Pre-Chirp-Domain Index Modulation for Full-Diversity Affine Frequency Division Multiplexing towards 6G

Affine frequency division multiplexing (AFDM), tailored as a superior multicarrier technique utilizing chirp signals for high-mobility communications, is envisioned as a promising candidate for the sixth-generation (6G) wireless network. AFDM is based on the discrete affine Fourier transform (DAFT) with two adjustable parameters of the chirp signals, termed as the pre-chirp and post-chirp parameters, respectively. We show that the pre-chirp counterpart can be flexibly manipulated for additional degree-of-freedom (DoF). Therefore, this paper proposes a novel AFDM scheme with the pre-chirp index modulation (PIM) philosophy (AFDM-PIM), which can implicitly convey extra information bits through dynamic pre-chirp parameter assignment, thus enhancing both spectral and energy efficiency. Specifically, we first demonstrate that the subcarrier orthogonality is still maintained by applying distinct pre-chirp parameters to various subcarriers in the AFDM modulation process. Inspired by this property, each AFDM subcarrier is constituted with a unique pre-chirp signal according to the incoming bits. By such arrangement, extra binary bits can be embedded into the index patterns of pre-chirp parameter assignment without additional energy consumption. For performance analysis, we derive the asymptotically tight upper bounds on the average bit error rates (BERs) of the proposed schemes with maximum-likelihood (ML) detection, and validate that the proposed AFDM-PIM can achieve the optimal diversity order under doubly dispersive channels. Based on the derivations, we further propose an optimal pre-chirp alphabet design to enhance the BER performance via intelligent optimization algorithms. Simulations demonstrate that the proposed AFDM-PIM outperforms the classical benchmarks under doubly dispersive channel.