Sensing With Communication Signals: From Information Theory to Signal Processing

TL;DR

This paper studies sensing with random communication signals within ISAC, revealing a fundamental deterministic-random tradeoff (DRT) that links the randomness of data payloads to sensing performance. It develops an information-theoretic framework (capacity-distortion) and a CRB-rate tradeoff for vector Gaussian ISAC channels, then connects these insights to practical signal design. The work analyzes ACF properties of random ISAC signals, introduces the iceberg-in-the-sea structure, and proposes design principles for modulation, constellation shaping, and pulse shaping to balance sensing and communication. It extends to MIMO via data-dependent and data-independent precoding, and outlines open problems and future directions, including 2D ambiguity, adaptive modulation, security, and AI-enabled ISAC. The results provide actionable guidelines for implementing 6G ISAC using random payload signals with tractable, scalable tradeoffs for real-world systems.

Abstract

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multi-input multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals.

Figures (13)

• Figure 1: The P2P ISAC model: An ISAC Tx transmits a unified signal to sense targets while communicating with a communication Rx. A dedicated sensing Rx is either collocated with the ISAC Tx (monostatic mode), or placed separately but connected with the ISAC Tx through a wired link (cooperative bistatic mode).
• Figure 2: An information-theoretic model for the P2P monostatic ISAC system.
• Figure 3: The C-D tradeoff boundary of the real-valued scalar Gaussian channel scenario with $B=10$, as well as the Pareto-optimal input distributions $P_{\mathsf{x}}(x)$ along the boundary.
• Figure 4: CRB-Rate tradeoff for a P2P monostatic ISAC system.
• Figure 5: A signal processing pipeline for P2P ISAC model in Fig. \ref{['fig:CRB_rate scenarios']}. The communication Rx aims to correctly detect symbols in the presence of multi-path interference, whereas the sensing Rx aims at extracting range parameters of multiple targets.