Uncovering the Iceberg in the Sea: Fundamentals of Pulse Shaping and Modulation Design for Random ISAC Signals

2025-01-03

AI Summary

In 6G integrated sensing and communication (ISAC) systems, random communication waveforms—such as QAM/PSK-modulated OFDM—suffer from poor range sidelobe suppression due to their stochastic autocorrelation function (ACF), limiting sensing resolution and detection accuracy. Method: This work jointly optimizes modulation design and Nyquist pulse shaping to enhance ACF sidelobe suppression. We propose an “iceberg-under-the-sea” statistical model that decouples the mean (iceberg) and variance (sea surface) of the ACF, enabling rigorous analysis of their coupling. A closed-form expression for the expected squared ACF of arbitrary modulated ISAC signals is derived analytically. Leveraging this, we identify OFDM’s optimal sidelobe properties under Nyquist shaping and design a novel Nyquist pulse tailored for ISAC. Results: Simulations demonstrate that the proposed pulse significantly outperforms the root-raised-cosine (RRC) filter in suppressing range sidelobes, thereby improving target resolvability and ranging precision.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Integrated Sensing and Communications (ISAC) is expected to play a pivotal role in future 6G networks. To maximize time-frequency resource utilization, 6G ISAC systems must exploit data payload signals, that are inherently random, for both communication and sensing tasks. This paper provides a comprehensive analysis of the sensing performance of such communication-centric ISAC signals, with a focus on modulation and pulse shaping design to reshape the statistical properties of their auto-correlation functions (ACFs), thereby improving the target ranging performance. We derive a closed-form expression for the expectation of the squared ACF of random ISAC signals, considering arbitrary modulation bases and constellation mappings within the Nyquist pulse shaping framework. The structure is metaphorically described as an ``iceberg hidden in the sea", where the ``iceberg'' represents the squared mean of the ACF of random ISAC signals, that is determined by the pulse shaping filter, and the ``sea level'' characterizes the corresponding variance, caused by the randomness of the data payload. Our analysis shows that, for QAM/PSK constellations with Nyquist pulse shaping, Orthogonal Frequency Division Multiplexing (OFDM) achieves the lowest ranging sidelobe level across all lags. Building on these insights, we propose a novel Nyquist pulse shaping design to enhance the sensing performance of random ISAC signals. Numerical results validate our theoretical findings, showing that the proposed pulse shaping significantly reduces ranging sidelobes compared to conventional root-raised cosine (RRC) pulse shaping, thereby improving the ranging performance.

Problem

• 6G Network
• ISAC Signal Design
• Ranging Performance

Innovation

• Nyquist pulse shaping
• ISAC system
• range accuracy enhancement