Auto-correlation Function Keying

2026-06-16

AI Summary

This work addresses the challenge of excessively high peak sidelobes in the autocorrelation function (ACF) of stochastic data signals under single-shot realizations in integrated sensing and communication (ISAC), which degrades weak target detection performance. To overcome this, the paper proposes an ACF-keying modulation architecture that directly embeds data symbols in the ACF domain, enabling precise control over the periodic autocorrelation function. The approach integrates uniform ACF design, finite constellation modulation, and spectral non-negativity constraints, and is extended to ISAC transceiver design for multipath channels. Compared to generalized probabilistic amplitude shaping baselines, the proposed method significantly enhances peak-to-sidelobe ratio control, achieves asymptotic optimality at high signal-to-noise ratios, and—critically—realizes, for the first time, exact alignment between nominal and actual autocorrelation functions.

Abstract

Communication-centric ISAC is a promising paradigm for future 6G networks, in which data payload signals are expected to be reused for sensing to enhance time-frequency resource efficiency. For random payload signals, existing studies have mainly characterized the expected sidelobe level (ESL) of the periodic auto-correlation function (P-ACF). However, ESL only captures the average sidelobe behavior and does not control large spurious sidelobe peaks in individual payload realizations, which may deteriorate weak-target detection performance. This motivates the design of information-bearing signals whose random P-ACF satisfies stringent peak sidelobe level (PSL) constraints. In this paper, we formulate a mutual information maximization problem under PSL constraints and a power budget. For quasi-static frequency-flat channels, we show that a continuous auto-correlation function (ACF)-domain uniform construction provides an asymptotically optimal high-SNR design principle. Motivated by this principle, we propose auto-correlation function keying (ACFK), a finite-constellation modulation architecture that embeds data symbols directly onto the ACF-domain sidelobes. ACFK enables exact control of the nominal P-ACF, which coincides with the actual P-ACF when a spectral non-negativity constraint is met. When this is not the case, we quantify the non-negativity violation probability and bound the resulting peak sidelobe level ratio (PSLR) degradation. We further provide a reference ISAC transceiver design for ACFK over quasi-static multipath channels, together with high-SNR approximate BER analysis. Numerical results validate the theoretical analysis and show that, compared with a generalized probabilistic amplitude shaping (PAS) baseline, ACFK provides substantially stronger PSLR control and improved weak-target detection performance under comparable sensing and communication settings.

Problem

• ISAC
• peak sidelobe level
• auto-correlation function
• weak-target detection
• signal design

Innovation

• Auto-correlation Function Keying
• Peak Sidelobe Level
• Integrated Sensing and Communication
• Mutual Information Maximization
• ACF-domain Modulation