Low-delay high-reliability satellite-ground covert communication system and method

Abstract

The invention discloses a low-delay and high-reliability satellite-ground covert communication system and method, and belongs to the technical field of wireless communication, and the method comprises the steps: monitoring a ground monitor Willie through a satellite Alice, and carrying out the communication with a plurality of ground receivers; the satellite Alice is provided with a planar array antenna, the ground receiver is provided with a single antenna, and the ground monitor Willie is provided with two antennas; a wireless channel link between the satellite Alice and the ground receiver is a downlink channel, the ground receiver comprises a hidden ground user and a confidential ground user, the satellite Alice respectively sends a hidden signal and a confidential signal to the hidden ground user and the confidential ground user, and the ground monitor Willie detects the transmission of the hidden signal, so that a communication system with low time delay and high concealment is obtained.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a low-latency, high-reliability, covert satellite-to-ground communication system.

[0002] This invention also relates to a low-latency, highly reliable satellite-to-ground covert communication method. Background Technology

[0003] Geostationary Earth Orbit (GEO) satellite communication links face significant security and efficiency challenges due to their wide coverage (a single satellite covers approximately one-third of the Earth's surface) and long transmission distance (orbital altitude of approximately 36,000 kilometers). On the one hand, their high-orbit characteristics result in severe path loss in satellite-to-ground links, requiring high-gain beams for reliable transmission. However, the electromagnetic characteristics of high-power directional signals are easily detected by enemy monitoring equipment through sidelobe radiation or direction of arrival (DOA) estimation. On the other hand, in dense access scenarios, the high-concurrency access demands of massive ground nodes (such as sensors, UAV swarms, and emergency terminals) make it difficult for traditional unicast communication modes to meet the dual requirements of low latency and high concealment.

[0004] The fixed orbital position and wide-area coverage of GEO satellites make them ideal targets for passive monitoring. Monitors can utilize the global broadcast characteristics of satellite signals to identify communication behavior and even locate ground nodes through energy detection or machine learning algorithms. Covert communication, by confining signal power below the environmental noise floor, can effectively evade detection, but its application in GEO satellite scenarios faces unique challenges: high orbits lead to severe signal attenuation, and low-power covert transmission may sacrifice reliability; while multi-node collaborative scheduling in dense access scenarios exacerbates the trade-off between latency and covertness.

[0005] Multicast technology, as an efficient communication method, can send the same data to multiple target nodes simultaneously, avoiding duplicate data transmission and significantly reducing transmission overhead and time consumption. Using multicast can effectively reduce latency and improve communication efficiency. Therefore, to address the above issues, a multicast-based transmission strategy provides a new approach for high-reliability, low-latency covert communication for GEO satellites. By dynamically dividing densely distributed ground nodes with similar service needs into multicast clusters, the satellite can utilize high-precision beamforming technology to provide directional coverage to the target clusters. This strategy has three advantages: First, the multicast mechanism reduces the number of repeated signal transmissions through spatial multiplexing, significantly reducing system latency. Theoretical analysis shows that... In densely populated access scenarios with multiple nodes, the number of multicast packets It is positively correlated with transmission latency, and the latency optimization ratio can reach [percentage missing]. Secondly, the fixed beam pointing characteristics of GEO satellites, combined with narrow beamforming technology, can concentrate signal energy in the target cluster area. By suppressing sidelobe radiation, signal leakage in non-target areas can be effectively avoided, thereby reducing the probability of being detected by wide-area monitoring equipment. Thirdly, multicast transmission optimizes power allocation through resource integration. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned problems by providing a low-latency, high-reliability satellite-to-ground covert communication system and method. This is achieved by constructing a distributed model of densely connected ground nodes with multiple ground nodes, designing a covert communication implementation method based on beamforming, and establishing a multicast-based transmission strategy to reduce the system's communication latency, thereby obtaining a low-latency, high-coverage communication system.

[0007] The technical solution adopted in this invention is as follows: A low-latency, high-reliability, covert satellite-to-ground communication system, comprising a satellite Alice, several ground receivers, and a ground monitor Willie, wherein the satellite Alice monitors the ground monitor Willie and communicates with the several ground receivers; The satellite Alice is equipped with a planar array antenna, the ground receiver is equipped with a single antenna, and the ground monitor Willie is equipped with two antennas; The wireless channel link between the satellite Alice and the ground receiver is a downlink channel. The ground receiver includes covert ground users and confidential ground users. The satellite Alice sends covert signals and confidential signals to the covert ground users and confidential ground users respectively. The ground monitor Willie detects the transmission of the covert signals.

[0008] The second technical solution adopted in this invention is a low-latency, high-reliability satellite-to-ground covert communication method, employing a low-latency, high-reliability satellite-to-ground covert communication system. The method specifically includes: Initialize all communication links in the system; Construct a covert planetary communication model for densely connected systems, the model comprising: A scenario model, wherein the scenario model is the covert communication system; The channel model specifically models the communication link between the satellite Alice and the ground receiver and the ground monitor Willie, while using beamforming to modify the satellite Alice signal transmission to directional transmission; Ground node model, which models ground nodes using the Boehringer-Pine process; A covert detection model was used to obtain the detection error probability of ground monitor Willie; Performance metrics are used to measure the covert communication model. Establish a multicast-based covert communication transmission protocol for the packet propagation of signals from the Alice satellite; The detection performance of the ground-based detector Willie and the covert communication performance of the aforementioned communication model were analyzed and optimized.

[0009] Furthermore, the channel model is constructed as follows: Link from satellite Alice to ground users The link between satellite Alice and ground monitor Willie All follow Ricean fading, and the link is modeled as follows: (1) In the formula, For Rice factor, For the direct component of the channel, For the scattering component, and The elements of are independent and identically distributed complex Gaussian random variables with zero mean and unit variance, i.e., satisfying . , This refers to the number of lateral antennas in a planar array antenna. This represents the number of longitudinal antennas in a planar array antenna.

[0010] Furthermore, the directional transmission of the satellite Alice is specifically as follows: The satellite Alice, several ground receivers, and the ground monitor Willie are located using a three-dimensional Cartesian coordinate system. The satellite Alice obtains the positions of the ground receivers and uses a beamforming method based on the position information to transmit its antenna beam to the ground receivers in a directional manner.

[0011] Furthermore, the covert detection model specifically uses short packet communication as the transmission method for covert communication in the satellite-to-ground downlink, defining a limited number of channel usage times as... Suppose that ground monitor Willie uses a binary hypothesis to determine whether satellite Alice is sending a covert signal to a ground user. Then, ground monitor Willie... The signal received during the use of each channel is as follows: (2) In the formula, The covert signal sent to Alice satisfies , for Index of the number of times the secondary channel has been used. , This represents Alice's transmission power. Represents path loss. This is the path loss index. It has zero mean and zero variance Additive white Gaussian noise; Ground-based monitor Willie used the minimum likelihood ratio test to distinguish between the null hypothesis and the alternative hypothesis. As a threshold, ground monitor Willie's decision criterion is as follows: (3) In the formula, and and represent the posterior probabilities of the null hypothesis and the alternative hypothesis, respectively. In order to make a decision based on the null hypothesis, To make decisions based on alternative hypotheses.

[0012] Detection errors include false alarm rate and false negative rate, as shown in the following formula: (4) (5) The detection error probability is the sum of the false alarm rate and the false negative rate: (6) The concealment constraint is represented as: (7) In the formula, For the sake of concealment, .

[0013] Furthermore, the performance metrics include: The confidentiality capacity, which is the maximum number of bits that can be transmitted at a given bit error rate, is specifically expressed by the following formula: (8) In the formula, and These represent the channel capacity at the secure ground receiver and the monitor Willie, respectively. The average decoding error probability output by the ground receiver is given by satellite Alice transmitting a packet containing data in each time slot. The probability of packet decoding error for short packets in Knight's information can be given as follows: (9) In the formula, For the transmission rate of the Alice satellite, , The signal-to-interference-plus-noise ratio (SIR) is given by the following formula: (10); Information timeliness is measured using the overall average information freshness (AoI), defined as the mean of the average AoI of all hidden ground users, as shown in the following formula: (11) In the formula, The number of users who are hidden on the ground.

[0014] Furthermore, the packet propagation is specifically as follows: A warning zone (GZ) is defined, encompassing ground users within a certain radius of the ground monitor Willie. Ground users within the GZ transmit information to the satellite Alice via point-to-point communication, while users outside the GZ use multicast transmission. Simultaneously, the DBSCAN algorithm is used to group ground users. After grouping, the ground users within each group are further subdivided according to their security level. The specific subdivision process is as follows: Security level information collection, obtaining the security level identifier for each ground user within the group. ; Coordinate mean calculation: For ground users with different security levels, their coordinates are extracted separately. For users with confidential transmission levels, let the set of users with that level be denoted as . The mean of its coordinates As shown in the following formula: (12) In the formula, express The number of elements in the set; similarly, for covert transmission level users, let the set of such users be . The mean of its coordinates As shown in the following formula: (13) Grouping: Based on the calculated mean coordinate value, the ground users within the group are divided into a secure transmission group and a covert transmission group. Using the mean coordinate value as the center and the distance from the ground receiver in the group that is farthest from the mean coordinate value to the mean coordinate value as the radius, the users within the group are divided into two subgroups: the secure transmission group and the covert transmission group. Once the beamforming direction is determined, the center coordinates of the secure transmission group and the covert transmission group are set as the beamforming illumination direction. The angle and direction of the transmitted beam are adjusted by the satellite Alice to focus the communication beam onto the target user group. After the segmentation is completed, the channel security capacity and AoI of covert transmission for ground users are calculated. Polling multicast optimization sorts the number of hidden users in different groups and prioritizes data transmission to groups with a larger number of hidden users.

[0015] Furthermore, special point processing involves handling points and outliers within the warning zone GZ separately, with point-to-point information transmission via the Alice satellite.

[0016] Furthermore, the performance of the ground detector Willie is measured as follows: (14) In the formula, The transmission power of the Alice satellite. For path loss, This is the path loss index.

[0017] Furthermore, the analysis of the covert communication performance of the communication model specifically involves the fact that each group contains multiple covert ground receivers. Therefore, the overall performance of the group is dominated by the network node with the worst channel conditions. Therefore, the average decoding error probability at the covert ground receiver with the worst channel quality in the packet is as follows: (15) In the formula, For signal-to-interference-plus-noise ratio The cumulative distribution function, , , For the transmission rate of the Alice satellite, As shown in the following formula: (16); The average information freshness (AoI) for each group is as follows: (17) The optimization process involves minimizing the information freshness (AoI) at the concealed ground receiver, which requires minimizing... Therefore, the optimized formula is constructed as follows: (18) (19) (20) (twenty one) In the formula, the constraint conditions To ensure concealment constraints, constraint conditions To ensure confidentiality, capacity constraints and conditions are required. Ensure the effectiveness of transmission power; The optimal transmit power is as follows: (twenty two) In the formula, KT This is the channel quality factor.

[0018] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention constructs a densely distributed ground node model with multiple ground nodes, designs a covert communication implementation method based on beamforming, constructs a ground node model for dense access, constructs a multicast-based transmission strategy to reduce system communication latency, designs a low-latency, high-reliability covert communication method for dense access, utilizes the planar array antenna of satellite equipment to achieve beamforming-based directional transmission, thereby assisting in the covert communication of the satellite-to-ground link, designs a multicast-based satellite-to-ground covert communication grouping strategy and transmission strategy, designs a grouping strategy based on the constructed ground node distribution, and designs a transmission strategy based on the final grouping results for covert transmission.

[0019] This invention also analyzes the detection performance of ground-based monitors, obtains concealment constraints, calculates the confidentiality capacity of the secure transmission link, analyzes the performance of a densely accessed, low-latency, high-reliability satellite-to-ground covert communication method, and derives the decoding error probability and average information freshness (AoI) at the receiver. An optimization problem for minimizing the average AoI of the covert link is established. Through analysis and solution of this optimization problem, the optimal solution satisfying the average AoI of the covert link is obtained under the premise of satisfying concealment and confidentiality.

[0020] Finally, simulation experiments were conducted to verify the correctness and superiority of the theoretical design and analysis, and to analyze the impact of different parameters on the performance of the multicast system. Furthermore, a performance comparison with traditional unicast communication methods further illustrates the superiority of the proposed method. Attached Figure Description

[0021] Figure 1 This is a model diagram of the densely connected downlink satellite-to-ground covert communication system of the present invention; Figure 2 This is a schematic diagram of the system flow of the present invention; Figure 3 This is a geometric relationship diagram between the planar antenna array and the ground node of the present invention; Figure 4 This is a distributed simulation diagram of the Matern cluster process of this invention; Figure 5 This is a schematic diagram of the multicast transmission protocol flow of the present invention; Figure 6 This is a schematic diagram illustrating the radius values ​​of the warning area in this invention; Figure 7 This is a subdivision diagram within the group of this invention; Figure 8 This is a schematic diagram of the ground node angle difference of the present invention; Figure 9This is a diagram of the secure transmission receiver and the covert transmission receiver with the worst channel quality according to the present invention. Figure 10 This is a schematic diagram illustrating the process of analyzing and optimizing the covert communication performance of this invention; Figure 11 This is a diagram showing the grouped simulation results of the present invention; Figure 12 This is a graph showing the variation of AoI with the radius of the warning area in this invention; Figure 13 This is a graph showing the variation of AoI with the radius of the warning area under certain special circumstances according to the present invention; Figure 14 This invention relates to AoI with hidden constraints. Change diagram; Figure 15 This invention relates to AoI with Matern cluster parameters. Change diagram; Figure 16 This is a graph showing the variation of AoI with the DBSCAN grouping algorithm parameter minPts. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings.

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0024] Example 1 This embodiment provides a downlink satellite-to-ground covert communication system for densely connected systems, and the scenario model is as follows: like Figure 1 As shown, the system in this embodiment includes a satellite transmitter Alice, a large number of ground receivers, and a ground monitor Willie. The ground receivers are divided into two types based on different security requirements: covert ground users and secure ground users. The satellite transmitter Alice is equipped with a planar array antenna, each ground monitor Willie is equipped with two antennas, and each ground receiver is equipped with a single antenna. The channel between the satellite transmitter Alice and the ground receivers is a downlink channel. The satellite transmitter Alice intends to send covert signals to covert ground users and secure signals to secure ground users. The covert and secure signals are orthogonal to each other. The satellite transmitter Alice evades detection by the ground monitor Willie while transmitting the covert signal.

[0025] Example 2 This embodiment provides a covert communication method based on beamforming and cooperative jamming techniques for densely intervening in satellite-to-ground communication links, such as... Figure 2 As shown, please follow these steps: Step 1: Initialize all links in the system; Step 2: Construct a downlink satellite-to-ground covert communication system for dense connections, including a scenario model, channel model, ground node model, detection model, and performance metrics, wherein the scenario model is as described in Example 1; Step 2.1: Construct a channel model, assuming that all communication links experience large-scale path loss and small-scale multipath fading, from Alice to the ground user. Link from Alice to Willie They all follow Ricean decay, modeled as follows: (1) In the formula, For Rice factor, For the direct component of the channel, For the scattering component, and The elements of are independent and identically distributed complex Gaussian random variables with zero mean and unit variance, i.e., satisfying . . This refers to the number of lateral antennas in a Uniform Planar Array (UPA) antenna. This refers to the number of longitudinal antennas in a planar array antenna. This embodiment uses a three-dimensional Cartesian coordinate system to model the positions of all nodes in the communication system, and sets the position of the listener Willie as the origin of the coordinate system. Specifically, using... , and These represent the locations of transmitter Alice, listener Willie, and receiver Bob, respectively. This embodiment assumes that satellite transmitter Alice can know the locations of all ground users through positioning technology, that is, she knows the locations of all receivers Bob.

[0026] Since the Alice satellite transmitter is equipped with a UPA antenna, the beamforming characteristics of the antenna array can be used to achieve directional transmission. Because the transmitter cannot obtain instantaneous satellite-to-ground state information, the traditional Maximum Ratio Transmitting (MRT) beamforming method cannot be used. Therefore, this embodiment employs a Location-Based Beamforming (LBB) method. The LBB method achieves directional transmission by pointing the antenna beam to the average position of the target cluster. This concentrates signal energy in the target area, effectively reducing signal diffusion and loss in non-target directions, thereby improving signal strength and quality. Furthermore, using beamforming technology to improve signal transmission accuracy also helps to evade detection by monitoring personnel.

[0027] like Figure 3 The figure shows the geometric relationship between the UPA equipped on the Alice satellite transmitter and the ground node. The beamforming direction based on LBB is based on this positional relationship, and the transmission phase is adjusted to achieve the purpose of beam pointing; in equation (1) It is determined by the Angle of Departure (AOD) from the UPA to the ground node, as shown in the following formula: (twenty three) In the formula, Indicates the Kronecker product. This refers to the guide vector of a uniform planar array (UPA). and These are the vertical and horizontal components of AOD, respectively. and These are the UPA steering vectors. and The components are as follows: (twenty four) (25) In the formula, , It is the distance between antenna elements. It is the wavelength.

[0028] Therefore, beamforming vector The expression is: (26) It's important to note that a LOS channel means there are no line-of-sight obstructions along the straight line between the transmitter Alice and the receiver Bob. This allows Alice to easily obtain information by observing Bob at line-of-sight. and In practice, the accuracy of line-of-sight observation will depend on the distance between the transmitter and receiver and the size of the physical entity. For simplicity, this embodiment does not consider the line-of-sight error of line-of-sight observation. In this sense, the uplink pilot transmission process is no longer necessary for position-based beamforming schemes.

[0029] Step 2.2: Constructing the ground node model. This embodiment is geared towards a densely accessed, covert satellite-to-ground communication scenario, therefore, it is necessary to model the ground nodes. This embodiment uses the Poisson Point Process (PPP) to model the ground nodes, specifically employing Matern clusters as the point process modeling method.

[0030] From a mathematical perspective, suppose It is a mother point process, and usually obeys the strength of The homogeneous Poisson process, i.e., the average number of mother points per unit area is Each mother point As the center of a cluster, it will be centered on the parent point with a radius of... Generate within the prototype region Individual points, It follows a uniform distribution, where It represents the average number of child points generated per parent point.

[0031] Points within the cluster are uniformly distributed within the circular region. For points falling within the circular region... Its conditional probability density function is: (27) In the formula, radius It follows the gamma function, and its CDF is: (28) In the formula, For shape parameters, For scale parameters, This is a gamma function.

[0032] This distribution setting makes the Matern cluster process more closely resemble the aggregation characteristics of 2D ground nodes in real-world scenarios; compared to other simple point process models, the Matern cluster process can not only capture the local aggregation characteristics of nodes, but also, through specific parameters as mentioned above... , , , By finely controlling the size, shape, and density of points within clusters, a more flexible and accurate means of modeling the distribution of two-dimensional nodes on the ground can be provided.

[0033] like Figure 4 The figure shown is a schematic diagram of the distributed simulation of the Matern cluster process, with parameters as follows: , , , , .

[0034] Step 2.3, Construct a covert detection model; In this embodiment, short packet communication is used as the transmission method for covert communication in the satellite-to-ground downlink, and the limited number of channel usage times is defined as... Suppose that the monitor Willie uses a binary hypothesis to determine whether Alice is sending a covert signal to a certain Bob, then Willie in the 1st... The signal received during the use of a channel can be given by the following formula: (2) In the formula, The covert signal sent to Alice satisfies , for Index of the number of times the secondary channel has been used. ; This represents Alice's transmission power. Represents path loss. These are path loss exponents, and they also apply to ground receivers. It has zero mean and zero variance Additive white Gaussian noise.

[0035] According to the Neyman-Pearson criterion, monitors use the minimum likelihood ratio test to distinguish between the null hypothesis and the alternative hypothesis. The threshold is used as the monitoring criterion for decision-making: (3) In the formula, and represent the posterior probabilities of the null hypothesis and the alternative hypothesis, respectively. In order to make a decision based on the null hypothesis, To make decisions based on alternative hypotheses.

[0036] Detection errors include two types: false alarm rate and false negative rate. The error probabilities are expressed as follows: (4) (5) Therefore, this embodiment defines the detection error probability, which is the sum of the false alarm rate and the false negative rate: (6) Considering the need for covert communication, the covert constraint can be expressed as: (7) In the formula, For the sake of concealment, .

[0037] Step 2.4, construct performance metrics, specifically including: Security capacity. In a communication system, security capacity refers to the maximum number of bits that can be transmitted at a given bit error rate. It is one of the important indicators for measuring the security of a communication system. In this embodiment, security capacity is defined as the maximum number of bits that can be transmitted at a given bit error rate. The signal received by the secure ground user can be represented as: (29) In the formula, A confidential signal sent to Alice This represents Alice's transmission power. Represents path loss. This is the path loss index. It has zero mean and zero variance Additive white Gaussian noise.

[0038] The same applies to Willie, the monitor.

[0039] (30) Based on the above formula, the instantaneous SINR at the monitor Willie and the secure ground receiver Bob can be obtained as follows: (31) (32) In the formula: (33) (34) in: (35) The above equation represents the beam gain in position-based beamforming, where, It is the vertical phase difference. It is the horizontal phase difference.

[0040] Therefore, the channel capacities of the secure transmission link and the eavesdropping link are expressed as follows: (36) (37) In the formula, and These represent the channel capacity at the secure receiver and the monitor Willie, respectively. According to the above definition, the security capacity is defined as: (8) The average decoding error probability at the receiver. Decoding error probability is a key factor in short packet covert communication. In this embodiment, it is assumed that the transmitter Alice sends a packet containing [missing information] in each time slot. The probability of packet decoding error for short packets in Knight's information can be given as follows: (9) In the formula, For the transmission rate of the Alice satellite transmitter, , For signal-to-interference-to-noise ratio: (10); Information timeliness. This embodiment uses information freshness as an indicator to measure information timeliness. AoI refers to the time elapsed during information transmission, and is an important indicator for measuring state update speed and communication latency. It is defined as the time since the covert receiver received the most recent data packet. At time 1, the average AoI at the covert receiver can be expressed as: (38) In the formula, The waiting time is the period before the covert receiver completes the transmission of the covert signal. This embodiment uses the overall average AoI to measure the system's information timeliness, defined as the mean of the average AoI of all covert users, which can be expressed as: (11) In the formula, The number of users who are hidden on the ground.

[0041] Step 3: Establish a multicast-based covert communication transmission protocol for the packet propagation of signals from the Alice satellite; the specific process is as follows... Figure 5 As shown: First, a grouping algorithm needs to be determined. Addressing the issue of non-uniform density distribution in large-scale node cluster analysis, this embodiment proposes DBSCAN as the grouping algorithm. Its core idea is to divide clusters based on the local density distribution characteristics of sample points. It innovatively establishes a clustering method based on density reachability and density connectivity, effectively identifying cluster structures of arbitrary shapes and automatically removing noise points. Unlike traditional clustering algorithms such as K-means and hierarchical clustering, DBSCAN does not require pre-specifying the number of clusters. Pre-specified cluster numbers often lack objective basis; instead, they are determined by parameters (neighborhood radius). The minimum number of samples (minPts) adaptively identifies dense regions in the data. Specifically, the parameters... The density threshold can effectively characterize the intensity of local data clustering, while minPts ensures the stability of clustering results by defining the critical conditions of core objects. This characteristic gives it a significant advantage when processing complex distributed data, and it is especially suitable for dense access scenarios with strong spatial correlation characteristics as described in this embodiment.

[0042] To achieve an effective balance between latency and concealment in covert communication, this embodiment proposes a multicast-based covert communication transmission protocol. This scheme precisely delineates warning zones; employs different transmission methods for points inside and outside the zones; utilizes the DBSCAN algorithm for user grouping; further subdivides groups based on security levels; comprehensively calculates capacity and AoI; and optimizes the polling multicast order. These measures aim to construct an efficient, secure, and reliable satellite-to-ground covert communication system to meet the diverse needs of different users in complex communication environments. The specific operation is as follows: Preparation stage During the preparation phase, information is collected, and a warning zone (GZ) is defined. The definition of the warning zone aims to balance system communication performance and security. Points within a certain range closest to the monitor, Willie, are designated as points within the warning zone. Points within the GZ use point-to-point transmission; points outside the GZ use multicast transmission to ensure transmission security with maximum beam precision. The specific steps of the preparation phase are as follows: Determine the radius of the warning zone: Based on the actual situation, determine the radius of the warning zone. This embodiment uses an exhaustive search method to exhaustively search for... Find a suitable value for it. ;like Figure 6 The blue concentric circles shown illustrate All possible values ​​are determined by enumerating the distances from all hidden receivers to the monitor, Willie. Figure 6 The receiver marked with a blue square at the center is a covert receiver, while the others are secure receivers.

[0043] Data preparation: Collect the geographic coordinates of ground users and convert them into a format that can be processed by the DBSCAN algorithm, i.e., each user corresponds to a sample point containing coordinates, denoted as . ,in ,in This represents the total number of users.

[0044] Determine the beamforming direction: Based on the user's location and security level, determine the beamforming direction.

[0045] Channel state information acquisition: Channel state information, including channel gain, is acquired for each ground user through a channel sounding mechanism between the satellite and the ground user. Noise power Parameters such as these.

[0046] User grouping phase To achieve efficient communication management, the DBSCAN algorithm is first used to group ground users. The specific steps are as follows: Parameter settings: Determine two key parameters, neighborhood radius. And the minimum number of points minPts. The parameters determine the neighborhood range of a point, and minPts specifies the minimum number of points required to become a core point within the neighborhood. The settings of these two parameters need to take into account factors such as user distribution density and expected group size.

[0047] Key point judgment: For each receiver point Calculate its in Points within the neighborhood That is, satisfying point The quantity, of which Represents Euclidean distance; if If so, then that point is determined to be the core point.

[0048] Starting with a core point, group all points within its neighborhood into the same category. If other core points exist within these neighborhoods, continue expanding the category until it cannot be expanded further. Repeat this process until all core points have been processed, thereby dividing geographically proximate users into different groups, laying the foundation for the development of subsequent targeted communication strategies.

[0049] Intragroup segmentation stage After user grouping is completed, users within each group are further subdivided according to security level. The specific process is as follows: Security level information collection: Obtain the security level identifier for each user within the group. This identifier can be determined through user registration information, communication request statements, or other security authentication mechanisms.

[0050] Coordinate mean calculation: Coordinates are extracted for users with different security levels. For users with a confidential transmission level, let the set of users for that level be denoted as . The mean of its coordinates The calculation is as follows: (12) In the formula, express The number of elements in the set. Similarly, for covert transmission level users (let the set of such users be ), ), its coordinate mean for: (13) Grouping: Based on the calculated mean coordinate values, users within a group are divided into a secure transmission group and a covert transmission group. Using the mean coordinate value as the center and the distance from the receiver furthest from the mean coordinate value within the group to the mean coordinate value as the radius, users within the group are further divided into two subgroups. For example... Figure 7 As shown.

[0051] Beamforming direction determination: The center coordinates of the secure transmission group and the covert transmission group are determined as the illumination direction of the beamforming, such as... Figure 7 As shown, by adjusting the angle and direction of the transmitted beam via satellite, the communication beam can be precisely focused on the target user group, thereby improving the strength and transmission efficiency of the communication signal.

[0052] Capacity and AoI Calculation Stage Considering the complexity of communication channel conditions, the corresponding confidentiality capacity and AoI for covert transmission are calculated based on the ground user with the worst channel conditions. The specific calculation steps are as follows: Worst-case channel user determination: Evaluate the channel conditions for all users in the group and compare the channel gain to noise power ratio for each user. By considering metrics such as channel conditions, we can identify the user with the worst channel conditions, i.e., the one that meets the criteria. Users.

[0053] Security capacity calculation: Based on the security capacity calculation formula in information theory, combined with the channel parameters of the worst-case channel user and the satellite transmit power. Based on factors such as these, the confidentiality capacity of this group was calculated.

[0054] Covert transmission AoI calculation: Defining a calculation model for information age, taking into account the time of information generation. Transmission delay and update frequency For covert transmission groups, based on factors such as the transmission situation of the worst channel user, the information freshness from generation to reception is calculated.

[0055] Polling multicast optimization phase.

[0056] Since the protocol proposed in this embodiment uses a polling multicast method, there is an unavoidable waiting time. To optimize this issue, the number of hidden users in different groups is sorted, and hidden users are processed first. Hidden User Count Statistics: Iterate through all groups and count the number of hidden users in each group. ,in , This represents the total number of groups.

[0057] Sorting operation: Using a suitable sorting algorithm, such as quicksort or bubble sort, sort the groups in descending order of the number of hidden users to obtain the sorted group index sequence. ,satisfy .

[0058] Multicast order determination: Based on the sorting results, the order of polling multicast is determined, prioritizing data transmission to groups with a larger number of covert users. This allows more covert users to be processed in a single round of polling, significantly reducing overall waiting time, improving communication efficiency, and meeting the timeliness requirements of covert communication.

[0059] Special point handling stage warning area Points within the network and outliers are processed separately. Outliers often mean that they are far away from other points. If they are forcibly grouped, it will cause the group to be too large, which will result in inaccurate grouping and will greatly affect the covertness of the transmission. Therefore, point-to-point transmission is required by the satellite transmitter Alice.

[0060] Step 4, Monitor detection performance analysis; The detection rules of the monitor can be derived from formula (3), but since this embodiment uses short packet communication, the strong number law cannot be used, which leads to... and It is very complex and difficult to analyze, so a lower bound is used to ensure the concealment constraint. According to Pinsker's inequality, the detection error probability can be further limited, as given by the following formula: (39) In the formula, The Kullback-Leibler (KL) divergence measures the distance from the Kullback-Leibler divergence to the Leibler divergence. arrive The difference between probability distributions, The expression can be given as: (40) This embodiment uses beamforming technology to concentrate the beam, so the LOS path occupies the majority of the channel. Therefore, for ease of calculation, Determined by beam gain, i.e.; (41) In the formula, by Figure 8 It can be seen that, and Let be the difference in elevation angle and the difference in azimuth angle between the line of sight of satellite transmitter Alice and monitor Willie, respectively. (42) therefore: (43) In the formula, (a) is because of the inequality Furthermore, we obtain: (14) Step 5: Analyze and optimize the performance of covert communication, such as... Figure 10 As shown.

[0061] Because the packet contains multiple covert receivers, its overall performance follows the "bottleneck effect," meaning it is dominated by the network node with the worst channel conditions. Channel conditions play a crucial role in network transmission, directly affecting data transmission rate, bit error rate, and transmission stability. When a node with poor channel conditions exists within the network packet, data transmission at that node faces numerous obstacles, such as low-rate transmission leading to data backlog, high bit error rates requiring frequent retransmissions, and unstable connections potentially causing data interruptions. Even if other nodes have good channel conditions and can efficiently process and transmit data, the next packet cannot be transmitted because the bottleneck node's data transmission is incomplete, ultimately dragging the network packet's performance down to a level similar to that of the bottleneck node.

[0062] In location-based beamforming, the location of each node within a network packet is closely related to channel conditions. Beamforming adjusts the phase and amplitude of the signal to concentrate signal energy in a specific direction, forming a beamline, thereby improving signal transmission quality. During this process, the node farthest from the beamline is often the node with the worst channel conditions. Figure 9 The text refers to the secure transmission receiver with the worst channel quality in a packet as... and covert transmission receiver are called .

[0063] Average decoding error probability at the receiver, receiver The decoding error probability at point is given by equation (9), since The function is difficult to analyze further, so an approximate expression for the decoding error probability is given as follows: (44) In the formula, and They are respectively: (45) (46) According to formula (44), the average decoding error probability at the covert receiver can be obtained as follows: (47) In the formula, for The cumulative distribution function, It can be given by formula (10). Since the expected value of the LOS component of the Rice channel is the beam gain mentioned earlier, refer to formula (41); therefore, we can obtain The cumulative distribution function is: (48) Therefore, the final average decoding error probability can be obtained as: (15) In the formula for: (16); The average information freshness (AoI) at a specific group can be calculated using equation (38), and the average AoI at a specific group can be expressed as: (17) As can be seen from the formula, the receiver with the worst current packet channel conditions is called... The information freshness (AoI) is closely related to its decoding error probability, which in turn is related to the transmission power of the transmitter Alice; to minimize the receiver's... The information freshness AoI at this location needs to be minimized. This embodiment constructs the following optimization problem: (18) (19) (20) (twenty one) In the formula, the constraint conditions This ensures the concealment of constraints and constraint conditions. The confidentiality capacity constraint was guaranteed, and the constraint conditions were as follows: This ensured the effectiveness of the transmission power.

[0064] First, address the constraints. According to formulas (8) and (36), we can obtain: (49) After handling the constraints Then, handle the constraints. and constraints Calculate the optimal transmit power The specific steps are as follows: Input system parameters ; Calculate the channel quality factor (50) If If the answer is no, return "no solution"; otherwise, calculate the power boundary. The power boundary is calculated as follows: (51) (52) The effective upper bound is calculated as follows: (53) if If the result is not found, return "no solution"; otherwise, continue calculating the optimal power. Set optimal power (twenty two).

[0065] Example 3 This embodiment will provide numerical results to prove the correctness of the given theoretical derivation and explain the influence of system parameters on concealment and average AoI.

[0066] The external parameters are set as follows: path loss factor Environmental noise Rice channel factor Total amount of data transmitted Number of data packets Hidden parameters .

[0067] like Figure 11 The figure shows that in , In the case of randomly generated multi-Matern clusters, the parameters of the Matern clusters are: number of cluster centers 20; intensity of the Boehringer process 0.5; average cluster size 5; shape parameter 2 of the gamma distribution followed by the cluster radius. Different colored dots represent different groups. Dots marked with blue squares are covert receivers, and the rest are secret receivers. Blue circles represent covert subgroups within a group, and orange-yellow circles represent secret subgroups within a group. The number on the group indicates the number of covert receivers in that group, and the order of multicast polling transmission needs to be determined based on the number of covert receivers in the group. Gray crosses represent outliers, which need to be processed separately for point-to-point transmission at the end. As shown in the figure, the DBSCAN grouping algorithm achieves good grouping results for randomly generated Matern clusters, laying the foundation for subsequent multicast transmission. Unless otherwise specified, the grouping parameters in subsequent experiments are as follows: , .

[0068] like Figure 12 The figure shows the simulation curves of the overall AoI of the system as a function of the radius of the warning area. All results are obtained by averaging 1000 simulations. The blue line in the figure represents the system AoI obtained using the packet multicast protocol proposed in Example 2, and the red line represents the system AoI obtained using traditional point-to-point unicast transmission. The value is determined according to Figure 6 The method shown yields the result, and it can be seen that as... As the threshold increases, the system's average AoI also gradually increases; this is because more and more points are joining the alert zone and becoming point-to-point transmitters, leading to an increase in the system's AoI. It can be seen that when... When the value is increased to 20, all points within the region become point-to-point transmissions, and the system's AoI becomes the same as traditional point-to-point unicast transmissions.

[0069] However, the system's average AoI does not always follow... It increases with the increase of, such as Figure 13 As shown, the system's average AoI follows First decrease and then increase, this is when When the value is small, some points very close to the monitor Willie will also be grouped. These groups are often far from the monitor Willie, and their concealment is poor, leading to an increase in the decoding error probability and consequently an increase in the system's average AoI. Therefore, The value needs to be determined based on the specific scenario. In this embodiment 2, exhaustive search is used to determine it. The value of . Of course, in most cases, the system's average AoI follows . The number of points increases monotonically with the increase in the number of points, because the participation of more points in the group always reduces the number of points in the unicast transmission.

[0070] like Figure 14 The figure shows the system's average AoI as a function of hidden constraints. The graph shows the changes. The blue line represents the system AoI obtained using the packet multicast protocol proposed in Embodiment 2, and the red line represents the system AoI obtained using traditional point-to-point unicast transmission. It can be seen that as... As ε increases, the system's average AoI gradually decreases. This is because as ε increases, the system's stealth requirements gradually decrease, allowing the transmitter Alice to use greater power to transmit stealth signals, thus reducing the system's average AoI. The figure also shows that the proposed packet multicast protocol has significant advantages over traditional point-to-point unicast transmission.

[0071] like Figure 15 The figure shows the system average AoI as a function of Matern cluster parameters. The transformation diagram, during the Matern cluster process, The parameter represents the mean of the Poisson distribution of the "child points" generated around each "parent point". That is... This determines the average number of "child points" generated around each "mother point". Therefore, it can be seen that whether it's the multicast protocol proposed in Example 2 or traditional point-to-point unicast transmission, with... As the value increases, the average AoI of the system gradually increases. This is because as the value increases... As the number of nodes increases, the number of child nodes surrounding each parent node also gradually increases, which leads to an increase in the system's average AoI. It can also be seen that under the unicast protocol, AoI follows the frequency of data transfer. The number of packets increases linearly with the increase of unicast, which is consistent with the characteristic that all points in the unicast protocol must transmit point-to-point. However, the increase of AoI in the multicast protocol system proposed in this embodiment is relatively gradual. This is because the increase of ground users will not cause the number of packets to increase proportionally, which also reflects the superiority of the packet multicast protocol.

[0072] like Figure 16The figure shows the variation of the system's average AoI with the DBSCAN grouping algorithm parameter minPts. DBSCAN is a density-based spatial clustering algorithm. In DBSCAN, the parameter minPts represents the minimum number of neighboring points a point needs to become a core point. The figure shows that as minPts increases, the system's average AoI first decreases and then increases. This is because, in the DBSCAN algorithm, the parameter minPts represents the minimum number of neighboring points a point needs to become a core point. In other words, in a sense, the parameter minPts represents a grouping threshold. When minPts is low, such as 1 or 2, almost every point can become a core point. This leads to a large number of points being incorrectly grouped into clusters, generating many meaningless clusters, and even misclassifying noisy outliers as part of clusters, resulting in very low clustering accuracy and quality. This leads to the formation of some very large groups. While this may seem to reduce the number of groups and improve system performance, excessively large groups can make the beam inaccurate, making it easier for Willie to detect covert signals. To maintain covertness, this introduces a large number of decoding errors, which increases the system's average AoI. When minPts is too large, the threshold for group formation increases significantly. Many points cannot form core points in the group, causing some dense areas that could be identified as clusters to be misjudged as noise points because they cannot meet the minPts requirement. In our proposed multicast protocol, these outlier noise points need to be handled separately by unicast. This is why, as minPts increases, the average AoI of the multicast protocol system eventually becomes consistent with that of the point-to-point unicast transmission scheme.

Claims

1. A low-latency high-reliable satellite-to-ground covert communication system, characterized in that, The system includes a satellite Alice, several ground receivers, and a ground monitor Willie, wherein the satellite Alice monitors the ground monitor Willie and communicates with the several ground receivers; The satellite Alice is equipped with a planar array antenna, the ground receiver is equipped with a single antenna, and the ground monitor Willie is equipped with two antennas; The wireless channel link between the satellite Alice and the ground receiver is a downlink channel. The ground receiver includes covert ground users and confidential ground users. The satellite Alice sends covert signals and confidential signals to the covert ground users and confidential ground users respectively. The ground monitor Willie detects the transmission of the covert signals.

2. A low-latency and high-reliability satellite-to-ground covert communication method, using the low-latency and high-reliability satellite-to-ground covert communication system of claim 1, characterized in that, The method specifically includes: Initialize all communication links in the system; Construct a covert planetary communication model for densely connected systems, the model comprising: A scenario model, wherein the scenario model is the covert communication system; The channel model specifically models the communication link between the satellite Alice and the ground receiver and the ground monitor Willie, while using beamforming to modify the satellite Alice signal transmission to directional transmission; Ground node model, which models ground nodes using the Boehringer-Pine process; A covert detection model was used to obtain the detection error probability of ground monitor Willie; Performance metrics are used to measure the covert communication model. Establish a multicast-based covert communication transmission protocol for the packet propagation of signals from the Alice satellite; The detection performance of the ground-based detector Willie and the covert communication performance of the aforementioned communication model were analyzed and optimized.

3. The low-latency and high-reliable satellite-to-ground covert communication method of claim 2, wherein, The channel model is constructed as follows: Satellite Alice to ground user link and satellite Alice to ground monitor Willie link Both subject to Rician fading, the links are modeled as: （1） wherein is the Rician factor, is the channel direct component, is the scattering component, and the elements of are independent and identically distributed zero-mean unit-variance complex Gaussian random variables, i.e., satisfy , is the number of transverse antennas of the planar array antenna, is the number of longitudinal antennas of the planar array antenna.

4. The low-latency and high-reliability satellite-to-ground covert communication method of claim 2, wherein, The directional transmission of the Alice satellite is as follows: The satellite Alice, several ground receivers, and the ground monitor Willie are located using a three-dimensional Cartesian coordinate system. The satellite Alice obtains the positions of the ground receivers and uses a beamforming method based on the position information to transmit its antenna beam to the ground receivers in a directional manner.

5. A low-latency, high-reliability satellite-to-ground covert communication method according to claim 2, characterized in that, The covert detection model specifically defines a limited number of channel use times as , and assumes that the ground monitor Willie uses a binary hypothesis to determine whether the satellite Alice is sending a covert signal to a certain ground user. The signal received by the ground monitor Willie in the th channel use is as follows: （2） wherein is the covert signal transmitted to Alice, satisfying , is the index of the number of times the secondary channel is used, , represents the transmit power of Alice, represents the path loss, is the path loss exponent, is an additive white Gaussian noise with zero mean and variance ​ The ground monitor Willie uses the minimum likelihood ratio test to distinguish between the null and alternative hypotheses, with threshold, the ground monitor Willie's decision rule is as follows: （3） wherein and P (H0|Y) and P (H1|Y) represent the posterior probabilities of the null hypothesis and the alternative hypothesis, respectively, P (H0|Y) is the probability of making a decision for the null hypothesis, P (H1|Y) is the probability of making a decision for the alternative hypothesis, and P (Y|H0) and P (Y|H1) are the likelihood functions under the null hypothesis and the alternative hypothesis, respectively. Detection errors include false alarm rate and false negative rate, as shown in the following formula: （4） （5） The detection error probability is the sum of the false alarm rate and the false negative rate: （6） The concealment constraint is represented as: （7） In the formula, For concealment requirements, .

6. The low-latency and high-reliability satellite-to-ground covert communication method of claim 2, wherein, The performance metrics include: The confidentiality capacity, which is the maximum number of bits that can be transmitted at a given bit error rate, is specifically expressed by the following formula: （8） where and Cwand Cwrepresent the channel capacities at the secure ground receiver and the monitor Willie, respectively. The average decoding error probability output by the ground receiver is given by satellite Alice transmitting a packet containing data in each time slot. The decoding error probability of short packets of Knight information can be given as: （9） In the formula, For the transmission rate of the Alice satellite, , The signal-to-interference-plus-noise ratio (SIR) is given by the following formula: （10）； Information timeliness is measured using the overall average information freshness (AoI), defined as the mean of the average AoI of all hidden ground users, as shown in the following formula: （11） In the formula, The number of users who are hidden on the ground.

7. A low-latency, high-reliability satellite-to-ground covert communication method according to claim 6, characterized in that, The packet propagation is described in the following details: A warning zone (GZ) is defined, encompassing ground users within a certain radius of the ground monitor Willie. Ground users within the GZ transmit information to the satellite Alice via point-to-point communication, while users outside the GZ use multicast transmission. Simultaneously, the DBSCAN algorithm is used to group ground users. After grouping, the ground users within each group are further subdivided according to their security level. The specific subdivision process is as follows: Security level information collection, obtaining the security level identifier for each ground user within the group. ; Coordinate mean calculation: For ground users with different security levels, their coordinates are extracted separately. For users with confidential transmission levels, let the set of users with that level be denoted as . The mean of its coordinates As shown in the following formula: （12） In the formula, express The number of elements in the set; similarly, for covert transmission level users, let the set of such users be . The mean of its coordinates As shown in the following formula: （13） Grouping: Based on the calculated mean coordinate value, the ground users within the group are divided into a secure transmission group and a covert transmission group. Using the mean coordinate value as the center and the distance from the ground receiver in the group that is farthest from the mean coordinate value to the mean coordinate value as the radius, the users within the group are divided into two subgroups: the secure transmission group and the covert transmission group. Once the beamforming direction is determined, the center coordinates of the secure transmission group and the covert transmission group are set as the beamforming illumination direction. The angle and direction of the transmitted beam are adjusted by the satellite Alice to focus the communication beam onto the target user group. After the segmentation is completed, the channel security capacity and AoI of covert transmission for ground users are calculated. Polling multicast optimization sorts the number of hidden users in different groups and prioritizes data transmission to groups with a larger number of hidden users.

8. The low-latency, high-reliability satellite-to-ground covert communication method according to claim 7, characterized in that, Special point processing involves handling points and outliers within the warning zone GZ separately, with point-to-point information transmission handled by the Alice satellite.

9. A low-latency, high-reliability satellite-to-ground covert communication method according to claim 2, characterized in that, The performance of the ground-based detector Willie is measured using the following formula: （14） In the formula, The transmission power of the Alice satellite. For path loss, This is the path loss index.

10. A low-latency, high-reliability satellite-to-ground covert communication method according to claim 2 or 6, characterized in that, The analysis of the covert communication performance of the communication model specifically involves the fact that each packet contains multiple covert ground receivers. Therefore, the overall performance of the packet is dominated by the network node with the worst channel conditions. Therefore, the average decoding error probability at the covert ground receiver with the worst channel quality in the packet is as follows: （15） In the formula, For signal-to-interference-plus-noise ratio The cumulative distribution function, , , For the transmission rate of the Alice satellite, As shown in the following formula: （16）； The average information freshness (AoI) for each group is as follows: （17） The optimization process involves minimizing the information freshness (AoI) at the concealed ground receiver, which requires minimizing... Therefore, the optimized formula is constructed as follows: （18） （19） （20） （21） In the formula, the constraint conditions To ensure concealment constraints, constraint conditions To ensure confidentiality, capacity constraints and conditions are required. Ensure the effectiveness of transmission power; The optimal transmit power is as follows: （22） In the formula, , , KT This is the channel quality factor.

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