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

## TL;DR

This paper introduces a new FMCW fuze system using chaotic modulation and a novel ranging algorithm to improve anti-jamming performance.

## Contribution

A novel FMCW fuze system using chaotic code-based frequency-phase composite modulation and a new ranging algorithm for anti-jamming is proposed.

## Key findings

- Chaotic modulation increases waveform entropy and disrupts jamming parameters.
- The NRIR algorithm effectively handles variable-slope modulation challenges.
- The design shows strong performance against DRFM and sweep-frequency jamming.

## Abstract

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.