A Robust Secure Beam Scheduling Method for GEO Satellite Communication Systems

Abstract

The present invention belongs to the field of satellite communication, and particularly relates to a robust secure beam scheduling method based on a GEO satellite communication system. The method includes: First, construct a GEO satellite communication network; construct a secure beam scheduling model for maximizing the sum rate of legitimate users in the GEO satellite communication network. Secondly, introduce an ellipsoid model to construct a bounded channel uncertainty model; construct a robust secure beam scheduling model according to the secure beam scheduling problem of maximizing the sum rate of legitimate users in the system and the bounded channel uncertainty model; solve the robust secure beam scheduling problem to obtain a beam scheduling scheme; the GEO satellite performs information transmission according to the beam scheduling scheme. The present invention improves the security and robustness of the GEO satellite communication system compared with traditional algorithms while ensuring the maximization of the sum rate of legitimate users in the system.

Description

Technical Field

[0001] The present invention belongs to the field of satellite communication, and particularly relates to a robust and secure beam scheduling method based on a GEO satellite communication system. Background Art

[0002] In recent years, geostationary orbit (GEO) satellite communication networks have been used to achieve continuous services within a specified coverage area and large-scale user connections. However, with the rapid growth of a large number of Internet of Things devices, the shortage of spectrum resources and information security issues have become increasingly prominent. Beamforming and artificial noise (AN) technologies are two main technologies to improve spectrum utilization and solve information security. The beamforming technology can make full use of the spatial degrees of freedom provided by multiple antennas to suppress the interference between beams under full frequency reuse. In addition, it can also achieve the directional transmission of information and weaken the interception ability of eavesdroppers for information. In a multi-eavesdropper network, the AN technology suppresses eavesdropping by reducing the communication quality of the eavesdropping channel without significantly affecting the reception quality of legitimate receivers. Therefore, a beam scheduling method that combines beamforming and AN technologies can effectively address the interference and eavesdropping problems in a GEO satellite communication system.

[0003] At present, many methods have studied the beam scheduling based on a GEO satellite communication system, but only considered the beam scheduling optimization problem under ideal channel conditions and mostly for unicast transmission. In actual GEO satellite communication, traditional unicast transmission cannot meet the current service requirements; in addition, in the face of complex communication scenarios, it is not feasible to assume perfect channel state information, and imperfect channel state information may lead to a decline in the performance of the beam scheduling method. Therefore, for the convenience of actual engineering applications, there is an urgent need for a robust and secure beam scheduling method based on a GEO satellite communication system to improve the system transmission rate. Summary of the Invention

[0004] In view of the deficiencies of the prior art, the present invention proposes a robust and secure beam scheduling method based on a GEO satellite communication system, which includes:

[0005] S1: Construct a GEO satellite communication network;

[0006] S2: Construct a secure beam scheduling model for maximizing the sum rate of legitimate users in the system according to the GEO satellite communication network;

[0007] S3: Introduce an ellipsoid model to construct a bounded channel uncertainty model;

[0008] S4: Construct a robust and secure beam scheduling model according to the secure beam scheduling problem of maximizing the sum rate of legitimate users in the GEO satellite communication system and the bounded channel uncertainty problem;

[0009] S5: Solve the robust secure beam scheduling problem to obtain a beam scheduling scheme;

[0010] S6: The GEO satellite performs information transmission according to the beam scheduling scheme.

[0011] Preferably, the GEO satellite communication network includes: a GEO satellite equipped with M single-reflector antennas, N beams, K legitimate users, and L eavesdroppers.

[0012] The GEO satellite transmits signals to K ground users through multicast transmission. There are L eavesdroppers in the same coverage area, attempting to steal the predetermined information of legitimate users. To reduce the communication quality of the eavesdropping channel without affecting the communication quality of the legitimate channel, AN is added at the satellite transmitter.

[0013] Preferably, the beam scheduling model for maximizing the sum rate of system legitimate users is expressed as:

[0014]

[0015] s.t.C1:||w|| 2 +Tr(Σ)≤P max ,

[0016]

[0017] C3:Σ≥0.

[0018] Among them, R k represents the transmission rate of the kth legitimate user, represents the minimum transmission security rate of the kth legitimate user, represents the minimum transmission security rate required by the kth legitimate user, w represents the satellite beamforming vector, Σ represents the artificial noise covariance, P max represents the maximum transmission power of the satellite, Tr(·) represents the trace of the matrix.

[0019] Furthermore, the minimum transmission security rate of the kth legitimate user is:

[0020]

[0021] Among them, h k represents the channel vector from the satellite to the kth legitimate user at the ground end, g l represents the channel vector from the satellite to the lth eavesdropper at the ground end, σ k 2 represents the noise power of additive Gaussian white noise at the legitimate user receiver, σ l 2 represents the noise power of additive Gaussian white noise at the eavesdropper receiver.

[0022] Furthermore, the channel vector from the satellite to the k-th legitimate user is expressed as:

[0023]

[0024] where, represents the parameter related to the free space loss of the k-th legitimate user, b k represents the far-field beam vector, r k represents the rain attenuation vector, θ k represents the channel phase vector.

[0025] Preferably, the bounded channel uncertainty model is expressed as:

[0026]

[0027]

[0028] where, and represent the uncertainty sets of the legitimate channel and the eavesdropping channel respectively; h k , and Δh k represent the actual channel vector, the estimated channel vector, and the estimated channel vector error from the satellite to the k-th legitimate user on the ground respectively, g l , and Δg l represent the actual channel vector, the estimated channel vector, and the estimated channel vector error from the satellite to the l-th eavesdropper on the ground respectively, ε k and ε l represent the upper bounds of the estimated channel vector errors of the legitimate channel and the eavesdropping channel respectively.

[0029] Preferably, the robust secure beam scheduling problem is expressed as:

[0030]

[0031] s.t.C1:Tr(W)+Tr(Σ)≤P max ,

[0032]

[0033] C3:Σ≥0,W≥0,

[0034] C4:Rank(W)=1,

[0035]

[0036] where, R k represents the transmission rate of the k-th legitimate user, W=ww H, where \(w\) represents the satellite beamforming vector, \(\Sigma\) represents the AN covariance, and \(P\) max represents the maximum transmit power of the satellite, \(Tr(\cdot)\) represents the trace of a matrix, represents the minimum transmission security rate of the \(k\)-th legitimate user, represents the minimum transmission security rate required by the \(k\)-th legitimate user, \(Rank(\cdot)\) represents the rank of a matrix, \(\Delta h\) k and \(\Delta g\) l respectively represent the estimated channel vector errors of the legitimate channel and the eavesdropping channel, and respectively represent the uncertainty sets of the legitimate channel and the eavesdropping channel.

[0037] Preferably, the process of solving the robust secure beam scheduling problem includes:

[0038] S51: Introduce slack variables to transform the objective function and the bounded uncertainty constraints into tractable forms, obtaining a rewritten robust secure beam scheduling problem;

[0039] S52: Use the exponential substitution method, successive convex approximation, Taylor series expansion, S-Procedure, and semidefinite relaxation method to transform the robust beam scheduling problem into a standard convex optimization problem;

[0040] S53: Use convex optimization tools to solve the convex optimization problem, obtaining the satellite beamforming vector and the artificial noise covariance, that is, the robust secure beam scheduling scheme.

[0041] Advantages of the present invention:

[0042] Aiming at the interference and eavesdropping problems caused by beam scheduling and information security in traditional satellite communication networks, and the traditional unicast transmission mode cannot support the access of a large number of users, the present invention introduces beamforming and AN technologies into the GEO satellite multicast communication system, considering the maximum transmit power of the GEO satellite and the minimum security rate constraint of legitimate users, and establishes a beam scheduling model for maximizing the sum rate of legitimate users. In addition, the present invention considers the imperfect channel state information of the legitimate channel and the eavesdropping channel, avoiding the performance degradation of the beam scheduling method. Different from the traditional beam scheduling methods that only guarantee the transmit power or the security rate, the present invention makes a trade-off optimization between the security rate and the transmit power, considering more comprehensively; at the same time, in the solving process, the present invention also proposes a new improved algorithm. In the new improved algorithm, methods such as successive convex approximation, semidefinite relaxation, and S-Procedure are used to ensure the limited satellite transmit power and the minimum security rate of users in the worst communication situation, control the convergence accuracy of the algorithm, and design an iterative algorithm with lower complexity. In addition, compared with the existing solutions, the present invention improves the security and robustness of the GEO satellite communication system. Description of the Drawings

[0043] Figure 1 It is the overall flowchart of the method of the present invention;

[0044] Figure 2 It is the system model diagram of the GEO satellite communication network in the present invention;

[0045] Figure 3 It is the curve graph of the sum rate of legitimate users of the present invention and the comparative method under different upper bounds of the estimated channel vector error.

[0046] Figure 4 It is the curve graph of the actual secure rate of legitimate users of the present invention and the comparative method under different upper bounds of the estimated channel vector error. Detailed implementation manners

[0047] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0048] The present invention proposes a robust beam scheduling method based on a GEO satellite communication system, as Figure 1 shown, the method includes the following content:

[0049] S1: Construct a GEO satellite communication network.

[0050] As Figure 2 shown, the present invention considers a GEO satellite communication network, which consists of a gateway, a GEO satellite, and ground terminals (legitimate users and eavesdroppers). Specifically, there is a GEO satellite in this network, which is equipped with M multi-feed single-reflector antennas to generate N beams to serve K legitimate users on the ground at the same time (N>K). It is assumed that there are L eavesdroppers in this network scenario, trying to eavesdrop on the predetermined information of any legitimate user. Define the beam set The set of legitimate users The set of eavesdroppers

[0051] S2: Construct a beam scheduling model for maximizing the sum rate of legitimate users of the system according to the GEO satellite communication network.

[0052] In the signal preparation and transmission stage, to prevent eavesdroppers from stealing user information, artificial noise is added at the satellite transmitting end to reduce the communication quality of the eavesdropping channel while minimizing the impact on the system transmission performance.

[0053] In some preferred embodiments of the present invention, the artificial noise can be obtained in the following manner:

[0054] Perform constellation mapping on the signal to be transmitted. According to the constellation mapping result, combined with the security rate and the transmission power, obtain the artificial noise of the signal to be transmitted. Then the artificial noise is expressed as:

[0055]

[0056] where z represents the artificial noise, x represents the signal to be transmitted, Σ represents the artificial noise covariance; sign(a) represents the sign function,

[0057] The artificial noise in this embodiment comprehensively considers the security rate and the transmission power. While ensuring that legitimate users can receive information normally, it blocks the theft of the transmitted signal by illegal eavesdropping users, and is more reasonable.

[0058] In the signal transmission stage, the ground-based eavesdroppers are far apart from each other and it is difficult for them to cooperate in eavesdropping. The minimum transmission security rate of the k-th legitimate user in the system is expressed as:

[0059]

[0060] where, represents the minimum security rate of the k-th legitimate user on the ground, represents the channel vector from the satellite to the k-th legitimate user on the ground, represents the channel vector from the satellite to the l-th eavesdropper on the ground, σ k 2 represents the noise power of the additive white Gaussian noise at the legitimate user's receiver, σ l 2 represents the noise power of the additive white Gaussian noise at the eavesdropper's receiver. The superscript H represents the conjugate matrix.

[0061] In the downlink of the GEO satellite communication system, considering the influence of factors such as satellite beam gain, rain attenuation effect, channel phase vector, and path loss, the channel vector from the satellite to the k-th legitimate user is expressed as:

[0062]

[0063] where ⊙ represents the Hadamard product, represents the parameter related to the free space loss of the k-th legitimate user, represents the far-field beam vector, represents the rain attenuation vector, represents the channel phase vector.

[0064] The beam scheduling model for maximizing the sum rate of the legitimate users in the system is expressed as:

[0065]

[0066] s.t.C1:||w|| 2 +Tr(Σ)≤P max ,

[0067]

[0068] C3:Σ≥0.

[0069] The constraints in the above formulas include: C1 is the maximum transmission power constraint of the satellite, C2 is the minimum secure rate constraint of the k-th legitimate user, and C3 is the positive semi-definite constraint of the artificial noise covariance; where, R k represents the transmission rate of the k-th legitimate user, represents the minimum transmission security rate of the k-th legitimate user, represents the minimum transmission security rate required by the k-th legitimate user, w represents the satellite beamforming vector, Σ represents the artificial noise covariance, and P max represents the maximum transmission power of the satellite, and Tr(·) represents the trace of a matrix.

[0070] S3: Introduce the ellipsoid model to construct a bounded channel uncertainty model.

[0071] Considering the additive model of uncertainty parameters, introduce the ellipsoid model. Compared with other parameter uncertainty sets, the ellipsoid uncertainty set can better reflect the correlation between uncertainty parameters and is more easily transformed into a tractable form in linear optimization, quadratic optimization, and conic quadratic optimization problems. Therefore, construct a bounded channel uncertainty model, expressed as:

[0072]

[0073]

[0074] where, and represent the uncertainty sets of the legitimate channel and the eavesdropping channel respectively; and Δh k represent the actual channel vector, estimated channel vector, and estimated channel vector error of the satellite to the k-th legitimate user on the ground respectively, and Δg l represent the actual channel vector, estimated channel vector, and estimated channel vector error of the satellite to the l-th eavesdropper on the ground respectively, and ε k and ε l represent the upper bounds of the estimated channel vector errors of the legitimate channel and the eavesdropping channel respectively.

[0075] S4: Construct a robust beam scheduling model according to the beam scheduling problem and the bounded channel uncertainty problem for maximizing the sum rate of legitimate users in the GEO satellite communication system.

[0076] The robust beam scheduling problem is expressed as:

[0077]

[0078] where, R k represents the transmission rate of the k-th legitimate user, W = ww H , represents the satellite beamforming vector, represents the artificial noise covariance, P max represents the maximum transmit power of the satellite, Tr(·) represents the trace of a matrix, represents the minimum transmission security rate of the k-th legitimate user, represents the minimum transmission security rate required by the k-th legitimate user, Rank(·) represents the rank of a matrix, Δh k and Δg l represent the estimated channel vector errors of the legitimate channel and the eavesdropping channel respectively, and represent the uncertainty sets of the legitimate channel and the eavesdropping channel respectively.

[0079] S5: Solve the robust beam scheduling problem to obtain a beam scheduling scheme.

[0080] The process of solving the robust beam scheduling problem includes:

[0081] S51: Introduce slack variables to transform the objective function and the bounded uncertainty constraints into a tractable form, obtaining a rewritten robust beam scheduling problem;

[0082] Use the following slack variables to process the objective function and the C2 constraint, transforming the uncertainty factors into a tractable form, obtaining:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] where, r k , r l , αk , β k , χ l and ω l are slack variables.

[0090] S52: By using the exponential substitution method, successive convex approximation, Taylor series expansion, S-procedure, and semi-definite relaxation method, the robust secure beam scheduling problem is transformed into a standard convex optimization problem;

[0091] By using the exponential substitution method, equations (2) and (3) are transformed into:

[0092]

[0093]

[0094]

[0095]

[0096] where and are slack variables.

[0097] By using successive convex approximation and Taylor series expansion, the non-convex constraints in equations (9) and (11) are transformed into convex constraints. Finally, equations (2) and (3) are transformed into:

[0098]

[0099]

[0100] where and respectively represent the last iteration results of variables and r l .

[0101] By using the S-Procedure method, the constraints containing uncertainty factors are transformed into deterministic constraints, and equations (4) to (7) are transformed into:

[0102]

[0103]

[0104]

[0105]

[0106] where λ1, λ2, λ3, and λ4 are slack variables.

[0107] By relaxing the rank-1 constraint of C4 in Equation (1) using the semidefinite relaxation method, the robust beam scheduling problem of Equation (1) is transformed into:

[0108]

[0109] where Θ = {r k , r l , α k , β k , χ l , ω l}, Λ = {λ1, λ2, λ3, λ4}.

[0110] S53: Use convex optimization tools to solve the convex optimization problem to obtain the satellite beamforming vector and the artificial noise covariance, that is, the robust secure beam scheduling scheme.

[0111] Equation (18) is a standard convex optimization problem. Therefore, the present invention directly uses convex optimization tools to solve this problem to obtain the satellite beamforming vector w and the artificial noise covariance Σ, that is, the robust beam scheduling scheme; the satellite in the GEO satellite communication system can perform information transmission according to the robust beam scheduling scheme.

[0112] S6: The GEO satellite performs information transmission according to the beam scheduling scheme.

[0113] In the context of imperfect channel information and the presence of eavesdroppers, the beam scheduling scheme proposed by the present invention aims to improve the transmission performance of the entire system, considering the minimum security rate constraint of users and the total satellite transmit power constraint under the worst communication conditions. Adhering to the concept of secure and green communication, it ensures the secure transmission of satellite communication and reduces the power consumption of satellite communication. An optimal beam scheduling scheme is obtained.

[0114] Evaluate the present invention:

[0115] Describe the application effect of the present invention in detail in combination with simulations:

[0116] 1) Simulation conditions

[0117] Assume that there is one GEO satellite, 2 legitimate users, and 2 eavesdroppers in this system. Assume that the current positions of the 2 legitimate users are represented as (-0.5×10 5 , 0) m, (0.5×10 5 , 0) m respectively. Assume that the coordinate range of the current position of the first eavesdropper is represented as {(x, y)| -2×10 5 m ≤ x ≤ -3×10 5 m, 1.5×10 5 m ≤ y ≤ 2.5×10 5m}, and the coordinate range of the current position of the second eavesdropper is represented as {(x, y)|2×10 5 m ≤ x ≤ 3×10 5 m, 1.5×10 5 m ≤ y ≤ 2.5×10 5 m}. Assume that the upper bounds of the estimated channel vector errors of the user channel and the eavesdropper channel are ε k = 0.05, ε l = 0.1, Assume the minimum security rate of the user The settings of other simulation parameters are given in Table 1:

[0118] Table 1 Simulation Parameter Table

[0119]

[0120] 2) Simulation Results

[0121] Figure 3 shows the relationship between the sum rate of the legitimate users of the present invention and the upper bound ε k of the legitimate channel estimation error. It can be seen that as ε k increases, the sum rate of the legitimate users decreases, and Figure 3 indicates that the sum rate of the legitimate users of the algorithm proposed by the present invention is significantly improved compared with the robust algorithm without AN and the non-robust algorithm without AN. Figure 4 shows the relationship between the actual security rate of the present invention and the number of eavesdroppers. It can be seen that as the number of eavesdroppers increases, the actual security rate of the user decreases. In addition, Figure 4 indicates that as the number of eavesdroppers increases, the security rate of the users of the robust algorithm without AN and the non-robust algorithm without AN is lower than the minimum security rate threshold, and the system is prone to interruption. However, the algorithm of the present invention considers the security rate of the users in the worst case and always satisfies the minimum security rate constraint, which reflects that the algorithm of the present invention can effectively improve the security performance of the system. In summary, compared with the traditional algorithm, the present invention has better robustness and security.

[0122] The above embodiments further elaborate on the purpose, technical solutions, and advantages of the present invention. It should be understood that the above embodiments are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made to the present invention within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0123] Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. The storage medium can include: ROM, RAM, magnetic disk, optical disk, etc.

[0124] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A robust security beam scheduling method based on a GEO satellite communication system, characterized in that Including: S1: Construct a GEO satellite communication network; S2: Construct a secure beam scheduling model for maximizing the sum rate of legitimate users in the GEO satellite communication network; S3: Introduce an ellipsoid model to construct a bounded channel uncertainty model; S4: Construct a robust secure beam scheduling model based on the secure beam scheduling problem of maximizing the sum rate of legitimate users in the GEO satellite communication system and the bounded channel uncertainty problem; S5: Solve the robust secure beam scheduling problem to obtain a beam scheduling scheme; S6: The GEO satellite performs information transmission according to the beam scheduling scheme.

2. The robust security beam scheduling method based on a GEO satellite communication system according to claim 1, characterized in that The GEO satellite communication network includes: One GEO satellite is equipped with M multi-feed single reflector antennas, generating N beams to serve K legitimate users and L eavesdroppers at the ground end simultaneously.

3. The robust security beam scheduling method based on a GEO satellite communication system according to claim 1, characterized in that The secure beam scheduling model for maximizing the sum rate of legitimate users in the system is expressed as: s.t.C1:||w|| 2 +Tr(Σ)≤P max , C2: C3: Σ≥0. Among them, R k represents the transmission rate of the k-th legitimate user, represents the minimum transmission security rate of the k-th legitimate user, represents the minimum transmission security rate required by the k-th legitimate user, w represents the satellite beamforming vector, Σ represents the artificial noise covariance, P max represents the maximum transmission power of the satellite, Tr(·) represents the trace of the matrix, K represents the number of legitimate users, C1 is the maximum transmission power constraint of the satellite, C2 is the minimum security rate constraint of the k-th legitimate user, and C3 is the positive semi-definite constraint of the artificial noise covariance.

4. The robust security beam scheduling method based on a GEO satellite communication system according to claim 3, characterized in that The minimum transmission security rate of the k-th legitimate user is: where h k represents the channel vector from the satellite to the k-th legitimate user at the ground terminal, and g l represents the channel vector from the satellite to the l-th eavesdropper at the ground terminal. σ k2 represents the noise power of additive white Gaussian noise at the legitimate user's receiver, and σ l 2 represents the noise power of additive white Gaussian noise at the eavesdropper's receiver. The superscript H represents the conjugate matrix, represents the set of eavesdroppers.

5. The robust security beam scheduling method based on a GEO satellite communication system according to claim 4, characterized in that The channel vector from the satellite to the k-th legitimate user at the ground end is expressed as: Among them, represents the parameter related to the free space loss of the k-th legitimate user, b k represents the far-field beam vector, r k represents the rain attenuation vector, θ k represents the channel phase vector, and ⊙ represents the Hadamard product.

6. The robust security beam scheduling method based on a GEO satellite communication system according to claim 1, characterized in that The bounded channel uncertainty model is expressed as: Among them, and represent the uncertainty sets of the legitimate channel and the eavesdropping channel, respectively; h k 、 and Δh k represent the actual channel vector, the estimated channel vector, and the estimated channel vector error of the k-th legitimate user from the satellite to the ground terminal, respectively; g l 、 and Δg l represent the actual channel vector, the estimated channel vector, and the estimated channel vector error of the l-th eavesdropper from the satellite to the ground terminal, respectively; ε k and ε l represent the upper bounds of the estimated channel vector errors of the legitimate channel and the eavesdropping channel, respectively.

7. The robust security beam scheduling method based on a GEO satellite communication system according to claim 1, characterized in that The robust secure beam scheduling problem is expressed as: s.t.C1:Tr(W)+Tr(Σ)≤P max , C2: C3: Σ≥0, W≥0, C4: Rank(W)=1, C5: where K represents the number of legitimate users, and R k represents the transmission rate of the k-th legitimate user, W = ww H , w represents the satellite beamforming vector, the superscript H represents the conjugate matrix, Σ represents the artificial noise covariance, and P max represents the maximum transmit power of the satellite, Tr(·) represents the trace of a matrix, represents the minimum transmission security rate of the k-th legitimate user, represents the minimum transmission security rate required by the k-th legitimate user, Rank(·) represents the rank of a matrix, Δh k and Δg l represent the estimated channel vector errors of the legitimate channel and the eavesdropping channel respectively, and represent the uncertainty sets of the legitimate channel and the eavesdropping channel respectively. C1 is the satellite maximum transmit power constraint, C2 is the minimum security rate constraint of the k-th legitimate user, C3 is the positive semi-definite constraint of the artificial noise covariance, and C4 is the rank-1 constraint.

8. A robust security beam scheduling method based on a GEO satellite communication system according to claim 1, characterized in that, The process of solving the robust secure beam scheduling problem includes: S51: Introduce slack variables to transform the objective function and the bounded uncertainty constraint into a tractable form, obtaining a rewritten robust secure beam scheduling problem; S52: Use the exponential substitution method, successive convex approximation, Taylor series expansion, S-Procedure algorithm, and semidefinite relaxation method to transform the robust secure beam scheduling problem into a standard convex optimization problem; S53: Use a convex optimization tool to solve the convex optimization problem to obtain the satellite beamforming vector and the artificial noise covariance, that is, the robust secure beam scheduling scheme.

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