Resource allocation method for secure communication of multi-beam low-orbit satellites

Abstract

The invention discloses a resource allocation method for multi-beam low-orbit satellite secure communication, and belongs to the field of resource allocation and secure communication of a multi-beam low-orbit satellite system. The implementation method comprises the following steps: constructing a satellite-ground channel model of an LEO legal satellite and a satellite-ground channel model of a GEO eavesdropping satellite; creating a binary optimization variable, constructing constraint conditions C1 and C2 of a multi-beam satellite communication system, a communication rate constraint condition C3 of a normal user and a hidden data transmission constraint condition C4 of a hidden user, and constructing an optimization problem of multi-beam satellite resource allocation; by introducing an auxiliary binary variable, an optimization problem of original multi-beam LEO satellite resource allocation is linearized and converted into a mixed integer linear programming (MILP) problem, and an optimization solver is applied to solve a resource allocation scheme of a multi-beam LEO legal satellite; and deploying the resource allocation scheme to an actual communication system to realize secure communication and communication resource allocation of the multi-beam LEO satellite network.

Description

Technical Field

[0001] The present invention belongs to the field of resource allocation and secure communication of a multi-beam low-orbit satellite system, and relates to the optimization problem of constructing a multi-beam low-orbit satellite resource allocation and the linear transformation of the problem. Background Art

[0002] With the widespread popularity of mobile communication technology, the demand for ubiquitous network access has increased significantly. As an important branch of modern communication technology, satellite communication systems have established a global seamless connection network with their unique advantages, becoming an ideal solution to fill the gap in ground network coverage and promote global interconnection. Compared with high-orbit (GEO) satellites and medium-orbit (MEO) satellites, low-orbit (LEO) satellites have the advantages of low orbit altitude, short signal propagation delay, and high spectrum efficiency. They can provide faster and more stable communication services, so they are likely to meet the strict requirements of industrial applications for delay and reliability. With the continuous development and application of LEO satellite technology, its role in remote industrial production will become increasingly important and become an important part of future communication networks. Due to the uneven geographical distribution of ground users and the diversity of communication needs, how to effectively schedule limited LEO satellite resources to meet the communication needs of various users is a major challenge. The traditional static single-beam satellite resource allocation strategy lacks flexibility and is difficult to cope with the diverse needs of industrial applications, resulting in low resource utilization and poor communication quality. Multi-beam satellites can flexibly allocate beams and frequency resources in each time slot through beam hopping technology, serve users in different regions, and effectively utilize on-board resources. In addition, multi-beam satellites minimize inter-beam interference and achieve robust interference management through strategic beam planning and precise spectrum management. However, with the continuous increase in user needs and the complexity of application scenarios, the contradiction between the limited onboard resources and the diversity of user needs has become increasingly prominent. In order to solve this problem, it is urgent to develop a resource allocation strategy that can not only improve resource utilization and communication efficiency, but also coordinate interference.

[0003] Although many scholars have conducted extensive research on satellite multi-beam networks, the security of wireless transmission between ground users and LEO satellites has not been fully considered. Due to the broadcast nature of wireless channels, satellite communication systems are vulnerable to eavesdropping and malicious interference. Some electronic reconnaissance satellites with specific functions may eavesdrop on important information transmitted by ground nodes without permission, causing security issues such as sensitive data leakage. In addition, the presence of signals may attract the attention of some active eavesdroppers, who can impose malicious interference to disrupt transmission. Traditionally, the security of satellite communications mainly relies on encryption technology and physical layer security (PLS). Encryption technology can protect the confidentiality and integrity of data, but requires complex key management and algorithm updates, and is still vulnerable to risks such as password cracking. Physical layer security uses modulation technology and channel characteristics to reduce the risk of eavesdropping without traditional encryption. However, eavesdroppers with advanced decoding capabilities can overcome their defenses and successfully obtain confidential information. In addition, both methods are vulnerable to interference attacks by active eavesdroppers, resulting in communication interruption due to the exposure of signal transmission behavior. Unlike the above-mentioned traditional methods, the purpose of covert communication technology is to ensure privacy and security by hiding wireless signals, thereby avoiding detection by unauthorized eavesdroppers. This method can hide the communication signal in the background noise through signal modulation and coding technology, or use spectrum expansion technology to make the signal difficult to detect and intercept. At present, the existing research on multi-beam LEO satellite resource allocation has not yet involved the issue of communication concealment. Considering the broad prospects of multi-beam LEO satellite networks in future industrial applications, it is of great practical significance to study how to combine covert communication technology in the resource allocation process to build a more secure and reliable satellite communication system. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that user signals are easily eavesdropped in the multi-beam low-orbit satellite resource scheduling scenario, and to provide a resource allocation method for secure communication of multi-beam low-orbit satellites. By analyzing the data transmission requirements of ground users and the beam hopping strategy of LEO satellites, the basic process of LEO satellite beam scheduling and user data transmission is described, and a satellite-to-ground communication resource scheduling scenario is constructed. Combined with the power loss characteristics of the satellite-to-ground link, the satellite-to-ground channel model of the LEO legitimate satellite and the satellite-to-ground channel model of the GEO eavesdropping satellite are constructed. Combined with the covert communication theory, the concealment constraint of the LEO satellite resource scheduling scenario is constructed; in order to maximize the communication rate of the concealed user while ensuring the concealment of the communication system, the optimization problem of LEO multi-beam satellite resource allocation is constructed and modeled as a mixed integer nonlinear programming (Mixed Integer Nonlinear Programming, MINLP) problem. By introducing auxiliary binary variables, the original optimization problem is linearized and converted into a mixed integer linear programming (Mixed Integer Linear Programming, MILP) problem, and the multi-beam LEO satellite resource allocation scheme is solved in combination with the optimization solver. Finally, the resource allocation scheme is deployed to the actual communication system for parameter configuration and dynamic adjustment, thereby achieving secure communication and multi-dimensional communication resource allocation in the low-orbit satellite network.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The present invention discloses a resource allocation method for multi-beam low-orbit satellite secure communication, comprising the following steps:

[0007] Step 1: Combined with the power loss characteristics of the satellite-to-ground link, the satellite-to-ground channel model of the LEO legitimate satellite and the satellite-to-ground channel model of the GEO eavesdropping satellite are constructed.

[0008] The resource allocation scenario for multi-beam LEO satellite secure communication includes I ground users, a LEO legal satellite at orbital altitude H, and an LEO satellite at orbital altitude H. e GEO eavesdropping satellites; the set of ground users is represented by Ground users are divided into two categories: normal users NUE and hidden users CUE that need to transmit hidden data; the number of hidden users is J, and the set is expressed as In order to meet the communication needs of ground users and realize flexible communication resource allocation, the LEO legal satellite adopts a beam hopping strategy to receive terminal data. The number of beam areas on the ground is N. Normal users and hidden users send uplink signals to the LEO legal satellite through different frequency bands. The number of frequency bands for normal users and hidden users is the same, both M. The carrier frequency of the transmitted signal is recorded as f, the system bandwidth is recorded as B, the length of the transmission time slot is δ, and the number of time slots is T. In the tth time slot, the i-th user selects power P on the mth frequency band. k Transmit data to a LEO legal satellite, where the power set is represented by {P k |k=1,2,...,K}.

[0009] Construct the satellite-to-ground channel model of LEO legal satellite, which can be expressed as:

[0010]

[0011] Among them, g(θ i,n ) represents the beam gain between the i-th user and the n-th beam area; Gt represents the maximum gain of the transmitting antenna, Gr represents the maximum gain of the receiving antenna. According to the Friis formula, the free space path loss of the electromagnetic wave L f It is expressed as:

[0012]

[0013] Where c is the speed of light, represents the distance between the LEO legal satellite and the i-th user, where s i Indicates the distance between the user and the satellite ground projection point.

[0014] The beam gain g(θ between the i-th user and the n-th beam area i,n ) is expressed as:

[0015]

[0016]

[0017] Among them, θ i,n is the angle at which the line connecting the i-th user and the LEO legal satellite deviates from the center of the n-th beam area; θ 3dB represents the deviation angle when the signal power is attenuated by half; functions J1(·) and J3(·) represent the first-order Bessel function of the first kind and the third-order Bessel function of the first kind, respectively.

[0018] The satellite-to-ground channel model of the GEO eavesdropping satellite is:

[0019]

[0020] Among them Gre is the maximum gain of the receiving antenna of the GEO eavesdropping satellite. Since the eavesdropping GEO satellite is far away from the ground and its orbital altitude is about 35786km, the signal deviation angle of the ground user can be ignored and the orbital altitude can be used to approximate the communication distance.

[0021] Step 2: Create binary optimization variables; construct constraints C1 and C2 of the multi-beam satellite communication system, the communication rate constraint C3 of normal users and the covert data transmission constraint C4 of covert users, and construct the optimization problem of multi-beam satellite resource allocation; constraint C1 means that in each time slot, each user can only choose one transmission power on the same frequency band; constraint C2 means that in each time slot, the number of LEO legal satellite transmission beams is; constraint C3 means that the communication rate of normal users should be greater than the minimum rate requirement; constraint C4 ensures the system's covert data transmission requirements;

[0022] Binary Optimization Variables represents the signal transmission status of the i-th user, It means that the i-th user in the t-th time slot uses power P k Transmitting data on frequency band m; In this case, the i-th user does not transmit data; in each time slot, each user can only choose one transmission power on the same frequency band, which is expressed as:

[0023]

[0024] In the tth time slot, the transmission signal power of the i-th user on the frequency band m is:

[0025]

[0026] Binary optimization variable c n,t ∈{0,1} represents the beam hopping scheduling of LEO legal satellites, c n,t =1 means that the nth beam area is lit in the tth time slot, c n,t =0 means that the nth beam is not lit in the tth time slot; in each time slot, the number of LEO legal satellite transmission beams is N0<N, expressed as:

[0027]

[0028] The uplink communication rate of the i-th normal user is expressed as:

[0029]

[0030] where σ 2represents the noise power of the LEO legal satellite channel; D represents the minimum communication requirement of normal users, that is, the rate threshold, then the communication rate constraint condition C3 of normal users is:

[0031]

[0032] In the satellite covert communication scenario, the goal of the GEO eavesdropping satellite is to detect whether there is covert data from the received signal, while the covert user attempts to transmit more covert data without being eavesdropped. The eavesdropping satellite determines the data transmission situation through the following binary hypothesis test:

[0033]

[0034] Among them Py e,l (t)] 1≤l≤L represents the signal sample set received by the eavesdropping satellite, and L=δB represents the number of samples collected by the eavesdropper. Indicates that ground users only send normal data. Indicates that the ground user sends both normal data and hidden data, n e,l is the noise at the GEO eavesdropping satellite. nue,l (t) is the normal signal received by the eavesdropping satellite at the tth time slot, x cue,l (t) is the hidden signal received by the eavesdropping satellite in the tth time slot, which can be expressed as:

[0035]

[0036]

[0037] where x i,m,l represents the lth symbol transmitted by the i-th user on frequency band m, satisfying the distribution x j,m,l represents the lth symbol transmitted by the jth hidden user on frequency band m, which also satisfies the distribution By analyzing the received signal, the eavesdropping satellite can make two kinds of wrong decisions: false alarm probability α and missed detection probability β. The concealment performance of the system is usually expressed as the total detection error probability p e =α+β. e ≥1-ε, the transmission requirements of the hidden user can be guaranteed, where ε is an arbitrarily small positive number. For a certain parameter ε, the following condition can meet the data transmission requirements of the hidden user:

[0038]

[0039] in express When true [y e,l (t)]1≤l≤L The probability distribution of express When true [y e,l (t)] 1≤l≤L The probability distribution of is the Kullback-Leibler (KL) divergence of the two probability distributions, expressed as:

[0040]

[0041] in represents the noise power of the GEO eavesdropping satellite channel. The upper bound of the KL divergence is expressed as:

[0042]

[0043] Then the hidden data transmission constraint condition C4 of the hidden user is expressed as:

[0044]

[0045] Under the above constraints, the optimization goal of the scheme proposed in the present invention is to maximize the total communication rate of hidden users. Based on the Successive Interference Cancellation (SIC) technology in the Non-Orthogonal Multiple Access (NOMA) technology, the LEO legal satellite can preferentially demodulate and remove the signals sent by normal users from the received signals. Therefore, the communication rate of hidden users is only affected by the interference of other hidden users. The goal of the optimization problem is to maximize the total communication rate of all hidden users; the set of optimization variables is expressed as and The optimization problem is then expressed as:

[0046]

[0047] Step 3: By introducing auxiliary binary variables, the original optimization problem is linearized and converted into a mixed integer linear programming MILP problem, and the optimization solver is used to solve the resource allocation plan of the multi-beam LEO legal satellite;

[0048] Auxiliary binary variable u t , represented as optimization variable and c n,t Combination of:

[0049]

[0050] Variable u t The length of is N+IKM, so theoretically u t Coexistence 2N+IKM There are many possible values, each of which corresponds to a resource allocation scheme for the tth time slot. This excessive number of possible values ​​greatly increases the complexity and computing time of the program, so it is necessary to eliminate some unreasonable possible values ​​to alleviate this problem. According to the constraints C1 and C2 proposed in step 2, the variable u t Reasonable values ​​can be reduced to:

[0051]

[0052] Define another auxiliary binary variable Indicates that in the tth time slot u t The value of is the qth one among all Q combinations, which corresponds to a unique satellite beam hopping scheduling scheme and user frequency band power allocation scheme; the beam scheduling scheme and user frequency band power allocation scheme executed by the system in the tth time slot are unique, which can be expressed as:

[0053]

[0054] In the tth time slot, for the qth resource allocation scheme, the variable u t The value of is uniquely determined, and its corresponding variable and c n,t The value of is also uniquely determined; therefore, in the tth time slot and under the qth resource allocation scheme, the communication rate of the ground user is expressed as:

[0055]

[0056]

[0057] in and c n,t,q Representation variables and c n,t The value under the qth resource allocation scheme is, represents the communication rate of the i-th normal user, represents the communication rate of the jth hidden user;

[0058] In the tth time slot, for the qth resource allocation, the parameter It is expressed as:

[0059]

[0060] The above parameters and All can be done by traversing the variable u in sequence tIt can be calculated by all Q values, so it can appear as a constant in the optimization problem. Then the original optimization problem P1 can be transformed into a mixed integer linear programming problem P2:

[0061]

[0062] Compared with the original optimization problem P1, the optimization problem P2 removes the logarithmic operation on the variables and the objective function and constraints are linear, so the optimization problem P2 belongs to the MILP problem. By solving the problem P2 with the optimization solver, the resource allocation scheme for the multi-beam LEO legal satellite can be obtained.

[0063] Step 4: Deploy the resource allocation scheme to the actual communication system to achieve secure communication and communication resource allocation of the multi-beam LEO satellite network;

[0064] The beam hopping resource allocation scheme solved in step 3 is handed over to the ground user terminal and the LEO legal satellite for execution, so as to realize the secure communication and multi-dimensional communication resource allocation of the multi-beam LEO legal satellite network;

[0065] On the ground user side, several communication base stations are set up as the starting point for data transmission. In terms of power, a flexible and adjustable transmission power of several watts to several hundred watts is configured to meet the communication needs under different distances and channel conditions. In terms of frequency, the base station uses a specific frequency band in the Ka band, uses orthogonal frequency division multiplexing OFDM modulation technology to achieve high-speed data transmission, and combines spread spectrum technology to enhance the concealment and anti-interference ability of the signal. In order to achieve wide signal coverage and reduce installation costs, the base station is equipped with an omnidirectional antenna to transmit uplink signals. In addition, the base station also has intelligent monitoring and dynamic adjustment functions, which can evaluate the communication quality in real time and adjust the transmission parameters as needed to maintain a stable communication connection.

[0066] On the LEO legal satellite side, the satellite carries a phased array antenna to implement a beam-hopping scheduling scheme, which accurately captures and efficiently utilizes base station signals by precisely controlling the direction and shape of the beam. In addition, high-precision time synchronization between satellites and ground base stations can be achieved through high-precision time references, complex signal processing technologies, and continuous monitoring and adjustment mechanisms. This intelligent resource allocation and communication management strategy not only improves communication efficiency, but also enhances the security and reliability of the communication system.

[0067] So far, the present invention has completed the steps of scenario construction, problem modeling, problem conversion and solution, and solution execution, thereby realizing covert communication and multi-dimensional communication resource allocation of multi-beam LEO satellite networks.

[0068] Beneficial effects:

[0069] 1. Different from the existing LEO satellite resource allocation scenario, the resource allocation method for multi-beam low-orbit satellite secure communication disclosed in the present invention takes into account the hidden transmission needs of ground users. By analyzing the data transmission needs of ground users and the LEO satellite beam hopping strategy, a satellite-to-ground communication network resource scheduling scenario is constructed.

[0070] 2. The present invention discloses a resource allocation method for secure communication of multi-beam low-orbit satellites. Combining the covert communication theory, the concealment constraint of LEO satellite resource scheduling scenario is constructed. In order to maximize the communication rate of concealed users while ensuring the concealment of the communication system, the optimization problem of multi-beam satellite resource allocation is constructed. The proposed optimization problem optimizes satellite beam hopping scheduling, frequency resource allocation and the transmission power of ground users in different time slots.

[0071] 3. The present invention discloses a resource allocation method for multi-beam low-orbit satellite secure communication. By introducing auxiliary binary variables, the original optimization problem is linearized into a MILP problem. Then, the optimization solver is applied to solve the optimal resource allocation scheme and deploy it to the actual communication system, thereby realizing the covert communication and multi-dimensional communication resource allocation of the LEO satellite network. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 This is a scenario diagram of a resource allocation method for multi-beam low-orbit satellite secure communications according to the present invention.

[0073] Figure 2 The present invention is a flow chart of a resource allocation method for multi-beam low-orbit satellite secure communications.

[0074] Figure 3 The present invention is a relationship diagram between the total rate of concealed users and the system bandwidth of a resource allocation method for multi-beam low-orbit satellite secure communications.

[0075] Figure 4 The present invention discloses a relationship diagram between user rate and rate threshold of a resource allocation method for multi-beam low-orbit satellite secure communication.

[0076] Figure 5 The diagram is a relationship diagram between user rate and parameter ε of a resource allocation method for multi-beam low-orbit satellite secure communication according to the present invention.

[0077] Figure 6 It is a scheme comparison diagram of a resource allocation method for multi-beam low-orbit satellite secure communication according to the present invention. DETAILED DESCRIPTION

[0078] The specific implementation of the present invention is further described below in conjunction with the technical solution.

[0079] like Figure 1As shown in Figure 1, the multi-beam LEO satellite resource scheduling scenario includes a LEO legitimate satellite, a GEO eavesdropping satellite, several ground users and several satellite beams. The orbital altitudes of the LEO satellite and the GEO satellite are 1000km and 35786km respectively. We assume that the satellite beam areas are adjacent to each other, and the beam radius can be calculated by r = Htanθ 3dB Calculation. We set up 5 beam areas corresponding to 5 ground users, including 2 hidden users. Specifically, we set user 4 and user 5 as hidden user 1 and hidden user 2. Regarding the positions of ground users and LEO satellites, we established a plane coordinate system on the ground. The coordinate origin (0,0) corresponds to the ground projection point of the LEO satellite, and the coordinates of the center points of each beam area are (-150km,0), (0,0), (150km,0), (-75km,-150km), (75km,-150km). The coordinates of users in each beam area are randomly generated. According to the characteristics of the LEO satellite communication system, the carrier frequency of the transmitted signal is set to 20GHz and the system bandwidth is set to 400MHz.

[0080] like Figure 2 As shown, the present embodiment discloses a resource allocation method for multi-beam low-orbit satellite secure communication, and the specific implementation steps are as follows:

[0081] Step 1: Combined with the power loss characteristics of the satellite-to-ground link, the satellite-to-ground channel model of the LEO legitimate satellite and the satellite-to-ground channel model of the GEO eavesdropping satellite are constructed.

[0082] The resource allocation scenario for multi-beam LEO satellite secure communication includes I ground users, a LEO legal satellite at orbital altitude H, and an LEO satellite at orbital altitude H. e GEO eavesdropping satellites; the set of ground users is represented by Ground users are divided into two categories: normal users NUE and hidden users CUE that need to transmit hidden data; the number of hidden users is J, and the set is expressed as In order to meet the communication needs of ground users and realize flexible multi-dimensional communication resource allocation, the LEO legal satellite adopts a beam hopping strategy to receive terminal data. The number of beam areas on the ground is N. Normal users and hidden users send uplink signals to the LEO legal satellite through different frequency bands. The number of frequency bands for normal users and hidden users is the same, both M. The carrier frequency of the transmitted signal is recorded as f, the system bandwidth is recorded as B, the length of the transmission time slot is δ, and the number of time slots is T. In the tth time slot, the i-th user selects power P on the mth frequency band. k Transmit data to a LEO legal satellite, where the power set is represented by {P k |k=1,2,...,K}.

[0083] Construct the satellite-to-ground channel model of LEO legal satellite, which can be expressed as:

[0084]

[0085] Among them, g(θ i,n ) represents the beam gain between the i-th user and the n-th beam area; Gt represents the maximum gain of the transmitting antenna, Gr represents the maximum gain of the receiving antenna. According to the Friis formula, the free space path loss of the electromagnetic wave L f It is expressed as:

[0086]

[0087] Where c is the speed of light, represents the distance between the LEO legal satellite and the i-th user, where s i Indicates the distance between the user and the satellite ground projection point.

[0088] The beam gain g(θ between the i-th user and the n-th beam area i,n ) is expressed as:

[0089]

[0090]

[0091] Among them, θ i,n is the angle at which the line connecting the i-th user and the LEO legal satellite deviates from the center of the n-th beam area; θ 3dB represents the deviation angle when the signal power is attenuated by half; functions J1(·) and J3(·) represent the first-order Bessel function of the first kind and the third-order Bessel function of the first kind, respectively.

[0092] The satellite-to-ground channel model of the GEO eavesdropping satellite is:

[0093]

[0094] Among them Gr e is the maximum gain of the receiving antenna of the GEO eavesdropping satellite. Since the eavesdropping GEO satellite is far away from the ground and its orbital altitude is about 35786km, the signal deviation angle of the ground user can be ignored and the orbital altitude can be used to approximate the communication distance.

[0095] Specifically in this embodiment, I=5, J=2, H=1000km, H e =35786km, δ=10ms, T=5, B=400, f=20GHz, N=5, optional power P k ∈{10W,100W}, K=2, Gt=20dB, Gr=30dB, Gr e =40dB,θ3dB =5°.

[0096] Step 2: Create binary optimization variables; construct constraints C1 and C2 of the multi-beam satellite communication system, the communication rate constraint C3 of normal users and the covert data transmission constraint C4 of covert users, and construct the optimization problem of multi-beam satellite resource allocation; constraint C1 means that in each time slot, each user can only choose one transmission power on the same frequency band; constraint C2 means that in each time slot, the number of LEO legal satellite transmission beams is N0; constraint C3 means that the communication rate of normal users should be greater than the minimum rate requirement; constraint C4 ensures the system's covert data transmission requirements;

[0097] Binary Optimization Variables represents the signal transmission status of the i-th user, It means that the i-th user in the t-th time slot uses power P k Transmitting data on frequency band m; In this case, the i-th user does not transmit data; in the t-th time slot, each user can only choose one transmission power on the same frequency band, which is expressed as:

[0098]

[0099] In the tth time slot, the transmission signal power of the i-th user on the frequency band m is:

[0100]

[0101] Binary optimization variable c n,t ∈{0,1} represents the beam hopping scheduling of LEO legal satellites, c n,t =1 means that the nth beam area is lit in the tth time slot, c n,t =0 means that the nth beam is not lit in the tth time slot; in the tth time slot, the number of LEO satellite transmission beams is N0<N, which is expressed as:

[0102]

[0103] The uplink communication rate of the i-th normal user is expressed as:

[0104]

[0105] where σ 2 represents the noise power of the LEO legal satellite channel; D represents the minimum communication requirement of normal users, that is, the rate threshold, then the communication rate constraint condition C3 of normal users is:

[0106]

[0107] In the satellite covert communication scenario, the goal of the GEO eavesdropping satellite is to detect whether there is covert data from the received signal, while the covert user attempts to transmit more covert data without being eavesdropped. The eavesdropping satellite determines the data transmission situation through the following binary hypothesis test:

[0108]

[0109] where [y e,l (t)] 1≤l≤L represents the signal sample set received by the eavesdropping satellite, and L=δB represents the number of samples collected by the eavesdropper. Indicates that ground users only send normal data. Indicates that the ground user sends both normal data and hidden data, n e,l is the noise at the GEO eavesdropping satellite. nue,l (t) is the normal signal received by the eavesdropping satellite at the tth time slot, x cue,l (t) is the hidden signal received by the eavesdropping satellite in the tth time slot, which can be expressed as:

[0110]

[0111]

[0112] where x i,m,l represents the lth symbol transmitted by the i-th user on frequency band m, satisfying the distribution x j,m,l represents the lth symbol transmitted by the jth hidden user on frequency band m, which also satisfies the distribution By analyzing the received signal, the eavesdropping satellite can make two kinds of wrong decisions: false alarm probability α and missed detection probability β. The concealment performance of the system is usually expressed as the total detection error probability p e =α+β. e ≥1-ε, the transmission requirements of the hidden user can be guaranteed, where ε is an arbitrarily small positive number. For a certain parameter ε, the data transmission requirements of the hidden user can be met if the following conditions are met:

[0113]

[0114] in express When true [y e,l (t)] 1≤l≤L The probability distribution of

[0115] express When true [y e,l (t)] 1≤l≤L The probability distribution of is the Kullback-Leibler (KL) divergence of the two probability distributions, which can be expressed as:

[0116]

[0117] in represents the noise power of the GEO eavesdropping satellite channel. The upper bound of the KL divergence can be expressed as:

[0118]

[0119] Then the hidden data transmission constraint condition C4 of the hidden user can be expressed as:

[0120]

[0121] Under the above constraints, the optimization goal of the scheme proposed in the present invention is to maximize the total communication rate of hidden users. Based on the Successive Interference Cancellation (SIC) technology in the Non-Orthogonal Multiple Access (NOMA) technology, the LEO legal satellite can preferentially demodulate and remove the signals sent by normal users from the received signals. Therefore, the communication rate of hidden users is only affected by the interference of other hidden users. The goal of the optimization problem is to maximize the total communication rate of all hidden users; the set of optimization variables is expressed as and Then the optimization problem can be expressed as:

[0122]

[0123] Specifically in this embodiment, N0=3, D=4Mbps, ε=0.1,σ 2 =-90dBW.

[0124] Step 3: By introducing auxiliary binary variables, the original optimization problem is linearized and converted into a mixed integer linear programming MILP problem, and the optimization solver is used to solve the resource allocation plan of the multi-beam LEO legal satellite;

[0125] Auxiliary binary variable u t , represented as optimization variable and c n,t Combination of:

[0126]

[0127] Variable u t The length of is N+IKM, so theoretically u tCoexistence 2 N+IKM There are many possible values, each of which corresponds to a resource allocation scheme for the tth time slot. This excessive number of possible values ​​greatly increases the complexity and computing time of the program, so it is necessary to eliminate some unreasonable possible values ​​to alleviate this problem. According to the constraints C1 and C2 proposed in step 2, the variable u t Reasonable values ​​can be reduced to:

[0128]

[0129] Define another auxiliary binary variable Indicates that in the tth time slot u t The value of is the qth one among all Q combinations, which corresponds to a unique satellite beam hopping scheduling scheme and user frequency band power allocation scheme; the beam scheduling scheme and user frequency band power allocation scheme executed by the system in the tth time slot are unique, which can be expressed as:

[0130]

[0131] In the tth time slot, for the qth resource allocation scheme, the variable u t The value of is uniquely determined, and its corresponding variable and c n,t The value of is also uniquely determined; therefore, in the tth time slot and under the qth resource allocation scheme, the communication rate of the ground user is expressed as:

[0132]

[0133]

[0134] in and c n,t,q Representation variables and c n,t The value under the qth resource allocation scheme is, represents the communication rate of the i-th normal user, represents the communication rate of the jth hidden user;

[0135] In the tth time slot, for the qth resource allocation, the parameter It is expressed as:

[0136]

[0137] The above parameters and All can be done by traversing the variable u in sequence tIt can be calculated by all Q values, so it can appear as a constant in the optimization problem. Then the original optimization problem P1 can be transformed into a mixed integer linear programming problem P2:

[0138]

[0139] Compared with the original optimization problem P1, the optimization problem P2 removes the logarithmic operation on the variables and the objective function and constraints are linear, so the optimization problem P2 belongs to the MILP problem. By solving the problem P2 with the optimization solver, the beam hopping resource allocation scheme of the multi-beam LEO legal satellite can be obtained;

[0140] Specifically in this embodiment, Q=10240, and the Gurobi solver is used to solve the optimization problem P2.

[0141] Step 4: Deploy the resource allocation scheme to the actual communication system to achieve secure communication and multi-dimensional communication resource allocation of the multi-beam LEO satellite network;

[0142] The beam hopping resource allocation scheme solved in step 3 is handed over to the ground user terminal and the LEO legal satellite for execution, so as to realize the secure communication and multi-dimensional communication resource allocation of the multi-beam LEO legal satellite network;

[0143] On the ground user side, several communication base stations are set up as the starting point for data transmission. In terms of power, a flexible and adjustable transmission power ranging from a few watts to several hundred watts is configured to meet the communication needs under different distances and channel conditions. In terms of frequency, the base station uses a specific frequency band in the Ka band, uses orthogonal frequency division multiplexing OFDM modulation technology to achieve high-speed data transmission, and combines spread spectrum technology to enhance the concealment and anti-interference ability of the signal. In order to achieve wide signal coverage and reduce installation costs, the base station is equipped with an omnidirectional antenna to transmit uplink signals. In addition, the base station also has intelligent monitoring and dynamic adjustment functions, which can evaluate the communication quality in real time and adjust the transmission parameters as needed to maintain a stable communication connection;

[0144] On the LEO legal satellite side, the satellite carries a phased array antenna to implement a beam-hopping scheduling scheme, which accurately captures and efficiently utilizes base station signals by precisely controlling the direction and shape of the beam. In addition, high-precision time synchronization between satellites and ground base stations can be achieved through high-precision time references, complex signal processing technology, and continuous monitoring and adjustment mechanisms. This intelligent resource allocation and communication management strategy not only improves communication efficiency, but also enhances the security and reliability of the communication system;

[0145] Specifically for this embodiment, the base station is equipped with an adjustable power amplifier, and its output power range is set between 10W and 100W. The frequency band of the transceiver module is 20GHz, and the OFDM modulator is configured as multiple subcarriers, each of which adopts QPSK modulation. The spread spectrum technology adopts direct sequence spread spectrum (DSSS). The phased array antenna of the LEO satellite is composed of a number of radiating units, and each unit controls the phase and amplitude electronically to achieve precise pointing and shape adjustment of the beam. The LEO satellite performs high-precision time synchronization with the ground base station through the NTP protocol.

[0146] in conclusion

[0147] According to the above parameters, the simulation results are sorted and plotted. Figure 3 As shown in Figure 2, as the system bandwidth and the number of LEO satellite beams increase, the total rate of hidden users increases accordingly. The impact of different rate thresholds on the rate of each user is shown in Figure 2. Figure 4 As shown in , as the rate threshold of normal users increases, the rate of hidden users decreases accordingly. This shows that when the total communication resources are limited, the system will balance resource allocation according to the communication needs of different users. The impact of different ε values ​​on the rate of each user is shown in Figure 5 As shown, when ε increases, the concealment of the system weakens, thereby increasing the rate of the concealed user. Figure 6 The performance of the multi-beam LEO satellite resource allocation scheme proposed in the present invention is compared with the beam polling scheduling scheme, and the results show that the scheme proposed in the present invention has better performance. In summary, the resource allocation method for multi-beam low-orbit satellite secure communication of the present invention can effectively realize the secure communication and multi-dimensional communication resource allocation of the LEO satellite network.

[0148] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A resource allocation method for multi-beam low-orbit satellite secure communication, characterized by: The following steps are included: Step 1: Construct the satellite-to-ground channel model of the LEO legitimate satellite and the satellite-to-ground channel model of the GEO eavesdropping satellite; Step 2: Create binary optimization variables; construct constraints C1 and C2 of the multi-beam satellite communication system, the communication rate constraint C3 of normal users and the covert data transmission constraint C4 of covert users, and construct the optimization problem of multi-beam satellite resource allocation; constraint C1 means that in each time slot, each user can only choose one transmission power on the same frequency band; constraint C2 means that in each time slot, the number of LEO legal satellite transmission beams is N0; constraint C3 means that the communication rate of normal users should be greater than the minimum rate requirement; constraint C4 ensures the system's covert data transmission requirements; Step 3: By introducing auxiliary binary variables, the original multi-beam satellite resource allocation optimization problem is linearized and converted into a mixed integer linear programming MILP problem, and the optimization solver is used to solve the resource allocation plan of the multi-beam LEO legal satellite; Step 4: Deploy the resource allocation scheme to the actual communication system to achieve secure communication and multi-dimensional communication resource allocation of the multi-beam LEO satellite network.

2. A resource allocation method for multi-beam low-orbit satellite secure communications as claimed in claim 1, characterized in that: The specific implementation method of step one is: The resource allocation scenario for multi-beam LEO satellite secure communication includes I ground users, a LEO legal satellite at orbital altitude H, and an LEO satellite at orbital altitude H. e GEO eavesdropping satellites; the set of ground users is represented by Ground users are divided into two categories: normal users NUE and hidden users CUE that need to transmit hidden data; the number of hidden users is J, and the set is expressed as In order to meet the communication needs of ground users and realize flexible communication resource allocation, the LEO legal satellite adopts a beam hopping strategy to receive terminal data. The number of beam areas on the ground is N. Normal users and hidden users send uplink signals to the LEO legal satellite through different frequency bands. The number of frequency bands for normal users and hidden users is the same, both M. The carrier frequency of the transmitted signal is recorded as f, the system bandwidth is recorded as B, the length of the transmission time slot is δ, and the number of time slots is T. In the tth time slot, the i-th user selects power P on the mth frequency band. k Transmit data to a LEO legal satellite, where the power set is represented by {P k |k=1,2,...,K}; The satellite-to-ground channel model of LEO legal satellite is: Among them, g(θ i,n ) represents the beam gain; Gt represents the maximum gain of the transmitting antenna, Gr represents the maximum gain of the receiving antenna. According to the Friis formula, the free space path loss of the electromagnetic wave is L f It is expressed as: Where c is the speed of light, represents the distance between the LEO legal satellite and the i-th user, where s i Indicates the distance between the user and the satellite ground projection point; Beam gain g(θ i,n ) is expressed as: Among them, θ i,n is the angle at which the line connecting the i-th user and the LEO legal satellite deviates from the center of the n-th beam area; θ 3dB represents the deviation angle when the signal power is attenuated by half; the functions J1(·) and J3(·) represent the first-order Bessel function of the first kind and the third-order Bessel function of the first kind, respectively; The satellite-to-ground channel model of the GEO eavesdropping satellite is: Among them Gr e is the maximum gain of the receiving antenna of the GEO eavesdropping satellite.

3. A resource allocation method for multi-beam low-orbit satellite secure communication as claimed in claim 1, characterized in that: The specific implementation method of step 2 is: Binary Optimization Variables represents the signal transmission status of the i-th user, It means that the i-th user in the t-th time slot uses power P k Transmitting data on frequency band m; In this case, the i-th user does not transmit data; in each time slot, each user can only choose one transmission power on the same frequency band, which is expressed as: Binary optimization variable c n,t ∈{0,1} represents the beam hopping scheduling of LEO legal satellites, c n,t =1 means that the nth beam area is lit in the tth time slot, c n,t =0 means that the nth area is not lit in the tth time slot; in each time slot, the number of LEO legal satellite transmission beams is N0<N, which is expressed as: The uplink communication rate of the i-th normal user is expressed as: where σ 2 represents the noise power of the LEO legal satellite channel; D represents the minimum rate requirement of normal users, that is, the rate threshold, then the communication rate constraint condition C3 of normal users is: The basic model of the covert communication system is expressed as: Where ε is an arbitrarily small positive number; It represents the probability distribution of GEO eavesdropping satellite receiving signal when the ground user sends normal data and covert data at the same time; represents the probability distribution of GEO eavesdropping satellite receiving signals when the ground user only sends normal data, is the KL divergence of the two probability distributions, expressed as: in represents the noise power of the GEO eavesdropping satellite channel; the upper bound of the KL divergence is expressed as: Then the hidden data transmission constraint condition C4 of the hidden user is expressed as: The goal of the optimization problem is to maximize the total communication rate of all hidden users; the set of optimization variables is expressed as and The optimization problem is then expressed as:

4. A resource allocation method for multi-beam low-orbit satellite secure communications as claimed in claim 1, characterized in that: The specific implementation method of step three is: Auxiliary binary variable u t , represented as optimization variable and c n,t Combination of: Variable u t The length of u is N+IKM, so u t Coexistence 2 N+IKM There are two kinds of value cases, each of which corresponds to a resource allocation scheme for the tth time slot; according to the constraints C1 and C2 constructed in step 2, the variable u t The reasonable values ​​are reduced to: Define another auxiliary binary variable Indicates that in the tth time slot u t The value of is the qth one among all Q combinations, which corresponds to a unique satellite beam hopping scheduling scheme and user frequency band power allocation scheme; the beam scheduling scheme and user frequency band power allocation scheme executed by the system in the tth time slot are unique, which can be expressed as: In the tth time slot, for the qth resource allocation scheme, the variable u t The value of is uniquely determined, and its corresponding variable and c n,t The value of is also uniquely determined; therefore, in the tth time slot and under the qth resource allocation scheme, the communication rate of the ground user is expressed as: in and c n,t,q Representation variables and c n,t The value under the qth resource allocation scheme is, represents the communication rate of the i-th normal user, represents the communication rate of the jth hidden user; In the tth time slot, for the qth resource allocation, the parameter It is expressed as: The above parameters and can be achieved by traversing the variable u in sequence t All Q values ​​can be calculated, so it can appear as a constant in the optimization problem. Then the original optimization problem P1 is transformed into a mixed integer linear programming problem P2: The problem P2 is solved by the optimization solver, and the resource allocation scheme for the multi-beam LEO legal satellite is obtained.

5. A resource allocation method for multi-beam low-orbit satellite secure communications as claimed in claim 1, characterized in that: The specific implementation method of step 4 is: The beam hopping resource allocation scheme solved in step 3 is handed over to the ground user terminal and the LEO legal satellite for execution, so as to realize the secure communication and multi-dimensional communication resource allocation of the multi-beam LEO legal satellite network; On the ground user side, several communication base stations are set up as the starting point of data transmission; in terms of power, flexible and adjustable transmission power ranging from a few watts to several hundred watts is configured to meet the communication needs under different distances and channel conditions; in terms of frequency, the base station selects a specific frequency band of the Ka band, uses orthogonal frequency division multiplexing OFDM modulation technology to achieve high-speed data transmission, and combines spread spectrum technology to enhance the concealment and anti-interference ability of the signal; in order to achieve wide signal coverage and reduce installation costs, the base station is equipped with an omnidirectional antenna to transmit uplink signals; in addition, the base station also has intelligent monitoring and dynamic adjustment functions, which can evaluate the communication quality in real time and adjust the transmission parameters as needed to maintain a stable communication connection; On the LEO legal satellite side, the satellite carries a phased array antenna to implement a beam-hopping scheduling scheme, which accurately captures and efficiently utilizes base station signals by precisely controlling the direction and shape of the beam; In addition, high-precision time synchronization between satellites and ground base stations is achieved through high-precision time reference, signal processing, and continuous monitoring and adjustment mechanisms.

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