## 1 Introduction
More robust encryption may pose risks as technology progresses, necessitating ongoing security development against evolving threats [12]. Security mechanisms operating at higher layers might not address attacks at the physical layer [13]. In IoT applications, considering the large number of devices and the possible alteration of communication by an adversary, an attack like a man-in-the-middle is easy to perform. While data theft might be prevented, interference in information transmission through broadcast signals could disrupt critical applications like vehicle-to-vehicle communication or medical IoT. Improving physical layer security addresses these concerns but is complex due to limited device resources. Hence, developing efficient and secure physical layer protection methods is a focal point in IoT security [5; 11; 14]. The chaos phenomenon presents a promising avenue for strengthening physical layer security in IoT systems. It offers diverse attributes such as a wide spectrum, noise-like waveform, narrow cross-correlation function, synchronization capability, and sensitivity to initial conditions while maintaining system determinism [13]. Integrating chaotic signals with coherent modulation techniques enhances security in IoT systems [15]. These signals find applications in fields like random number generation [16; 17], encryption [18; 19; 20; 21], radar systems [22; 23; 24], and IoT communications [25; 26; 27]. The versatility of chaotic signals in generating analog signals and digital logistic maps drives interest, particularly in FPGA-based image encryption using chaotic logistic maps [28; 29; 30]. Such systems provide secure communication channels for transmitting images across IoT sensing systems to domains like smart healthcare [31; 32], where security and privacy are crucial. Ongoing efforts involve developing and studying communication systems based on analog chaos oscillators [33; 34; 35]. Simpler analog chaos oscillators can replace digital chaotic communication for resource-constrained IoT sensors and nodes. Various chaotic oscillators, including Colpitts [36], have been extensively studied [37; 38; 39; 40; 41]. Colpitts chaos oscillators, in particular, have garnered attention for their simple schematic. [PERSON] [42; 43] specified that a chaos oscillator must have at least three state variable elements (inductor, capacitor) to accumulate energy, an active element to support fluctuation, and a nonlinear element to ensure system nonlinear dynamics. The Colpitts chaos oscillator, comprising a transistor as both the active and nonlinear element, along with an inductor and capacitors, allows for a more straightforward configuration of the fundamental frequency by adjusting reactive element values [44; 45; 46; 47]. [PERSON] et al. developed a Colpitts chaos oscillator operating in the frequency range of 500 MHz to 15 GHz [48]. Due to its specific autocorrelation function shape, it finds application in UWB radar detection systems [22; 23]. Moreover, that system can effectively utilize a wide spectrum, providing access to different spectral channels and avoiding transmitter detection. Researchers have also explored Colpitts chaos oscillator signals' numerical, statistical, and informational parameters [49; 50; 51; 52], conducting Lyapunov exponent analysis to identify parameter regions resulting in chaotic behavior [53]. The simplicity of the Colpitts chaos oscillator circuit has made it a notable choice for data transmission. [PERSON] et al. were the first to showcase Colpitts chaos oscillator synchronization in a drive-response system, enabling the development of a coherent communication system [54]. [PERSON] et al. introduced binary phase-shift keying based on chaotic oscillators [55], while [PERSON] et al. suggested chaotic modulation using a schematic power supply [56]. Additionally, [PERSON] et al. explored and studied security enhancements in OFDM systems by employing Discrete-nonlinear Colpitts oscillator-based communication [57].