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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
Summary
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.
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.
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