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α-Fair Multistatic ISAC Beamforming for Multi-User MIMO-OFDM Systems via Riemannian Optimization

Hyeonho Noh, Jonggyu Jang

Abstract

This paper proposes an $α$-fair multistatic integrated sensing and communication (ISAC) framework for multi-user multi-input multi-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems, where communication users act as passive bistatic receivers to enable multistatic sensing. Unlike existing works that optimize aggregate sensing metrics and thus favor geometrically advantageous targets, we minimize the $α$-fairness utility over per-target Cramér--Rao lower bounds (CRLBs) subject to per-user minimum data rate and transmit power constraints. The resulting non-convex problem is solved via the Riemannian conjugate gradient (RCG) method with a smooth penalty reformulation. Simulation results validate the effectiveness of the proposed scheme in achieving a favorable sensing fairness--communication trade-off.

α-Fair Multistatic ISAC Beamforming for Multi-User MIMO-OFDM Systems via Riemannian Optimization

Abstract

This paper proposes an -fair multistatic integrated sensing and communication (ISAC) framework for multi-user multi-input multi-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems, where communication users act as passive bistatic receivers to enable multistatic sensing. Unlike existing works that optimize aggregate sensing metrics and thus favor geometrically advantageous targets, we minimize the -fairness utility over per-target Cramér--Rao lower bounds (CRLBs) subject to per-user minimum data rate and transmit power constraints. The resulting non-convex problem is solved via the Riemannian conjugate gradient (RCG) method with a smooth penalty reformulation. Simulation results validate the effectiveness of the proposed scheme in achieving a favorable sensing fairness--communication trade-off.

Paper Structure

This paper contains 20 sections, 28 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Scenario and Protocol
  3. System and Signal Model
  4. Performance Metrics
  5. $\alpha$-Fairness Multistatic Sensing Optimization
  6. Methodology
  7. Solution for Beamforming Variables
  8. Penalty-Based Reformulation
  9. Riemannian Conjugate Gradient Method
  10. Simulation Results
  11. Performance Analysis
  12. Computational Complexity
  13. Conclusion
  14. Derivation of FIM
  15. Derivation of $\nabla \bar{F}_\alpha(\mathbf{z})$
  16. ...and 5 more sections

Figures (6)

  • Figure 1: Illustration of the proposed multistatic ISAC scenario.
  • Figure 2: Position of the BS and sensing targets.
  • Figure 3: Convergence of sum CRLB and data rate for different penalty parameters $\rho$.
  • Figure 4: CRLB performance of 10 targets with different $\alpha$: (a) per-target CRLB and (b) sum and max CRLB.
  • Figure 5: Trade-off between CRLB and data rate for monostatic, multistatic (SDR), and the proposed multistatic schemes.
  • ...and 1 more figures