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Joint Angle and Delay Cramér-Rao Bound Optimization for ISAC

Chao Hu, Yuan Fang, Ling Qiu

TL;DR

The paper addresses joint sensing and communication in ISAC by deriving a CRB for simultaneous angle and delay estimation at a multi-antenna BS and optimizing transmit beamforming to minimize the CRB under rate and power constraints. It delivers a closed-form, projection-based solution for the single-target/single-user scenario and proves a sparsity structure that enables low-complexity optimization in the multi-target/multi-user setting via SDR, with rank-one recovery. Numerical results show significant improvements in positioning accuracy over conventional beamformers while reducing the need for large antenna counts. Overall, the work provides a rigorous, scalable framework for joint angle-delay localization in ISAC communications with practical constraints.

Abstract

In this paper, we study a multi-input multi-output (MIMO) beamforming design in an integrated sensing and communication (ISAC) system, in which an ISAC base station (BS) is used to communicate with multiple downlink users and simultaneously the communication signals are reused for sensing multiple targets. Our interested sensing parameters are the angle and delay information of the targets, which can be used to locate these targets. Under this consideration, we first derive the Cramér-Rao bound (CRB) for joint angle and delay estimation. Then, we optimize the transmit beamforming at the BS to minimize the CRB, subject to the communication rate requirement and the maximum transmit power constraint. In particular, we obtain the closed-form optimal solution in the case of single-target and single-user, and in the case of multi-target and multi-user scenario, the sparsity of the optimal solution is proven, leading to a reduction in computational complexity during optimization. The numerical results demonstrate that the optimized beamforming yields excellent positioning performance and effectively reduces the requirement for a large number of antennas at the BS.

Joint Angle and Delay Cramér-Rao Bound Optimization for ISAC

TL;DR

The paper addresses joint sensing and communication in ISAC by deriving a CRB for simultaneous angle and delay estimation at a multi-antenna BS and optimizing transmit beamforming to minimize the CRB under rate and power constraints. It delivers a closed-form, projection-based solution for the single-target/single-user scenario and proves a sparsity structure that enables low-complexity optimization in the multi-target/multi-user setting via SDR, with rank-one recovery. Numerical results show significant improvements in positioning accuracy over conventional beamformers while reducing the need for large antenna counts. Overall, the work provides a rigorous, scalable framework for joint angle-delay localization in ISAC communications with practical constraints.

Abstract

In this paper, we study a multi-input multi-output (MIMO) beamforming design in an integrated sensing and communication (ISAC) system, in which an ISAC base station (BS) is used to communicate with multiple downlink users and simultaneously the communication signals are reused for sensing multiple targets. Our interested sensing parameters are the angle and delay information of the targets, which can be used to locate these targets. Under this consideration, we first derive the Cramér-Rao bound (CRB) for joint angle and delay estimation. Then, we optimize the transmit beamforming at the BS to minimize the CRB, subject to the communication rate requirement and the maximum transmit power constraint. In particular, we obtain the closed-form optimal solution in the case of single-target and single-user, and in the case of multi-target and multi-user scenario, the sparsity of the optimal solution is proven, leading to a reduction in computational complexity during optimization. The numerical results demonstrate that the optimized beamforming yields excellent positioning performance and effectively reduces the requirement for a large number of antennas at the BS.
Paper Structure (10 sections, 3 theorems, 21 equations, 4 figures)

This paper contains 10 sections, 3 theorems, 21 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmit Beamforming Design
  4. Single-Target and Single-User Case
  5. Multi-Target and Multi-User Case
  6. Numerical Results
  7. Conclusion
  8. Proof of Theorem \ref{['CRLB']}
  9. Proof of Theorem \ref{['S_D']}
  10. Proof of Proposition \ref{['M_D']}

Key Result

Theorem 1

The FIM $\boldsymbol{F}$ for estimating $\boldsymbol{\varsigma}$ is given by where

Figures (4)

  • Figure 1: An illustration of the system.
  • Figure 2: The transmit beampattern for single-target and single-user case, where the target and CU are located respectively at azimuth angles $0^{\circ}$ and $40^{\circ}$.
  • Figure 3: The estimation CRB versus $P_T$.
  • Figure 4: Normalized CRB of parameters at different angles, where the targets are located at azimuth angles $-30^{\circ},0^{\circ}, 15^{\circ}$, respectively, and the CUs are at azimuth angles $10^{\circ},40^{\circ}, 80^{\circ}$, respectively.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Proposition 1