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Rethinking the fundamental performance limits of integrated sensing and communication systems

Zhouyuan Yu, Xiaoling Hu, Chenxi Liu, Mugen Peng

TL;DR

The paper tackles fundamental limits of integrated sensing and communication (ISAC) in band-limited, continuous-time systems, addressing the limitations of prior discrete-time analyses. It develops a unified information-theoretic model that incorporates time, frequency, and spatial properties, introducing the sensing mutual information $I_s$ to connect sensing accuracy with information gain and linking it to the mean squared error (MSE). By defining the communication mutual information $I_c$ and establishing the CMI-SMI and CMI-MSE regions, the authors characterize the trade-offs and derive insights for waveform design and resource allocation. A key finding is the opposite waveform requirements for communication (prefer random-amplitude, Gaussian-like signals) and sensing (prefer constant-modulus, low-correlation signals) while both benefit from low phase randomness; moreover, time-frequency resource allocation scales linearly with performance, enabling practical design guidelines. The results are supported by analytical derivations and numerical experiments showing region shapes, waveform effects, and resource allocation implications for ISAC systems.

Abstract

Integrated sensing and communication (ISAC) has been recognized as a key enabler and feature of future wireless networks. In the existing works analyzing the performances of ISAC, discrete-time systems were commonly assumed, which, however, overlooked the impacts of temporal, spectral, and spatial properties. To address this issue, we establish a unified information model for the band-limited continuous-time ISAC systems. In the established information model, we employ a novel sensing performance metric, called the sensing mutual information (SMI). Through analysis, we show how the SMI can be utilized as a bridge between the mutual information domain and the mean squared error (MSE) domain. In addition, we illustrate the communication mutual information (CMI)-SMI and CMI-MSE regions to identify the performance bounds of ISAC systems in practical settings and reveal the trade-off between communication and sensing performances. Moreover, via analysis and numerical results, we provide two valuable insights into the design of novel ISAC-enabled systems: i) communication prefers the waveforms of random amplitude, sensing prefers the waveforms of constant amplitude, both communication and sensing favor the waveforms of low correlations with random phases; ii) There exists a linear positive proportional relationship between the allocated time-frequency resource and the achieved communication rate/sensing MSE.

Rethinking the fundamental performance limits of integrated sensing and communication systems

TL;DR

The paper tackles fundamental limits of integrated sensing and communication (ISAC) in band-limited, continuous-time systems, addressing the limitations of prior discrete-time analyses. It develops a unified information-theoretic model that incorporates time, frequency, and spatial properties, introducing the sensing mutual information to connect sensing accuracy with information gain and linking it to the mean squared error (MSE). By defining the communication mutual information and establishing the CMI-SMI and CMI-MSE regions, the authors characterize the trade-offs and derive insights for waveform design and resource allocation. A key finding is the opposite waveform requirements for communication (prefer random-amplitude, Gaussian-like signals) and sensing (prefer constant-modulus, low-correlation signals) while both benefit from low phase randomness; moreover, time-frequency resource allocation scales linearly with performance, enabling practical design guidelines. The results are supported by analytical derivations and numerical experiments showing region shapes, waveform effects, and resource allocation implications for ISAC systems.

Abstract

Integrated sensing and communication (ISAC) has been recognized as a key enabler and feature of future wireless networks. In the existing works analyzing the performances of ISAC, discrete-time systems were commonly assumed, which, however, overlooked the impacts of temporal, spectral, and spatial properties. To address this issue, we establish a unified information model for the band-limited continuous-time ISAC systems. In the established information model, we employ a novel sensing performance metric, called the sensing mutual information (SMI). Through analysis, we show how the SMI can be utilized as a bridge between the mutual information domain and the mean squared error (MSE) domain. In addition, we illustrate the communication mutual information (CMI)-SMI and CMI-MSE regions to identify the performance bounds of ISAC systems in practical settings and reveal the trade-off between communication and sensing performances. Moreover, via analysis and numerical results, we provide two valuable insights into the design of novel ISAC-enabled systems: i) communication prefers the waveforms of random amplitude, sensing prefers the waveforms of constant amplitude, both communication and sensing favor the waveforms of low correlations with random phases; ii) There exists a linear positive proportional relationship between the allocated time-frequency resource and the achieved communication rate/sensing MSE.
Paper Structure (16 sections, 4 theorems, 36 equations, 8 figures)

This paper contains 16 sections, 4 theorems, 36 equations, 8 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model
  4. Communication-Sensing Performance Analysis
  5. Communication Performance Characterization
  6. Sensing Performance Characterization
  7. Communication-Sensing Performance Region
  8. Special Cases and Discussion
  9. Waveform Design in ISAC system
  10. Time-Frequency-Spatial Resource Allocation in ISAC Systems
  11. Time-Frequency Resources Allocation in ISAC systems
  12. Spatial Resources Allocation in ISAC systems
  13. Numerical Results
  14. Relationship between SMI and MSE
  15. Communication-Sensing Performance Region
  16. ...and 1 more sections

Key Result

Proposition 1

With SMI being $I_{\mathrm{s}}$ and the auto-covariance matrix of $\mathbf{s}$ being $\mathbf{R}_{\mathrm{s}}$, the MSE $\varepsilon$ is given by

Figures (8)

  • Figure 1: The ISAC scenario considered in this paper.
  • Figure 2: Illustration of the communication-sensing performance region.
  • Figure 3: Relationship between SMI and MSE with various values of $K$.
  • Figure 4: Relationship between SMI and MSE with various values of $\rho _{\mathrm{s}}$.
  • Figure 5: Communication-sensing performance region with various values of $U_{\mathrm{ISAC}}$.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Lemma 1
  • proof
  • Theorem 1