A Design of FMCW Fuze System and Ranging Algorithm Based on Frequency–Phase Composite Modulation Using Chaotic Codes

TY - JOUR

T1 - A Design of FMCW Fuze System and Ranging Algorithm Based on Frequency–Phase Composite Modulation Using Chaotic Codes

AU - Zhang, Jincheng

AU - Hao, Xinhong

AU - Hou, Chaowen

AU - Wang, Jianqiu

N1 - Publisher Copyright: © 2026 by the authors.

PY - 2026/3

Y1 - 2026/3

N2 - To address the vulnerability of traditional linear frequency-modulated continuous wave (FMCW) fuze to jamming due to fixed modulation parameters, this paper proposes a novel fuze waveform design scheme using chaotic code-based frequency and phase composite modulation along with a Normalized Rate-Invariant Ranging algorithm (NRIR). Leveraging the ergodicity and initial value sensitivity of the Logistic chaotic map, a dual-dimensional composite modulation system is constructed. In the frequency domain, the frequency modulation slope undergoes periodic binary variation according to chaotic states to break the signal periodicity. In the phase domain, phase encoding is implemented based on chaotic binary sequences to further improve waveform entropy and complexity, effectively destabilizing the parameter stability required for coherent jamming. To resolve the distance–Doppler coupling challenges and spectral dispersion issues caused by variable-slope modulation, the NRIR algorithm is developed. By introducing a resampling transformation operator, the non-stationary rate-varying beat frequency signal is mapped to a normalized “constant-slope” space, enabling coherent accumulation and ranging of targets. Using the ambiguity function as an analytical tool, theoretical analyses, simulation experiments, and test results demonstrate that this design scheme exhibits excellent performance in suppressing DRFM jamming and sweep-frequency jamming, providing theoretical support and technical approaches for fuze anti-jamming design.

AB - To address the vulnerability of traditional linear frequency-modulated continuous wave (FMCW) fuze to jamming due to fixed modulation parameters, this paper proposes a novel fuze waveform design scheme using chaotic code-based frequency and phase composite modulation along with a Normalized Rate-Invariant Ranging algorithm (NRIR). Leveraging the ergodicity and initial value sensitivity of the Logistic chaotic map, a dual-dimensional composite modulation system is constructed. In the frequency domain, the frequency modulation slope undergoes periodic binary variation according to chaotic states to break the signal periodicity. In the phase domain, phase encoding is implemented based on chaotic binary sequences to further improve waveform entropy and complexity, effectively destabilizing the parameter stability required for coherent jamming. To resolve the distance–Doppler coupling challenges and spectral dispersion issues caused by variable-slope modulation, the NRIR algorithm is developed. By introducing a resampling transformation operator, the non-stationary rate-varying beat frequency signal is mapped to a normalized “constant-slope” space, enabling coherent accumulation and ranging of targets. Using the ambiguity function as an analytical tool, theoretical analyses, simulation experiments, and test results demonstrate that this design scheme exhibits excellent performance in suppressing DRFM jamming and sweep-frequency jamming, providing theoretical support and technical approaches for fuze anti-jamming design.

KW - ambiguity function

KW - anti-intercept ability

KW - chaotic bi-phased code modulation

KW - chaotic code

KW - linear frequency modulation

KW - radio fuze

UR - https://www.scopus.com/pages/publications/105032625592

U2 - 10.3390/s26051434

DO - 10.3390/s26051434

M3 - Article

AN - SCOPUS:105032625592

SN - 1424-8220

VL - 26

JO - Sensors

JF - Sensors

IS - 5

M1 - 1434

ER -