AFDMA with Heterogeneous Post-Chirp Parameters: Supporting User-Specific Waveform Configurations

Abstract

This paper investigates a downlink affine frequency division multiple access (AFDMA) framework supporting flexible user-specific waveform configurations with heterogeneous post-chirp parameters. The proposed framework is in sharp contrast to conventional disjoint chirp-subcarrier allocation, which may destroy inter-user orthogonality when users employ heterogeneous post-chirp parameters. Such a loss of orthogonality manifests as cross-basis leakage onto user-allocated chirp subcarriers, which we characterize by analyzing the cross-projection between user-specific discrete affine Fourier transform bases. Specifically, we express the cross-projection entries as quadratic Gauss sums whose quadratic coefficients depend on pairwise post-chirp differences. This yields a sufficient pairwise residue-class orthogonality rule that preserves inter-user orthogonality by satisfying the leakage-free condition. The resulting chirp-subcarrier allocation problem with pairwise modular constraints is reduced to the residue-class level. To solve this problem, we develop a two-stage framework that recursively searches for a feasible representative allocation and deterministically assigns the remaining residue classes. We prove that the problem is either infeasible or admits an optimal full-loading solution. Simulations show that the proposed allocation avoids the bit error rate (BER) floors and signal-to-interference-plus-noise ratio (SINR) ceiling of conventional localized allocation, achieves near-single-user BER, and provides comparable BER while reducing receiver complexity compared with conventional common-maximum-post-chirp AFDMA.