Blind Parameter Estimation Method for PSK Modulated Frequency-Hopping Signals Based on Improved Maximum Likelihood

ZHANG Tianhao; ZHANG Yushu; XU Zhongqiu; TANG Xinyi; DANG Wenhua; LI Guangzuo

doi:10.11999/JEIT260005

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ZHANG Tianhao, ZHANG Yushu, XU Zhongqiu, TANG Xinyi, DANG Wenhua, LI Guangzuo. Blind Parameter Estimation Method for PSK Modulated Frequency-Hopping Signals Based on Improved Maximum Likelihood[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260005

Citation:

ZHANG Tianhao, ZHANG Yushu, XU Zhongqiu, TANG Xinyi, DANG Wenhua, LI Guangzuo. Blind Parameter Estimation Method for PSK Modulated Frequency-Hopping Signals Based on Improved Maximum Likelihood[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260005

Citation:

ZHANG Tianhao, ZHANG Yushu, XU Zhongqiu, TANG Xinyi, DANG Wenhua, LI Guangzuo. Blind Parameter Estimation Method for PSK Modulated Frequency-Hopping Signals Based on Improved Maximum Likelihood[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260005

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Blind Parameter Estimation Method for PSK Modulated Frequency-Hopping Signals Based on Improved Maximum Likelihood

doi: 10.11999/JEIT260005 cstr: 32379.14.JEIT260005

ZHANG Tianhao^{1, 2, 3},
ZHANG Yushu^{1, 2},
XU Zhongqiu^{1, 2},
TANG Xinyi^{1, 2},
DANG Wenhua^{1, 2},
LI Guangzuo^{1, 2
,
,}

1.
Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
2.
Research Department of Cyber-electromagnetic Space Information Technology, Aerospace Information Research Institute, Beijing 100094, China
3.
School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Science and Disruptive Technology Program, AIRCAS (2025-AIRCAS-SDTP-06)

Received Date: 2026-01-04
Accepted Date: 2026-03-09
Rev Recd Date: 0026-03-09

Available Online: 2026-03-18

Abstract

Abstract

Objective Blind parameter estimation of non-cooperative Frequency-Hopping (FH) signals is a key task in electronic reconnaissance and countermeasure systems. Estimation methods based on time-frequency analysis typically suffer from limited resolution or high computational cost. Methods based on compressive sensing also rely heavily on consistency between the predefined dictionary and the actual signal characteristics, and their estimation accuracy is often degraded by grid mismatch or modulation-induced energy dispersion. Maximum Likelihood (ML)-based methods provide high theoretical estimation accuracy at relatively low computational cost. However, existing studies usually assume an ideal unmodulated signal model with a single frequency transition. Therfore, severe model mismatch arises when these ML-based methods are applied to digitally modulated FH signals, such as Phase Shift Keying (PSK), or to multi-hop signals. In addition, conventional iterative solutions in ML-based methods are prone to divergence or convergence to local optima. To address these issues, an improved ML-based method is proposed for blind parameter estimation of PSK-modulated FH signals. Methods To process received multi-hop signals, a signal-slicing method based on the Short-Time Fourier Transform (STFT) is proposed to extract slices that contain individual frequency transitions. To reduce the model mismatch caused by digital modulation in conventional ML-based methods, a model-matching signal extraction method based on the ML objective function is developed for PSK-modulated FH signals. Furthermore, a weighted iterative algorithm is designed for ML estimation to improve convergence and thus achieve robust and accurate estimation of FG parameters. Results and Discussions To verify the effectiveness of the model-matching signal extraction method, ablation experiments are conducted under several modulation schemes, including Binary PSK (BPSK), Quadrature PSK (QPSK), and 8-ary PSK (8PSK). The results show that the proposed method (Group D) significantly reduces the Mean Square Error (MSE) of hopping-frequency estimation compared with the method without the proposed extraction procedure (Group ND). These findings indicate that the proposed method effectively reduces model mismatch (Fig. 5). Simulation results also show that the designed weighted iterative algorithm provides better convergence than linear-weighting and non-weighting schemes (Fig. 6). The experiments further confirm that the algorithm is insensitive to initial frequency offsets, and offsets of up to 2 MHz are tolerated at an Signal-to-Noise Ratio (SNR) of –10 dB with little performance degradation (Fig. 7). Comparative experiments with representative existing methods also show that the proposed method achieves higher estimation accuracy (Fig. 8). Conclusions An improved ML-based method is proposed for blind parameter estimation of PSK-modulated FH signals. By using an STFT-based signal-slicing method, the applicability of the ML-based estimator is extended to continuous multi-hop signals. To reduce the model mismatch caused by PSK modulation, a model-matching signal extraction method is developed to isolate valid signal segments that satisfy the ML model. Furthermore, a weighted iterative algorithm with a dynamic weighting function is proposed to address the instability of the conventional iterative ML solver. Simulation results confirm that the proposed method effectively reduces model mismatch, provides superior convergence, and remains insensitive to initial frequency offsets. High estimation accuracy is achieved for both hopping frequency and hopping time.
- Frequency-Hopping (FH),
- Blind parameter estimation,
- Maximum Likelihood (ML),
- Short-Time Fourier Transform (STFT),
- Phase Shift Keying (PSK)

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References(18)

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