDM Systems in Time-Scaled Wideband Doubly-Dispersive Channels

The recently proposed affine frequency division multiplexing (AFDM) modulation has been considered as a promising technology for narrowband doubly-dispersive channels. However, the time-scaling effects, i.e., pulse widening and pulse shortening phenomena, in extreme wideband doubly-dispersive channels have not been considered in the literature. In this paper, we investigate such wideband transmission and develop an efficient transmission structure with chirp-periodic prefix (CPP) and chirp-periodic suffix (CPS) for AFDM systems. We derive the input-output relationship of AFDM systems under time-scaled wideband doubly-dispersive channels and demonstrate the sparsity in discrete affine Fourier (DAF) domain equivalent channels. We further optimize the AFDM chirp rate to accommodate the time-scaling characteristics in wideband doubly-dispersive channels and verify the performance of the derived chirp rate by pairwise error probability (PEP) analysis. Simulation results demonstrate the superiority of AFDM systems with our optimized chirp rate over the existing competitive modulation schemes in time-scaled wideband doubly-dispersive channels. Index Terms-AFDM, wideband doubly-dispersive channels, time-scaling effects, pairwise error probability.