Affine Frequency Division Multiplexing with Index Modulation: Full Diversity Condition, Performance Analysis, and Low-Complexity Detection

Abstract: Affine frequency division multiplexing (AFDM) is a novel modulation technique based on chirp signals that has been recently proposed as an effective solution for highly reliable communications in high-mobility scenarios. In this paper, we focus on the design of robust index modulation (IM) schemes under the multiple-antenna AFDM transmission framework. To this end, the cyclic delay diversity (CDD) technique is employed to harvest the transmit diversity gain. As a result, we propose two novel AFDM-IM schemes with transmit diversity, termed as CDD-AFDM-IM-I and CDD-AFDM-IM-II. We analyze the full diversity conditions and parameter settings of the proposed CDD-AFDM-IM schemes for both integer and fractional Doppler cases over linear time-varying (LTV) channels. Moreover, we prove that IM enables AFDM to have stronger diversity protection when the full diversity condition is not satisfied. Asymptotically tight upper bounds on the average bit error rates (BERs) of the proposed schemes with maximum-likelihood (ML) detection are derived in closed-form. Furthermore, we propose a low-complexity double-layer message passing (DLMP) algorithm for practical large-dimensional signal detection in the proposed CDD-AFDM-IM systems. Comparison with existing detections shows that the proposed DLMP algorithm achieves a better tradeoff between the BER performance and the computational complexity. Finally, BER simulation results confirm that our proposed CDD-AFDM-IM schemes with both the ML and DLMP detections outperform the benchmark schemes over the LTV channels.