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Fisher Information Limits of Satellite RF Fingerprint Identifiability for Authentication

Haofan Dong, Ozgur B. Akan

Abstract

RF fingerprinting authenticates satellite transmitters by exploiting hardware-specific signal impairments, yet existing methods operate without theoretical performance guarantees. We derive the Fisher information matrix (FIM) for joint estimation of in-phase/quadrature (IQ) imbalance and power amplifier (PA) nonlinearity parameters, establishing Cramér-Rao bounds (CRBs) whose structure depends on constellation moments. A necessary condition for full IQ identifiability is that the identifiability factor~$β$ exceeds zero; for binary phase-shift keying (BPSK), $β= 0$ yields a rank-deficient FIM, rendering IQ parameters unidentifiable. This provides a plausible theoretical explanation for OrbID's near-random performance (area under the ROC curve, AUC~$= 0.53$) on Orbcomm. From the FIM, we define a discrimination metric that predicts which hardware parameters dominate authentication for a given modulation. For constant-modulus PSK signals, PA nonlinearity features are predicted to dominate while IQ features are ineffective. We validate the framework on 24~Iridium satellites using two recording campaigns, achieving cross-file PA fingerprint correlation $r = 0.999$ and confirming all four CRB predictions. A discrimination-ratio-weighted (DR-weighted) authentication test achieves AUC~$= 0.934$ from six features versus $0.807$ with equal weighting, outperforming machine-learning classifiers (AUC~$\leq 0.69$) on the same data.

Fisher Information Limits of Satellite RF Fingerprint Identifiability for Authentication

Abstract

RF fingerprinting authenticates satellite transmitters by exploiting hardware-specific signal impairments, yet existing methods operate without theoretical performance guarantees. We derive the Fisher information matrix (FIM) for joint estimation of in-phase/quadrature (IQ) imbalance and power amplifier (PA) nonlinearity parameters, establishing Cramér-Rao bounds (CRBs) whose structure depends on constellation moments. A necessary condition for full IQ identifiability is that the identifiability factor~ exceeds zero; for binary phase-shift keying (BPSK), yields a rank-deficient FIM, rendering IQ parameters unidentifiable. This provides a plausible theoretical explanation for OrbID's near-random performance (area under the ROC curve, AUC~) on Orbcomm. From the FIM, we define a discrimination metric that predicts which hardware parameters dominate authentication for a given modulation. For constant-modulus PSK signals, PA nonlinearity features are predicted to dominate while IQ features are ineffective. We validate the framework on 24~Iridium satellites using two recording campaigns, achieving cross-file PA fingerprint correlation and confirming all four CRB predictions. A discrimination-ratio-weighted (DR-weighted) authentication test achieves AUC~ from six features versus with equal weighting, outperforming machine-learning classifiers (AUC~) on the same data.

Paper Structure

This paper contains 34 sections, 6 theorems, 28 equations, 12 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. RF Fingerprinting
  4. CRB for Hardware Impairment Estimation
  5. Threat Model and Adversary Capabilities
  6. System Model
  7. Transmitted Signal
  8. Hardware Impairment Model
  9. Received Signal Model
  10. Satellite Channel Characteristics
  11. Cramér-Rao Bounds for HWI Parameter Estimation
  12. Fisher Information Matrix
  13. PA-IQ Coupling Structure
  14. Channel Marginalization
  15. Numerical Verification
  16. ...and 19 more sections

Key Result

Theorem 1

For the signal model in eq:rx_signal with known symbols from a unit-power constellation ($\mathbb{E}[|x|^2]=1$), in the small-impairment regime ($|\varepsilon| \ll 1$, $|\alpha_3| \ll 1$), the FIM has the block structure where the IQ sub-block is with the directional sensitivities $J_{\varepsilon\varphi} = \frac{1{+}\varepsilon}{2}\,\mathrm{Im}\{e^{-2j\varphi}\mu_{20}\}$, and the IQ identifiabi

Figures (12)

  • Figure 1: System overview of CRB-based satellite RF fingerprinting. Each satellite's RF chain (IQ mixer $\to$ PA $\to$ antenna) introduces hardware-specific distortions parameterized by $\boldsymbol{\theta}_k = [\varepsilon_k, \varphi_k, \mathrm{Re}(\alpha_{3,k}), \mathrm{Im}(\alpha_{3,k})]^T$. The ground receiver extracts HWI features from the received IQ signal and uses the FIM-induced discrimination metric to authenticate transmitters.
  • Figure 2: FIM structure for QPSK at $\varepsilon = 0.05$, $\varphi = 3^{\circ}$, $N = 76$, $\gamma = 20$ dB. (a) Absolute FIM entries normalized by $N\gamma$. (b) Normalized correlation matrix $\rho_{ij}$. At this operating point, $\rho(\varepsilon, \mathrm{Re}(\alpha_3)) = 0.725$, close to the small-impairment limit $\mu_4/\sqrt{2\mu_6} = 1/\sqrt{2} \approx 0.707$ for QPSK (Corollary \ref{['cor:coupling']}). Values are computed from the exact numerical FIM at the stated operating point; the closed-form approximation (Theorem \ref{['thm:fim']}) gives $[\mathbf{J}_{\mathrm{PA}}]/(N\gamma) \approx 2\mu_6 = 2.0$, with the $17\%$ difference attributable to the $O(\varepsilon^2)$ terms at $\varepsilon = 0.05$.
  • Figure 3: CRB vs. SNR for $N = 76$ known symbols. (a) $\mathrm{CRB}(\varepsilon)$: BPSK is unidentifiable ($\beta = 0$); QPSK and 16-QAM overlap ($\beta = 1$). The dotted line shows QPSK with PA-IQ coupling ignored, revealing a $2\times$ CRB inflation. (b) $\mathrm{CRB}(\mathrm{Re}(\alpha_3))$: all modulations follow $\propto 1/(N\gamma\mu_6)$, where $\mu_6 = \mathbb{E}[|x|^6]$. QAM has lower CRB due to $\mu_6 > 1$ (e.g., $\mu_6 = 1.96$ for 16-QAM). Gray lines show scaling with $N = 32$ and $N = 256$.
  • Figure 4: Monte Carlo CRB validation ($N = 76$, 300 trials per SNR). (a) QPSK ($\beta = 1$): all four parameter MSEs (solid markers) track their respective CRBs (dashed), confirming the bound is tight and achievable. At 30 dB SNR, MSE/CRB$\,\approx 1.0$ for all parameters. (b) BPSK ($\beta = 0$): MSE for $\mathrm{Re}(\alpha_3)$ tracks the PA sub-block CRB (identifiable), while MSE for $\varepsilon$ and $\varphi$ remain constant across SNR (unidentifiable, CRB$\,= \infty$), confirming the rank-deficiency prediction of Proposition \ref{['prop:bpsk']}. The divergence of MSE($\mathrm{Im}(\alpha_3)$) from its sub-block CRB at high SNR is consistent with the $(\varphi, \mathrm{Im}(\alpha_3))$ confounding identified in Remark \ref{['rem:paradox']}.
  • Figure 5: Modulation-dependent FIM properties. (a) FIM rank drops to 2 for BPSK ($\beta = 0$). (b) Per-parameter diagonal entries $[\mathbf{J}]_{ii}/(N\gamma)$ on a log scale. For BPSK, $[\mathbf{J}]_{\varepsilon\varepsilon} \approx 0$ while $[\mathbf{J}]_{\varphi\varphi} = 2.20$ is large---yet $\varphi$ is unidentifiable due to collinearity (Remark \ref{['rem:paradox']}). (c) Normalized correlation $\rho(\varphi, \mathrm{Im}(\alpha_3))$: BPSK exceeds $0.99$ (near-perfect collinearity), while QPSK drops to $0.684$.
  • ...and 7 more figures

Theorems & Definitions (9)

  • Theorem 1: Closed-Form FIM
  • Remark 1: Scaling Laws
  • Corollary 1
  • Proposition 1: BPSK Signal Collapse
  • Remark 2: The Large-FIM-Diagonal Paradox
  • Corollary 2: OrbID Prediction
  • Remark 3: DQPSK vs. OFDM
  • Theorem 2: Discrimination Bound
  • Lemma 1: Amplitude Variance as PA Proxy