Chaotic Complex-Valued Hopfield Neural Network for Secure OFDM Communication

The extension of chaotic dynamics into the complex domain offers a promising avenue to overcome the limitations of real-valued chaotic systems in terms of complexity and applicability. This paper presents a comprehensive study on a complex-valued Hopfield neural network (CVHNN) for generating high-complexity chaos and its application in physical layer security. First, a novel CVHNN model is proposed, and its dynamics are rigorously analyzed. Detailed characterization via Lyapunov exponents and bifurcation diagrams confirms the existence of rich chaotic regimes. Second, the CVHNN is successfully implemented on a FPGA platform, validating its physical realizability as a high-speed entropy source. Finally, a secure Orthogonal Frequency-Division Multiplexing (OFDM) scheme is developed, which intrinsically leverages the native complex-valued chaos. The proposed scheme employs a multi-domain encryption strategy, where a single complex chaotic sample directly encrypts a corresponding OFDM symbol in the code, modulation, and time-frequency domains. Overall, this work presents a framework containing chaotic system design, hardware implementation, and application development for complex-valued chaos, offering both a new theoretical foundation in chaotic neural networks and a practical physical-layer security solution for industrial wireless communications.