## 1 Introduction
For multiple-input-multiple-output (MIMO) systems with DM, hybrid MIMO phased-array time-direction modulation [31] and the mixed-beam design for signal and noise projection matrices [32; 33] have been proposed to improve confidentiality performance with MIMO directionality. By synergizing the polarization state of the transmitted signal with DM for differential signal emission, researchers have induced a significant reduction in received power and distortion in the constellation diagram for undesired directions, which substantially increases the demodulation difficulty for eavesdroppers [34; 35]. Combining the above research results, the current research is far from sufficient to improve the covertness of signals in complex electromagnetic environments and the robustness of signals in antagonistic environments. In addition, several challenges are as follows:  
1. In satellite communications, MQPSK modulation is commonly used but can lead to high BER and significant signal energy loss from the RF front-end power amplifier. To address these issues, polarization modulation (PM) can be employed. When the modulation order \(M>2\), the distance between adjacent constellation points in PM's three-dimensional constellation is significantly larger, resulting in better BER performance compared to MQPSK. Additionally, PM is not affected by the nonlinear distortion of the power amplifier. 2. Currently, the MP-WFRFT secure transmission algorithm is increasingly utilized to enhance the anti-interception performance of communication systems. However, there is a lack of clear numerical analysis regarding its effectiveness in improving anti-interception performance in PM. In this paper, for the VPAPM scheme, the selection of horizontal and vertical direction parameters in the MP-WFRFT algorithm has varying impacts on the anti-interception performance. 3. Given the current challenges of poor anti-interception performance and low secrecy rates in satellite communication, relying on a single secure transmission technique is insufficient. While MP-WFRFT processes the signal from the perspective of the time-frequency transform domain, it lacks beam directivity in the air domain. In contrast, DM enhances anti-interception performance by leveraging the beam directivity of MIMO in the air domain, serving as a complementary approach to MP-WFRFT. The specific work and contributions of this paper are detailed below:  
1. PM does not introduce additional distortions to amplitude and phase, offering enhanced immunity to interference. The paper proposes a VPAPM scheme, grounded in the fundamental principles of polarization modulation and variable polarization modulation, which effectively suppresses interference by leveraging polarization orthogonality. Additionally, the PAPM scheme is employed to enhance both the data transmission rate and the energy efficiency of the power amplifier. 2. Based on VPAPM modulation scheme, this study delves into the influence of MP-WFRFT scanning parameter periodicity on the anti-interception capabilities of satellite communication systems. As the results show, firstly, the anti-scanning capabilities of a single parameter in a scale vector vary from one another. Specifically, parameter \(m_{1}\) shows no effect, \(m_{2}\) is the most effective, \(m_{3}\) is the second most effective, and \(m_{4}\) is the least effective. Secondly, the \(\cos\varphi\) direction outperforms the \(\sin\gamma e^{i\varphi}\) direction in terms of anti-interception capabilities. 3. This paper proposes directional variable polarization modulation with MP-WFRFT to improve the anti-interception capabilities of satellite communication systems. The analysis of performance simulation indicates that the fusion algorithm of MP-WFRFT and DM substantially improves the anti-interception performance compared to individual secure transmission methods, improving anti-interception performance by at least an order of magnitude at signal-to-noise ratio above 10 dB.