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

TL;DR

This work targets robust, high-rate communications in time-frequency doubly dispersive channels typical of 6G scenarios. It introduces AFDM-PIM, a pre-chirp-domain index-modulated AFDM scheme that assigns subcarrier-specific pre-chirp values to encode extra bits without energy cost, while preserving subcarrier orthogonality and enabling full diversity under appropriate conditions. The authors derive an input–output model in the DAFT domain, develop PEP-based BER upper bounds, quantify diversity through a rank-based criterion, and analyze spectral efficiency gains against classical AFDM and OFDM-IM baselines. A PSO-based method designs the pre-chirp alphabet to maximize Euclidean distance and improve BER, with simulations showing notable BER and SE improvements over benchmarks in doubly dispersive channels.

Abstract

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.

Figures (8)

• Figure 1: The block diagram of AFDM system.
• Figure 2: Transceiver structure of the proposed AFDM-PIM scheme.
• Figure 3: Example of the effective channel matrix of a three-path channel.
• Figure 4: BER Performance comparison between the $c_2$ alphabet designed by Algorithm \ref{['Alg1']} and the initial $c_2$ solution, given two different numbers of paths.
• Figure 5: Performance comparison between the proposed AFDM-PIM scheme and the OFDM-IM scheme given two different spectral efficiencies.

Theorems & Definitions (6)

• Theorem 1
• proof
• Theorem 2: MGF
• Theorem 3
• proof
• proof