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Multi-Target Position Error Bound and Power Allocation Scheme for Cell-Free mMIMO-OTFS ISAC Systems

Yifei Fan, Shaochuan Wu, Haojie Wang, Mingjun Sun, Jianhe Wang

TL;DR

This work addresses multi-target position estimation in a CF mMIMO-OTFS ISAC system. It derives closed-form CRLB and PEB expressions for positioning, accompanied by a low-complexity PEB approximation, and develops a max-min SINR power allocation algorithm that enforces a sensing PEB constraint via iterative convex optimization with quadratic transforms. The results verify the accuracy of the PEB expressions, quantify the coordination gains from ISAC, and demonstrate the CF architecture's advantages over traditional cellular ISAC, especially in high-mobility scenarios with OTFS. The study provides practical insights for joint sensing and communication design and highlights the impact of antenna density and Doppler-rich environments on performance.

Abstract

This paper investigates multi-target position estimation in cell-free massive multiple-input multiple-output (CF mMIMO) architectures, where orthogonal time frequency and space (OTFS) is used as an integrated sensing and communication (ISAC) signal. Closed-form expressions for the Cramér-Rao lower bound and the positioning error bound (PEB) in multi-target position estimation are derived, providing quantitative evaluations of sensing performance. To enhance the overall performance of the ISAC system, a power allocation algorithm is developed to maximize the minimum user communication signal-to-interference-plus-noise ratio while ensuring a specified sensing PEB requirement. The results validate the proposed PEB expression and its approximation, clearly illustrating the coordination gain enabled by ISAC. Further, the superiority of using the multi-static CF mMIMO architecture over traditional cellular ISAC is demonstrated, and the advantages of OTFS signals in high-mobility scenarios are highlighted.

Multi-Target Position Error Bound and Power Allocation Scheme for Cell-Free mMIMO-OTFS ISAC Systems

TL;DR

This work addresses multi-target position estimation in a CF mMIMO-OTFS ISAC system. It derives closed-form CRLB and PEB expressions for positioning, accompanied by a low-complexity PEB approximation, and develops a max-min SINR power allocation algorithm that enforces a sensing PEB constraint via iterative convex optimization with quadratic transforms. The results verify the accuracy of the PEB expressions, quantify the coordination gains from ISAC, and demonstrate the CF architecture's advantages over traditional cellular ISAC, especially in high-mobility scenarios with OTFS. The study provides practical insights for joint sensing and communication design and highlights the impact of antenna density and Doppler-rich environments on performance.

Abstract

This paper investigates multi-target position estimation in cell-free massive multiple-input multiple-output (CF mMIMO) architectures, where orthogonal time frequency and space (OTFS) is used as an integrated sensing and communication (ISAC) signal. Closed-form expressions for the Cramér-Rao lower bound and the positioning error bound (PEB) in multi-target position estimation are derived, providing quantitative evaluations of sensing performance. To enhance the overall performance of the ISAC system, a power allocation algorithm is developed to maximize the minimum user communication signal-to-interference-plus-noise ratio while ensuring a specified sensing PEB requirement. The results validate the proposed PEB expression and its approximation, clearly illustrating the coordination gain enabled by ISAC. Further, the superiority of using the multi-static CF mMIMO architecture over traditional cellular ISAC is demonstrated, and the advantages of OTFS signals in high-mobility scenarios are highlighted.

Paper Structure

This paper contains 14 sections, 2 theorems, 37 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. System Model
  5. Downlink Communication Model
  6. Multi-Target Sensing Model
  7. CRLB Derivation
  8. The Original CRLB Expression
  9. Approximate Fisher Information
  10. Proposed Power Allocation Algorithm
  11. Numerical Results
  12. Conclusion
  13. Entries of the FIM in \ref{['eq:FIM']}
  14. Proof of Proposition \ref{['prop1']}

Key Result

Proposition 1

By considering only the beam directed toward the corresponding target, an approximation of the FIM for multi-target position estimation of target $t$ in eq:positionFIM can be obtained by $\mathbf{F}_{\mathbf{p}_t}=\sum_{p=1}^{N_{\mathrm{tx}}}\sum_{r=1}^{N_{\mathrm{rx}}}\eta_{pt}\hat{\mathbf{F}}_{\ma

Figures (4)

  • Figure 1: Illustration of the multi-target CF-ISAC system setup.
  • Figure 2: The sensing PEB versus different target number and RCS variance.
  • Figure 3: Tradeoff between the SE and the sensing PEB constraint in both cellular and CF systems.
  • Figure 4: The average per-user communication SE versus different user and target velocities.

Theorems & Definitions (2)

  • Proposition 1
  • Lemma 1