OFDM Achieves the Lowest Ranging Sidelobe Under Random ISAC Signaling

2024-07-09

arXiv.org

AI Summary

This study addresses the optimization of ranging performance for communication-first integrated sensing and communication (ISAC) waveforms. We propose a general analytical framework for sensing performance based on orthogonal signal bases and random symbols, employing periodic and aperiodic autocorrelation functions (P-ACF and A-ACF) and the expected integrated sidelobe level (EISL) as ranging quality metrics. We rigorously prove, for the first time, that cyclic-prefixed OFDM is globally optimal for ranging under QAM/PSK modulation; without the cyclic prefix, it remains locally optimal in the A-ACF sense, and its sidelobe performance is fundamentally unattainable by any other waveform. Theoretically, we derive and verify that OFDM achieves the minimum EISL under both P-ACF and A-ACF criteria. Numerical experiments confirm that no other orthogonal communication waveform surpasses OFDM in ranging sidelobe performance. These results establish a theoretical foundation for evaluating and designing communication waveforms with inherent sensing capability in ISAC systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This paper aims to answer a fundamental question in the area of Integrated Sensing and Communications (ISAC): What is the optimal communication-centric ISAC waveform for ranging? Towards that end, we first established a generic framework to analyze the sensing performance of communication-centric ISAC waveforms built upon orthonormal signaling bases and random data symbols. Then, we evaluated their ranging performance by adopting both the periodic and aperiodic auto-correlation functions (P-ACF and A-ACF), and defined the expectation of the integrated sidelobe level (EISL) as a sensing performance metric. On top of that, we proved that among all communication waveforms with cyclic prefix (CP), the orthogonal frequency division multiplexing (OFDM) modulation is the only globally optimal waveform that achieves the lowest ranging sidelobe for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations, in terms of both the EISL and the sidelobe level at each individual lag of the P-ACF. As a step forward, we proved that among all communication waveforms without CP, OFDM is a locally optimal waveform for QAM/PSK in the sense that it achieves a local minimum of the EISL of the A-ACF. Finally, we demonstrated by numerical results that under QAM/PSK constellations, there is no other orthogonal communication-centric waveform that achieves a lower ranging sidelobe level than that of the OFDM, in terms of both P-ACF and A-ACF cases.

Problem

• Optimal communication-centric ISAC waveform for ranging
• Lowest ranging sidelobe for QAM/PSK constellations
• Comparison of OFDM with other orthogonal waveforms

Innovation

• CP-OFDM minimizes ranging sidelobe for QAM/PSK
• OFDM is optimal for cyclic prefix waveforms
• OFDM achieves local EISL minimum without CP