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Fundamental Limits of Bistatic Integrated Sensing and Communications over Memoryless Relay Channels

Yao Liu, Min Li, Lawrence Ong, Aylin Yener

TL;DR

It is found that the hybrid-partial-decode-and-compress-forward scheme achieves optimal sensing performance when the communication task is ignored, and the upper and lower bounds are shown to coincide for three specific classes of relay channels.

Abstract

The problem of bistatic integrated sensing and communications over memoryless relay channels is considered, where destination concurrently decodes the message sent by the source and estimates unknown parameters from received signals with the help of a relay. A state-dependent discrete memoryless relay channel is considered to model this setup, and the fundamental limits of the communication-sensing performance tradeoff are characterized by the capacity-distortion function. An upper bound on the capacity-distortion function is derived, extending the cut-set bound results to address the sensing operation at the destination. A hybrid-partial-decode-and-compress-forward coding scheme is also proposed to facilitate source-relay cooperation for both message transmission and sensing, establishing a lower bound on the capacity-distortion function. It is found that the hybrid-partial-decode-and-compress-forward scheme achieves optimal sensing performance when the communication task is ignored. Furthermore, the upper and lower bounds are shown to coincide for three specific classes of relay channels. Numerical examples are provided to illustrate the communication-sensing tradeoff and demonstrate the benefits of integrated design.

Fundamental Limits of Bistatic Integrated Sensing and Communications over Memoryless Relay Channels

TL;DR

It is found that the hybrid-partial-decode-and-compress-forward scheme achieves optimal sensing performance when the communication task is ignored, and the upper and lower bounds are shown to coincide for three specific classes of relay channels.

Abstract

The problem of bistatic integrated sensing and communications over memoryless relay channels is considered, where destination concurrently decodes the message sent by the source and estimates unknown parameters from received signals with the help of a relay. A state-dependent discrete memoryless relay channel is considered to model this setup, and the fundamental limits of the communication-sensing performance tradeoff are characterized by the capacity-distortion function. An upper bound on the capacity-distortion function is derived, extending the cut-set bound results to address the sensing operation at the destination. A hybrid-partial-decode-and-compress-forward coding scheme is also proposed to facilitate source-relay cooperation for both message transmission and sensing, establishing a lower bound on the capacity-distortion function. It is found that the hybrid-partial-decode-and-compress-forward scheme achieves optimal sensing performance when the communication task is ignored. Furthermore, the upper and lower bounds are shown to coincide for three specific classes of relay channels. Numerical examples are provided to illustrate the communication-sensing tradeoff and demonstrate the benefits of integrated design.

Paper Structure

This paper contains 33 sections, 11 theorems, 133 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization and Notation
  4. System Model
  5. Upper and Lower Bounds on Capacity-Distortion Function $C(D)$
  6. Upper Bound on $C(D)$
  7. Lower Bound on $C(D)$
  8. A Numerical Example
  9. Minimum Distortion of Capacity-Distortion Tradeoff Region
  10. When the Sensing Parameter and the Channel to the Relay Are Independent
  11. When the Sensing Parameter and the Channel to the Destination Are Independent
  12. Optimal Capacity-Distortion Functions for Specific Bistatic ISAC Relay Channels
  13. Relay Channels with Orthogonal Sender Components: Optimal Tradeoff Achieved by Partial-Decode-Forward Strategy
  14. State-Dependent Cover-Kim Relay Channels: Optimal Tradeoff Achieved by Compress-Forward Strategy
  15. Two-hop Relay Channels: Optimal Tradeoff Achieved by Hybrid-Partial-Decode-and-Compress-Forward Strategy
  16. ...and 18 more sections

Key Result

Theorem 1

The capacity-distortion function $C(D)$ is upper bounded as where $\hat{S}_d$ is a deterministic function of $X,X_1,Y,T$ given as and the joint distribution of variables $XX_1SS_{d}YY_1T\hat{S}_{d}$ is where $P_{SS_{d}}P_{YY_1|XX_1S}$ is fixed by the channel, $P_{\hat{S}_{d}|XX_1YT}$ is fixed by the chosen estimator equ:stateEstimator, and $P_{XX_1}P_{T|XX_1Y_1}$ is to be optimized. It suffice

Figures (10)

  • Figure 1: A motivating scenario of bistatic ISAC over relay channels.
  • Figure 2: The logical connections between theorems, propositions, and numerical examples in this paper.
  • Figure 3: Bistatic ISAC over SD-DM relay channels.
  • Figure 4: An illustration of our achievable coding scheme.
  • Figure 5: Rate-distortion tradeoff for the channel considered in Example \ref{['example:generalAchievable']}.
  • ...and 5 more figures

Theorems & Definitions (34)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Remark 1
  • Remark 2
  • Theorem 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Example 1
  • ...and 24 more