Pre-Chirp-Domain Index Modulation for Affine Frequency Division Multiplexing

TL;DR

The paper addresses the challenge of reliable high-mobility communications by introducing AFDM-PIM, a pre-chirp index-modulated enhancement to the DAFT-based AFDM framework. By assigning distinct pre-chirp parameters across AFDM subcarriers and encoding index bits into the pre-chirp realizations, AFDM-PIM achieves additional spectral and energy efficiency without extra transmit power. A key theoretical result is that varying the pre-chirp parameter across subcarriers preserves orthogonality, enabling the proposed index modulation scheme, while practical receivers employing ML or ML-MMSE detectors recover both data symbols and chirp-indices. Simulations show substantial BER improvements over classical AFDM, OFDM, and IM-aided OFDM in doubly dispersive channels, demonstrating AFDM-PIM’s potential for robust, high-rate communications in 6G-like high-mobility scenarios.

Abstract

Affine frequency division multiplexing (AFDM), tailored as a novel multicarrier technique utilizing chirp signals for high-mobility communications, exhibits marked advantages compared to traditional orthogonal frequency division multiplexing (OFDM). AFDM is based on the discrete affine Fourier transform (DAFT) with two modifiable parameters of the chirp signals, termed as the pre-chirp parameter and post-chirp parameter, respectively. These parameters can be fine-tuned to avoid overlapping channel paths with different delays or Doppler shifts, leading to performance enhancement especially for doubly dispersive channel. In this paper, we propose a novel AFDM structure with the pre-chirp index modulation (PIM) philosophy (AFDM-PIM), which can embed additional information bits into the pre-chirp parameter design for both spectral and energy efficiency enhancement. Specifically, we first demonstrate that the application of distinct pre-chirp parameters to various subcarriers in the AFDM modulation process maintains the orthogonality among these subcarriers. Then, different pre-chirp parameters are flexibly assigned to each AFDM subcarrier according to the incoming bits. By such arrangement, aside from classical phase/amplitude modulation, extra binary bits can be implicitly conveyed by the indices of selected pre-chirping parameters realizations without additional energy consumption. At the receiver, both a maximum likelihood (ML) detector and a reduced-complexity ML-minimum mean square error (ML-MMSE) detector are employed to recover the information bits. It has been shown via simulations that the proposed AFDM-PIM exhibits superior bit error rate (BER) performance compared to classical AFDM, OFDM and IM-aided OFDM algorithms.

Figures (4)

• Figure 1: Transceiver structure of the proposed AFDM-PIM scheme.
• Figure 2: BER performance comparison between the proposed AFDM-PIM and AFDM at 2 bits/s/Hz, where $N$=8, $d_{\max}$ = 4 and $\alpha_{\max}$ = 2.
• Figure 3: BER performance comparison between the proposed AFDM-PIM and OFDM at 2 bits/s/Hz, where $N$=8, $P=3$, $d_{\max}$ = 1 and $\alpha_{\max}$ = 1.
• Figure 4: BER performance comparison between the ML detector and ML-MMSE detector at 1.25 bits/s/Hz, where $N = 8$, $d_{\max} = 2$, $\alpha_{\max} = 2$ and BPSK is employed.