Auto-correlation Function Keying

Abstract

We propose ACFK: Auto-correlation Function Keying, a new integrated sensing and communication (ISAC) waveform that carries random communication data while directly controlling the peak sidelobe level (PSL) of the periodic auto-correlation function (P-ACF). In contrast to existing works aiming at controlling the expected sidelobe level (ESL), which fails to characterize realization-specific sidelobe behaviors, we formulate a mutual information maximization problem under PSL and power constraints, and show that a continuous ACF-domain uniform distribution is asymptotically optimal at high signal-to-noise ratio (SNR) over quasi-static frequency-flat channels. Motivated by this principle, ACFK maps finite-constellation symbols onto auto-correlation function (ACF)-domain sidelobes and uses independent phase symbols to exploit the remaining degrees of freedom. The resulting waveform enables exact control of the nominal P-ACF, which coincides with the actual P-ACF when the power spectral non-negativity condition is satisfied. We further analyze the non-negativity violation probability and bound the corresponding peak sidelobe level ratio (PSLR) degradation. A reference ISAC transceiver and its high-SNR approximate bit error rate (BER) analysis are also provided. Numerical results show that ACFK achieves stronger PSLR control, and improved weak-target detection performance, than a generalized probabilistic amplitude shaping (PAS) baseline at similar data rate and BER.

25 pages, 15 figures, submitted to IEEE Transactions on Information Theory