A satellite-ground fusion security transmission method based on intelligent non-stationary control

Abstract

The application discloses a kind of based on intelligent non-stationary control's satellite-ground fusion security transmission method, comprising the following steps;Step one: construct time-frequency dual-dimensional satellite-ground fusion transmission model, the construction of overall application scene is carried out;Step two: based on time-frequency dual-dimensional satellite-ground fusion transmission model, the acquisition of low interference continuous usable frequency slot is carried out, and frequency slot set is obtained;Step three: by the information sequence in the frequency slot set is changed into orthogonal non-stationary waveform signal, it simultaneously presents the dynamic non-stationary characteristic of no rule in time, space, frequency and multiple dimensions, to obtain final sequence;Step four: the performance analysis of the non-stationary control sequence obtained;Step five: based on performance analysis, by theoretical derivation, the security and reliability of the proposed method overall are tested.The application has the characteristics of strong anti-interference ability, high transmission stability, excellent security performance, adaptive complex time-varying channel environment.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication technology, specifically relating to a satellite-ground integrated secure transmission method based on intelligent non-stationary control. Background Technology

[0002] In recent years, with the increasing complexity of the electromagnetic environment for communication, the security and reliability of converged satellite-terrestrial communication networks have faced enormous challenges. On the one hand, the types and scale of services carried by satellite-terrestrial communication networks have exploded, leading to a surge in traffic and increasingly scarce spectrum resources. The probability of spectrum conflicts and internal system interference has risen exponentially. On the other hand, the inherent openness of satellite communication and the continuous evolution and upgrading of intelligent interference and eavesdropping techniques have severely impacted the security and reliability of data transmission systems. To address these issues, non-stationary control technology analyzes and processes dynamic information of the communication environment, integrating control mechanisms into the satellite signal transmission process. This provides core support for system adaptation to highly dynamic scenarios for anti-eavesdropping and anti-interference, and has therefore received widespread attention in academia and industry. However, existing non-stationary control methods are insufficient to cope with rapidly changing interference and security threats, resulting in bottlenecks in the reliability, security, and overall spectrum utilization of satellite communication systems.

[0003] Due to their broadcast characteristics and open space, satellite communication channels are inevitably susceptible to eavesdropping and interference from malicious nodes. These actions not only compromise the quality of communication links but also pose a direct threat to the stable operation of critical infrastructure, presenting a significant challenge to communication security. Ensuring reliable and secure transmission of satellite-to-ground data and improving the anti-interference and anti-eavesdropping capabilities of satellite communication systems has become an urgent task. In recent years, dynamic non-stationary control and intelligent anti-interference, as advanced satellite communication security enhancement technologies, have received widespread attention. Unlike traditional fixed-frequency control or simple power control, these technologies focus on real-time perception of the spectrum environment during communication, acquiring interference characteristics, and using dynamic spectrum agility and intelligent decision-making to avoid or suppress interference and reduce the risk of information eavesdropping, thereby ensuring the continuity and security of communication. Related technological fields are developing rapidly, and numerous research teams both domestically and internationally are dedicated to improving the dynamics and resilience of satellite communication in complex electromagnetic environments through technologies such as artificial intelligence and cognitive radio.

[0004] Nevertheless, with the acceleration of global informatization, the types and scale of services carried by satellite communications are growing explosively, the degree of frequency slot reuse is continuously increasing, and the probability of spectrum conflicts and interference is rising exponentially. At the same time, driven by electromagnetic spectrum competition and electronic countermeasures, external interference and eavesdropping methods targeting satellite communications are constantly evolving and upgrading, making the spectrum environment more complex. Under these constraints, current mainstream satellite communication security enhancement schemes are unable to fully exert their effectiveness, and the reliability and security of communication systems are under serious threat.

[0005] This demonstrates that, given the severe scarcity of spectrum resources and the continuous evolution of malicious tactics, the number of users involved in information transmission and their demand for secure and reliable transmission are constantly increasing. Without effective satellite security transmission solutions, the likelihood of transmission failures and eavesdropping on personal privacy during communication will intensify, severely impacting communication performance. Therefore, designing efficient satellite communication security solutions to enhance the anti-interference and anti-eavesdropping capabilities of information transmission between satellite and ground stations is crucial for satellite communication networks.

[0006] The main technical defects in the existing technology are: Dynamic interference scenarios: In transmission scenarios with intelligent jammers or dynamically changing electromagnetic environments, existing anti-jamming schemes based on preset rules or traditional optimization theories exhibit significant lag and vulnerability. When faced with intelligent jammers (such as tracking jammers) capable of sensing the communication spectrum usage status and dynamically adjusting their jamming strategies, these schemes lack dynamic response mechanisms. The patterns of their transmission control methods or spectrum allocation patterns are easily learned and predicted by adversaries, leading to the failure of interference avoidance and a sharp decline in communication link reliability.

[0007] Hybrid scenarios involving both interference and eavesdropping: While dynamic anti-interference measures can adapt well to complex electromagnetic environments and effectively improve the reliability and security of communication systems, existing intelligent control technologies can unintentionally weaken security in the pursuit of anti-interference performance. For example, to improve link reliability, some solutions tend to increase dwell time or repeat frequency hopping on frequency bands with high signal-to-noise ratios. This non-uniform, statistically characteristic frequency usage pattern facilitates signal feature extraction and communication pattern recognition by eavesdroppers, thereby greatly increasing the probability of data transmission being eavesdropped on and reducing system security.

[0008] Therefore, given the evolving nature of satellite communication security threats towards intelligence and complexity, and the continued scarcity of spectrum resources, there is an urgent need to develop intelligent non-stationary control schemes with environmental perception and learning capabilities to address the limitations in the anti-interference and anti-eavesdropping performance of satellite communication systems. Summary of the Invention

[0009] In order to overcome the shortcomings of the existing technology, the purpose of this invention is to provide a satellite-ground integrated secure transmission method based on intelligent non-stationary control. This method has the characteristics of strong anti-interference ability, high transmission stability, excellent security performance, and adaptability to complex time-varying channel environments.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A satellite-ground integrated secure transmission method based on intelligent non-stationary control includes the following steps; Step 1: Construct a time-frequency dual-dimensional satellite-to-ground fusion transmission model and build an overall application scenario; Step 2: Based on the time-frequency dual-dimensional satellite-to-ground fusion transmission model, obtain low-interference, continuously available frequency slots to obtain a frequency slot set; Step 3: By transforming the information sequence within the frequency gap set into orthogonal non-stationary waveform signals, it simultaneously exhibits irregular dynamic non-stationary characteristics in multiple dimensions such as time, space, and frequency, thereby obtaining the final sequence for users to transmit information. Step 4: Analyze the uniformity, randomness, and complexity of the non-stationary control sequence used by the user to prove that the transmission method can guarantee that the information is uniform and random, making it difficult for eavesdroppers to detect. Even if the information is detected, the transmission method has a certain degree of complexity, making it difficult for the eavesdropper to crack, thus ensuring the security of the transmission method. Step 5: Based on performance analysis, the performance of the entire system utilizing the frequency slot set acquisition module and non-stationary control sequence is analyzed. By calculating the signal-to-interference-plus-noise ratio of the receiver, the reliable communication probability and security rate are obtained, and simulation verification is performed to ensure that the transmission method proposed in this invention can enhance the security and reliability of the system.

[0011] Step one specifically involves: i) System model construction: A satellite-ground integrated transmission communication scenario model is constructed, including satellites, ground base stations (TBS), licensed users, active interference sources, and some randomly distributed passive eavesdropping devices. The satellites and TBS share the same spectrum resources, and the proposed intelligent non-stationary control scheme is applied for data transmission in overlapping coverage areas. It is assumed that… Indicates an authorized user connected to the satellite. This indicates a user associated with TBS. The satellite-to-ground communication network integrates agents for spectrum sensing, learning, and security decision-making tasks to respond to environmental changes; in addition, there are passive eavesdroppers hidden within the constructed communication environment, attempting to eavesdrop on information sent to users from satellites or TBS. ii) Time-frequency resource allocation and transmission cycle layering: Based on the model, the time-frequency resources and communication cycle during transmission are divided. To cope with the complex spectrum environment, the total bandwidth is divided into equally spaced q segments. n A non-overlapping frequency band, assuming This represents the set of divided frequency slots, with the total transmission time divided into m distinct time slots. In addition, an information transmission process can be divided into a perception stage, a learning stage, and a communication stage.

[0012] The specific functions of each module within a communication cycle are as follows: Sensing Phase: In this phase, the spectrum sensing module continuously senses the spectrum status of the communication environment and predicts the future spectrum status by collecting the characteristics of interference signals. This status serves as an effective input for subsequent slot set selection. Learning Phase: In this phase, based on the prediction results, the learning module uses the information transmitted back from the receiver to classify the divided frequency slots into usable and unusable slots according to the magnitude of interference, thereby obtaining the set of usable frequency slots. Assuming... Represents the available frequency slot set, where It refers to the number of available frequency slots selected; Communication Phase: In this phase, it is assumed that all authorized users transmit their data packets on the allocated discrete-time channels, and the method used for transmission is the intelligent non-stationary control sequence proposed in this invention; authorized users will randomly occupy a frequency slot to transmit data packets according to these sequences.

[0013] Step two specifically involves: i) Markov model establishment: In the scenario of this invention, the decision model needs to make a decision based on the current spectrum information when selecting a set of available frequency slots. This process naturally has Markov properties. The selection process of the available set of frequency slots is modeled as a Markov decision process (MDP). The process consists of a state space, an action space, a reward function, and an optimization function. ii) Improved DQN-based low-interference slot set acquisition algorithm: When updating the Q network, it will randomly draw from the experience pool D. Using a sample, training efficiency is improved by breaking the correlation between samples, and the target Q is calculated. and with mean squared error The training network is updated using this as a loss function; The improved algorithm is as follows: First, Long Short-Term Memory Networks (LSTM) are introduced to handle the temporal evolution of interference and predict the spectral state of subsequent states. Subsequently, this acquired predictive information will be compared with the spectral state obtained at the current moment. Combining these into inputs to the agent in a strengthened state, represented as... This state integrates instantaneous observations of the current environment with predictions of future risks based on historical inferences; The improved DQN algorithm makes more comprehensive and forward-looking decisions when evaluating the Q value of each slot. It not only focuses on whether the slot is currently available, but also assesses whether the slot will remain safe in the near future. If a slot is currently available, but LSTM predicts that it is very likely to be interfered with in the next second, the Q value of that slot will be significantly reduced, thereby guiding the agent to prioritize slots that are currently available and more stable and less likely to be interfered with in the future. Based on the combined action of the selected N frequency bands, i.e., selection The overall reward is used to update the Q-value after the action selection. Therefore, the loss function can be calculated as follows: After obtaining the list of available frequency slots, these frequency slots need to be sorted in descending order of Q value, and the top N frequency slots are selected as the final set.

[0014] Step three specifically involves: i) Generate the basic nonstationary control sequence: The sequence used for data transmission is generated in two parts: the first step is to generate a family of basic sequences with comprehensive performance, and the second step is to adaptively remap this sequence to the set of available frequency slots obtained in the previous step; cryptographic theorems are applied to the basic sequences through the principle of equivalence. The generation; by considering the TOD and network identification key of the entire communication system, The generation steps are represented as follows: in It is a sub-part separated from TOD. It is a subkey obtained from the network identification key. This is the segment number where the entire system performs the separation operation. Assume... Indicates the number of iterations. and They represent as well as These two parameters are 1 when the number of iterations is 8 or 16, and 0 for other values; This represents the XOR operation, and also... and This represents the transformation box used for nonlinear transformations in cryptography. It is the result of the iterative operation.

[0015] ii) Iteratively generate sequence families: After generating the basic sequence, it needs to be expanded into a set of K sequences to provide K authorized users with transmission sequences that are difficult for jammers or passive eavesdroppers to trace; this is achieved through the sequence obtained in the previous step. Perform K rounds of iteration to obtain K distinct sequences, assuming... The generated sequence family is represented by the following steps. iii) Obtaining the reference value factor: After obtaining the basic sequence, the sequence is remapped through the following steps to generate an intelligent non-stationary control sequence; this sequence generates a new sequence based on the acquired number of frequency slots to adapt to complex communication environments when the number of available frequency slots changes; first, the reference factor is obtained. As shown below: in, This refers to the total number of frequency slots divided in the communication model of this invention. It is the number of frequency slots in the acquired set of available frequency slots; It is the floor function, and then the resulting family of basic sequences is... and Compare to obtain the desired mapping order The specific steps are as follows: iv) Dynamic generation of non-stationary control sequences: Finally, using these mapping orders, the available frequency slot set, and the generated family of basic sequences, the final sequence is obtained: .

[0016] Step four specifically involves: 1) Homogeneity analysis: Two scenarios may occur during the mapping process: normal order and overflow order. First, we discuss the distribution of the intelligent non-stationary control sequence when the normal order occurs, i.e., without overflow, due to the generated base sequence. If a uniform distribution is satisfied, then The probability is: .

[0017] Therefore, for Furthermore, we can obtain: Based on the mapping process described above, for ,have indivual ,make Therefore, we get: Continue to prove the generated sequence Uniformity, due to It can be rewritten in this form: Assumption It is The sequence of bases satisfies uniformity, resulting in: And assume It is A sequence of numbers in base S, and independent of S. If Represented as Assuming It is a sequence The range, then for , The probability is: Since X and S are independent, the expression can be further expressed as: Here, through the one-to-one mapping relationship between a and b, we obtain: Substitute it in, and you will get ,Right now It conforms to a uniform distribution; Finally, this proof leads to the conclusion that if S is uniformly distributed and X is independent of S, then the sequence... It also conforms to a uniform distribution; Therefore, we obtain The generated intelligent nonstationary control sequence satisfies a uniform distribution when there is no overflow computation; For the overflow portion, the probability distribution is: ; when hour, Get the maximum value ; but When N is large enough, =0, therefore, the probability of overflow computation events can be ignored. In summary, the generated sequence is uniform.

[0018] 2) Randomness analysis Randomness must satisfy: ; Assumption and These are the two parts of the generated sequence. Using conditional probability, we obtain: ; make Then there is ; according to The following was subsequently obtained: The joint distribution function is ; Assumption Then we have: ; Therefore, the generated sequence is random; 3) Complexity analysis: Complexity analysis is performed using fuzzy entropy (FuEn) theory, defined by: ; in ; It is the observation length. It is the dimension of the observed space; The detection value of the detected sequence is obtained. According to the definition of fuzzy entropy, the larger the FuEn of the sequence, the greater the complexity of the sequence.

[0019] Step five specifically involves: i) Collision probability analysis: Authorized users need to occupy Only a series of consecutive time slots can successfully complete their transmission; assuming and They represent and In the The frequency slots occupied by each time slot, of which Assume that within the transmission period of these two data packets there are l The time slots overlap; in this case, in the time slots middle, and The two consecutive time slots overlap, and The l Each time slot is only with The L The time slots overlap; at the same time, since data transmission in different time slots is independent of each other, and The probability of no collision between two transmitted data packets is: Assumption In the The first time slot occupies the first The probability of a frequency gap is Since each frequency slot has the same probability of being occupied, we obtain Similarly, assuming In the The first time slot occupies the first The probability of a frequency gap is We can obtain: .

[0020] Substituting it in, we get: ; To obtain the maximum conflict-free probability, the Lagrange multiplier method and Taylor expansion are introduced for solution. Here, we introduce... As a constraint, set For the Lagrange multipliers, the non-conflict probability maximization algorithm based on the Lagrange multiplier method is used to find them. The maximum value; The algorithm is specifically as follows: 1) Introduce constraint functions and construct the Lagrange multiplier expression: ; 2) For each Taking its partial derivative and setting it to 0, we have ; 3) To Taking its partial derivative and setting it to 0, we have ; 4) For the generated q Solve one more equation; 5) Find the optimal solution ,maximize ; Calculations show that when hour, Having the maximum value yields the maximum probability of no conflict: The probability of a data packet arriving at the transmission channel is further obtained. By approximating it using a Taylor series, the final conflict-free probability is obtained. The probability of a conflict between the two can be expressed as: W represents the number of users it supports.

[0021] ii) System reliability and security analysis: 1) Channel modeling: In the established communication model, without loss of generality, the ground link experiences independent flat Rayleigh fading; therefore, the base station and user... Base stations and jammers jammer and user The channels between them all conform to an exponential distribution; For satellite channels, free-space path loss, rain attenuation, and satellite beam gain will be taken into account and modeled as a composite fading distribution: .

[0022] Represents free space path loss, specifically expressed as , It is the carrier wave, d represents the distance from the beam center to the satellite coverage center, and h represents the satellite altitude; It is satellite beam gain. , Indicates the maximum satellite antenna gain. and These are first-order and third-order Bessel functions. It's a 3dB elevation angle.

[0023] Rain attenuation coefficient is expressed as , It is a rain attenuation coefficient that follows a logarithmic exponential distribution. For phase; 2) Reliability Analysis: The probability that an authorized user can receive information is defined as the reliable transmission probability; the SINR of an authorized user is represented as: ; in, It is the power of the information received by the authorized user. It is the interference power from an external jammer. It is the interference power from the ground system caused by the collision. It is background noise characterized by a zero-mean complex Gaussian random variable; The power received by the authorized user is represented as follows: ; It is the satellite's transmission power. This represents the probability that an authorized user will randomly occupy a specific frequency slot. This represents the collision probability derived earlier; It is the channel gain between the licensed user and the satellite. The channel gain between the licensed user and the ground base station is distributed as described previously; therefore, the specific expression for SINR can be obtained: ; Assuming a decoding threshold Then the reliable transmission probability is ,make Based on the previous channel model, assume that Y follows a parameter of... Based on the exponential distribution of X, and consulting relevant materials, the log-exponential distribution of X is approximately equal to the gamma distribution. Therefore, the probability density functions of X and Y are: ; Substituting the probability density function, the specific reliable transmission probability can be calculated using the following formula: ; In the formula, Y needs to be greater than 0, therefore To simplify the calculation, let ,get . 3) Security Analysis: The received power of the eavesdropper is: Indicates eavesdropper, It is the channel gain between the eavesdropper and the satellite; The interference power obtained by the eavesdropper is expressed as: That's the power of the jammer. It is the channel gain between the eavesdropper and the ground base station. Let represent the channel gain between the jammer and the eavesdropper; substituting these two equations, the eavesdropper's SINR is expressed as: By substitution and The system's safe speed Represented as: The safety rate formula derived here provides a clear metric for verifying the safety of the system; the system's safety can only be guaranteed when the result is greater than zero; furthermore, the larger the result, the safer the system. This provides a corresponding metric for comparing the safety of various methods in simulations.

[0024] A system for implementing a satellite-ground integrated secure transmission method based on intelligent non-stationary control includes an available frequency slot set acquisition module, a spectrum dynamic control access protocol generation module, and a system reliability and security performance evaluation module. The available frequency slot set acquisition module is used to perceive and predict the time-frequency domain interference situation and spectrum occupancy status of the satellite-ground fusion link, and uses an improved reinforcement learning method to dynamically select the available frequency slot set that meets the transmission reliability constraints, laying the foundation for the generation of subsequent information transmission sequences.

[0025] The spectrum dynamic control access protocol generation module is used to generate an initial high-security basic sequence by using the time stamp (TOD) and network identification key of the satellite-ground fusion communication system through nonlinear transformation, and to generate a sequence family to adapt to multi-user transmission through a multi-round cyclic iteration method, as well as to generate a non-stationary transmission waveform sequence for signal transmission in the acquired available frequency slot set. The system reliability and security performance evaluation module is used to construct a multi-dimensional evaluation index system, including indicators such as sequence randomness, uniformity, and complexity, as well as system reliable transmission probability and security rate indicators. Through a combination of theoretical analysis and simulation verification, the module quantitatively evaluates the reliable transmission performance and security defense capabilities of the proposed transmission method under complex electromagnetic environments and malicious attack scenarios, providing support for system optimization and engineering deployment.

[0026] The beneficial effects of this invention are: This invention proposes a secure transmission protocol for space-to-ground convergence in complex electromagnetic environments, based on intelligent non-stationary control. This protocol breaks through the limitations of traditional single-dimensional control by intelligently managing and allocating time-frequency resources. It guides users to orderly occupy available spectrum resources for data transmission using non-stationary control sequences, avoiding spectrum conflicts caused by disorderly contention while improving the system's anti-interference performance and anti-eavesdropping capabilities. Furthermore, addressing the issue of transmission collisions caused by multiple users occupying the same frequency slot when sharing spectrum resources in space-to-ground networks, this invention derives optimal frequency slot usage rules through mathematical derivation, effectively reducing the probability of transmission conflicts between users in space-to-ground converged systems. This protocol achieves synergistic optimization of interference avoidance and orderly transmission, laying the foundation for the secure and reliable operation of space-to-ground converged communication.

[0027] This invention proposes an improved reinforcement learning-based method for selecting available frequency slot sets. This method first utilizes LSTM deep analysis of historical spectrum state data to capture the temporal evolution patterns of interference, such as the velocity and direction of linear frequency sweep interference, and the statistical patterns and dwell times of random burst interference, thereby predicting the spectral interference probability of subsequent time slots. Based on the obtained probabilities, a reinforcement learning network is further used to dynamically decide on the available frequency slot set, outputting a continuously available frequency slot set with low interference probability, rather than being limited to currently available slots. Ultimately, this enables intelligent control transmission signals to still operate in frequency bands with good communication quality even with sensing lag, improving the reliability of satellite-to-ground transmission under dynamic interference environments.

[0028] This invention introduces cryptographic theory and non-stationary transmission theory. By dynamically transforming the information sequence into orthogonal non-stationary waveform signals within the available frequency slot set, it simultaneously exhibits irregular dynamic non-stationary characteristics in multiple dimensions such as time, space, and frequency. This prevents intelligent jammers and eavesdroppers from reconstructing the overall sequence transmission waveform from the obtained partial sequences, and makes it impossible for them to predict the authorized user's spectrum usage rules. This fundamentally cuts off the complete acquisition of information transmission by jammers and eavesdroppers. Furthermore, since the rules for acquiring the available frequency slot set are also unknown to unauthorized users, generating non-stationary control sequences within the acquired available set further enhances the system's security and reliability. Through this dual-protection mechanism, this method provides a framework that efficiently integrates system security and reliability, enabling the system to achieve secure data transmission while resisting various dynamic interferences.

[0029] This invention proposes derivation formulas for uniformity and randomness, and constructs a complete theoretical verification system. Regarding the derivation of uniformity, based on probability theory principles, derivation methods are established for two scenarios: normal mapping and overflow mapping, demonstrating the uniformity of the sequence across all scenarios. For randomness, a derivation method based on conditional probability and joint distribution is established, combined with the iterative characteristics of the block cipher of the basic sequence, demonstrating the independence of each part of the sequence. This derivation method provides rigorous theoretical support for the core performance of the sequence, avoiding the limitations of relying solely on simulation results, making the uniformity and randomness of the sequence provable and universal, further proving the security foundation of the entire transmission system. Attached Figure Description

[0030] Figure 1 This is a framework diagram of the technical solution of the present invention.

[0031] Figure 2 This is a system model diagram of the present invention.

[0032] Figure 3 This is a diagram of the transmission scheme of the present invention.

[0033] Figure 4 This is the network diagram of the improved slot set selection algorithm of this invention.

[0034] Figure 5 This is a diagram of the intelligent non-stationary control sequence generation algorithm of the present invention.

[0035] Figure 6 This is a collision diagram of data transmission in the system of this invention.

[0036] Figure 7 This is a comparison diagram of the randomness of the sequence in this invention.

[0037] Figure 8 This is a spectrum showing the success rate of frequency slot selection in this invention.

[0038] Figure 9 This is a comparison chart of the sequence complexity of the present invention.

[0039] Figure 10 This is a graph showing the prediction success rate of the present invention under different allowable error ranges.

[0040] Figure 11 This is a comparison chart of the reliable transmission probability of the scheme under different decoding thresholds of the present invention.

[0041] Figure 12 This is a comparison chart of the safe rate of the present invention under different number of frequency slots. Detailed Implementation

[0042] The present invention will now be described in further detail with reference to the accompanying drawings.

[0043] like Figure 1 As shown, a satellite-ground integrated secure transmission method based on intelligent non-stationary control includes the following steps; Step 1: Construct a time-frequency dual-dimensional satellite-to-ground fusion transmission model: i) System model construction: To facilitate research, this invention constructs a satellite-ground integrated transmission communication scenario model, such as... Figure 2 As shown in the figure, the model includes satellites, terrestrial base stations (TBS), licensed users, active interference sources, and some randomly distributed passive eavesdropping devices. To improve spectrum utilization, the satellites and TBS share the same spectrum resources, and the proposed intelligent non-stationary control scheme is applied for data transmission in the overlapping coverage area. It is assumed that… Indicates an authorized user connected to the satellite. This represents users associated with the TBS. Additionally, the satellite-to-ground communication network integrates agents for spectrum sensing, learning, and security decision-making tasks to respond appropriately to environmental changes. Furthermore, some passive eavesdroppers are hidden within this established communication environment, attempting to intercept information transmitted from satellites or the TBS to users. Besides eavesdroppers, the model also considers active jammers that interfere with normal data transmission.

[0044] ii) Time-frequency resource allocation and transmission cycle layering: Based on the model, the time-frequency resources and communication cycle during transmission are divided, as illustrated in the diagram below. Figure 3 As shown. To cope with the complex spectrum environment, the total bandwidth is divided into equally spaced q... n A non-overlapping frequency band, assuming This represents the set of divided frequency slots, with the total transmission time divided into m distinct time slots. In addition, an information transmission process can be divided into three parts: the perception stage, the learning stage, and the communication stage.

[0045] The specific functions of each module within a communication cycle are as follows: Sensing Phase: In this phase, the spectrum sensing module continuously senses the spectrum status of the communication environment. By collecting characteristics of interference signals, such as duration and direction of motion, it predicts future spectrum status, which can serve as effective input for subsequent slot set selection.

[0046] Learning Phase: In this phase, based on the prediction results, the learning module can use the information fed back from the receiver to classify the divided frequency slots into usable and unusable slots according to the magnitude of interference, thereby obtaining the set of usable frequency slots. Assuming... Represents the available frequency slot set, where It represents the number of available frequency slots selected.

[0047] Communication Phase: In this phase, it is assumed that all authorized users transmit their data packets on the allocated discrete-time channels, using the intelligent non-stationary control sequence proposed in this invention. Authorized users will randomly occupy a frequency slot according to these sequences to transmit data packets, thereby ensuring the security and reliability of the entire transmission process. The satellite-to-ground network transmission scheme based on intelligent non-stationary control can address the challenges of complex spectrum environments with mixed interference and eavesdroppers through the integration of three phases. Therefore, it can achieve efficient spectrum resource allocation and secure information transmission, significantly improving the security and reliability of the system.

[0048] Step 2: Obtaining Low-Interference Continuously Available Frequency Bands: i) Markov model establishment: In the scenario of this invention, the decision model needs to make a decision based on the current spectrum information when selecting a set of available frequency slots, a process that naturally exhibits Markov properties. Therefore, the selection process of the available frequency slot set can be modeled as a Markov decision process (MDP). The process consists of a state space, an action space, a reward function, and an optimization function.

[0049] 1) State space: Assuming the spectrum sensing module uses energy detection to perceive the state of the spectrum environment, power spectral density (PSD) is introduced here to represent the state of each frequency slot. Due to the presence of unauthorized users and malicious jammers, the power received by the sensor in a time slot t can be expressed as: Where S and Jn represent the number of users and jammers, respectively. This represents the power spectral density of the user's baseband signal, and N0 represents Gaussian white noise. This represents the baseband signal power spectral density of the jammer. Additionally... and This represents the channel gain between the user and the jammer. Therefore, the power component in the i-th frequency slot at time slot t can be obtained, which can be expressed as: Here, This indicates the interval between the divided frequency slots. This is the initial frequency of the calculation. Based on the analysis of the PSD, the state space used by this system can be obtained. From this state space, we can obtain the available frequency slots, the interfered frequency slots, and the degree of interference, which provides key input for the agent to finally select the set of available frequency slots.

[0050] 2) Motion space: To ensure the reliability and security of data transmission between satellite and ground, the learning decision model needs to select an appropriate frequency slot as the carrier for information transmission in each time slot. Defined as the action space of the agent during selection, it corresponds to all frequency slot resources allocated in the system. Within this action space, the agent can autonomously select the frequency slot to occupy in the next time slot. Unlike traditional methods where the agent only performs a single action selection, the agent designed in this invention needs to select multiple frequency slots within a single time slot to construct a set of available frequency slots for information transmission; that is, the agent needs to complete the collaborative selection of multiple actions. For this model, the transition probability... Since the instability of the environment is difficult to model, this invention adopts model-free reinforcement learning, and achieves adaptive response to the environment through interactive sampling and neural network function approximation.

[0051] 3) Reward function: When the selected time slot encounters interference, transmission will be affected or even interrupted, resulting in a significant decline in communication quality. In each time slot t, the intelligent agent, based on its state space, selects from the available spectrum... A subset of available channels. To guide the agent in making reliable and robust slot selection decisions, this scheme designs a reward function that integrates multi-dimensional incentives. This function includes three core components: a successful transmission incentive, a failed transmission penalty, and a slot quantity incentive. Its design goal is to encourage the agent to prioritize slots with lower interference probabilities, thereby ensuring transmission reliability while selecting as many available slots as possible. Based on the above design, the reward function can be defined as follows: in, It is a fuzzy factor, meaning that the specific reward value can be adjusted.

[0052] 4) Optimize the function: The agent's goal is to find the optimal strategy that maximizes the expected cumulative reward over time. In this invention, it is assumed that... The value function representing the optimal state is defined from the state. The maximum expected return to begin with and follow the optimal strategy. This can be expressed as: in The optimal action-value function represents the agent's state. Using the expected reward obtained after performing action a, the optimal Q-function satisfies the Bellman optimality equation: In this formula, This represents the discount factor. It's an instant reward, also, This represents the transition probability. In the system model established in this invention, a neural network function is used to approximate the transition probability. .

[0053] During transmission, the agent learns and estimates the Q-value corresponding to each state-action pair, enabling it to select the most suitable set of frequency slots in each time slot to maximize the reliability and security of long-term communication in dynamic environments. Therefore, the process of the agent finding the optimal low-interference frequency slot set is transformed into finding the value of maximizing the Q-function, thus realizing a mathematical representation of the problem and laying a foundation for subsequent optimization.

[0054] ii) Improved DQN-based low-interference slot set acquisition algorithm: Q-learning is often used to solve the MDP problem proposed in the previous step, but due to the large state-action space in this invention, it significantly increases the computational burden and reduces learning efficiency. To address this issue, Deep Reinforcement Learning (DQN) is used. Unlike the previously mentioned Q-learning, DQN employs an experience replay method, processing each transition pair consisting of the current state, action, next state, and reward. The experience is stored in an experience pool and randomly drawn from this pool during training. DQN uses a dual-network structure for training, consisting of a target network and a training network. When updating the Q-network, experience is randomly drawn from the experience pool D. Using a sample, training efficiency is improved by breaking the correlation between samples, and the target Q is calculated. and with mean squared error The loss function is used to update the trained network.

[0055] However, in order to adapt to the complex electromagnetic environment and spectrum sharing characteristics of the satellite-ground fusion transmission model of this invention, this invention addresses the adaptation defects of the traditional DQN algorithm in this scenario and makes corresponding improvements to the traditional DQN algorithm, thereby forming an optimized algorithm that has both interference time-frequency feature extraction capability and multi-frequency slot collaborative decision-making capability. The improved algorithm structure is shown below.

[0056] First, unlike common DQNs that rely solely on the current state for decision-making, this method introduces Long Short-Term Memory Networks (LSTMs) to handle the temporal evolution of interference and predict the spectral state of subsequent states, thus compensating for the insufficient utilization of historical information in traditional state management. The unique gating mechanism of LSTMs (including input gates, forget gates, and output gates) allows it to act as a "memory unit," selectively retaining important historical information and forgetting redundant information, thereby accurately capturing the temporal dependencies of interference patterns. By analyzing past... Spectral state of each time slot By performing in-depth analysis, LSTM can extract the dynamic characteristics of interference from historical data and output accurate predictions of the probability of interference in future time slots, thus obtaining the spectral interference status at subsequent times. For example, for linear frequency sweeping interference, LSTM can learn its sweeping speed and direction; for random burst interference, it can analyze its statistical regularity and dwell time. These temporal characteristics learned from history are crucial information that traditional DQN states cannot provide at all. Subsequently, this acquired predictive information will be combined with the current spectral state. Combining these inputs into a strengthened state for the agent can be represented as follows: This approach integrates instantaneous observations of the current environment with future risk predictions based on historical inferences. Therefore, the improved DQN algorithm, when evaluating the Q-value of each slot, has a more comprehensive and forward-looking decision-making basis. It not only focuses on whether a slot is currently available but also assesses whether it will remain safe in the near future. If a slot is currently available but LSTM predicts it is highly likely to be compromised by interference in the next second, its Q-value will be significantly reduced, guiding the agent to prioritize currently available slots that are more stable and less likely to be interfered with in the future. By introducing LSTM for in-depth mining and feature extraction of historical interference information, this scheme successfully integrates the time-frequency dynamics of interference into the decision-making process, greatly enhancing its adaptability to non-stationary interference environments and the long-term reliability of decisions.

[0057] Furthermore, the proposed scheme requires obtaining a set of available frequency slots with high Q values. Therefore, unlike DQN with single-action output, this method requires a combination of actions based on the selected N frequency slots, i.e., selecting... The overall reward is used to update the Q-value after the action selection. Therefore, the loss function can be calculated as follows: After obtaining the list of available frequency slots, these slots need to be sorted in descending order of their Q values, and the top N slots are selected as the final set. This method, by updating the Q value for each slot in the combination, not only avoids the computational difficulties caused by multi-band combination explosion, but also more accurately reflects the actual contribution of each slot, thereby guiding the strategy to select the set of slots with the least interference.

[0058] This design avoids the inefficient selection of frequency slots caused by traditional equalization Q-value updates by precisely quantifying the actual value of each slot to the overall transmission reliability. Furthermore, by combining the action space and overall reward feedback, it avoids the computational complexity caused by the explosion of multiple slot combinations, enabling the agent to efficiently select the set of continuously available frequency slots with the lowest interference probability. Specifically, as follows... Figure 4 As shown.

[0059] Step 3: Dynamic generation of intelligent non-stationary control sequences: i) Generate the basic nonstationary control sequence: In this invention, the sequence used for data transmission is generated in two parts: the first step is to generate a family of basic sequences with comprehensive performance, and the second step is to adaptively remap this sequence to the set of available frequency slots obtained in the previous step. Cryptographic theorems can be applied to the basic sequences using the equivalence principle. The generation of [the system] is achieved by considering the TOD (Transmission of Data) and network identification key of the entire communication system. The generation steps can be represented as follows: in It is a sub-part separated from TOD. It is a subkey obtained from the network identification key. This is the segment number where the entire system performs the separation operation. Assume... Indicates the number of iterations. and They represent as well as These two parameters are 1 when the number of iterations is 8 or 16, and 0 for other values. This represents the XOR operation, and also... and This represents the transformation box used for nonlinear transformations in cryptography. It is the result of the iterative operation.

[0060] ii) Iteratively generate sequence families: After generating the basic sequence, it needs to be expanded into a set of K sequences to provide K authorized users with transmission sequences that are difficult for jammers or passive eavesdroppers to trace, thereby improving the system's spectrum utilization and security. Therefore, the sequence obtained in the previous step... Perform K rounds of iteration to obtain K distinct sequences, assuming... The generated sequence family is represented by the following steps. iii) Obtaining the reference value factor: After obtaining the basic sequence, the sequence can be remapped through the following steps to generate the intelligent non-stationary control sequence used in this invention. This sequence can generate a corresponding new sequence based on the number of available frequency slots, adapting to complex communication environments when the number of available frequency slots changes. First, the reference factor is obtained. As shown below: in, This refers to the total number of frequency slots divided in the communication model of this invention. It is the number of frequency slots in the acquired set of available frequency slots.

[0061] It is the floor function. Then, the generated basic sequence family... and Compare to obtain the desired mapping order The specific steps are as follows: iv) Dynamic generation of nonstationary control sequences Finally, using these mapping orders, the available set of frequency slots, and the generated family of basic sequences, the final sequence can be obtained: According to the proposed generation scheme, the generation method of this sequence can be combined with the low-interference, continuously available frequency slot acquisition method to generate an intelligent non-stationary spectrum control sequence for transmission. This sequence can select frequency slots with low interference probabilities and simultaneously generate a set of intelligent non-stationary transmission sequences with dynamic non-stationary characteristics from these frequency slot sets. This enhances its adaptability in complex environments and ensures the reliability and security of the communication system. The overall flowchart is as follows: Figure 5 As shown.

[0062] Step 4: Performance Analysis of Non-Stationary Control Sequences This invention utilizes relevant theories from probability theory to propose two theorems and a method to measure the overall performance of sequences. This probability-based analysis method not only provides a rigorous theoretical foundation for evaluating sequence performance but also helps to better understand and optimize the performance of sequences in practical applications.

[0063] 1) Homogeneity analysis: As discussed earlier, two scenarios may occur during the mapping process: normal order and overflow order. First, we discuss the distribution of the intelligent non-stationary control sequence when the normal order occurs, i.e., without overflow, due to the generated base sequence. If a uniform distribution is satisfied, then The probability is: .

[0064] Therefore, for Furthermore, we can obtain: Based on the mapping process described above, for ,have indivual ,make Therefore, we can obtain: Furthermore, we will continue to prove the generated sequence. Uniformity, due to It can be rewritten in this form: Here, we will first prove a theorem to facilitate understanding of... Analysis of properties, assumptions It is The sequence of bases satisfies uniformity, which gives us: And assume It is A sequence of numbers in base S, and independent of S. If Represented as Assuming It is a sequence The range, then for , The probability is: Since X and S are independent, this expression can be further expressed as: Here, we can see the one-to-one mapping relationship between a and b, and we can obtain: Substituting it in, we can obtain ,Right now It conforms to a uniform distribution.

[0065] Finally, this proof leads to the conclusion that if S is uniformly distributed and X is independent of S, then the sequence... It also conforms to a uniform distribution.

[0066] Therefore, we obtain The generated intelligent non-stationary control sequence satisfies a uniform distribution when there is no overflow computation.

[0067] For the overflow portion, the probability distribution is: , when hour, Get the maximum value but When N is large enough, =0, therefore, the probability of overflow computation events can be ignored. In summary, the generated sequence is uniform.

[0068] Uniformity refers to the equal probability that each element of the sequence and each frequency slot in data transmission are used by authorized users. This can make the signal frequency domain have no obvious characteristics, improve the anti-interference and anti-interception capabilities of the communication system. Therefore, uniformity analysis of the transmission sequence is an indispensable part of ensuring the security of the transmission system. 2) Randomness analysis Randomness means that any two sequences of a smart non-stationary control sequence are independent of each other; that is, they must satisfy: Assumption and These are the two parts of the generated sequence. Using conditional probability, we can obtain: make Then there is ; according to The following can be obtained: ; The joint distribution function is Analysis of the randomness of the sequence can verify that any element in the sequence is independent and has no statistical correlation, thus making the frequency slot occupancy of authorized users non-recursive and improving the security of satellite-to-ground communication. Since the basic sequence generated by this invention is obtained by employing a similar block cipher iterative scheme, based on the principle of equivalent design and without loss of generality, it is assumed that... Then we have: Therefore, the generated sequence is random.

[0069] 3) Complexity analysis: Methods for evaluating sequence complexity primarily focus on linear complexity detection. However, these methods are limited to sequences generated based on finite field theory and are not suitable for detecting sequences generated based on chaos theory or other advanced sequence types. To measure the complexity of the proposed control sequence, this paper applies fuzzy entropy (FuEn) theory. Fuzzy entropy is defined as follows: in It is the observation length. It is the dimension of the observation space.

[0070] The detection value of the detected sequence can be obtained. According to the definition of fuzzy entropy, the larger the FuEn of the sequence, the greater the complexity of the sequence.

[0071] Sequence complexity reflects the difficulty of recovering a complete sequence from a partial sequence. The higher the complexity, the more difficult the recovery. Even if a high-complexity sequence is intercepted, unauthorized users will find it difficult to decipher the complete information from the fragments, thus improving the anti-eavesdropping capabilities of communication systems. Therefore, sequence complexity can be used to assess the security of communication systems.

[0072] Step 5: Performance Analysis of the Satellite-to-Ground Transmission System Based on Intelligent Non-Stationary Control i) Collision probability analysis: It is worth noting that the intelligent non-stationary control-based scheme applied in this invention, due to the sharing of the same spectrum resources between satellite and terrestrial networks, may lead to collisions and transmission interference as authorized users connected to different systems simultaneously occupy the same frequency slots. Within a single cycle, the collision model caused by information transmission from different systems is as follows: Figure 6 As shown.

[0073] This figure shows the selection and satellite user ( ) and users who choose to use ground base stations ( The data packet transmission process. Authorized users need to occupy... Only a series of consecutive time slots can successfully complete their transmission. Let... and They represent and In the The frequency slots occupied by each time slot, of which Assume that within the transmission period of these two data packets there are lThe time slots overlap. In this case, in the time slots middle, and The two consecutive time slots overlap, and The l Each time slot is only with The L The time slots overlap. At the same time, since data transmission in different time slots is independent of each other, and The probability of no collision between two transmitted data packets is: Assumption In the The first time slot occupies the first The probability of a frequency gap is Since each frequency slot has the same probability of being occupied, we obtain Similarly, assuming In the The first time slot occupies the first The probability of a frequency gap is We can obtain: .

[0074] Substituting it in, we get: , To obtain the maximum conflict-free probability, the Lagrange multiplier method and Taylor expansion are introduced for solution. Here, we introduce... As a constraint, set To find the Lagrange multipliers, follow these steps: The maximum value.

[0075] Algorithm 1: Non-conflict probability maximization algorithm based on Lagrange multiplier method: 1) Introduce constraint functions and construct the Lagrange multiplier expression: 2) For each Taking its partial derivative and setting it to 0, we have 3) To Taking its partial derivative and setting it to 0, we have 4) For the generated q Solve one more equation.

[0076] 5) Find the optimal solution ,maximize Calculations show that when hour, Having the maximum value yields the maximum probability of no conflict: The probability of a data packet arriving at the transmission channel is further obtained. By approximating it using a Taylor series, the final conflict-free probability is obtained. The probability of a conflict between the two can be expressed as: W represents the number of users it supports.

[0077] ii) System reliability and security analysis: 1) Channel modeling: In this analysis, it should first be clarified that, without loss of generality, the communication model established in this invention... The terrestrial link experiences independent, flat Rayleigh fading, therefore the base station and user... Base stations and jammers jammer and user The channels between them all conform to an exponential distribution.

[0078] For satellite channels, free-space path loss, rain attenuation, and satellite beam gain will be taken into account and modeled as a composite fading distribution: .

[0079] Represents free space path loss, specifically expressed as , It is the carrier wave, d represents the distance from the beam center to the satellite coverage center, and h represents the satellite altitude.

[0080] It is satellite beam gain. , Indicates the maximum satellite antenna gain. and These are first-order and third-order Bessel functions. It's a 3dB elevation angle.

[0081] Rain attenuation coefficient can be expressed as , It is a rain attenuation coefficient that follows a logarithmic exponential distribution. For phase.

[0082] 2) Reliability Analysis: Based on Wiener's work, during data transmission, information can only be received normally if the authorized user's SINR is greater than the decoding threshold. According to this theory, this invention defines the probability that an authorized user can receive information as the reliable transmission probability. In the system established in this invention, the authorized user's SINR can be expressed as: in, It is the power of the information received by the authorized user. It is the interference power from an external jammer. It is the interference power from the ground system caused by the collision. It is background noise characterized by a zero-mean complex Gaussian random variable.

[0083] In the proposed model, the information received by the authorized user is transmitted using an intelligent non-stationary control sequence. Therefore, interference from external jammers can be ignored. Consequently, the power received by the authorized user can be expressed as: It is the satellite's transmission power. This represents the probability that an authorized user will randomly occupy a specific frequency slot. This represents the collision probability derived previously. It is the channel gain between the licensed user and the satellite. This represents the channel gain between the licensed user and the ground base station, and its distribution is as described previously. Therefore, the specific expression for SINR can be obtained: Assuming a decoding threshold Then the reliable transmission probability is To simplify the subsequent calculations, let Based on the previous channel model, assume that Y follows a parameter of... From the available information, the log-exponential distribution of X can be approximated by the gamma distribution. Therefore, the probability density functions of X and Y are: , Substituting the probability density function, the specific reliable transmission probability can be calculated using the following formula: , In the formula, Y needs to be greater than 0, therefore To simplify the calculation, let ,get . This formula analyzes the reliability of communication systems based on non-stationary control transmission methods from the receiver's perspective. By deriving a closed-form formula for calculating the reliable transmission probability based on the signal-to-interference-plus-noise ratio of the signals received by authorized users, it provides a quantitative assessment of the transmission reliability of satellite communication systems. The higher the reliable transmission probability, the stronger the system's reliability. This provides a clear and solid theoretical basis for optimizing system transmission parameters and improving communication reliability in complex electromagnetic environments based on actual communication needs. It can be seen that the system's transmission reliability probability is related to the data transmission length and the set of available frequency slots. Therefore, the formulation of this closed-form formula can provide a solid foundation for system transmission reliability analysis.

[0084] 3) Security Analysis: Also based on Wiener's eavesdropping channel model, secure transmission can only be achieved when the difference between the SINR of the authorized user and the SINR of the eavesdropper is greater than 0. For the eavesdropper, the intelligent non-stationary control sequence applied by the authorized user is unknown; therefore, the eavesdropper can only reside on one or more frequency slots to acquire the data sent to the user. The received power received by the eavesdropper is: Indicates eavesdropper, It is the channel gain between the eavesdropper and the satellite.

[0085] Meanwhile, due to the lack of corresponding anti-interference measures, the eavesdropper will receive interference power from an external jammer when receiving information. The interference power obtained by the eavesdropper can be expressed as: That's the power of the jammer. It is the channel gain between the eavesdropper and the ground base station. Let represent the channel gain between the jammer and the eavesdropper. Substituting these two equations, the eavesdropper's SINR can be expressed as: By substitution and The system's safe speed It can be represented as: The safety rate formula derived here provides a clear metric for verifying the safety of the system. The system's safety can only be guaranteed when the result is greater than zero. Furthermore, the larger the result, the safer the system. This provides a corresponding indicator for comparing the safety of various methods in simulations.

[0086] This invention, combining spectrum sensing with intelligent non-stationary control as its core, proposes a space-to-ground integrated secure transmission method for complex electromagnetic environments, aiming to improve spectrum utilization efficiency while ensuring communication reliability and security. Specifically, it constructs a space-to-ground integrated transmission model in both time and frequency dimensions. It obtains the available frequency slots for information transmission through spectrum sensing and further designs a method for generating non-stationary control sequences. By transforming the information sequence into orthogonal non-stationary waveform signals within the frequency slot set, it simultaneously exhibits irregular dynamic non-stationary characteristics in multiple dimensions such as time, space, and frequency. This guides users to occupy available frequency slots in an orderly manner while enhancing the anti-interference performance and security of information transmission. To further enhance the system's anti-interference capability, this invention combines reinforcement learning theory to propose a low-interference frequency slot set acquisition method based on feature mining and dynamic decision-making. It combines short-term prediction of spectrum interference states using a long short-term memory network with dynamic screening using a deep Q-network to output a continuously available frequency slot set with low interference probability. This achieves forward-looking spectrum resource selection and release while improving the reliability of the transmission system. Finally, by conducting reliability and security analysis on the space-to-ground communication system and calculating the reliable transmission probability and security capacity, it provides a theoretical basis for system optimization design. This invention, through the synergy of intelligent spectrum sensing, non-stationary sequence generation, and orthogonal resource allocation, forms a unified architecture for space-ground network security transmission. It is expected to improve the limited interference and eavesdropping resistance of space-ground communication systems in complex electromagnetic environments, thereby enhancing spectrum utilization and communication survivability. This provides effective theoretical support and technical assurance for safeguarding space information infrastructure and maintaining national space security. System Performance Analysis To more intuitively demonstrate the performance of this invention, for sequence performance, the statistical performance of the Intelligent Non-stationary Control Sequence (INCS) generated by this invention is simulated by comparing it with some existing sequences: a finite-field FH sequence (FFS) with 2^k-2^m slots, a 6th-order coupled-mapped lattice chaotic sequence (CMLS), and a 4th-order Chebyshev chaotic sequence (CHS). Simultaneously, regarding reliability and security, this chapter demonstrates the success rate of the system in selecting stable and available slots to compare the system's ability to avoid fixed-mode interference, and also shows the sequence's anti-prediction performance to compare the system's ability to resist tracking interference. Furthermore, comparative simulation graphs of the system's reliable transmission probability and secure rate are presented to confirm that the method proposed in this invention can improve the reliability and security of satellite communication in complex electromagnetic environments.

[0087] 1) Sequence performance By comparing the standard chi-square test values, the homogeneity of the sequence can be obtained. If the chi-square value is less than the chi-square test reference value, it can be considered a homogeneous sequence. Table 1 clearly shows that, regardless of the number of low-frequency or high-frequency slots, all results of the INCS established in this invention are equal to 100%, while the result of CMLS is 0%. Although the results of FFS and CHS are greater than 90%, they are still lower than those of INCS. This indicates that, compared with other methods, INCS can maintain good homogeneity across different frequency slots.

[0088] Table 1. Comparison of Sequence Uniformity Figure 7 The test results for the randomness of the sequences are displayed. It can be seen that as the observation length increases, all test results for INCS are less than the reference value, while most test results for sequences based on chaos theory (CMLS and CHS) and finite field theory (FFS) are much greater than the reference value. In particular, all values ​​for CHS and FFS are greater than the reference value. This indicates that, compared to other schemes, the proposed INCS exhibits the best randomness, maintaining good uniformity across different observation lengths and reducing the probability of being cracked. Compared to other schemes, the short period of FFS means that the sequence will repeat in a shorter time, which significantly reduces the randomness of the sequence. Furthermore, it is worth noting that, compared to the CMLS method, the proposed method is not limited by the finite word length effect, and the mathematical operations in the generation process are more accurate. Therefore, it can generate high-performance sequences in dynamic and complex electromagnetic scenarios.

[0089] 2) Anti-interference performance analysis In complex electromagnetic environments, interference encountered during communication can be broadly categorized into two types: fixed-mode interference and learning-based intelligent interference. Fixed-mode interference typically exhibits distinct characteristics, such as frequency sweeping interference, multi-tone interference, and broadband interference. These characteristics can be extracted by neural networks to predict interference patterns over several future time slots. The proposed available frequency slot selection scheme based on an improved LSTM-DQN combination in this invention leverages this characteristic to select frequency slots that are stable and available throughout the entire transmission cycle.

[0090] Figure 8The average success rate of frequency slot selection for the proposed scheme is shown, representing the system's resilience to fixed-mode interference. The graph of the average success probability intuitively reflects the reliability of the proposed method. As can be seen from the graph, the frequency selection success rate of the LSTM+DQN combined method eventually stabilizes at 96% to 98% with faster convergence. This is because the LSTM network can learn the characteristics and patterns of interference, thus providing DQN with a forward-looking prediction of interference probability, guiding the agent to select frequency slots with lower interference probabilities. This method outperforms the DQN method (88%-90%) which relies solely on current observations and strategy-free random selection (approximately 65%). It can be concluded that when facing interference in complex electromagnetic environments, the proposed method can capture the temporal dependence of interference, integrate information from multiple dimensions, and improve the performance of reliable decision-making.

[0091] Besides fixed-pattern interference, with the development of artificial intelligence, learning-based intelligent interference methods are emerging in large numbers. These interference methods can also perform spectrum sensing, obtain historical information about the sequences used in data transmission, analyze and predict subsequent sequences, and thus target interference for data transmission frequency slots. To demonstrate the ability to resist these intelligent interferences, sequence complexity and anti-predictability are effective indicators for evaluating the method proposed in this invention. Figure 9 and Figure 10 Simulation graphs showing the sequence complexity and the accuracy of sequence prediction using an LSTM network are displayed.

[0092] When faced with AI-based tracking and interference, increased complexity makes it difficult for unauthorized users to obtain the transmission sequences of authorized users, thus preventing them from being eavesdropped on and interfered with. Figure 9 As can be seen, regardless of the number of slots, the FuEn of the sequences generated by our proposed scheme is greater than that of other schemes. Therefore, we can conclude that the system's anti-interference capability and security can be improved with the help of INCS. Furthermore, the figure also shows that increasing the number of slots is beneficial to increasing the sequence complexity, which is consistent with the fact that more slots make the sequence more difficult to predict. However, as the observation length increases, the complexity of sequences other than CHS decreases. This is mainly because as the observation length increases, the periodicity of the sequence gradually becomes more apparent. Although CHS is not sensitive to changes in observation length, its FuEn value is always smaller than that of other sequences. Figure 10The graph shows the prediction success rate. A lower prediction success rate means it's more difficult for interferers or eavesdroppers to deduce subsequent transmission sequences from past information. As can be seen from the graph, sequences generated based on chaotic mapping and DQN show a faster increase in prediction accuracy as the error range increases, and reach a high level even within a small error range. While the success rate of the dynamically generated scheme is lower than the previous two schemes, its prediction success rate can still exceed 60% as the error range expands. Compared to other schemes, the INCS proposed in this paper has the lowest prediction success rate. For example, within the same error range (e.g., when the error is ≤6%), its accuracy is significantly lower than sequences generated by other schemes, indicating that this method can effectively resist tracking interference and improve system reliability and security. This is mainly because the proposed method not only achieves frequency selection through LSTM-DQN but also introduces a high-security sequence generated based on cryptographic principles to guide frequency mapping. Both processes are typically random and difficult to predict, thus significantly improving anti-prediction performance.

[0093] 3) System reliability and security analysis The transmission reliability of the proposed intelligent non-stationary control scheme and other multi-domain joint schemes was further analyzed. Figure 11 The performance of the proposed scheme is compared with methods based on artificial noise and dynamic control in terms of reliable transmission probability. Results show that, with a fixed decoding threshold... Under the given conditions, the proposed intelligent non-stationary control scheme exhibits the highest reliable transmission probability, which further increases with increasing transmission power, indicating that the scheme can effectively guarantee reliable system transmission. In contrast, the artificial noise-assisted method, due to the introduction of additional noise, requires higher transmission power to reach the decoding threshold under the same conditions; while the dynamic control-based method, although considering currently available frequency slots, may find these resources unavailable due to interference in subsequent transmission cycles, resulting in a higher degree of interference susceptibility than this scheme. Furthermore, it can be seen that when the decoding threshold... As the probability of reliable transmission decreases from 1 to 2, the overall reliability of each scheme decreases, indicating that the system reliability will be constrained and the performance will be reduced in more complex transmission environments. However, the proposed scheme still performs the best. Finally, the simulation results of the proposed method agree well with the theoretical values, further verifying the correctness of the theoretical analysis.

[0094] Figure 12This paper presents the security rate performance of different secure communication schemes under varying transmission power. The comparison results show that, with the same number of frequency slots, the proposed scheme has a significantly higher security rate than methods based on artificial noise assistance and dynamic control, indicating that it possesses superior security transmission capabilities in eavesdropping channel environments. The performance advantage of the proposed scheme mainly stems from its selection mechanism for the available frequency slot set, which effectively reduces the interference probability of legitimate receivers. Simultaneously, since no similar strategy is implemented against eavesdroppers, the signal-to-interference-plus-noise ratio (SNR) difference between legitimate and eavesdropping links is further widened, thereby improving the system's security rate. In contrast, the dynamic control-based scheme does not fully consider the mobility of interference, resulting in higher received interference power than this scheme; while the artificial noise assistance method indirectly affects the main channel performance while interfering with the eavesdropping channel, causing a decrease in security rate. Furthermore, with increasing transmission power, the security rate of all schemes shows an upward trend, indicating that a favorable transmission environment helps enhance system security performance. Increasing the number of available frequency slots has also been proven to further improve system security, because with more frequency slots, the difficulty for eavesdroppers using stationary eavesdropping schemes to intercept information increases accordingly. In summary, the proposed solution of this invention achieves the best security performance through optimized spectrum resource selection and interference management, and is suitable for reliable communication in dynamic eavesdropping environments.

Claims

1. A satellite-ground integrated secure transmission method based on intelligent non-stationary control, characterized in that, Includes the following steps; Step 1: Construct a time-frequency dual-dimensional satellite-to-ground fusion transmission model and build an overall application scenario; Step 2: Based on the time-frequency dual-dimensional satellite-to-ground fusion transmission model, obtain low-interference, continuously available frequency slots to obtain a frequency slot set; Step 3: By transforming the information sequence within the frequency gap set into orthogonal non-stationary waveform signals, making it exhibit irregular dynamic non-stationary characteristics simultaneously in multiple dimensions of time, space, and frequency, the final sequence is obtained for users to transmit information. Step 4: Analyze the uniformity, randomness, and complexity of the non-stationary control sequence used by the user to prove that the transmission method can guarantee that the information is uniform and random, making it difficult for eavesdroppers to detect, and even if the information is detected, the eavesdropper cannot crack it. Step 5: Perform performance analysis on the entire system using the frequency gap set acquisition module and the non-stationary control sequence. Calculate the signal-to-interference-plus-noise ratio (SINR) of the receiver to obtain the reliable communication probability and secure rate, and then verify this through simulation.

2. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 1, characterized in that, Step one specifically involves: i) Construct a satellite-ground integrated transmission communication scenario model, including satellites, ground base stations, authorized users, active interference sources, and some randomly distributed passive eavesdropping devices; the satellite and TBS share the same spectrum resources, and the proposed intelligent non-stationary control scheme is applied for data transmission in the overlapping coverage area, assuming... Indicates an authorized user connected to the satellite. This refers to users associated with TBS; the satellite-to-ground communication network integrates agents for spectrum sensing, learning, and security decision-making tasks to respond to changes in the environment; in addition, there are passive eavesdroppers hidden in the communication environment of the model, attempting to eavesdrop on information sent from satellites or TBS to users; ii) Based on the model, the time-frequency resources and communication period during transmission are divided, and the total bandwidth is divided into equally spaced q intervals. n A number of non-overlapping frequency slots are used to cope with complex spectral environments, assuming This represents the set of divided frequency slots, with the total transmission time divided into m distinct time slots. In addition, an information transmission process can be divided into a perception stage, a learning stage, and a communication stage.

3. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 2, characterized in that, The specific functions of each module within a communication cycle are as follows: During the perception phase, the spectrum sensing module continuously senses the spectrum status of the communication environment and predicts the future spectrum status by collecting the characteristics of interference signals. This status serves as an effective input for subsequent slot set selection. During the learning phase, based on the prediction results, the learning module uses the information transmitted back from the receiver to classify the divided frequency slots into usable and unusable slots according to the magnitude of interference, thereby obtaining the set of usable frequency slots. Assuming... Represents the available frequency slot set, where It refers to the number of available frequency slots selected; During the communication phase, all authorized users transmit their data packets on the allocated discrete-time channels, using intelligent non-stationary control sequences as the transmission method; authorized users will randomly occupy a frequency slot to transmit data packets according to these sequences.

4. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 1, characterized in that, Step two specifically involves: i) Model the selection process of the available slot set as a Markov decision process; The process consists of a state space, an action space, a reward function, and an optimization function. ii) When updating the Q network, experience pool D will be randomly selected. Using a sample, training efficiency is improved by breaking the correlation between samples, and the target Q is calculated. and with mean squared error The training network is updated using this as a loss function; The improved algorithm is as follows: First, a long short-term memory network is introduced to handle the temporal evolution of interference and to predict the spectral state of subsequent states. Subsequently, this acquired predictive information will be compared with the spectral state obtained at the current moment. Combining these into inputs for a strengthened agent state is represented as follows: This state integrates instantaneous observations of the current environment with predictions of future risks based on historical inferences; The improved DQN algorithm makes more comprehensive and forward-looking decisions when evaluating the Q value of each slot. It not only focuses on whether the slot is currently available, but also assesses whether the slot will remain safe in the near future. If a slot is currently available, but LSTM predicts that its subsequent slots are very likely to be occupied by interference, then the Q value of that slot will be lowered, thereby guiding the agent to prioritize slots that are currently available and more stable and less likely to be interfered with in the future. Based on the combined action of the selected N frequency bands, i.e., selection The overall reward is used to update the Q-value after the action selection. Therefore, the loss function can be calculated as follows: After obtaining the list of available frequency slots, these frequency slots need to be sorted in descending order of Q value, and the top N frequency slots are selected as the final set.

5. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 1, characterized in that, Step three specifically involves: i) Generate the basic nonstationary control sequence: The sequence used for data transmission is generated in two parts: the first step is to generate a family of basic sequences with comprehensive performance, and the second step is to adaptively remap this sequence to the set of available frequency slots obtained in the previous step; cryptographic theorems are applied to the basic sequences through the principle of equivalence. The generation; by considering the TOD and network identification key of the entire communication system, The generation steps are represented as follows: in It is a sub-part separated from TOD. It is a subkey obtained from the network identification key. It is the segment number where the entire system performs the separation operation; assuming Indicates the number of iterations. and They represent as well as; This represents the XOR operation, and also... and This represents the transformation box used for nonlinear transformations in cryptography. It is the result of the iterative operation; ii) After generating the basic sequence, it needs to be expanded to generate a set of K sequences, providing K authorized users with transmission sequences that are difficult for jammers or passive eavesdroppers to trace; using the sequences obtained in the previous step... Perform K rounds of iteration to obtain K distinct sequences, assuming... The generated sequence family is represented by the following steps: iii) After obtaining the basic sequence, the sequence is remapped through the following steps to generate an intelligent non-stationary control sequence; this sequence generates a new sequence based on the number of available frequency slots to adapt to complex communication environments when the number of available frequency slots changes; first, the reference factor is obtained. As shown below: in, It is the total number of frequency slots divided in the communication model. It is the number of frequency slots in the acquired set of available frequency slots; It is the floor function, and then the resulting family of basic sequences is... and Compare to obtain the desired mapping order The specific steps are as follows: iv) Finally, using the mapping order, the available frequency slot set, and the generated family of basic sequences, the final sequence is obtained: 。 6. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 5, characterized in that, Step four specifically involves: 1) Two scenarios may occur during the mapping process: normal order and overflow order. First, we discuss the distribution of the intelligent non-stationary control sequence when the normal order occurs, i.e., when there is no overflow, due to the generated base sequence. If a uniform distribution is satisfied, then The probability is: 。 Therefore, for Furthermore, we obtain: Based on the mapping process described above, for ,have indivual ,make Therefore, we get: Continue to prove the generated sequence Uniformity, due to It can be rewritten in this form: Assumption It is The sequence of bases satisfies uniformity, resulting in: And assume It is A sequence of bases and independent of S, if Represented as Assuming It is a sequence The range, then for , The probability is: Since X and S are independent, the expression can be further expressed as: Here, through the one-to-one mapping relationship between a and b, we obtain: Substitute it in, and you will get ,Right now It conforms to a uniform distribution; Finally, this proof leads to the conclusion that if S is uniformly distributed and X is independent of S, then the sequence... It also conforms to a uniform distribution; Therefore, we obtain The generated intelligent nonstationary control sequence satisfies a uniform distribution when there is no overflow computation; For the overflow portion, the probability distribution is: ， when hour, Get the maximum value ; but When N is large enough, =0, therefore, the probability of an overflow calculation event is ignored; Uniformity means that each element of the sequence and each frequency slot in data transmission have an equal probability of being used by authorized users, which can make the signal frequency domain have no obvious characteristics and improve the anti-interference and anti-interception capabilities of the communication system. 2) Randomness must satisfy: ; Assumption and These are the two parts of the generated sequence. Using conditional probability, we obtain: ； make Then there is ; according to The following was subsequently obtained: The joint distribution function is ; Assumption Then we have: ； Analysis of the randomness of the sequence can verify that any element in the sequence is independent and has no statistical correlation, thus making the frequency slot occupancy of authorized users non-recursive and improving the security of satellite-to-ground communication. 3) Apply fuzzy entropy theory to perform complexity analysis, based on the definition of fuzzy entropy: ； in ； It is the observation length. It is the dimension of the observed space; The detection value of the detected sequence is obtained. According to the definition of fuzzy entropy, the larger the FuEn of the sequence, the greater the complexity of the sequence. Sequence complexity reflects the difficulty of recovering a complete sequence from a partial sequence. The higher the complexity, the greater the difficulty of recovery. Even if a high-complexity sequence is intercepted, unauthorized users will find it difficult to decipher the complete information from the fragments, which can improve the anti-eavesdropping capabilities of communication systems.

7. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 6, characterized in that, Step five specifically involves: i) Authorized users need to occupy Only a series of consecutive time slots can successfully complete their transmission; assuming and They represent and In the The frequency slots occupied by each time slot, of which Assume that within the transmission period of these two data packets there are l The time slots overlap; in this case, in the time slots middle, and The two consecutive time slots overlap, and The l Each time slot is only with The L The time slots overlap; at the same time, since data transmission in different time slots is independent of each other, and The probability of no collision between two transmitted data packets is: Assumption In the The first time slot occupies the first The probability of a frequency gap is Since each frequency slot has the same probability of being occupied, we obtain Similarly, assuming In the The first time slot occupies the first The probability of a frequency gap is ,get: . Substituting it in, we get: ， We introduce the Lagrange multiplier method and Taylor expansion to solve for the maximum conflict-free probability. Here, we introduce... As a constraint, set For the Lagrange multipliers, the non-conflict probability maximization algorithm based on the Lagrange multiplier method is used to find them. The maximum value; ii) In the established communication model, without loss of generality, the terrestrial link experiences independent flat Rayleigh fading; therefore, the base station and user... Base stations and jammers jammer and user The channels between them all conform to an exponential distribution; For satellite channels, free-space path loss, rain attenuation, and satellite beam gain will be taken into account and modeled as a composite fading distribution: ; Represents free space path loss, specifically expressed as , It is the carrier wave, d represents the distance from the beam center to the satellite coverage center, and h represents the satellite altitude; It is satellite beam gain. , Indicates the maximum satellite antenna gain. and These are first-order and third-order Bessel functions. It's a 3dB elevation angle; Rain attenuation coefficient is expressed as , It is a rain attenuation coefficient that follows a logarithmic exponential distribution. For phase; The probability that an authorized user can receive information is defined as the reliable transmission probability; the SINR of an authorized user is represented as: in, It is the power of the information received by the authorized user. It is the interference power from an external jammer. It is the interference power from the ground system caused by the collision. It is background noise characterized by a zero-mean complex Gaussian random variable; The power received by the authorized user is represented as follows: It is the satellite's transmission power. This represents the probability that an authorized user will randomly occupy a specific frequency slot. This represents the collision probability derived previously. It is the channel gain between the licensed user and the satellite. The channel gain between the licensed user and the ground base station is distributed as described previously; therefore, the specific expression for SINR is obtained: Assuming a decoding threshold Then the reliable transmission probability is ,make Based on the previous channel model, assume that Y follows a parameter of... Based on the exponential distribution of X, and consulting relevant materials, the log-exponential distribution of X is approximately equal to the gamma distribution. Therefore, the probability density functions of X and Y are: ； Substituting the probability density function, the specific reliable transmission probability can be calculated using the following formula: ， In the formula, Y needs to be greater than 0, therefore To simplify the calculation, let ,get . This formula analyzes the reliability of communication systems based on non-stationary control transmission methods from the receiver's perspective. It derives a closed-form calculation formula for reliable transmission probability based on the signal-to-interference-plus-noise ratio of the signals received by licensed users, and provides a quantitative assessment of the transmission reliability of satellite communication systems. The received power of the eavesdropper is: Indicates eavesdropper, It is the channel gain between the eavesdropper and the satellite; The interference power obtained by the eavesdropper is expressed as: That's the power of the jammer. It is the channel gain between the eavesdropper and the ground base station. Let represent the channel gain between the jammer and the eavesdropper; substituting these two equations, the eavesdropper's SINR is expressed as: By substitution and The system's safe speed Represented as: The safety rate formula obtained here provides a clear indicator to verify the safety of the system; the safety of the system can only be guaranteed when the result is greater than zero; moreover, the larger the result, the safer the system.

8. The satellite-ground fusion secure transmission method based on intelligent non-stationary control according to claim 7, characterized in that, The optimal frequency slot usage rule was derived, effectively reducing the probability of transmission conflicts between users in a satellite-to-ground fusion system. The algorithm is as follows: 1) Introduce constraint functions and construct the Lagrange multiplier expression: ； 2) For each Taking its partial derivative and setting it to 0, we have ; 3) To Taking its partial derivative and setting it to 0, we have ; 4) For the generated q Solve one more equation; 5) Find the optimal solution ,maximize ; Calculations show that when hour, Having the maximum value yields the maximum probability of no conflict: ； The probability of a data packet arriving at the transmission channel is further obtained. By approximating it using a Taylor series, the final conflict-free probability is obtained. The probability of a conflict between the two is expressed as: W represents the number of users it supports; This formula yields the maximum collision-free probability of inter-system collisions between satellite and terrestrial communication systems, thereby minimizing inter-system interference when receiving information from authorized users and enhancing the reliability and security of the communication system.

9. A system for implementing the satellite-ground fusion secure transmission method based on intelligent non-stationary control as described in any one of claims 1-8, characterized in that, This includes a module for acquiring available frequency slot sets, a module for generating spectrum dynamic control access protocols, and a module for evaluating system reliability and security performance. The available frequency slot set acquisition module is used to perceive and predict the time-frequency domain interference situation and spectrum occupancy status of the satellite-ground fusion link, and to dynamically filter the available frequency slot set that meets the transmission reliability constraints using an improved reinforcement learning method. The spectrum dynamic control access protocol generation module is used to generate an initial high-security basic sequence by using the timestamp and network identification key of the satellite-ground fusion communication system through nonlinear transformation, and to generate a sequence family to adapt to multi-user transmission through a multi-round cyclic iteration method, as well as to generate a non-stationary transmission waveform sequence for signal transmission in the acquired available frequency slots. The system reliability and security performance evaluation module is used to construct a multi-dimensional evaluation index system, including sequence randomness, uniformity and complexity indicators, as well as system reliable transmission probability and security rate indicators. Through a combination of theoretical analysis and simulation verification, the module quantifies the reliable transmission performance and security defense capability of the proposed transmission method under complex electromagnetic environments and malicious attack scenarios, providing support for system optimization and engineering deployment.

10. The application of the satellite-ground fusion secure transmission method based on intelligent non-stationary control as described in any one of claims 1-8, characterized in that, The method is applied to various space-ground integrated secure communication systems and related equipment; The method is applicable to secure transmission in space-ground integrated systems under complex electromagnetic environments, including wireless communication and satellite communication application scenarios involving personal privacy, corporate secrets, or national security. The system includes an integrated intelligent non-stationary control module to guide users to access the communication system in an orderly manner; an intelligent frequency slot selection module to select available frequency slots, including a spectrum prediction unit integrating a long short-term memory network and a frequency slot set selection unit integrating deep reinforcement learning, used to select a set of continuously available frequency slots with low interference probability in complex electromagnetic environments as the medium for information transmission; and a hardware module for sequence generation to transform the information sequence into a transmission waveform sequence with dynamic non-stationary characteristics in multiple dimensions. The reliable transmission probability and security rate calculation and analysis module is used to monitor the security and reliability of data transmission in the system in real time, thereby providing data to ensure the secure and reliable communication of the entire system. The aforementioned systems and equipment can be deployed independently or integrated into existing communication infrastructure as add-on modules, and are suitable for various communication network environments that require high reliability and security.

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