## 1 Introduction
Since the chaos implemented in the FPGA itself is discrete in nature, careful consideration must be taken of the width of the data bus in the fixed-point (sometimes floating-point) data format as well as methods for solving discrete ODEs. These choices affect the accuracy of the computation as well as the robustness and properties of the chaotic signals in the system, which may be critical for the system's performance quality. Two types of chaotic communication systems can be pointed out--those with coherent and non-coherent detection [7]. Coherent systems (such as chaos shift keying (CSK) [8]), which require chaotic synchronization between the transmitter and receiver, excel in privacy but demand precise parameter matching, as stable chaotic synchronization in the presence of channel noise is a challenging task. Non-coherent systems, on the other hand, simplify receiver design at the cost of reduced security. Non-coherent chaotic communication systems (such as differential chaotic shift keying (DCSK) [9]) are more popular, but they mainly use nonlinear wide-band properties of the chaotic signals for communication purposes. As they do not use chaotic synchronization, they do not need any chaos generator at the receiver. Key challenges in chaotic secure communication include achieving stable synchronization, particularly in coherent systems, and mitigating parameter mismatches between the transmitter and receiver. The trade-off between the security of a chaotic communication channel and its robustness to noise is another challenge that needs to be addressed in the design. The predictability of chaos and simplicity of non-coherent communication schemes weaken the security of the system, while the increased complexity of the chaotic system risks making it less resilient to the channel noise and interferences. The search for new, more efficient and viable chaotic modulation methods is a relevant task and a necessary step to allow secure chaotic communications to become more popular among other communication methods. While the topic of chaotic secure communications has been of interest to researchers for about three decades now, this subject is still vastly understudied. This could be related to the increased complexity of chaos theory and to the low popularity of chaotic communications in comparison to conventional communication systems. As scarce as this area of research is, the use of FPGAs to implement chaos generators has been gradually increasing in recent years. For instance, [PERSON] et al. [10] proposed an FPGA realization of an image encryption system that employs 16-Chaotic Phase Shift Keying in a coherent communication scheme. A similar approach was used in the work of [PERSON] et al. [11], where the authors effectively deployed an FPGA realization of an image encryption scheme using DCSK chaotic modulation together with the code division multiple access (CDMA) technique for multichannel communication. In another study, [PERSON] and [PERSON] [12] addressed several challenges of cascaded chaos-based secure communication systems, while analyzing the security and efficiency of an FPGA-implemented system with various cascade levels. [PERSON] et al. [13] focused their research on a novel digital chaotic encrypted communication scheme, which was implemented both in an FPGA and as software on the ESP32 Arduino platform. These studies, published in 2024, highlight the growing interest in and successful applications of FPGA technology for chaotic encryption and secure data transmission. Regarding earlier research on FPGA-implemented chaotic communication systems, only a limited number of relevant papers [14; 15; 16; 17; 18; 19; 20] have been identified. Some design parameters of these works were reviewed and compared in our previous study [21]. Table 1 provides an overview of the design features of the reviewed FPGA-based chaotic communication systems. Notably, the FM-ACSK system stands out as the only design with passband operation capabilities.