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Joint Active and Passive Beamforming Design for Reconfigurable Intelligent Surface Enabled Integrated Sensing and Communication

Zhe Xing, Rui Wang, Xiaojun Yuan

TL;DR

This paper proposes a novel joint active and passive beamforming design for RIS-enabled ISAC system in consideration of the target size, and demonstrates the approach to be superior when detecting targets with practical sizes.

Abstract

To exploit the potential of the RIS in supporting ISAC, this paper proposes a novel joint active and passive beamforming design for RIS-enabled ISAC system in consideration of the target size. First, the detection probability for target sensing is derived in closed-form based on the illumination power on an approximated scattering surface area of the target, and a new concept of ultimate detection resolution (UDR) is defined for the first time to measure the target detection capability. Then, an optimization problem is formulated to maximize the SNR at the UE under a minimum detection probability constraint. To solve the non-convex problem, a novel alternative optimization approach is developed. In this approach, the solutions of the communication and sensing beamformers are obtained by our proposed bisection-search based method. The optimal receive combining vector is derived from an equivalent Rayleigh-quotient problem. To optimize the RIS phase shifts, the Charnes-Cooper transformation is conducted to cope with the fractional objective, and a novel convexification process is proposed to convexify the detection probability constraint with matrix operations and a real-valued first-order Taylor expansion. After the convexification, a successive convex approximation (SCA) based algorithm is designed to yield a suboptimal phase-shift solution. Finally, the overall optimization algorithm is built, followed by detailed analysis on its computational complexity, convergence behavior and problem feasibility condition. Extensive simulations are carried out to testify the analytical properties of the proposed beamforming design, and to reveal two important trade-offs, namely, communication vs. sensing trade-off and UDR vs. sensing-duration trade-off. In comparison with several existing benchmarks, our proposed approach is validated to be superior when detecting targets with practical sizes.

Joint Active and Passive Beamforming Design for Reconfigurable Intelligent Surface Enabled Integrated Sensing and Communication

TL;DR

This paper proposes a novel joint active and passive beamforming design for RIS-enabled ISAC system in consideration of the target size, and demonstrates the approach to be superior when detecting targets with practical sizes.

Abstract

To exploit the potential of the RIS in supporting ISAC, this paper proposes a novel joint active and passive beamforming design for RIS-enabled ISAC system in consideration of the target size. First, the detection probability for target sensing is derived in closed-form based on the illumination power on an approximated scattering surface area of the target, and a new concept of ultimate detection resolution (UDR) is defined for the first time to measure the target detection capability. Then, an optimization problem is formulated to maximize the SNR at the UE under a minimum detection probability constraint. To solve the non-convex problem, a novel alternative optimization approach is developed. In this approach, the solutions of the communication and sensing beamformers are obtained by our proposed bisection-search based method. The optimal receive combining vector is derived from an equivalent Rayleigh-quotient problem. To optimize the RIS phase shifts, the Charnes-Cooper transformation is conducted to cope with the fractional objective, and a novel convexification process is proposed to convexify the detection probability constraint with matrix operations and a real-valued first-order Taylor expansion. After the convexification, a successive convex approximation (SCA) based algorithm is designed to yield a suboptimal phase-shift solution. Finally, the overall optimization algorithm is built, followed by detailed analysis on its computational complexity, convergence behavior and problem feasibility condition. Extensive simulations are carried out to testify the analytical properties of the proposed beamforming design, and to reveal two important trade-offs, namely, communication vs. sensing trade-off and UDR vs. sensing-duration trade-off. In comparison with several existing benchmarks, our proposed approach is validated to be superior when detecting targets with practical sizes.
Paper Structure (26 sections, 4 theorems, 75 equations, 11 figures, 1 table, 3 algorithms)

This paper contains 26 sections, 4 theorems, 75 equations, 11 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Statement
  3. Communication Performance Metric
  4. Sensing Performance Metric
  5. Problem Statement
  6. Joint Active and Passive Beamforming Optimization
  7. Optimization of $\mathbf{w}_{c}$, $\mathbf{w}_{s}$ with Fixed $\mathbf{w}_{rx}$, $\bm{\omega}$
  8. Optimization of $\mathbf{w}_{rx}$ with Fixed $\mathbf{w}_{c}$, $\mathbf{w}_{s}$ and $\bm{\omega}$
  9. Optimization of $\bm{\omega}$ with Fixed $\mathbf{w}_{c}$, $\mathbf{w}_{s}$ and $\mathbf{w}_{rx}$
  10. Charnes-Cooper Transformation for $(\mathrm{P8})$
  11. Convexification of Constraint (\ref{['Overall_problem']}e)
  12. SCA-based Algorithm Design
  13. Overall Algorithm Design for Solving $(\mathrm{P1})$
  14. Convergence Analysis
  15. Computational Complexity Analysis
  16. ...and 11 more sections

Key Result

Proposition 1

By introducing $\mathbf{Q}=\mathbf{q}\mathbf{q}^\mathrm{H}$, $f(\mathbf{q})$ in (Simplify-29) can be transformed into where $\mathbf{v}(\mathbf{Q})\in \mathbb{C}^{(N+1)^2 \times 1}$ is a vector with respect to $\mathbf{Q}$, given by where $\mathbf{S}_i$ for $i=1,2,\cdots,(N+1)^2$ are specified in (S_i) in Appendix A, and are independent of $\mathbf{Q}$.

Figures (11)

  • Figure 1: The considered RIS-ISAC system, where the RIS is leveraged to reflect the ISAC signal from the BS to the UE and the target for communication and sensing purposes. A portion of the signal wave scattered by the target is then reflected back to the BS for target detection.
  • Figure 2: Illustration of the joint sensing and communication scheme over the time line.
  • Figure 3: The visual illustration of the scattering surface area of the possible target.
  • Figure 4: The convergence behaviors of Algorithm 2 at $T=1$ and $T=2$, when the numbers of BS antennas and RIS reflectors are: (a) $M=16,N=64$, and (b) $M=16,N=72$.
  • Figure 5: Convergence behavior of Algorithm 3 at $M=32$.
  • ...and 6 more figures

Theorems & Definitions (13)

  • Definition 1
  • Remark 1
  • Proposition 1
  • proof
  • Remark 2
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • ...and 3 more