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Hybrid Mono- and Bi-static OFDM-ISAC via BS-UE Cooperation: Closed-Form CRLB and Coverage Analysis

Xiaoli Xu, Yong Zeng

TL;DR

This work presents a BS-UE cooperative ISAC framework that blends BS mono-static sensing with UE-assisted bi-static sensing using OFDM signals, enabling joint target localization and velocity estimation without extra spectrum. A closed-form CRLB is derived for target position and velocity as functions of the target and UE positions, revealing significant gains when the BS-Target-UE geometry is favorable and allowing velocity estimation beyond radial components. The authors validate the CRLBs with FFT-based estimation and a weighted MSE fusion approach, and they develop a coverage analysis showing non-monotonic sensing area with BS-UE separation and a UE-density-driven PEB distribution under random UE placement. Practical implications include UE selection strategies to maximize sensing performance and guidelines for network deployment to optimize sensing coverage. The framework accommodates extensions such as prior angle information, synchronization errors, joint estimation, multi-UE cooperation, and 3D location tracking, providing a tractable tool for planning ISAC-enabled cellular networks.

Abstract

This paper proposes a hybrid mono- and bi-static sensing framework, by leveraging the base station (BS) and user equipment (UE) cooperation in integrated sensing and communication (ISAC) systems. This scheme is built on 3GPP-supported sensing modes, and it does not incur any extra spectrum cost or inter-cell coordination. To reveal the fundamental performance limit of the proposed hybrid sensing mode, we derive closed-form Cramér-Rao lower bound (CRLB) for sensing target localization and velocity estimation, as functions of target and UE positions. The results reveal that significant performance gains can be achieved over the purely mono- or bi-static sensing, especially when the BS-target-UE form a favorable geometry, which is close to a right triangle. The analytical results are validated by simulations using effective parameter estimation algorithm and weighted mean square error (MSE) fusion method. Based on the derived sensing bound, we further analyze the sensing coverage by varying the UE positions, which shows that sensing coverage first improves then degrades as the BS-UE separation increases. Furthermore, the sensing accuracy for a potential target with best UE selection is derived as a function of the UE density in the network.

Hybrid Mono- and Bi-static OFDM-ISAC via BS-UE Cooperation: Closed-Form CRLB and Coverage Analysis

TL;DR

This work presents a BS-UE cooperative ISAC framework that blends BS mono-static sensing with UE-assisted bi-static sensing using OFDM signals, enabling joint target localization and velocity estimation without extra spectrum. A closed-form CRLB is derived for target position and velocity as functions of the target and UE positions, revealing significant gains when the BS-Target-UE geometry is favorable and allowing velocity estimation beyond radial components. The authors validate the CRLBs with FFT-based estimation and a weighted MSE fusion approach, and they develop a coverage analysis showing non-monotonic sensing area with BS-UE separation and a UE-density-driven PEB distribution under random UE placement. Practical implications include UE selection strategies to maximize sensing performance and guidelines for network deployment to optimize sensing coverage. The framework accommodates extensions such as prior angle information, synchronization errors, joint estimation, multi-UE cooperation, and 3D location tracking, providing a tractable tool for planning ISAC-enabled cellular networks.

Abstract

This paper proposes a hybrid mono- and bi-static sensing framework, by leveraging the base station (BS) and user equipment (UE) cooperation in integrated sensing and communication (ISAC) systems. This scheme is built on 3GPP-supported sensing modes, and it does not incur any extra spectrum cost or inter-cell coordination. To reveal the fundamental performance limit of the proposed hybrid sensing mode, we derive closed-form Cramér-Rao lower bound (CRLB) for sensing target localization and velocity estimation, as functions of target and UE positions. The results reveal that significant performance gains can be achieved over the purely mono- or bi-static sensing, especially when the BS-target-UE form a favorable geometry, which is close to a right triangle. The analytical results are validated by simulations using effective parameter estimation algorithm and weighted mean square error (MSE) fusion method. Based on the derived sensing bound, we further analyze the sensing coverage by varying the UE positions, which shows that sensing coverage first improves then degrades as the BS-UE separation increases. Furthermore, the sensing accuracy for a potential target with best UE selection is derived as a function of the UE density in the network.
Paper Structure (19 sections, 8 theorems, 73 equations, 11 figures, 1 table, 1 algorithm)

This paper contains 19 sections, 8 theorems, 73 equations, 11 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model
  4. SNR Analysis
  5. Target Parameter Estimation
  6. CRLB for Hybrid Mono- and Bi-static Sensing
  7. CRLB for Target Localization
  8. Insights and Possible Extension of the Analysis
  9. Incorporate the prior information on $\theta$
  10. Account for the random synchronization error
  11. CRLB for Target Velocity Estimation
  12. Summary of the Analytical Results
  13. Verification of the Analytical Results
  14. Coverage Analysis for Hybrid Sensing
  15. Sensing Coverage Analysis
  16. ...and 4 more sections

Key Result

Theorem 1

The CRLB for target localization in OFDM-ISAC with BS-UE cooperation can be expressed in closed-form in terms of the target location $\mathbf q$ and UE location $\mathbf q_U$, given by where $\mathcal{I}_{\tau_B}$, $\mathcal{I}_{\theta}$, and $\mathcal{I}_{\tau_U}$ are Fisher information for estimating individual parameters, given in eq:FishTauB, eq:FishTheta0 and eq:FishTauU0, respectively. $r_B

Figures (11)

  • Figure 1: The hybrid mono- and bi-static ISAC mode with BS-UE cooperation.
  • Figure 2: An illustration of BS-target-UE geometry
  • Figure 3: The comparison of PEB achievable by the BS mono-static versus hybrid sensing with given UE position.
  • Figure 4: The comparison of PEB with given target position.
  • Figure 5: Target velocity and measured Doppler by BS and UE.
  • ...and 6 more figures

Theorems & Definitions (16)

  • Theorem 1
  • proof
  • Corollary 1
  • Corollary 2
  • Example 1
  • Theorem 2
  • Example 2
  • Lemma 1
  • Example 3
  • Lemma 2
  • ...and 6 more