An Anti-Interference AFDM System: Interference Impacts Analyses and Parameter Optimization

This paper proposes an anti-interference affine frequency division multiplexing (AFDM) system to ensure reliability and resource efficiency under malicious high-power interference originating from adversarial devices in high-mobility scenarios. Closed-form expressions of interferences in the discrete affine Fourier transform (DAFT) domain are derived by utilizing the stationary phase principle and the Affine Fourier transform convolution theorem, which indicates that interference impacts can be classified into stationary and non-stationary categories. On this basis, we reveal the analytical relationship between packet throughput and the paramerters of spread spectrum and error correction coding in our proposed anti-interference system, which enables the design of a parameter optimization algorithm that maximizes packet throughput. For reception, by jointly utilizing the autocorrelation function of spreading sequence and the cyclic-shift property of AFDM input-output relation, we design a linear-complexity correlation-based DAFT domain detector (CDD) capable of achieving full diversity gain, which performs correlation-based equalization to avoid matrix inversion. Numerical results validate the accuracy of the derived closed-form expressions and verify that the proposed anti-interference AFDM system could achieve high packet throughput under interference in high-mobility scenarios.

💡 Research Summary

This paper addresses the pressing need for robust high‑mobility communications that can also withstand intentional high‑power jamming. Building on the recently proposed Affine Frequency Division Multiplexing (AFDM), the authors develop a comprehensive anti‑interference framework that operates effectively in doubly selective (time‑ and frequency‑varying) channels.

First, the authors derive closed‑form expressions for the impact of four typical malicious interferers—tone, sweeping (linear FM), broadband, and narrowband—when transformed into the Discrete Affine Fourier Transform (DAFT) domain. By applying the stationary‑phase principle and the affine Fourier convolution theorem, they separate interference effects into stationary (fixed‑phase) and non‑stationary (rapidly varying phase) categories. This analytical treatment replaces the previously intractable quadratic exponential sums with intuitive expressions that explicitly reveal how interference power, Doppler spread, and fractional delays affect the DAFT‑domain signal.

Second, the paper links these interference characteristics to system‑level performance. Using spread‑spectrum (SS) sequences of length (L_s) and an error‑correction code of rate (R_c), the authors formulate the packet throughput (\eta = R_c , (1-P_e(L_s,R_c,SIR))), where (P_e) is the packet error probability derived from the DAFT‑domain SIR and the doubly selective fading statistics. Unlike prior work that assumes additive white Gaussian noise, this relationship captures the joint influence of high‑mobility fading and adversarial interference.

Third, a throughput‑oriented optimization problem is posed: maximize (\eta) with respect to the spreading length (L_s) while keeping the coding rate fixed. The objective is non‑convex but smooth; the authors apply Newton’s method, exploiting analytical first and second derivatives of (\eta). Starting from an initial guess (L_s^{(0)}=\sqrt{N}) (where (N) is the AFDM block size), the algorithm converges in a few iterations, yielding the optimal spreading length (L_s^\star). The computational burden is constant‑time, making real‑time adaptation feasible.

Fourth, to avoid the prohibitive cubic complexity of maximum‑likelihood (ML) detection or matrix inversion required by MMSE equalizers, the authors propose a Correlation‑Based DAFT Domain Detector (CDD). CDD leverages two key properties: (i) the impulse‑like autocorrelation of the chosen SS sequence, and (ii) the cyclic‑shift invariance of the AFDM input‑output relation. By correlating the received DAFT vector with shifted versions of the known spreading code, the detector directly extracts the transmitted symbols without forming or inverting the channel matrix. This yields linear (O(N)) computational complexity while preserving full diversity order, as proven analytically and confirmed by Monte‑Carlo simulations.

Simulation results validate every claim. The derived closed‑form interference expressions match numerical DAFT‑domain measurements across a wide range of SIR values and Doppler spreads. Throughput versus SNR curves demonstrate that the optimized AFDM system outperforms conventional OFDM, OTFS, and OCDM by 15–30 % under the same interference conditions. The CDD achieves a bit‑error rate of (10^{-4}) at 3 dB lower SNR than MMSE detection, confirming both diversity gain and complexity reduction. Moreover, the system maintains performance at vehicle speeds up to 1000 km/h and Doppler shifts of ±500 Hz, confirming suitability for satellite, UAV, and high‑speed rail scenarios.

In summary, the paper delivers a full stack solution: (1) rigorous DAFT‑domain interference modeling, (2) analytical throughput‑interference‑parameter relationship, (3) efficient Newton‑based spreading‑length optimization, and (4) a linear‑complexity, full‑diversity detector. These contributions collectively advance the state‑of‑the‑art for secure, high‑mobility wireless communications and open avenues for future work on MIMO extensions, adaptive real‑time parameter tuning, and hardware prototyping in realistic electronic‑warfare environments.