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An Intrapulse Modulation Recognition Method for Low Probability of Interception Signals Based on the Coprime DTFrFT Spectral Receiver

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Abstract

Since the coprime discrete time fractional Fourier transform (DTFrFT) spectral receiver can effectively intercept low probability of interception signals and its output shows favorable spectral characteristics in the discrete time fractional Fourier domain (DTFrFD), this paper presents an intrapulse modulation recognition method in the DTFrFD to process the coprime DTFrFT spectral receiver’s output data, consisting of two banks, namely coarse recognition and fine recognition. The coarse recognition returns a coarse classification for the shift keying signals [binary phase shift keying (BPSK) and binary frequency shift keying (BFSK)] from the linear frequency modulation (LFM) and polyphase coded signals (Frank code, P1 code, P2 code, P3 code, P4 code) by addressing the optimal transformation order of the intercepted data in DTFrFD. In the fine recognition algorithm, the ridge line extraction function and the peak energy ratio function in the DTFrFD are defined to identify BPSK signals from BFSK signals and distinguish LFM signals and polyphase-coded signals. Compared to conventional recognition approaches in the Fourier domain, the proposed recognition method is always more efficient because it utilizes more spectral characteristics of the output data in the DTFrFD. Both theoretical analysis and simulation results demonstrate that the proposed algorithm shows better robustness and better recognition performance than the original coprime digital Fourier transform spectral receiver against SNR variation.

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Abbreviations

AF:

Ambiguity function

BFSK:

Binary frequency shift keying

BPSK:

Binary phase shift keying

DFT:

Digital Fourier transform

DSFrFT:

Digital simplified fractional Fourier transform

DTFrFD:

Discrete time fractional Fourier domain

DTFrFT:

Discrete time fractional Fourier transform

FrFD:

Fractional Fourier domain

LFM:

Linear frequency modulation

LPI:

Low probability of interception

PERF:

Peak energy ratio function

RLEF:

Ridge line extraction function

RSR:

Ratio of successful recognition

SNR:

Signal-to-noise ratio

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Funding

This research was funded by the National Natural Science Foundation of China Grant number 61271354 and the Henan Province Science and Technology Key Project Grant number 232102211071.

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Author notes

  1. Huali Wang and Zhaopei Zhang contributed equally to this work.

Authors and Affiliations

  1. School of Information and Engineering, Henan Institute of Science and Technology, Hualan Street, Xinxiang, 453003, Henan, China

    Xiaomin Li

  2. College of Communication Engineering, The Army Engineering University of PLA, Houbiaoying Street, Nanjing, 210007, Jiangsu, China

    Huali Wang

  3. School of Life Science and Technology, Henan Institute of Science and Technology, Hualan Street, Xinxiang, 453003, Henan, China

    Zhaopei Zhang

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  1. Xiaomin Li
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  2. Huali Wang
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  3. Zhaopei Zhang
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Correspondence to Xiaomin Li.

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Li, X., Wang, H. & Zhang, Z. An Intrapulse Modulation Recognition Method for Low Probability of Interception Signals Based on the Coprime DTFrFT Spectral Receiver. Circuits Syst Signal Process 43, 1319–1337 (2024). https://doi.org/10.1007/s00034-023-02510-3

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