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)

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 critical task in electronic reconnaissance and countermeasures. Estimation methods based on time-frequency analysis typically suffer from limited resolution or high computational complexity. Furthermore, methods based on compressive sensing rely heavily on the consistency between the predefined dictionary and the actual signal characteristics, and the estimation precision will be significantly compromised by grid mismatch or modulation-induced energy dispersion. Maximum Likelihood (ML)-based methods offer the advantage of high theoretical estimation accuracy with relatively low computational complexity. However, existing studies typically assume an ideal unmodulated signal model with a single frequency transition. Consequently, these ML-based methods suffer from severe model mismatch when processing FH signals with digital modulation, such as Phase Shift Keying (PSK), or multi-hop signals. Moreover, the conventional iterative solution of ML-based methods is prone to divergence or trapping in local optima. To address these limitations, this paper proposes an improved ML-based method for the blind parameter estimation of PSK-modulated FH signals. Methods To handle received multi-hop signals, a signal slicing technique based on the Short-Time Fourier Transform (STFT) is proposed to extract slices containing individual frequency transitions. Subsequently, to mitigate the model mismatch caused by digital modulation in conventional ML-based methods, a model-matching signal extraction approach based on the ML objective function is developed for PSK-modulated FH signals. Furthermore, a weighted iterative solving algorithm for ML estimation is designed to enhance convergence, thereby achieving robust and accurate estimation of frequency-hopping parameters. Results and Discussions To validate the effectiveness of the model-matching signal extraction approach, ablation experiments were carried out under various modulation schemes, including binary PSK (BPSK), quadrature PSK (QPSK), and 8-ary PSK (8PSK). The results indicate that the proposed approach (Group D) significantly reduces the Mean Square Error (MSE) of hopping frequency estimation compared to that without the proposed extraction (Group ND). These results demonstrate that the proposed method effectively mitigates the model mismatch (Fig. 5). Simulation results also illustrate that the designed weighted iterative algorithm achieves superior convergence performance compared with linear weighting and non-weighting schemes (Fig. 6). Moreover, the experiments verify the algorithm's insensitivity to initial frequency offsets, showing that it tolerates offsets of up to 2 MHz at SNR of -10 dB with little performance degradation (Fig. 7). Finally, comparative analysis with representative existing methods indicates that the proposed method outperforms the others in terms of estimation accuracy (Fig. 8). Conclusions To achieve blind parameter estimation for PSK-modulated FH signals, this paper proposes an improved ML-based method. By utilizing a signal slicing technique based on the STFT, the proposed method successfully extends the applicability of the ML-based estimator to continuous multi-hop signals. To mitigate the model mismatch induced by PSK modulation, a model-matching signal extraction approach is developed to isolate valid signal segments that conform to the ML model. Furthermore, a weighted iterative algorithm incorporating a dynamic weighting function is introduced to address the instability of the conventional iterative ML solver. Simulation results confirm that the proposed method effectively eliminates model mismatch and ensures superior convergence performance with insensitivity to initial frequency offsets. Moreover, it is shown to achieve high estimation precision for both hopping frequencies and hopping times.
- 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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