## 1 Introduction  
Satellite communication technology is pivotal across a spectrum of applications, including the establishment of integrated air, space, and submarine networks [1, 2]; low-orbit communications [3]; satellite internet of things [4, 5]; satellite navigation [6, 7]; and advanced millimeter-wave satellite communications [8]. It particularly excels in the realms of information warfare and unmanned combat, demonstrating distinct advantages [9]. Despite these strengths, satellite communications encounter challenges such as scarce spectrum resources and stringent carrier synchronization accuracy demands during their evolution. Polarization, an additional dimension of electromagnetic waves beyond time, frequency, and spatial domains, offers a novel avenue for information transmission by utilizing the polarization state as an information carrier itself. However, the open nature and broad reach of satellite communication channels render the security of polarized information vulnerable to eavesdropping, underscoring the critical need to boost the anti-interception capabilities of satellite communications. Anti-interception strategies for satellite communication systems can be broadly categorized into two primary approaches: conventional cryptographic methods and physical layer secure transmission techniques [10; 11; 12]. The former concentrates on the cryptographic manipulation of message content, leveraging the intricacy of algorithms and encryption keys to safeguard data confidentiality. In contrast, physical layer security techniques concentrate on manipulating the waveform, structure, and form of the transmitted signal, harnessing the inherent properties of the wireless channel to enhance communication security. Among these physical layer techniques, the multi-parameter weighted-type fractional Fourier transform (MP-WFRFT) has garnered significant interest due to its channel state information independence. Despite various definitions from different perspectives, fractional Fourier transforms (FRFT) are fundamentally and logically equivalent, hence collectively termed classical fractional Fourier transform (CFRFT) [13; 14; 15]. To mitigate the complexity of FRFT, weighted-type fractional Fourier transform (WFFFT) [16] has been proposed for digital communication systems, with in-depth studies on its applications in such systems [17; 18; 19]. Another key technique is directional modulation (DM), which involves the precise manipulation of signal emission direction to ensure a targeted amplitude response in the desired direction while suppressing it in undesired directions. Research has made significant strides in satellite communication security and efficiency. Polarization modulation has been incorporated into satellite communication systems, and the theoretical error symbol rate formula has been derived for Gaussian channels. Simulation results have validated that polarization modulation surpasses the incoherent demodulation of differential phase shift keying (DPSK) in terms of error symbol rate [20]. The study demonstrated that the polarization-amplitude-phase joint modulation scheme significantly improves power amplifier efficiency when compared to conventional orthogonal amplitude modulation. Additionally, an optimal pre-compensation algorithm has been proposed to effectively counteract the polarization losses of wireless channels [21; 22; 23; 24]. To enhance the safety of polarization modulation, introducing a robust transmission technique that leverages double-layer multi-parameter weighted-type fractional Fourier transform (DL-MPWFRFT), which has been demonstrated to provide superior protection against eavesdropping, is a very effective approach [25]. Due to the limitations of traditional DM, including poor scanning resistance, weak decryption capabilities, and low secrecy rates, studies have incorporated artificial noise [26], multiple access [27], linear sparse array techniques [28], enhanced DM [29], and precoding [30] to boost security performance.