Non-Orthogonal Affine Frequency Division Multiplexing for Spectrally Efficient High-Mobility Communications

TL;DR

Simulation results demonstrate that the proposed nAFDM can achieve near identical BER compared to conventional AFDM, while outperforms other waveform counterparts and the proposed soft iterative detection (ID) scheme can attain a trade-off between BER and complexity.

Abstract

This paper proposes a novel non-orthogonal affine frequency division multiplexing (nAFDM) waveform for reliable high-mobility communications with enhanced spectral efficiency (SE). The key idea is to introduce a bandwidth compression factor into the AFDM modulator to enable controllable subcarrier overlapping. We first detail the proposed nAFDM transceiver and derive the corresponding input-output signal relationship. Then, an efficient nAFDM signal generation method based on the inverse discrete Fourier transform (IDFT) is proposed, enabling practical implementation using existing inverse fast Fourier transform (IFFT) modules without additional hardware complexity. Next, to characterize the impact of non-orthogonal modulation, we derive a closed-form expression of inter-carrier interference (ICI), showing its dependence on the bandwidth compression factor. To mitigate the resulting interference, we propose a soft iterative detection algorithm and a low-complexity implementation approach that leverages the distribution characteristics of ICI. Simulation results demonstrate that 1) in terms of bit error rate (BER), the proposed nAFDM can achieve near identical BER compared to conventional AFDM, while outperforms other waveform counterparts; 2) nAFDM is capable of striking higher SE compared to other existing waveforms; and 3) the proposed nAFDM achieves an attractive BER vs. SE trade-off, and the proposed soft iterative detection (ID) scheme can attain a trade-off between BER and complexity.

Figures (17)

• Figure 1: System block diagram of the proposed nAFDM waveform.
• Figure 2: Structure of the effective channel matrix $\mathbf{H}_i$ under different Doppler shifts and compression factors: (a) AFDM with $\nu_i=1$; (b) AFDM with $\nu_i=0.4$; (c) nAFDM ($\alpha=0.9$) with $\nu_i=1$; (d) nAFDM ($\alpha=0.9$) with $\nu_i=0.4$; (e) nAFDM ($\alpha=0.8$) with $\nu_i=1$; (f) nAFDM ($\alpha=0.8$) with $\nu_i=0.4$. The system parameters are set to $N=16$, $l_i=1$, and $c_1=c_2=\frac{3}{2N}$.
• Figure 3: Modulation and demodulation processes of the proposed nAFDM scheme using IDFT and DFT operations: (a) Modulation; (b) Demodulation.
• Figure 4: Correlation amplitude $\left|C_ \alpha(m_1, m_2)\right|$ for nAFDM under different compression factors ($N = 16$).
• Figure 5: Structure of the correlation matrix $\mathbf{C}_\alpha$ for nAFDM under different compression factors ($N = 16$).