A Novel One-Dimensional Chaotic System and Its Application in Chaotic Communication Systems
DOI:
https://doi.org/10.54097/nm089129Keywords:
1D-SCNM, Chaotic Communication, Nonlinear Fusion.Abstract
Chaotic systems are widely applied in secure communications, and one-dimensional (1D) chaotic systems are preferred for resource-constrained scenarios due to their structural simplicity and ease of hardware implementation. However, traditional 1D systems (Logistic, Sine, Chebyshev maps) suffer from narrow/discontinuous chaotic intervals, insufficient sequence complexity, and weak initial sensitivity, leading to chaotic degradation in digital implementation and poor communication performance in practical channels. To address these issues, this paper proposes a novel 1D Sin-Coupled Nonlinear Map (1D-SCNM) based on “nonlinear fusion + parameter coupling”. It retains the low-complexity advantage of 1D systems while achieving wide continuous chaotic intervals, high-complexity sequences, and strong initial sensitivity. Evaluated via bifurcation diagrams, Lyapunov exponents (LE) and sample entropy (SE), 1D-SCNM was applied as a carrier in DCSK/NR-DCSK systems, with BER tested under AWGN and Rayleigh fading channels. Results show 1D-SCNM’s chaotic interval covers full parameters (LE/SE exceeding traditional systems); NR-DCSK (P=16) achieves a BER of 2.3×10⁻³ (14 dB Eb/N₀, AWGN), 97.2% improvement over DCSK (15.46 dB gain), with stable advantages in Rayleigh channels. This work provides a high-performance, easily implementable chaotic carrier for secure communications.
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