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.

翻译：仿频分复用（AFDM）作为一种利用啁啾信号实现高移动性通信的先进多载波技术，被视作第六代（6G）无线网络的有力候选方案。AFDM基于离散仿傅里叶变换（DAFT），其啁啾信号包含两个可调参数，分别称为预啁啾参数和后啁啾参数。本文论证了预啁啾参数可被灵活调控以提供额外的自由度。为此，本文提出一种基于预啁啾索引调制（PIM）思想的新型AFDM方案（AFDM-PIM），该方案通过动态分配预啁啾参数隐式传输额外信息比特，从而同时提升频谱效率和能量效率。具体而言，我们首先证明在AFDM调制过程中对不同子载波施加不同预啁啾参数仍能保持子载波正交性。基于此特性，每个AFDM子载波可根据输入比特序列配置独特的预啁啾信号。通过这种设计，额外的二进制比特可嵌入预啁啾参数分配的索引模式中，且无需额外能量消耗。在性能分析方面，我们推导了所提方案在最大似然（ML）检测下平均误码率（BER）的渐近紧上界，并验证了AFDM-PIM在双弥散信道中能够达到最优分集阶数。基于推导结果，我们进一步提出通过智能优化算法设计最优预啁啾字母表以提升BER性能。仿真结果表明，所提出的AFDM-PIM在双弥散信道下性能优于经典基准方案。