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As a superior multicarrier technique utilizing chirp signals for high-mobility communications, affine frequency division multiplexing (AFDM) is envisioned to be a promising candidate for sixth-generation (6G) wireless networks. AFDM is based on the discrete affine Fourier transform (DAFT) with two adjustable parameters of the chirp signals, termed the pre-chirp and post-chirp parameters, respectively. Whilst the post-chirp parameter complies with stringent constraints to combat the time-frequency doubly selective channel fading, we show that the pre-chirp counterpart can be flexibly manipulated for an additional degree of freedom. 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, we allow each AFDM subcarrier to carry a unique pre-chirp signal according to the incoming bits. By such an arrangement, extra bits can be embedded into the index patterns of pre-chirp parameter assignment without additional energy consumption. We derive asymptotically tight upper bounds on the average bit error probability (BEP) of the proposed schemes with the maximum-likelihood detection, and validate that the proposed AFDM-PIM can achieve full diversity under doubly dispersive channels. Based on the derived result, we further propose an optimal pre-chirp alphabet design to enhance the bit error rate (BER) performance via intelligent optimization algorithms. Simulation results demonstrate that the proposed AFDM-PIM outperforms the classical benchmarks.
Liu et al. (Wed,) studied this question.