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Continuous-Aperture Array-Based ISAC Over Fading Channels

Boqun Zhao, Chongjun Ouyang, Xingqi Zhang, Yuanwei Liu

Abstract

A framework of continuous-aperture array (CAPA)-based integrated sensing and communications (ISAC) under a fading communication channel is proposed. A continuous operator-based signal model is developed, and the statistics of the communication channel gain are characterized via Landau's eigenvalue theorem. On this basis, the performance of the CAPA-based ISAC system is analyzed by considering three continuous beamforming designs: i) the sensing-centric (S-C) design that optimizes sensing performance, ii) the communication-centric (C-C) design that optimizes communication performance, and iii) the Pareto-optimal design that balances the sensing-communication trade-off. For the S-C and C-C design, closed-form expressions for the sensing rate (SR), ergodic communication rate (CR), and outage probability are derived, and high-signal-to-noise ratio asymptotic analysis is conducted to obtain the multiplexing and diversity gains. For the Pareto-optimal design, the Pareto-optimal beamformer achieving the Pareto boundary is derived, and the achievable SR-CR region is characterized. Numerical results demonstrate that the proposed CAPA-ISAC scheme outperforms both conventional spatially discrete arrays-based ISAC and CAPA-based frequency-division sensing and communications.

Continuous-Aperture Array-Based ISAC Over Fading Channels

Abstract

A framework of continuous-aperture array (CAPA)-based integrated sensing and communications (ISAC) under a fading communication channel is proposed. A continuous operator-based signal model is developed, and the statistics of the communication channel gain are characterized via Landau's eigenvalue theorem. On this basis, the performance of the CAPA-based ISAC system is analyzed by considering three continuous beamforming designs: i) the sensing-centric (S-C) design that optimizes sensing performance, ii) the communication-centric (C-C) design that optimizes communication performance, and iii) the Pareto-optimal design that balances the sensing-communication trade-off. For the S-C and C-C design, closed-form expressions for the sensing rate (SR), ergodic communication rate (CR), and outage probability are derived, and high-signal-to-noise ratio asymptotic analysis is conducted to obtain the multiplexing and diversity gains. For the Pareto-optimal design, the Pareto-optimal beamformer achieving the Pareto boundary is derived, and the achievable SR-CR region is characterized. Numerical results demonstrate that the proposed CAPA-ISAC scheme outperforms both conventional spatially discrete arrays-based ISAC and CAPA-based frequency-division sensing and communications.
Paper Structure (30 sections, 20 theorems, 111 equations, 7 figures, 1 table)

This paper contains 30 sections, 20 theorems, 111 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Motivations and Contributions
  4. Organization and Notations
  5. System Model
  6. System Description
  7. Sensing Model
  8. Communication Model
  9. Communication Channel Statistics
  10. Performance Analysis
  11. Sensing-Centric Design
  12. Performance of Sensing
  13. Performance of Communications
  14. Communications-Centric Design
  15. Performance of Communications
  16. ...and 15 more sections

Key Result

Lemma 1

The autocorrelation function of $\hat{h}_{\rm{c}}( z )$ is given by

Figures (7)

  • Figure 1: Illustration of CAPA-based ISAC.
  • Figure 2: Illustration of the eigenvalues of $K(z,z')$.
  • Figure 3: ECR versus transmit SNR.
  • Figure 4: OP versus transmit SNR.
  • Figure 5: SR versus transmit SNR.
  • ...and 2 more figures

Theorems & Definitions (23)

  • Lemma 1
  • Lemma 2
  • Corollary 1
  • Remark 1
  • Lemma 3
  • Theorem 1
  • Corollary 2
  • Theorem 2
  • Corollary 3
  • Theorem 3
  • ...and 13 more