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Joint Transmit and Reflective Beamforming for Multi-Active-IRS-Assisted Cooperative Sensing

Yuan Fang, Xianghao Yu, Jie Xu

TL;DR

This paper addresses DoA-based sensing of a non-LoS target using a distributed set of active IRSs to provide multi-view observations at a base station. It derives closed-form CRB expressions for DoA estimation with respect to each IRS and formulates a non-convex max-CRB minimization problem that jointly optimizes BS transmit beamforming and IRS reflective beamforming. An alternating optimization framework combining SDP for transmit design and SDR/SCA with Gaussian randomization for reflective design yields high-quality solutions, with convergence guarantees. Numerical results show active IRSs offer significant gains over passive ones, and that BS power budget and IRS amplification limits jointly bound sensing performance, while transmit-beamforming design is especially impactful.

Abstract

This paper studies multi-active intelligent-reflecting-surface (IRS) cooperative sensing, in which multiple active IRSs are deployed in a distributed manner to help the base station (BS) provide multi-view sensing. We focus on the scenario where the sensing target is located in the non-line-of-sight (NLoS) area of the BS. Based on the received echo signal, the BS aims to estimate the target's direction-of-arrival (DoA) with respect to each IRS. In addition, we leverage active IRSs to overcome the severe path loss induced by multi-hop reflections. Under this setup, we minimize the maximum Cramér-Rao bound (CRB) among all IRSs by jointly optimizing the transmit beamforming at the BS and the reflective beamforming at the multiple IRSs, subject to the constraints on the maximum transmit power at the BS, as well as the maximum transmit power and the maximum power amplification gain at individual IRSs. To tackle the resulting highly non-convex max-CRB minimization problem, we propose an efficient algorithm based on alternating optimization, successive convex approximation, and semi-definite relaxation, to obtain a high-quality solution. Finally, numerical results are provided to verify the effectiveness of our proposed design and the benefits of active IRS-assisted sensing compared to the counterpart with passive IRSs.

Joint Transmit and Reflective Beamforming for Multi-Active-IRS-Assisted Cooperative Sensing

TL;DR

This paper addresses DoA-based sensing of a non-LoS target using a distributed set of active IRSs to provide multi-view observations at a base station. It derives closed-form CRB expressions for DoA estimation with respect to each IRS and formulates a non-convex max-CRB minimization problem that jointly optimizes BS transmit beamforming and IRS reflective beamforming. An alternating optimization framework combining SDP for transmit design and SDR/SCA with Gaussian randomization for reflective design yields high-quality solutions, with convergence guarantees. Numerical results show active IRSs offer significant gains over passive ones, and that BS power budget and IRS amplification limits jointly bound sensing performance, while transmit-beamforming design is especially impactful.

Abstract

This paper studies multi-active intelligent-reflecting-surface (IRS) cooperative sensing, in which multiple active IRSs are deployed in a distributed manner to help the base station (BS) provide multi-view sensing. We focus on the scenario where the sensing target is located in the non-line-of-sight (NLoS) area of the BS. Based on the received echo signal, the BS aims to estimate the target's direction-of-arrival (DoA) with respect to each IRS. In addition, we leverage active IRSs to overcome the severe path loss induced by multi-hop reflections. Under this setup, we minimize the maximum Cramér-Rao bound (CRB) among all IRSs by jointly optimizing the transmit beamforming at the BS and the reflective beamforming at the multiple IRSs, subject to the constraints on the maximum transmit power at the BS, as well as the maximum transmit power and the maximum power amplification gain at individual IRSs. To tackle the resulting highly non-convex max-CRB minimization problem, we propose an efficient algorithm based on alternating optimization, successive convex approximation, and semi-definite relaxation, to obtain a high-quality solution. Finally, numerical results are provided to verify the effectiveness of our proposed design and the benefits of active IRS-assisted sensing compared to the counterpart with passive IRSs.
Paper Structure (10 sections, 2 theorems, 38 equations, 4 figures)

This paper contains 10 sections, 2 theorems, 38 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Estimation CRB Derivation for Active IRS
  4. Joint Transmit and Reflective Beamforming for Target Estimation
  5. Optimal Transmit Beamforming Design
  6. Reflective Beamforming Design
  7. Numerical Results
  8. Conclusion
  9. Proof of Proposition \ref{['prop_FIM_bs']}
  10. Proof of Lemma \ref{['FIM_appr_lem']}

Key Result

Proposition 1

We define the derivatives of ${{\mathbf{a}}}$ with respect to $\theta_{l}$ and $\phi_{l}$ as $\dot{{\mathbf{a}}}_{\theta_{l}}$ and $\dot{{\mathbf{a}}}_{\phi_{l}}$, respectively. Then, the FIM for estimating ${\mathbf{F}}_{l}$ is given by where with $\mathbf{C}_{\theta_{l},l} = \mathbf{G}_{l}^{T}\mathbf{\Psi}_{l} \left({\dot{{\mathbf{a}}}_{\theta_{l}} {\mathbf{a}} _l^T + {{ {\mathbf{a}} }_l}{\dot

Figures (4)

  • Figure 1: Multi-IRS-assisted cooperative sensing.
  • Figure 2: The achieved max-CRB versus the maximum transmit power $P_{\text{t}}$ at the BS with $P_{\text{s}} = 0.1$ W, $M=16$, and $N_v = N_h = 4$.
  • Figure 3: The achieved max-CRB versus the maximum transmit power $P_{\text{s}}$ at the IRSs with $M=16$, $N_v = N_h = 4$, and $a_{\text{max}}=8$.
  • Figure 4: The achieved max-CRB versus the number of antennas $M$ at the BS with $P_{\text{t}} = 20$ W, $P_{\text{s}} = 0.1$ W $N_v = N_h = 4$, and $a_{\text{max}}=8$.

Theorems & Definitions (2)

  • Proposition 1
  • Lemma 1