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Cramer--Rao Bounds for Magneto-Inductive Integrated Sensing and Communications

Haofan Dong, Ozgur B. Akan

Abstract

Magnetic induction (MI) enables communication in RF-denied environments (underground, underwater, in-body), where the medium conductivity imprints a deterministic signature on the channel. This letter derives a closed-form Cramér--Rao bound (CRB) for the joint estimation of range and medium conductivity from MI pilot observations in an integrated sensing and communication (ISAC) framework. The Fisher information matrix reveals that the joint estimation penalty converges to 3\,dB in the near-field regime, meaning conductivity sensing adds at most a factor-of-two loss in ranging precision. Monte Carlo maximum-likelihood simulations confirm that the CRB is achievable under practical operating conditions.

Cramer--Rao Bounds for Magneto-Inductive Integrated Sensing and Communications

Abstract

Magnetic induction (MI) enables communication in RF-denied environments (underground, underwater, in-body), where the medium conductivity imprints a deterministic signature on the channel. This letter derives a closed-form Cramér--Rao bound (CRB) for the joint estimation of range and medium conductivity from MI pilot observations in an integrated sensing and communication (ISAC) framework. The Fisher information matrix reveals that the joint estimation penalty converges to 3\,dB in the near-field regime, meaning conductivity sensing adds at most a factor-of-two loss in ranging precision. Monte Carlo maximum-likelihood simulations confirm that the CRB is achievable under practical operating conditions.
Paper Structure (9 sections, 2 theorems, 14 equations, 4 figures)

This paper contains 9 sections, 2 theorems, 14 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. MI-ISAC Scenario
  4. MI Channel Model
  5. Signal Model
  6. Problem Formulation
  7. Cramér--Rao Bound Analysis
  8. Numerical Results
  9. Conclusion

Key Result

Theorem 1

Let $\rho$ denote the FIM correlation coefficient $\rho \triangleq J_{12}/\sqrt{J_{11}\,J_{22}}$. Then and the joint estimation penalties for $r$ and $\sigma_{\mathrm{m}}$ are

Figures (4)

  • Figure 1: MI-ISAC system model. Two coaxial coils (radius $a$, $N$ turns) are separated by range $r$ in a lossy medium (conductivity $\sigma_{\mathrm{m}}$, permeability $\mu_0$). The transmitter sends $L$ pilot symbols; the receiver jointly estimates $\bm{\theta} = [r,\, \sigma_{\mathrm{m}}]^{\mathrm{T}}$ from the received signal, while also decoding communication data.
  • Figure 2: Joint vs. single-parameter CRB for (a) range and (b) conductivity estimation across four medium types. Solid: joint estimation; faded: known-parameter bound. Cross markers: MLE with $N_{\mathrm{mc}} = 5000$.
  • Figure 3: Joint estimation penalty vs. range for four medium conductivities. Horizontal line: 3 dB near-field limit. Cross markers: MLE empirical penalty ($N_{\mathrm{mc}} = 5000$, $\sigma_{\mathrm{m}} = 0.01$ S/m).
  • Figure 4: CRB vs. pilot count $L$ for (a) range and (b) conductivity estimation at multiple distances ($\sigma_{\mathrm{m}} = 0.01$ S/m). Open markers: MLE validation. Dashed lines: cm- and mm-level accuracy thresholds.

Theorems & Definitions (2)

  • Theorem 1
  • Corollary 1: Near-field limit