## 1 Introduction  
In the era of increasing threats to information security, developing robust and cost-effective solutions for secure communication has become a critical challenge, particularly in scenarios requiring resistance to eavesdropping and interference. Chaos signals, characterized by their wide continuous spectra, randomness, and ease of generation, offer a promising low-cost carrier solution for spread spectrum communication. These signals have unique properties that make them highly suitable for secure communication systems. By embedding information into chaotic signals, chaos-based communication systems inherit the well-established advantages of traditional spread spectrum systems--such as low detection probability, high interference resistance, and the ability to mitigate multipath effects. Additionally, chaotic signals further enhance data security due to their inherent unpredictability and complexity [1, 2]. Chaotic digital modulation techniques, known for their simple circuitry and resistance to interception, are highly resilient to adverse channel conditions, making them particularly useful for secure communication in dynamic environments [3, 4]. However, in practical applications, systems that rely on chaotic synchronization may face challenges due to the complexity of achieving and maintaining synchronization in real time. To address this, non-coherent chaos-based communication systems, which eliminate the need for synchronization, have emerged as a more feasible and attractive solution for real-world secure communication scenarios. Differential chaos shift keying (DCSK) is a non-coherent digital modulation scheme that leverages chaotic signals. In DCSK, half of the bit duration is allocated to transmitting a reference chaotic signal, which reduces both energy efficiency and data rate [5]. Despite this, DCSK-based communication systems are well-suited for wireless sensor networks due to their low power consumption, simplicity, and robustness against channel distortion. Over time, various enhancements have been introduced to improve the energy efficiency, data rate, and error performance of DCSK systems. Reference [6] proposed the short reference differential chaos shift keying (SR-DCSK) technique to shorten the reference time slot length and improve the energy efficiency. Reference [7] improved SR-DCSK to realize wireless transmission of information and power, simplify system design and save energy. Reference [8] proposed high efficiency DCSK (HE-DCSK), which improved the data transmission efficiency by two times. Reference [9] points out that a chaotic reference sequence as a carrier reduces security. To improve the BER, reference [10] introduces the LSTM-OFDM-DCSK technique, while reference [11] proposes two-dimensional frequency and time diversity-assisted OFDM-DCSK for enhanced security. Reference [12] proposed a multicarrier DCSK (MC-DCSK) system to improve the data rate and security through a simple design, and references [13; 14] further optimized its bit rate and peak-to-average power ratio. The multiuser MC-DCSK (ANC-MU-MC-DCSK) system proposed in reference [15] improves spectral efficiency and energy consumption, and reference [16] improves the reliability of multiuser transmissions through sparse code expansion. Multi-carrier chaotic modulation proposed in reference [17] is robust in time-varying hydroacoustic channels. In order to reduce the performance degradation caused by noise affecting the reference and data signals in traditional DCSK systems, reference [18] proposes a noise reduction DCSK (NR-DCSK) system, which reduces noise variance and improves system performance by averaging multiple chaotic samples. Furthermore, coding technology has been utilized to further enhance DCSK in references [19; 20; 21]. To enhance the data rate and energy efficiency of DCSK systems, several improvement schemes were proposed in reference [22; 23; 24; 25].