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Direct and Regularized Inverse De-Embedding for Single-Carrier Signal Recovery in Measurement Front-Ends.

Haonan Gu1,2,3, Yingxin Jin1,2,3, Yongnan Rao1,2,3

  • 1National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China.

Sensors (Basel, Switzerland)
|June 26, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a frequency-domain de-embedding compensation framework to improve single-carrier signal recovery accuracy. The Wiener-type inverse compensation method shows superior performance in reducing noise and distortion in measurement chains.

Keywords:
Wiener inverse filteringde-embeddingill-posed inverse problemmeasurement front-endregularized inverse compensationsingle-carrier signal

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Area of Science:

  • Electrical Engineering
  • Signal Processing
  • Measurement Science

Background:

  • Single-carrier signal measurement chains suffer from accuracy degradation due to amplitude/phase distortion, delay distortion, and noise amplification.
  • De-embedding these signals is an ill-conditioned inverse problem, sensitive to noise and weak frequency responses.
  • Existing compensation methods require a unified framework for evaluation.

Purpose of the Study:

  • To investigate direct inverse and regularized inverse de-embedding compensation methods for single-carrier signals.
  • To establish a unified frequency-domain compensation framework.
  • To evaluate the applicability of different compensation methods under various measurement chain conditions and noise levels.

Main Methods:

  • Formulated single-carrier signal de-embedding as an ill-conditioned inverse problem within a linear time-invariant system model.
  • Developed a unified frequency-domain compensation framework including Direct, Tikhonov, Wiener-type, and Truncated inverse methods.
  • Evaluated methods using simulated narrowband signals and four distinct measurement-chain models, followed by measured experiments.

Main Results:

  • The Wiener-type inverse compensation method demonstrated superior Normalized Mean Square Error (NMSE) performance compared to Direct, Tikhonov, and Truncated methods.
  • Compensation effectiveness is dependent on measurement chain characteristics (e.g., ill-conditioning, magnitude response) and noise levels.
  • Frequency-domain de-embedding improved measured NMSE from -18.78 dB to -37.95 dB.

Conclusions:

  • The proposed frequency-domain de-embedding framework offers a practical approach for enhancing single-carrier signal recovery.
  • The Wiener-type method is particularly effective under tested conditions, while others offer limited gains in specific scenarios.
  • The study clarifies the applicability of different inverse compensation techniques based on measurement chain properties and noise.