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Distortion Is Not Noise: On the Limits of the Kappa Model for Monostatic ISAC

Haofan Dong, Ozgur B. Akan

TL;DR

This work derives PA-aware sensing Cram\'er--Rao bounds and a PN-aware CRB that reveals an irreducible velocity-error floor, and quantifies when $\kappa$-based bounds overestimate sensing degradation.

Abstract

Monostatic ISAC sensing differs from communication because the transmitter can monitor its distorted transmit waveform. Thus, the aggregate $κ$ distortion model, which treats impairments as unknown noise, is appropriate for communication but pessimistic for monostatic sensing. We derive PA-aware sensing Cramér--Rao bounds (CRBs) and a PN-aware CRB that reveals an irreducible velocity-error floor, and quantify when $κ$-based bounds overestimate sensing degradation. Simulations validate the analysis and show robustness to practical DPD template errors (less than 1~dB overhead at a typical $-25$~dB NMSE).

Distortion Is Not Noise: On the Limits of the Kappa Model for Monostatic ISAC

TL;DR

This work derives PA-aware sensing Cram\'er--Rao bounds and a PN-aware CRB that reveals an irreducible velocity-error floor, and quantifies when -based bounds overestimate sensing degradation.

Abstract

Monostatic ISAC sensing differs from communication because the transmitter can monitor its distorted transmit waveform. Thus, the aggregate distortion model, which treats impairments as unknown noise, is appropriate for communication but pessimistic for monostatic sensing. We derive PA-aware sensing Cramér--Rao bounds (CRBs) and a PN-aware CRB that reveals an irreducible velocity-error floor, and quantify when -based bounds overestimate sensing degradation. Simulations validate the analysis and show robustness to practical DPD template errors (less than 1~dB overhead at a typical ~dB NMSE).
Paper Structure (20 sections, 4 theorems, 6 equations, 5 figures)

This paper contains 20 sections, 4 theorems, 6 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. OFDM-ISAC Signal Model
  4. PA Nonlinearity
  5. Phase Noise
  6. Observation Models
  7. PA-Aware Analysis
  8. Physics-Based Sensing CRB
  9. $\kappa$/Bussgang Overestimation
  10. Communication Under PA
  11. PN-Aware Analysis
  12. Augmented FIM and Schur Complement
  13. Joint PA+PN Separability
  14. Communication Under PN
  15. Numerical Results
  16. ...and 5 more sections

Key Result

Theorem 1

The CRB for delay and Doppler estimation under PA nonlinearity is where $\tilde{E}_{20}^{(Z)} \!= \!\sum_{k,m}(k')^2|Z[k,m]|^2$ and $\tilde{E}_{02}^{(Z)} \!= \!\sum_{k,m}(m')^2|Z[k,m]|^2$ are spectral moments of the PA output. The degradation relative to the ideal case is $\Delta_{\mathrm{sens}}^{\mathrm{PA}} = 10\log_{10}(\tilde{E}_{20}^{(X)}/\tilde{E}_{20}^{(Z)}

Figures (5)

  • Figure 1: Monostatic OFDM-ISAC system. Upper: The ISAC base station transmits PA-distorted, phase-noise-affected waveforms for simultaneous sensing and communication. Lower: Signal flow showing that $Z[k,m]$ is deterministically known at the co-located sensing receiver (✓) but unknown at the remote communication receiver ($\times$)---the asymmetry that the $\kappa$ model fails to capture.
  • Figure 2: PA sensing CRB analysis. (a) $\kappa$ model overestimation ratio vs. SNR: the physics-based CRB is validated by MC (hollow circles near 0 dB); the $\kappa$ model diverges at high SNR. (b) Overestimation vs. IBO at fixed SNR values.
  • Figure 3: (a) Velocity CRB vs. SNR: L-shaped curves reveal the transition from noise-limited to PN floor-limited regimes. The ideal baseline (dashed) diverges from all PN curves by $>$40 dB at high SNR. MC validates $\beta{=}100$ Hz. (b) DPD template error sensitivity: range CRB overhead vs. template NMSE at IBO $=5$ dB, SNR $=20$ dB. Star marks typical DPD accuracy ($-25$ dB).
  • Figure 4: Joint IBO--$\beta$ design map at SNR $=20$ dB. Color shows velocity CRB (m/s); white contours are velocity thresholds, blue dashed contours are communication rates (bits/s/Hz). Contour orthogonality directly visualizes the separability in Corollary \ref{['cor:joint']}. Star marks a typical operating point.
  • Figure 5: (a) Sensing--communication Pareto frontier at SNR $= 10, 20, 30$ dB: the physics-based model (solid) shows significantly smaller sensing cost than the $\kappa$ model (dashed), with the gap widening at higher SNR. (b) Bidirectional asymmetry (IBO $=5$ dB, $\beta{=}100$ Hz): PA predominantly degrades communication while PN predominantly degrades sensing. Annotations show the sensing-to-communication degradation-factor ratio $10^{(\Delta_{\mathrm{sens}}-\Delta_{\mathrm{comm}})/10}$.

Theorems & Definitions (4)

  • Theorem 1: PA-Aware Sensing CRB
  • Theorem 2: Overestimation Gap
  • Theorem 3: PN-Aware Sensing CRB
  • Corollary 1: Orthogonal Design Space