Symbol-level secure transmission method based on satellite beam cooperation

Abstract

The invention discloses a symbol-level secure transmission method based on satellite beam cooperation, and belongs to the field of physical layer security in a wireless communication technology. Based on the multi-beam cooperative transmission technology, a symbol-level beam pointing drift and symbol mapping randomization method is adopted, and spatial randomness is introduced around a target user, so that a non-target user cannot receive an effective signal, and the anti-eavesdropping capability of a symbol-level secure transmission system is further improved. According to the method, random drift of asymmetric array segmentation and beam pointing is introduced on the basis of beam forming, and information leakage of a side lobe area is controlled. By introducing interference and randomizing beam pointing, leaked signal energy is dispersed to an unexpected direction, and the possibility that an eavesdropper eavesdrops through sidelobe signals is reduced. According to the method, the adaptive Armijo algorithm is constructed, so that the optimization process of the multi-objective optimization problem of the symbol-level secure transmission system is accelerated, and the convergence of the optimization result in a high-dimensional space is ensured.

Description

Technical Field

[0001] The present invention relates to a symbol-level secure transmission method based on satellite beam collaboration, belonging to the field of physical layer security in wireless communication technology. Technical Background

[0002] Satellite communication has become a key component of the global telecommunications network, providing extensive coverage and reliable transmission. Due to its inherent broadcast nature and vast coverage area, satellite communication is vulnerable to various security threats such as eavesdropping. Traditional methods for ensuring information security usually rely on upper-layer security technologies. However, these methods may impose a significant processing overhead on the satellite platform. Physical layer security technology (PLS) ensures secure transmission by leveraging the unique characteristics of the wireless channel, thereby reducing the reliance on complex encryption algorithms. Beamforming can be regarded as a basic PLS technology, which ensures security by creating a significant energy difference between the legitimate and eavesdropping channels. However, when the eavesdropper has a highly sensitive receiver, the advantages of beamforming may be weakened. The directed modulation (DM) method is another typical PLS method, which introduces artificial noise (AN) into beamforming to prevent information from leaking through the sidelobes.

[0003] However, a significant limitation of beamforming-based PLS methods is that they cannot guarantee security within the main lobe region. This problem is particularly evident in satellite communication. Even when the beam width is very narrow, the insecure region under the main lobe can become quite large. With the advancement of PLS technology, cooperative communication has shown great potential in resisting eavesdropping. This potential stems from the additional design flexibility provided by spatial cooperation, which can be used to enhance secure communication design. Summary of the Invention

[0004] To solve the problem of information transmission leakage caused by the inability to guarantee security within the main lobe region, the object of the present invention is to provide a symbol-level secure transmission method based on satellite beam collaboration, which reduces sidelobe leakage and narrows the transparent communication area through random drift of the beam pointing; and adopts a multi-objective optimization and adaptive Armijo step-size algorithm to improve the convergence speed and robustness of the optimization of the symbol-level secure transmission optimization problem. The present invention also has the advantages of high security and high efficiency.

[0005] The object of the present invention is achieved by the following technical solutions.

[0006] A symbol-level secure transmission method based on satellite beam collaboration disclosed by the present invention includes the following steps:

[0007] Step 1: Model the array transmission channel based on multi-antenna theory to obtain the transmission channel models of each sub-array.

[0008] The satellite array is a uniform planar array (UPA) with N isotropic antennas in a line, where the antennas are evenly placed with a spacing of d ≤ λ / 2, and λ is the wavelength. The UPA adopts a hybrid analog-digital architecture and uses switched power amplifiers to divide the UPA into two sub-arrays. Each sub-array is driven by a separate radio frequency chain and can transmit data independently.

[0009] The i-th sub-array consists of N i = N i，v × N i，h antennas, where N i，v and N i，h represent the number of antennas in the vertical and horizontal dimensions respectively. For ease of analysis, we use polar coordinates (ρ, θ) to represent the position of the receiving user in the x-y plane, where ρ is the distance and θ is the azimuth angle. The target user is located at the origin, and the satellite is located at a height of H directly above the target user. The elevation angle of the i-th sub-array beam pointing to the user is calculated as φ = arctan(ρ / H). Therefore, the channel matrix of the i-th sub-array to the receiver at (ρ, θ) can be expressed as:

[0010]

[0011] where:

[0012]

[0013] represent the channel vectors along the vertical and horizontal directions respectively. represents the tensor product of the channel vectors.

[0014] Applying hybrid analog-digital precoding to direct the i-th beam towards (ρ i , θ i ). For the k-th symbol interval, the transmitted symbol is represented by , and the noise-free received signal y i (ρ, θ) from the i-th beam is expressed as:

[0015] y i (k, ρ, θ) = h i (ρ, θ) w i (ρ i , θ i ) s(k) (2)

[0016] Equation (2) is the transmission channel model of each sub-array.

[0017] Step 2: Through random symbol mapping design, achieve transparent transmission in the beam overlapping area and randomize the signals in other areas.

[0018] For the k-th symbol interval, the mapping function f(·) = {f1(·), f2(·)} is used to randomly map s(k) to the transmission symbols of two sub-arrays. The mapping process is expressed as:

[0019] f i : s(k) → x i (k), i = 1, 2 (3)

[0020] The transmission symbol of the i-th beam

[0021] In this case, the noiseless superimposed signal received by the ground user at (ρ, θ) can be expressed as:

[0022]

[0023] To ensure transparent service for users at (ρ0, θ0), the beam cross-transmission method imposes a constraint where r > 0 is a proportionality constant.

[0024] Step 3: Introduce spatial randomness into the sidelobes through symbol-level variable beam steering design to reduce information leakage.

[0025] The symbol-level variable beam steering design realizes interference in the undesired direction through the random drift of the beam steering at the symbol rate. The movable trajectory in the x-y plane is expressed as r = g(ψ), that is, the beam steering trajectory function, where ψ ∈ [0, 2π] is the polar angle. The radii of the insecure coverage areas formed by the two beams on the ground are R1 and R2 respectively. The probability density function f i (r, ψ) can be expressed as:

[0026]

[0027] where δ(r - g(ψ)) is the Dirac function, ensuring that the beam only appears on the trajectory r = g(ψ);

[0028] For the k-th symbol interval, the position pointed to by the i-th beam is mathematically expressed as (r i (k), ψ i (k)), where ψ i (k) is the polar angle, and r i (k) = g(ψ i (k)) is the corresponding radial distance along the trajectory. The precoding vector w i (r i (k), ψ i (k)) can be expressed as:

[0029]

[0030] Step 4: Manufacture spatial randomness through an asymmetric array division design to further narrow the non-secure area.

[0031] Construct a method for asymmetrically dividing a satellite array into two sub-arrays. This division will create a difference that, through random and continuous movement of the beam pointing, will be converted into interference in an undesired direction. The difference between the sub-arrays is characterized by the array division parameter Taking ξ into (6), the precoding vector is transformed into:

[0032]

[0033] Using the above asymmetric array division design, the noiseless superimposed signal can be expressed as:

[0034]

[0035] Step 5: Establish a multi-objective optimization model to minimize the non-secure area and sidelobe information leakage.

[0036] The objective is to minimize the non-secure area S within the main lobe by optimizing the variables introduced in Steps 2 to 4: the symbol mapping function f(·), the beam pointing trajectory function g(ψ), and the array division parameter ξ (abbreviated as f, g, and ξ respectively), LM and eliminate the non-secure area S within the sidelobe LS . Define the minimum security capacity (SC) at the sidelobe as C min , and eliminate S by maximizing C min such that LS C is the maximum tolerable information leakage. Then, formulate the multi-objective linear weighted optimization problem as follows: U r≥∈, (13)

[0037]

[0038] where ε is the minimum signal-to-noise ratio required for a legitimate user to successfully receive.

[0039]

[0040] Step 6: Construct an adaptive Armijo algorithm to handle the complex multi-objective optimization problem and achieve symbol-level secure transmission based on satellite beam collaboration according to the symbol-level secure transmission results.

[0041] Constrain the beam pointing trajectory to lie on a circle with a radius of R, which can be extended to any shape. Combining the gradient descent method and the Armijo rule, accelerate the convergence by ensuring sufficient reduction of the objective function in each iteration. For ξ, at the (k + 1)-th iteration, its gradient is expressed as:

[0042]

[0043] Among them, represents a small step size. The update step size of ξ is where α is a scaling factor used to ensure sufficient reduction of the objective function. α ∈ (0, 1) is a constant scaling factor that satisfies the Armijo condition, which is expressed as:

[0044]

[0045] If this condition is not satisfied, α will be interactively reduced by multiplying it with the coefficient γ ∈ (0, 1). This process will be repeated iteratively until and so as to obtain the optimal parameters. The computational complexity is O(KL), where k is the number of iterations and L is the average number of step size adjustments in each iteration.

[0046] The symbol-level secure transmission result is obtained by optimizing the multi-objective optimization problem, and the symbol-level secure transmission based on satellite beam collaboration is realized according to the symbol-level secure transmission result.

[0047] Beneficial effects:

[0048] 1. Aiming at the problems of wide ground coverage range of satellite beams, large hidden range of eavesdropping threats, and insufficient security, a symbol-level secure transmission method based on satellite beam collaboration disclosed by the present invention is based on multi-beam cooperative transmission technology, and adopts symbol-level beam pointing drift and symbol mapping randomization methods to introduce spatial randomness around the target user, so that non-target users cannot receive effective signals, further improving the anti-eavesdropping ability of the symbol-level secure transmission system.

[0049] 2. Aiming at the problem that the signal leakage in the sidelobe region in the traditional beamforming method may be captured by eavesdroppers, a symbol-level secure transmission method based on satellite beam collaboration disclosed by the present invention effectively controls the information leakage in the sidelobe region by introducing asymmetric array segmentation and random drift of beam pointing on the basis of beamforming. By introducing interference and randomizing the beam pointing, the leaked signal energy is dispersed to undesired directions, thereby reducing the possibility of eavesdropping by eavesdroppers through sidelobe signals.

[0050] 3. To address the challenges in solving multi-objective optimization problems, a symbol-level secure transmission method based on satellite beam collaboration disclosed in the present invention constructs an adaptive Armijo algorithm to accelerate the optimization process of the multi-objective optimization problem in the symbol-level secure transmission system and ensure the convergence of the optimization results in high-dimensional space. Compared with traditional gradient descent methods, the present invention demonstrates higher efficiency and stronger robustness in dealing with complex multi-objective optimization problems, ensuring that the symbol-level secure transmission system can operate efficiently on resource-constrained satellite platforms and achieve the expected performance. Brief Description of the Drawings

[0051] Figure 1 is the flowchart for realizing satellite secure communication based on beam collaboration.

[0052] Figure 2 is the schematic diagram of the variable beam pointing system based on symbol mapping.

[0053] Figure 3 is the schematic diagram for comparing the BER performance of the proposed scheme and the traditional scheme, where: Figure 3 (a) is the schematic diagram of beamforming, Figure 3 (b) is the schematic diagram of multi-beam intersection, Figure 3 (c) is the proposed design, Figure 3 (d) is the proposed design of asymmetric partitioning.

[0054] Figure 4 is the schematic diagram of the SC performance and the positions of legitimate users. Detailed Embodiment

[0055] To enable those skilled in the art to more deeply understand the implementation idea of the solution of the present invention, the technical solutions in the embodiments of the present invention will be carefully and clearly described below with reference to 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 embodiments. All other implementation cases 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.

[0056] As Figure 1 shown, a symbol-level secure transmission method based on satellite beam collaboration disclosed in this example is specifically implemented as follows:

[0057] Step 1. Based on multi-antenna theory, model the array transmission channel to obtain the transmission channel models of each sub-array.

[0058] The symbol-level variable beam pointing design method based on symbol mapping is realized relying on a satellite communication system. Consider a satellite communication downlink secure transmission system with a multi-antenna satellite and a single-antenna receiver.

[0059] Low Earth Orbit satellites operate at an altitude of approximately between 160 km and 2000 km. At a certain moment, it is at an orbital altitude of 600 km and is equipped with 2600 antennas. The information leakage within the secure area is set to be less than I m = 0.1 bit / channel, the signal modulation method is QPSK modulation, and the carrier frequency is 30 GHz.

[0060] The satellite array is a uniform planar array (UPA) of g with N isotropic antennas, where the antennas are uniformly placed with a spacing of d ≤ λ / 2, and λ is the wavelength. The UPA adopts a hybrid analog-digital architecture and uses a switched power amplifier to divide the UPA into two sub-arrays. Each sub-array is driven by a separate radio frequency chain and can transmit data independently. Let the i-th sub-array consist of N i = N i，v ×N i，h antennas, where N i，v and N i，h represent the number of antennas in the vertical and horizontal dimensions respectively. For ease of analysis, we use polar coordinates (ρ, θ) to represent the position of the receiving user in the x-y plane, where ρ is the distance and θ is the azimuth angle. The target user is located at the origin, and the satellite is at a height of H directly above the target user. The elevation angle of the i-th sub-array beam pointing to the user is calculated as φ = arctan(ρ / H). Therefore, the channel matrix of the i-th sub-array to the receiver at (ρ, θ) can be expressed as:

[0061]

[0062] where:

[0063]

[0064] represent the channel vectors along the vertical and horizontal directions. represents the tensor product of the channel vectors.

[0065] Apply hybrid analog-digital precoding to direct the i-th beam towards (ρ i , θ i ). For the k-th symbol interval, the transmitted symbol is represented by , and the noise-free received signal y i (ρ, θ) from the i-th beam can be expressed as:

[0066] y i (k, ρ, θ) = h i (ρ, θ)w i (ρ i , θ i )s(k)

[0067] Step 2: Propose a random symbol mapping design to achieve transparent transmission in the beam overlapping region and randomize signals in other regions, such as Figure 2 shown.

[0068] For the k-th symbol interval, use the mapping function f(·) = {f1(·), f2(·)} to randomly map the source symbol s(k) to the transmission symbols of the two sub-arrays. The transmitted symbol of the i-th beam, denoted as can be expressed as:

[0069] f i : s(k) → x i (k), i = 1, 2

[0070] In this case, the noise-free superimposed signal received by the ground user at (ρ, θ) can be expressed as:

[0071]

[0072] To ensure transparent service for users at (ρ0, θ0), this method imposes the constraint where r > 0 is a proportionality constant.

[0073] Step 3: Propose a symbol-level variable beam pointing design to introduce spatial randomness into the sidelobes to reduce information leakage.

[0074] This design achieves interference in the undesired direction through the random drift of the beam pointing at the symbol rate. The movable trajectory in the x-y plane is expressed as r = g(ψ), where ψ ∈ [0, 2π] is the polar angle and r is the radial distance as a function of the polar angle ψ. Assume that the radii of the insecure coverage areas formed by the two beams on the ground are R1 and R2 respectively. The probability density function f i (r, ψ) of the i-th beam moving along the trajectory can be expressed as:

[0075]

[0076] where δ(r - g(ψ)) is the Dirac function to ensure that the beam only appears on the trajectory r = g(ψ). For the k-th symbol interval, the position of the k-th beam pointing is mathematically expressed as (r i (k), ψ i (k)), where ψ i (k) is the polar angle and r i (k) = g(ψ i (k)) is the corresponding radial distance along the trajectory. The precoding vector w i (r i (k), ψ i (k)) can be expressed as:

[0077]

[0078] Step 4: Propose an asymmetric array partitioning design to create spatial randomness and further narrow the non-secure region.

[0079] This partitioning creates differences that, through random and continuous movement of the beam direction, are converted into interference in undesired directions. The differences between sub-arrays are characterized by the parameter Therefore, the precoding vector is transformed into

[0080]

[0081] Using the above design, the noise-free superimposed signal

[0082] Step 5: Establish a multi-objective optimization model to minimize the non-secure region and sidelobe information leakage.

[0083] The objective is to minimize the non-secure region S within the main lobe and eliminate the non-secure region S within the sidelobe by optimizing the beam direction trajectory function g, the array partitioning parameter ξ, and the symbol mapping function f. LM Define the minimum security capacity (SC) at the sidelobe as C LS and eliminate S by maximizing C min such that min C LS is the maximum tolerable information leakage. Then, formulate the multi-objective linear weighted optimization problem as follows: C U r≥∈,

[0084]

[0085] where ε is the minimum signal-to-noise ratio required for successful reception by legitimate users, set to 0.5.

[0086] Set the weight coefficient W

[0087] to 0.05 and W e to 0.95. s

[0088] Step 6: Propose an adaptive Armijo algorithm to handle the complex multi-objective optimization problem.

[0089] Constrain the beam direction trajectory to lie on a circle with radius R, which can be extended to any shape. Combine the gradient descent method and the Armijo rule to accelerate convergence by ensuring sufficient reduction of the objective function in each iteration. For ξ, at the (k + 1)-th iteration, its gradient is expressed as:

[0090]

[0091] Among them, represents a small step size. The update step size of ξ is where α is a scaling factor used to ensure sufficient reduction of the objective function. α ∈ (0, 1) is a constant scaling factor that satisfies the Armijo condition, which is expressed as:

[0092]

[0093] If this condition is not satisfied, α will be interactively reduced by multiplying it with the coefficient γ ∈ (0, 1). This process will be repeated iteratively until and so as to obtain the optimal parameters. The computational complexity is O(KL), where k is the number of iterations and L is the average number of step size adjustments in each iteration. δ, α, and γ are set to 0.01, 1, and 0.5 respectively.

[0094] Step 7: Use the multi-objective optimization algorithm to solve the beam pointing trajectory function g, the array segmentation parameter ξ, and the symbol mapping function f. The specific steps are as follows:

[0095] 1) Input ξ (0) , R (0) , f (0) , δ, σ, γ, W s , W e .

[0096] 2) Initialize k = 0, ξ (0) = 1, R (0) = 0, γ = 0.5.

[0097] 3) When and , enter loop ①:

[0098] 4) Calculate the gradient Initialize α = 1, β = 1.

[0099] 5) Set

[0100] 6) Fix ξ (k+1) and R (k) , optimize f (k) to minimize V, which is represented by DNN as

[0101] 7) Fix ξ (k) and R (k+1) , optimize f (k) to minimize V, which is represented by DNN as

[0102] 8) When Enter loop ②:

[0103] 9) Update α = γα, then repeat 5) and 6).

[0104] 10) End loop ②.

[0105] 11) When Enter loop ③:

[0106] 12) Update β = γβ, then repeat 5) and 7).

[0107] 13) End loop ③.

[0108] 14) k = k + 1.

[0109] 15) End loop ①.

[0110] 16) Output the optimized variables ξ (k) , R (k) , f (k) .

[0111] As Figure 3 shown, the present invention compares the BER performance of the proposed scheme with the baseline scheme, including traditional beamforming and multi-beam cooperative transmission. The proposed scheme exhibits a narrower security beam width around the target direction and significantly reduces the sidelobe information leakage through asymmetric array division. This is because the array differences during beam pointing drift not only cause interference in the undesired direction but also increase the dispersion of the leakage energy.

[0112] As Figure 4 shown, it can be observed that the scheme forms an insecure area with a radius of 6.3 km, while the multi-beam cooperative transmission forms an unstable area with a radius of 19.2 km. Therefore, compared with the existing multi-beam cooperative transmission scheme, the insecure area of our proposed scheme is reduced by 67.14%. In addition, our scheme reduces the sidelobe information leakage by 18.19%.

[0113] The above specific description further details the purpose and technical solution of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A symbol-level secure transmission method based on satellite beam cooperation, characterized in that: Model the array transmission channel through multi - antenna theory to obtain the transmission channel models of each sub - array, and design random symbol mapping to achieve transparent transmission in the beam overlapping region, while randomizing the signals in other regions. Then, through symbol - level variable beam pointing design, introduce spatial randomness to the sidelobes to reduce information leakage. In addition, create spatial randomness through asymmetric array division design to further narrow the non - secure region. To minimize the non - secure region and sidelobe information leakage, a multi - objective optimization model is established, and the complex multi - objective optimization problem is processed through the adaptive Armijo algorithm, thereby obtaining the symbol - level secure transmission result and realizing symbol - level secure transmission based on satellite beam cooperation.

2. A symbol-level secure transmission method based on satellite beam cooperation, characterized in that: It includes the following steps: Step 1: Model the array transmission channel based on multi - antenna theory to obtain the transmission channel models of each sub - array; The satellite array is a uniform planar array (UPA) with N isotropic antennas, where the antennas are uniformly placed with a spacing of d ≤ λ / 2, and λ is the wavelength; the UPA adopts a hybrid analog - digital architecture and uses switched power amplifiers to divide the UPA into two sub - arrays; each sub - array is driven by a separate radio - frequency chain and can transmit data independently; The i-th subarray consists of N i = N i，v × N i，h antennas, where N i，v and N i，h represent the number of antennas in the vertical and horizontal dimensions respectively; polar coordinates (ρ, θ) are used to represent the position of the receiving user in the x-y plane, where ρ is the distance and θ is the azimuth angle; the target user is located at the origin and the satellite is located at a height H directly above the target user; the elevation angle of the i-th subarray beam pointing to the user is calculated as φ = arctan(ρ / H); thus, the channel matrix from the i-th subarray to the receiver at (ρ, θ) is expressed as: Where: respectively represent the channel vectors along the vertical and horizontal directions; represent the tensor product of the channel vectors; Apply digital-analog hybrid precoding to direct the i-th beam towards (ρ i , θ i ); for the k-th symbol interval, the transmitted symbol is represented by , and the noise-free received signal y i (ρ, θ) is expressed as: y i (k, ρ, θ) = h i (ρ, θ)w i (ρ i , θ i )s(k) (2) Equation (2) is the transmission channel model of each sub - array obtained. Step 2: Through random symbol mapping design, achieve transparent transmission in the beam overlapping region and randomize the signals in other regions; Step 3: Through symbol - level variable beam pointing design, introduce spatial randomness to the sidelobes to reduce information leakage; Step 4: Create spatial randomness through asymmetric array division design to further narrow the non - secure region; Step 5: Establish a multi - objective optimization model to minimize the non - secure region and sidelobe information leakage; Step 6: Construct an adaptive Armijo algorithm to process the complex multi - objective optimization problem, obtain the symbol - level secure transmission result through optimizing the multi - objective optimization problem, and realize symbol - level secure transmission based on satellite beam cooperation according to the symbol - level secure transmission result.

3. The symbol-level secure transmission method based on satellite beam collaboration according to claim 2, wherein: The implementation method of Step 2 is as follows: For the k - th symbol interval, use the symbol mapping function f(·)={f1(·), f2(·)} to randomly map s(k) to the transmission symbols of the two sub - arrays, and the mapping process is expressed as: f i : s(k) → x i (k), i = 1, 2 (3) Transmission symbol of the i-th beam The noise - free superposition signal received by the ground user at (ρ, θ) is expressed as: To ensure transparent service for users at the overlapping region (ρ0, θ0), the beam cross - transmission method imposes constraints where r > 0 is a proportionality constant.

4. The symbol-level secure transmission method based on satellite beam collaboration according to claim 2, characterized in that: The implementation method of Step 3 is as follows: Symbol-level variable beam steering design achieves interference in undesired directions through random drift of beam steering at the symbol rate; the movable trajectory in the x-y plane is expressed as r = g(ψ), i.e., the beam steering trajectory function, where ψ ∈ [0, 2π] is the polar angle; the radii of the unsafe coverage areas formed by two beams on the ground are R1 and R2 respectively; the probability density function f i (r, ψ) is expressed as: Where δ(r - g(ψ)) is the Dirac function, ensuring that the beam only appears on the moving trajectory r = g(ψ); For the k-th symbol interval, the position pointed by the i-th beam is mathematically expressed as (r i (k), ψ i (k)), where ψ i (k) is the polar angle of the i-th beam, and r i (k) = g(ψi(k)) is the corresponding radial distance along the trajectory; the precoding vector w i (r i (k), ψ i (k)) is expressed as:

5. The symbol-level secure transmission method based on satellite beam collaboration according to claim 2, wherein: The implementation method of Step 4 is as follows: A method for non-uniformly dividing a satellite array into two sub-arrays, the division generates a difference, and through the random and continuous movement of the beam pointing, the difference is converted into interference in an undesired direction; the difference between the two sub-arrays is characterized by an array division parameter Taking ξ into (6), the precoding vector is converted to: Using the above - mentioned asymmetric array division design, the noise - free superposition signal is expressed as:

6. The symbol-level secure transmission method based on satellite beam cooperation according to claim 2, characterized in that: The implementation method of Step 5 is as follows: The goal is to minimize the unsafe area S in the main lobe by optimizing the variables introduced in steps 2 to 4: the symbol mapping function f(·), the beam pointing trajectory function g(ψ), and the array partition parameter ξ, which are abbreviated as f, g, and ξ respectively. LM , eliminate the unsafe area S in the side lobe LS ; Define the minimum safety capacity SC at the side lobe as C min , and by maximizing C mm To eliminate S LS ,make C U is the maximum tolerable information leakage; then, the multi-objective linear weighted optimization problem is formulated as follows: r≥∈，(13) Where ε is the minimum signal - to - noise ratio required for the legitimate user to successfully receive.

7. The symbol-level secure transmission method based on satellite beam cooperation according to claim 2, wherein: The implementation method of Step 6 is as follows: The beam pointing trajectory is constrained to lie on a circle with radius R, which can be extended to any shape; combining the gradient descent method and the Armijo rule, the convergence is accelerated by ensuring sufficient reduction of the objective function in each iteration; for ξ, at the (k + 1)-th iteration, its gradient is expressed as: Among them, represents a small step size; the update step size of ξ is where α is a scaling factor used to ensure sufficient reduction of the objective function; α ∈ (0, 1) is a constant scaling factor that satisfies the Armijo condition, which is expressed as: If this condition is not met, α will be interactively decreased by multiplying it with the coefficient β ∈ (0, 1); this process will be repeated iteratively until and the optimal parameters are obtained; the computational complexity is O(KL), where k is the number of iterations and L is the average number of step adjustments in each iteration; Obtain the symbol - level secure transmission result through optimizing the multi - objective optimization problem, and realize symbol - level secure transmission based on satellite beam cooperation according to the symbol - level secure transmission result.

8. The symbol-level secure transmission method based on satellite beam collaboration according to claim 6, characterized in that: Solution The method is as follows: 1) Input ξ (0) , R (0) , f (0) , δ, σ, γ, W s , W e ; 2) Initialize \(k = 0\), \(\xi\) (0) = 1, \(R\) (0) = 0, \(\gamma=0.5\); 3) When and , enter Loop ①: 4) Calculate the gradient Initialize α = 1 and β = 1; 5) Set 6) Fix ξ (k+1) and R (k) and optimize f (k) to minimize V, expressed using DNN as 7) Fix ξ (k) and R (k+1) and optimize f (k) to minimize V, expressed using DNN as 8) When Enter loop ②: 9) Update α = γα, and then repeat 5) and 6); 10) End loop ②; 11) When Enter loop ③: 12) Update β = γβ, and then repeat 5) and 7); 13) End loop ③; 14) k = k + 1; 15) End loop ①; 16) Output the optimized variable ξ (k) , R (k) , f (k) .

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