Security beamforming method and system based on dynamic beam allocation

Abstract

The present invention discloses a secure beamforming method and system based on dynamic beam allocation. The method of the present invention uses dynamic beam allocation and designs a beamforming method that minimizes the total transmit power at the transmitting end of a large-scale low-orbit satellite constellation. The secure rate of each user in the large-scale multi-beam low-orbit satellite constellation system is not less than the minimum secure rate #imgabs0#, the signal-to-interference-plus-noise ratio of each user is not less than the minimum signal-to-interference-plus-noise ratio #imgabs1#, and the satellite transmit power is limited to P th , the number of beams provided by the satellite constellation to provide services to users is less than U k As a constraint, an optimization problem is established and solved to minimize the total transmit power of the satellite constellation while ensuring the safe transmission of each user. Through dynamic beam allocation and the rational design of beamforming coefficients for the transmission signals of a large-scale low-orbit satellite constellation, the safe transmission of satellite users in the system is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the field of wireless secure communications, and in particular relates to a secure beamforming method based on dynamic beam allocation, in particular to a secure beamforming method based on dynamic beam allocation in a large-scale multi-beam low-orbit satellite constellation system. Background Art

[0002] With the rapid growth in demand for wireless communications, satellite communication systems, with their wide coverage and high transmission rates, will play a vital role in the 6G integrated air, space, land, and sea networks. Within satellite communication systems, low-Earth orbit (LEO) satellites have attracted significant attention due to their reduced path loss and transmission latency. A key transmission requirement for large-scale LEO satellite constellations is communication security. In recent years, beamforming technology, which achieves secure transmission at the physical layer, has been widely adopted in multi-beam satellite communication systems.

[0003] Existing physical layer security transmission solutions for satellite communication systems are mostly designed for multi-beam, high-orbit, single-satellite communication systems. Directly applying these solutions to large-scale low-orbit satellite constellations would waste beam resources, limiting the optimal anti-eavesdropping effect achieved during user communications and potentially causing unnecessary power loss. Furthermore, the unique advantages of low-orbit satellite communication systems cannot be fully utilized. Therefore, it is necessary to design a more reasonable security transmission solution for large-scale, multi-beam, low-orbit satellite constellations. Summary of the Invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a secure beamforming method based on dynamic beam allocation in a large-scale multi-beam low-orbit satellite constellation system. Compared with existing research, this method proposes a dynamic beam allocation scheme in a large-scale multi-beam low-orbit satellite constellation system, and minimizes the total transmission power of the satellite constellation while meeting the secure and reliable transmission requirements of each user and the satellite power budget.

[0005] To achieve the above object, the present invention adopts a technical solution: a secure beamforming method based on dynamic beam allocation, comprising the following steps:

[0006] Model and analyze the signal transmission model in a large-scale multi-beam low-orbit satellite constellation system. Calculate the received signal-to-interference-and-noise ratio (SINR) based on the received signal at each satellite user, thereby calculating the safe data rate for each user.

[0007] The safe rate of each user in a large-scale multi-beam low-orbit satellite constellation system is not less than the minimum safe rate The signal-to-interference-and-noise ratio of each user is not less than the minimum signal-to-interference-and-noise ratio The satellite transmission power is limited by the maximum transmission power P of each satellite thAnd the number of beams provided by the satellite constellation to provide services to users is less than U k As a constraint, an optimization problem is established to minimize the total transmit power of the satellite constellation;

[0008] The beam allocation variables are fixed and the optimization problem is converted into a convex second-order cone programming problem, which can be solved to obtain the satellite's transmit beamforming vector. The beam allocation variables are searched for the optimal solution through a genetic algorithm. Ultimately, the satellite constellation will perform beam allocation and beamforming according to the optimal solution obtained from the optimization problem and complete data transmission.

[0009] In a large-scale multi-beam low-orbit satellite constellation, satellite users and eavesdroppers are all single-antenna users. A single satellite can generate N beams. The total area served by these N beams constitutes the communication range of a single satellite. The diameter of each beam is D. The distance between the eavesdropper and the legitimate user is εD, 0.15≤ε<1. In this system, there are K users randomly distributed in a circular area. The users in the circular area are located in the communication coverage of multiple LEO satellites in this constellation. The minimum elevation angle at which a satellite in this constellation can communicate with a user is α. When the elevation angle of the satellite relative to the user is greater than α, the satellite can transmit signals to the user. The set of satellites whose communication range can cover any of the K users is expressed as gather Contains the numbers of J satellites, that is, User k is also in Q k The satellite set is represented as The set of satellites whose elevation angle relative to user k is greater than 0 is expressed as When user k is within the communication range of satellite j, the beam directly covering user k and the adjacent beams of the beam can provide a higher signal-to-noise ratio for user k. The number of beams that a single satellite can provide services to users is not less than one. The set of beams that satellite j can provide services to user k is expressed as The constellation system can utilize up to beams transmit useful signals for user k;

[0010] All LEO satellites in the constellation can share the user's transmission information. The same beam of the satellite can serve multiple users, and a user can also receive signals from multiple beams. All satellites in the constellation operate on the same frequency band. Different beams of the same satellite use full-frequency multiplexing. Communications between different users will interfere with each other. Satellite users' communications may be eavesdropped by a nearby eavesdropper. All beam resources in the network need to be dynamically allocated in real time and combined with beamforming technology to achieve secure transmission for users. The maximum number of beams that can be processed by the satellite system for single-user transmission is O. k , the communication of user k must be completed by at least one beam, and the number of beams does not exceed U k =min{I k ,O k}.

[0011] During the solution process, the satellite downlink channel is obtained based on the fact that the satellite links in the large-scale multi-beam low-orbit satellite constellation are all static slow-fading channels and the channels between different beams are independent.

[0012] The received signal at each user is used to calculate the received signal-to-interference-noise ratio at the user, and the eavesdropper e who eavesdrops on user k is used to calculate the received signal-to-interference-noise ratio at the user. k For example, the received signal to noise ratio at user k and eavesdropper e k Received signal-to-interference-and-noise ratio at and Finally, the receiving security rate C at user k can be k for:

[0013]

[0014] The optimization problem of minimizing the total transmit power of the satellite constellation is:

[0015]

[0016] Where, Indicates whether the i-th beam from satellite j carries the useful signal of user k, represents the beamforming coefficient of beam i from satellite j transmitting the useful signal to user k, represents the beam set that satellite j can provide service to user k, C k represents the receiving security rate at user k, Indicates the minimum security rate required for user k to achieve communication security; Represents a collection of users: Represents user k and eavesdropper e k The received signal-to-interference-and-noise ratio at represents the minimum SINR required for user k to successfully decode the signal; Pth Indicates the maximum transmission power of each satellite, Represents the set of satellites in the system, U k Q represents the maximum number of beams that the satellite system can handle for single-user transmission. k represents the number of satellites within the visible range of user k; constraint (9b) represents the communication security rate constraint for each user; constraint (9c) represents the reception SINR constraint for each user; constraint (9d) represents the power constraint for each satellite; constraint (9e) represents the constraint on the sum of the number of beams used by the satellite to transmit signals to user k; constraint (9f) represents the beam allocation criterion constraint for transmitting useful signals to the user.

[0017] Fix the beam allocation variables in the optimization problem The optimization problem is converted into the following convex optimization problem:

[0018]

[0019] In the formula, the available beam can transmit signal s to user k k The beamforming vector at this time is w k , W k represents the semidefinite slack variable obtained from this vector, h k represents the channel gain vector of the beam used by the satellite system to transmit useful signals to user k, g k The beam of the satellite system used to transmit the useful signal to user k is k The channel gain vector is x; the indicator vector of whether the beam generated by the satellite within the visible range of user k is allocated to user k for transmission is x k , X k represents the semidefinite slack variable obtained from this vector h k,m represents the channel gain vector of the beam of the satellite system transmitting useful signals to user k to user m, g k,m The beam of the satellite system transmitting the useful signal to user k is m The channel gain vector, Ψ1 and Ψ2 represent the intermediate variables obtained in the simplification process of constraint condition (9b);

[0020] The optimization problem can be solved using the mathematical tool CVX, and the optimal beamforming vector of the satellite can be obtained.

[0021] A search algorithm based on a genetic algorithm is used to solve the optimal beam allocation variables and the beamforming vector of the satellite, including the following steps:

[0022] Initialize the beam allocation variables and randomly generate the first generation population And solve the transformed convex optimization problem to calculate the utility function of each individual in the population;

[0023] The individuals in the existing population are selected, mutated and crossed to obtain new individuals. When the number of new individuals is equal to the population size PO, the new population replaces the old population and one iteration is completed. The iterative operation is repeated until the maximum number of iterations is reached. When the maximum number of iterations is reached, the iteration stops. At this time, the individual with the largest utility function in the population is the optimal beam allocation variable. The beam allocation variable is fixed. The value of is the value of the individual and the optimal beamforming vector at this time can be calculated.

[0024] On the other hand, based on the concept of the method of the present invention, a security beamforming system based on dynamic beam allocation is also provided, comprising a security rate solving module, an optimization problem building module, and an optimization problem solving module;

[0025] The safe rate calculation module is based on a large-scale multi-beam low-orbit satellite constellation system. It models and analyzes the signal transmission model in this system, calculates the received signal-to-interference-and-noise ratio (SINR) from the received signal at each satellite user, and thus calculates the safe rate for each user.

[0026] The optimization problem construction module is to ensure that the safe rate of each user in the large-scale multi-beam low-orbit satellite constellation system is not less than the minimum safe rate. The signal-to-interference-and-noise ratio of each user is not less than the minimum signal-to-interference-and-noise ratio Satellite transmission power is limited by P th , the number of beams provided by the satellite constellation to provide services to users is less than U k As a constraint, an optimization problem is established to minimize the total transmit power of the satellite constellation;

[0027] The optimization problem solving module fixes the beam allocation variables, transforming the original optimization problem into a convex second-order cone programming problem. This problem can then be solved to obtain the satellite's transmit beamforming vector. The optimal solution for the beam allocation variables is then searched for using a genetic algorithm. This optimal solution serves as the basis for the satellite's beam allocation and beamforming operations to complete data transmission.

[0028] The present invention also provides a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, and the processor reads the computer executable program from the memory and executes it. When the processor executes the computer executable program, it can implement the security beamforming method based on dynamic beam allocation described in the present invention.

[0029] A computer-readable storage medium is also provided. The computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the secure beamforming method based on dynamic beam allocation according to the present invention can be implemented.

[0030] Compared with the prior art, the present invention has at least the following beneficial effects:

[0031] The secure beamforming method based on dynamic beam allocation in a large-scale multi-beam low-orbit satellite constellation system described in the present invention addresses the situation where beam resources are abundant in a large-scale low-orbit satellite constellation. Under the condition of limited satellite transmit power, an optimization problem is established to minimize the total transmit power of the satellite constellation while satisfying the minimum safe rate constraints of satellite users and the minimum signal-to-interference-and-noise ratio constraints. The optimization problem is solved to minimize the total transmit power of the large-scale low-orbit satellite constellation while ensuring secure and reliable transmission for users.

[0032] Moreover, the present invention considers the problem of minimizing the transmission power when the beam allocation variables are given, and then converts the non-convex constraints into second-order cone constraints to obtain an easy-to-solve convex optimization problem, and solves the optimal beam allocation variables and the satellite's beamforming vector through a search algorithm based on a genetic algorithm, ultimately satisfying the satellite's transmission power constraints and the reliable communication needs of satellite users, and minimizing the total transmission power of a large-scale low-orbit satellite constellation system while ensuring the safe transmission of satellite users. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a model diagram of a large-scale low-orbit satellite constellation system.

[0034] Figure 2 This is a comparison diagram of the transmission power required for a secure beamforming method based on dynamic beam allocation in a large-scale low-orbit satellite constellation system of the present invention and a comparative solution within one satellite orbit operation cycle.

[0035] Figure 3 This is a comparison diagram of the required transmission power of a security beamforming method based on dynamic beam allocation in a large-scale low-orbit satellite constellation system of the present invention and a comparative solution under different user security rate requirements.

[0036] Figure 4 This is a comparison diagram of the required transmit power of a secure beamforming method based on dynamic beam allocation in a large-scale low-orbit satellite constellation system according to the present invention and a comparative solution under different signal-to-interference-and-noise ratio requirements of users.

[0037] Figure 5 This is a comparison chart of the signal-to-interference-plus-noise ratio (SINR) and safety rate that can be achieved by users under different SIN requirements for a security beamforming method based on dynamic beam allocation in a large-scale low-orbit satellite constellation system according to the present invention and a comparative solution.

[0038] Figure 6 This is a comparison diagram of the transmission power required for a secure beamforming method based on dynamic beam allocation in a large-scale low-orbit satellite constellation system of the present invention and a comparative solution when the number of beams provided by the satellite constellation to serve a single user is different. DETAILED DESCRIPTION

[0039] The present invention is described in further detail below with reference to the accompanying drawings:

[0040] The secure beamforming method based on dynamic beam allocation in a large-scale multi-beam low-orbit satellite constellation system of the present invention comprises the following steps:

[0041] Step 1): Reference Figure 1 , establish the following system model:

[0042] Consider the downlink transmission of a large-scale multi-beam low-orbit satellite constellation. Satellite users and eavesdroppers are all single-antenna users. A single satellite can generate N beams. The total area served by these N beams constitutes the communication range of a single satellite. The diameter of each beam is D, and the distance between the eavesdropper and the legitimate user is εD, 0.15≤ε<1. In this system, there are K users randomly distributed in a specific circular area. The users in the circular area are located in the communication coverage of multiple LEO satellites in this constellation. The minimum elevation angle at which a satellite in this constellation can communicate with a user is α. When the elevation angle of the satellite relative to the user is greater than α, the satellite can transmit signals to the user. The set of satellites whose communication range can cover any of the K users is expressed as gather Contains the numbers of J satellites, that is, User k is also in Q k The satellite set is represented as Where q k [j] represents the number of the jth satellite whose communication range can cover user k. Similarly, the set of satellites with an elevation angle greater than 0 relative to user k is represented as In the formula represents the number of the pth satellite whose elevation angle relative to user k is greater than 0; when user k is within the communication range of satellite j, transmission using the beam directly covering user k and the adjacent beams of the beam is likely to provide a higher signal-to-noise ratio for user k. Therefore, the number of beams that a single satellite can provide services to a user is not less than one. The set of beams that satellite j can provide services to user k is expressed as In the formula represents the number of the i-th beam that satellite j can serve for user k. Therefore, the constellation system can utilize at most A beam transmits a useful signal for user k.

[0043] Assuming that all LEO satellites in the constellation can share the user's transmission information, the same beam of the satellite can serve multiple users, and a user can also receive signals from multiple beams. All satellites in the constellation operate on the same frequency band, and different beams of the same satellite use full-frequency multiplexing, so the communications between different users will interfere with each other. Assuming that a satellite user's communication may be eavesdropped by an eavesdropper nearby, all beam resources in the network need to be dynamically allocated in real time and combined with beamforming technology to achieve secure transmission for the user. Due to the limited onboard processing capacity of the satellite system, the maximum number of beams that can be processed for a single user's transmission is O. k Therefore, the communication of user k must be completed by at least one beam, and the number of beams does not exceed U k =min{I k ,O k Consider the eavesdropper as a potential eavesdropper, that is, the eavesdropper of interest is a legitimate user in the network, but the transmission time slot of interest does not involve the transmission of the potential eavesdropper's useful signal, so it can be assumed that the channel state information of all users is known information.

[0044] Step 2): Calculate the received signal-to-interference-and-noise ratio (SINR) of the single-antenna satellite user’s received signal, and thus calculate the safe rate at the user:

[0045] All links are modeled using static slow-fading channels. Assuming that the channels between different beams of the same satellite are independent, and considering the effects of free-space path loss, beam gain, and small-scale fading, the downlink channel gain of a single satellite beam can be expressed as:

[0046]

[0047] Among them, C L =λ / 4πd represents the free space path loss, λ is the wavelength, and d is the distance between the satellite and the user. Beam gain The value of can be approximated as b max represents the maximum beam gain, represents the angle between the user and the satellite beam center, represents the 3-dB angle. J1(.) and J3(.) represent the first-order and third-order Bessel functions of the first kind, respectively. Small-scale fading The Lutz channel is used for modeling. The Lutz distribution divides the channel into two states: the Rician distribution representing a "good state" and the log-normally shadowed Rayleigh distribution representing a "bad state". The probability density expression of the received power S under the Rician distribution is: I0(·) represents the first-order modified Bessel function. The received power under the log-normally shadowed Rayleigh distribution obeys p Rayl (S|S0)=1 / S0 exp(-S / S0), where the short-term average received power S0 follows the distribution Therefore, the probability density expression of the received power in the Lutz model is: Where A represents the percentage of time that a “bad channel” exists, A = -0.0177θ + 1.0095 and when θ ≥ 57.0339°, A = 0, where θ represents the elevation angle of the satellite; μ and σ 2 σ represents the mean and variance of the Rayleigh distribution, σ = -0.0979θ + 8.2036dB, and σ = 0dB when θ ≥ 83.8321°. c represents the Rice factor, c = 0.3282θ - 3.9554dB. μ satisfies a piecewise function: when θ ≤ 15°, μ = -11dB; when 15° < θ ≤ 25°, μ = -0.6θ - 2dB; when 25° < θ ≤ 35°, μ = 0.4θ - 27dB; when 35° < θ ≤ 45°, μ = 0.3θ - 23.5dB; when 45° < θ ≤ 55°, μ = -0.2θ - 1dB; and when 55° < θ, μ = -12dB. The channel phase of each link follows a uniform distribution between [0, 2π].

[0048] The useful signal of user k is denoted as s k , s k Satisfy E(s k 2 )=1. In this method, the satellite set needs to be considered The matching problem between the satellite beam and user k in the image is introduced, thus introducing the variable if = indicates that the i-th beam from satellite j carries the useful signal of user k, and vice versa, it means that the i-th beam from satellite j does not carry the useful signal of user k. The useful signal sent to user k can be expressed as:

[0049]

[0050] The total transmitted signal of the satellite constellation can be expressed as:

[0051]

[0052] Theoretically, the interference signal received by user k comes from the signals of other users transmitted by all satellites whose elevation angle is greater than 0. Therefore, user k and the eavesdropper eavesdropping on user k can be k The received signal at is expressed as:

[0053]

[0054]

[0055] Where, They represent the beam i from satellite j to user k and eavesdropper e, respectively. k The channel gain at ; represents the beamforming coefficient of beam i from satellite j transmitting useful signals to user k; n i ,i∈{s,e} represents user k and eavesdropper e k The zero-mean complex Gaussian white noise received at κ is the Boltzmann constant, B s represents the signal bandwidth, and T represents the noise temperature.

[0056] From this we can calculate the user k and the eavesdropper e k The signal-to-interference-noise ratios at are:

[0057]

[0058]

[0059] Finally, the receiving security rate at user k can be expressed as:

[0060]

[0061] Step 3): Set the communication security rate constraint of each user in the large-scale low-orbit satellite constellation system to The received signal-to-interference-and-noise ratio constraint of each user is The maximum transmission power of each satellite is P th The maximum number of beams that a satellite can use to transmit signals to user k is I k .

[0062] Step 4): The communication security rate constraint of each user in the large-scale low-orbit satellite constellation system set in step 3) is The received signal-to-interference-and-noise ratio constraint of each user is The maximum transmission power of each satellite is P th The maximum number of beams that a satellite can use to transmit signals to user k is I k, the user's safe transmission rate is not less than the minimum safe rate The actual received signal-to-interference-and-noise ratio of the user is not lower than the minimum signal-to-interference-and-noise ratio The satellite's transmission power is not higher than P th As well as the limited number of beams that the satellite can use when transmitting signals to users as constraints, an optimization problem of minimizing the total transmission power of the satellite constellation is established.

[0063] The optimization problem of minimizing the total transmit power of a satellite constellation can be expressed as:

[0064]

[0065] Where, Indicates whether the i-th beam from satellite j carries the useful signal of user k, represents the beamforming coefficient of beam i from satellite j transmitting the useful signal to user k, represents the beam set that satellite j can provide service to user k, C k represents the receiving security rate at user k, Indicates the minimum security rate required for user k to achieve communication security; Represents a collection of users: Represents user k and eavesdropper e k The received signal-to-interference-and-noise ratio at represents the minimum SINR required for user k to successfully decode the signal; P th Indicates the maximum transmission power of each satellite, Represents the set of satellites in the system, U k Q represents the maximum number of beams that the satellite system can handle for single-user transmission. k represents the number of satellites within the visible range of user k; constraint (9b) represents the communication security rate constraint for each user; constraint (9c) represents the reception SINR constraint for each user; constraint (9d) represents the power constraint for each satellite; constraint (9e) represents the constraint on the sum of the number of beams used by the satellite to transmit signals to user k; constraint (9f) represents the beam allocation criterion constraint for transmitting useful signals to the user.

[0066] Step 5): Fix the beam allocation variables The original optimization problem can be converted into a convex second-order cone programming problem, which can be solved to obtain the satellite's transmit beamforming vector. The beam allocation variables will be searched through a genetic algorithm to obtain the optimal solution.

[0067] In order to solve the proposed convex optimization problem conveniently, the original optimization problem is first rewritten. In order to rewrite the constraints (9b) and (9c), the present invention sets the satellite set I can be used to transmit useful signals to user k k The channel gain of a beam to user k is expressed as a vector This I k The indicator vector indicating whether the beam is actually allocated to user k for transmission is expressed as This I k The beam transmits a signal s k The beamforming vector when is represented as a vector Where, Represents a satellite set Satellite α points to user k The channel gain of a beam to user k is, Represents a satellite set Satellite α points to user k The indicator vector of whether the beam carries the useful signal of user k: Represents a satellite set Satellite α points to user k The beamforming vector of the useful signal transmitted by user k is:

[0068] Similarly, the satellites are assembled I used when transmitting signals to user m m The channel gain of a beam to user k is expressed as Where, Represents a satellite set Satellite β points to user m The channel gain of a beam to user k is: At the same time, the indicator vector Where, Represents a satellite set The indicator vector of whether satellite β will cause interference to user k when sending user m signal:

[0069] Finally, user k and eavesdropper e can be k The SINR expression at is rewritten as:

[0070]

[0071]

[0072] Where, X k Indicates diag(x k ), X m Indicates diag(x m ), Y k,m Indicates diag(y k,m );g k Represents a satellite set The beam transmitting the useful signal to user k has no significant effect on the eavesdropper e. k Channel gain g k,m Represents a satellite set The beam transmitting the useful signal to user m has a negative impact on the eavesdropper e. k The channel gain,

[0073] Similarly, in order to rewrite the constraint (9d), the indicator vector is introduced In the formula represents satellite q k [α] is the indicator vector of satellite j:

[0074] Therefore, constraint (9d) can be rewritten as:

[0075]

[0076] Where D k,j Indicates diag(d k,j );

[0077] The final optimization problem can be rewritten as:

[0078]

[0079] When the beam allocation variable When fixed, the original optimization problem is still non-convex, and the optimization problem is recorded as the beam coefficient optimization problem. To solve this problem, a semidefinite relaxation is introduced to convert the quadratic expression into a linear form, and then a solvable convex optimization problem is obtained by converting the non-convex constraint (13b) into a convex second-order cone constraint. First, the semidefinite relaxation variable is introduced. Then the optimization problem (13) can be rewritten as shown in formula (14).

[0080]

[0081] Where:

[0082] Η k express Hk,m express G k express G k,m express It can be seen that the constraint (14b) in the optimization problem is non-convex, so it is converted into a second-order cone constraint to eliminate its non-convexity. First, the constraint is expanded as:

[0083]

[0084] After simplification, it can be rewritten into an equivalent form:

[0085]

[0086] Then further transform the right side of equation (16):

[0087]

[0088] Where:

[0089] The matrix conversion formulas used at the equal sign are: a——Tr(F T R)=[vec(F)] T vec(R); f——Tr(R 2 )=[Tr(R)] 2 .

[0090] Therefore, constraint (14b) can be rewritten as:

[0091]

[0092] Where:

[0093]

[0094]

[0095] According to the formula Formula (18) can be rewritten as:

[0096]

[0097] Finally, constraint (14b) can be rewritten as a second-order cone constraint:

[0098]

[0099] Given a beam allocation vector Removing the rank 1 constraint, the optimization problem can be written as:

[0100]

[0101] At this point, the non-convex beam coefficient optimization problem can be converted into a convex optimization problem, and the mathematical tool CVX can be used to solve the optimization problem. The final optimal vector is expressed as Notice: The rank of is not necessarily 1, because of the introduction of relaxation conditions. When the rank is 1, the eigenvalue decomposition method can be used to obtain When its rank is not 1, the Gaussian random method can be used to find a set of approximate optimal solutions In the formula, the available beam can transmit signal s to user k k The beamforming vector at this time is w k , W k represents the semidefinite slack variable obtained from this vector, h k represents the channel gain vector of the beam used by the satellite system to transmit useful signals to user k, g k The beam of the satellite system used to transmit the useful signal to user k is k The channel gain vector is x; the indicator vector of whether the beam generated by the satellite within the visible range of user k is allocated to user k for transmission is x k , X k represents the semidefinite slack variable obtained from this vector h k,m represents the channel gain vector of the beam of the satellite system transmitting useful signals to user k to user m, g k,m The beam of the satellite system transmitting the useful signal to user k is m The channel gain vector, Ψ1 and Ψ2 represent the intermediate variables obtained in the simplification process of constraint condition (9b).

[0102] Beam allocation variables The optimal solution can be found through a genetic algorithm search. This paper refers to the problem of searching for the optimal beam allocation vector as the beam allocation problem. A genetic algorithm is a heuristic optimization search algorithm based on the natural evolutionary mechanisms of biological organisms, effectively solving global optimization problems. The genetic algorithm's solution process can be viewed as an evolutionary process, where the initialized population evolves generation after generation, ultimately reproducing the most suitable population. By designing appropriate selection, mutation, and crossover schemes, the genetic algorithm employs a randomized yet directed search method to find the optimal solution.

[0103] For the beam allocation problem of a multi-beam low-orbit satellite constellation, the GA is first initialized and randomly generates a population of individuals, PO. Each individual in the population can be used as a solution to the beam allocation problem. The fitness of each individual, i.e., the utility function value, is calculated. Some individuals are selected based on the utility function value. The selected individuals will undergo mutation and crossover operations with a certain probability, thus generating the next generation. Individuals with larger utility function values ​​are more likely to be selected. When the number of newly generated individuals reaches PO, the newly generated individuals will form a new population to replace the old population, and a new round of selection, mutation, and crossover operations will be performed until the maximum number of iterations is reached or an individual with a utility function value greater than a given threshold is generated. The detailed steps of initialization, selection, mutation, and crossover operations are as follows:

[0104] 1) Initialization

[0105] The purpose of initialization is to generate the first generation of individuals. The specific steps are: randomly generate PO individuals, each of which contains A one-dimensional vector of 0-1 random numbers. Let l represent the current number of iterations, then the mth individual generated by initialization can be expressed as:

[0106]

[0107] Where, Represents a satellite set The beam allocation vector for user k is, constitute Each element is called a gene of an individual.

[0108] 2) Select

[0109] The purpose of the selection operation is to select the parents that will produce the next generation of individuals. Proportional selection is a commonly used selection strategy, in which the probability of an individual being selected is proportional to the value of its utility function. The specific implementation algorithm used in this invention is the Roulette Wheel Selection (RWS) algorithm. The detailed operation steps are as follows.

[0110] Selecting the cube of the inverse proportional function as the utility function can make the probability of individuals with high utility function values ​​being selected large enough. The utility function value of each individual is recorded as f(x (l) [m]):

[0111]

[0112] Where, Representing variables The optimal useful signal beamforming vector for the optimization problem.

[0113] From this we can get the probability of individual m being selected in the lth iteration:

[0114]

[0115] Then the cumulative probability of the individual being selected can be expressed as:

[0116]

[0117] The above cumulative probability represents the sum of the probabilities of all individuals from individual 1 to individual m being selected, which is equivalent to the span on the roulette wheel. After the calculation is completed, a random number δ is randomly generated that obeys the uniform distribution U(0,1). When the number falls in the interval [Θ(x (l) [m]),Θ(x (l) [m+1])) represents individual x (l) [m] is selected to produce the next generation.

[0118] 3) Variation

[0119] Mutation is a way to generate new individuals. The probability of mutation is expressed as m The mutation operation will randomly select a gene in the selected individual and modify the value of the gene to obtain a new individual. c If the value of is too large, the performance of GA will degenerate, or even be equivalent to the ordinary random algorithm, thus losing the superiority of GA. c In order to determine the real number, this paper adopts an improved genetic algorithm to achieve a balance between maintaining population diversity and ensuring algorithm convergence by adaptively modifying the mutation probability.

[0120]

[0121] Where: f represents the utility function value of the parent individual; represents the average utility function value of individuals in the existing population; f max It represents the maximum utility function value of individuals in the existing population, ξ1 and ξ2 represent the given probability values, and the general value is ξ1=ξ2=0.5.

[0122] It should be noted that when the individual with the largest utility function value in the population is found, m The value of will become 0, at which point we directly save the individual to the next generation of the population. This method, also known as Elitist Strategy (ES) selection, can prevent the optimal solution generated during evolution from being destroyed by mutation.

[0123] 4) Cross

[0124] Crossover is another way to generate new individuals. The probability of a crossover is expressed asc , the crossover operation randomly exchanges some genes of the two selected individuals, thus obtaining two new individuals. c If the value is too large, the probability of the population generating new individuals will be greater, and the probability of excellent individuals remaining in the population will be lower. Similarly, the improved genetic algorithm is used here, c The value of changes adaptively according to the iterative process:

[0125]

[0126] Where f' represents the larger utility value of the two parent individuals, ξ3 and ξ4 represent the given probability values, which are generally taken as ξ3 = ξ4 = 1.

[0127] It is also important to note that when the individual with the largest utility function value in the population is found, c The value of will become 0. According to elitist selection, we directly retain the individual to the new population.

[0128] Because the direction of mutation and crossover operations is random, there is no guarantee that the resulting new individuals will meet the constraints. In this case, one approach is to discard the new individual and perform the mutation or crossover operation again. Another approach is to set the utility function of the individual to 0, which means that the individual will not be used to produce the next generation. Here we choose the first approach.

[0129] Summarizing the above process, a search algorithm based on genetic algorithm is finally proposed, as shown in Table 1:

[0130] Table 1 Search algorithm based on genetic algorithm

[0131]

[0132]

[0133] In the simulation experiment, four comparison schemes were designed, namely, a safe beamforming scheme based on random beam allocation and a safe beamforming scheme based on random beam allocation combined with artificial noise assistance, a safe beamforming scheme based on minimum angle beam allocation and a safe beamforming scheme based on minimum angle beam allocation combined with artificial noise assistance. Among them, the difference between the safe beamforming scheme based on minimum angle beam allocation and the safe beamforming scheme based on random beam allocation and our proposed scheme lies in the different ways of beam allocation. The minimum angle beam allocation scheme refers to selecting the beam with the smallest off-axis angle between the beam center and the user among the available beams of the satellite. k The random beam allocation scheme is to randomly select O beams from the available beams of the satellite. k The simulation scenario and parameter settings are shown in Table 2.

[0134] Table 2 Simulation parameter settings

[0135]

[0136] refer to Figure 2 , the satellite constellation transmission power required when the scheme proposed in the present invention and the comparative scheme are used during one orbital operation of the satellite constellation is compared. The number of users is set to 10, the maximum transmission power of a single satellite is set to 50dBW, the number of beams that the satellite constellation can provide for each user is set to 5, the minimum safety rate requirement required by the satellite user is set to 2bit / s / Hz, and the minimum signal-to-interference-and-noise ratio requirement required by the user is set to 1. In the figure, AN represents a safety beamforming scheme with beam allocation combined with artificial noise assistance, and NAN represents a safety beamforming scheme that only transmits useful signals and performs beam allocation. Figure 2 It can be seen that during the entire orbital operation cycle, the proposed secure beamforming scheme based on dynamic beam allocation can ensure the safe transmission of satellite users with the minimum transmission power by optimizing the beam-user matching pair. This is because the proposed dynamic beam allocation scheme searches for the optimal beam-user matching pair through a genetic algorithm at every moment, and the beam with the smallest off-axis angle between the beam center and the user cannot guarantee that the satellite can ensure the safe transmission of the user with the minimum transmission power at every moment. Figure 2 We can see that without effective beam-user matching, even the seemingly advantageous minimum-angle beam allocation scheme for secure transmission may not achieve optimal results. Secondly, we can see that the performance of the random beam allocation scheme is slightly worse than that of the minimum-computation beam allocation scheme, and that this scheme requires significantly higher transmit power at certain times. Finally, we can see that, for both comparison schemes, the scheme that introduces artificial noise requires less power than the scheme that does not. This is because the artificial noise signal can interfere with eavesdroppers in a targeted manner, allowing the satellite to appropriately reduce the transmit power of the useful signal to achieve the desired secure transmission performance. However, it should be noted that the artificial noise signal's effectiveness in reducing required transmit power is only significant when the channel quality of the legitimate user is poor.

[0137] refer to Figure 3, set the number of users to 10, set the maximum transmit power of a single satellite to 50dBW, set the minimum signal-to-interference-and-noise ratio requirement for the user to 1, and set the safety rate constraint required by the user to 1-2.8bit / s / Hz. Compared with the comparative scheme, regardless of the value of the minimum safety rate required by the user, the satellite constellation transmit power required by the scheme proposed in the present invention is the smallest. As the minimum safety rate required by the user increases, the satellite constellation transmit power required for multiple users to achieve safe transmission at the same time increases. This is because when the minimum safety rate required for safe transmission by the user increases, the satellite must transmit useful signals at a higher power to improve the user's signal-to-interference-and-noise ratio, thereby increasing the user's safety rate and ultimately achieving the purpose of ensuring user safe transmission. It can also be seen that the total satellite constellation transmit power required to achieve safe transmission for the safe transmission scheme based on random beam allocation is greater than that for the safe transmission scheme based on minimum angle beam allocation. This shows that the secure transmission scheme based on minimum angle beam allocation is better than the secure transmission scheme based on random beam allocation in reducing satellite transmission power. This is because the secure transmission scheme based on random beam allocation transmits signals by randomly selecting beams at each moment. The randomness of beam allocation and the randomness of the channel together lead to an increased possibility that the beam allocated to the user by the secure transmission scheme based on random beam allocation is not suitable for secure transmission. The secure transmission scheme based on minimum angle beam allocation can select the beam with the largest beam gain. k Beams are allocated to users for secure transmission. To a certain extent, beams with better channel quality for legitimate users are selected for transmission. Therefore, the required transmission power is less than that of the secure transmission scheme based on random beam allocation.

[0138] refer to Figure 4, set the number of users to 10, the maximum transmit power of a single satellite to 50dBW, the minimum safety rate requirement required by the user to 2bit / s / Hz, and the user's signal-to-interference-and-noise ratio requirement to 1-10. Compared with the comparative scheme, regardless of the minimum signal-to-interference-and-noise ratio required by the user, the satellite constellation transmit power required by the scheme proposed in this invention is the lowest. Secondly, we can see that as the user's minimum signal-to-interference-and-noise ratio constraint increases, the satellite transmit power required by all schemes remains unchanged when the user's minimum signal-to-interference-and-noise ratio requirement is in the range of 1-4. This is because in this scheme, we set the user's minimum safety rate constraint to 2bit / s / Hz. Even if we set the minimum signal-to-interference-and-noise ratio requirement to 1, in order to meet the minimum safety rate requirement, the satellite must increase its transmit power to meet this constraint. When the signal-to-interference-and-noise ratio requirement is greater than 4, as the user's minimum signal-to-interference-and-noise ratio increases, the satellite constellation transmit power required for multiple users to achieve simultaneous secure transmission increases. This is because when the user's SIR constraint is set to 4.66, the maximum safe rate that the user can achieve under ideal conditions is 2.5 bits / s / Hz. If the minimum safe rate constraint is still set to 2.5 bits / s / Hz, the satellite transmit power will need to be significantly increased to meet the SIR constraint. The figure shows that when the SIR constraint is greater than 4, the required satellite transmit power shows a steady upward trend as the minimum SIR required for successful user decoding increases.

[0139] refer to Figure 5 ,use Figure 4 For the simulation parameters, when the user's minimum SIN is between 1 and 4, the actual SIN that the user can achieve is always greater than the required minimum SIN. This is because the actual SIN must meet the user's minimum secure rate constraint of 2.5 bits / s / Hz, meaning the actual SIN must be greater than 4.66. In reality, however, an eavesdropper's SIN is not zero. When the SIN is around 0.1, the transmission rate can reach around 0.14. Therefore, the actual SIN required for legitimate users is around 5, which is consistent with our simulation results.

[0140] refer to Figure 6 , the number of users is set to 10, the user signal to interference and noise ratio constraint is set to 1, and the user minimum security rate is set to 2.5 bit / s / Hz. k For how much, the satellite constellation transmission power required by the solution proposed in the present invention is the smallest. k As the number of satellites increases, the required transmission power of the satellite constellation decreases, because kThe increase in means that the number of beams that the satellite can process to transmit signals to a single user increases, which leads to an increase in interference between users. These interferences can be used as green interference to interfere with eavesdroppers. Beamforming technology can reduce the signal-to-interference-to-noise ratio of eavesdroppers. Therefore, the signal-to-interference-to-noise ratio required by legitimate users can also be appropriately reduced, and the useful signal transmission power required by users to achieve secure transmission is also reduced. Figure 6 We can also observe that when O k When the number is less than 5, there are almost no feasible solutions for the secure transmission schemes based on minimum-angle beam allocation and random beam allocation. This indicates that the beams allocated to users by these secure transmission schemes are likely unsuitable for secure transmission and may even fail to meet the user's secure transmission requirements. This simulation result further verifies the effectiveness of the secure transmission scheme proposed in this invention.

[0141] On the other hand, the present invention also provides a secure beamforming system based on dynamic beam allocation, comprising a secure rate solving module, an optimization problem building module, and an optimization problem solving module;

[0142] The safe rate calculation module is based on a large-scale multi-beam low-orbit satellite constellation system. It models and analyzes the signal transmission model in this system, calculates the received signal-to-interference-and-noise ratio (SINR) from the received signal at each satellite user, and thus calculates the safe rate for each user.

[0143] The optimization problem construction module is to ensure that the safe rate of each user in the large-scale multi-beam low-orbit satellite constellation system is not less than the minimum safe rate. The signal-to-interference-and-noise ratio of each user is not less than the minimum signal-to-interference-and-noise ratio Satellite transmission power is limited by P th , the number of beams provided by the satellite constellation to provide services to users is less than U k As a constraint, an optimization problem is established to minimize the total transmit power of the satellite constellation;

[0144] The optimization problem solving module fixes the beam allocation variables, transforming the original optimization problem into a convex second-order cone programming problem. This problem can then be solved to obtain the satellite's transmit beamforming vector. The optimal solution for the beam allocation variables is then searched for using a genetic algorithm. This optimal solution serves as the basis for the satellite's beam allocation and beamforming operations to complete data transmission.

[0145] The present invention also provides a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, and the processor reads the computer executable program from the memory and executes it. When the processor executes the computer executable program, it can implement the security beamforming method based on dynamic beam allocation described in the present invention.

[0146] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the method for secure beamforming based on dynamic beam allocation according to the present invention can be implemented.

[0147] The computer device may be a laptop computer, a desktop computer or a workstation.

[0148] The processor may be a central processing unit (CPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), or an off-the-shelf field programmable gate array (FPGA).

[0149] The memory of the present invention may be an internal storage unit of a laptop computer, desktop computer or workstation, such as a memory or a hard disk; or an external storage unit, such as a mobile hard disk or a flash memory card.

[0150] Computer-readable storage media may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media may include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSD) or optical disks, etc. Among them, random access memory may include resistance random access memory (ReRAM) and dynamic random access memory (DRAM).

[0151] The above content is a detailed description of the present invention, and it cannot be considered that the present invention is limited to this. For ordinary technicians in the technical field to which the present invention belongs, they can make several simple deductions or substitutions without departing from the concept of the present invention, which should be regarded as belonging to the scope of patent protection determined by the submitted claims of the present invention.

Claims

1. A secure beamforming method based on dynamic beam allocation, characterized in that: The following steps are involved: Model and analyze the signal transmission model in a large-scale multi-beam low-orbit satellite constellation system. Calculate the received signal-to-interference-and-noise ratio (SINR) based on the received signal at each satellite user, thereby calculating the safe data rate for each user. The safe rate of each user in the large-scale multi-beam low-orbit satellite constellation system is not less than the minimum safe rate The signal-to-interference-and-noise ratio of each user is not less than the minimum signal-to-interference-and-noise ratio The satellite transmission power is limited by the maximum transmission power P of each satellite th And the number of beams provided by the satellite constellation to provide services to users is less than U k As a constraint, an optimization problem is established to minimize the total transmit power of the satellite constellation; The beam allocation variables are fixed and the optimization problem is converted into a convex second-order cone programming problem, which can be solved to obtain the satellite's transmit beamforming vector. The beam allocation variables are searched for the optimal solution using a genetic algorithm. Ultimately, the satellite constellation will perform beam allocation and beamforming according to the optimal solution obtained from the optimization problem and complete data transmission. Fix the beam allocation variables in the optimization problem The optimization problem is converted into the following convex optimization problem: In the formula, the available beam can transmit signal s to user k k The beamforming vector at this time is w k , W k represents the semidefinite slack variable obtained from this vector, h k represents the channel gain vector of the beam used by the satellite system to transmit useful signals to user k, g k The beam of the satellite system used to transmit the useful signal to user k is k The channel gain vector is x; the indicator vector of whether the beam generated by the satellite within the visible range of user k is allocated to user k for transmission is x k , X k represents the semidefinite slack variable obtained from this vector h k,m represents the channel gain vector of the beam of the satellite system transmitting useful signals to user k to user m, g k,m The beam of the satellite system transmitting the useful signal to user k is m The channel gain vector; Ψ1 and Ψ2 represent the intermediate variables obtained in the simplification process of constraint condition (9b); This optimization problem can be solved using the mathematical tool CVX, and the optimal beamforming vector of the satellite can be obtained; A search algorithm based on a genetic algorithm is used to solve the optimal beam allocation variables and the beamforming vector of the satellite, which includes the following steps: Initialize the beam allocation variables and randomly generate the first generation population And solve the transformed convex optimization problem to calculate the utility function of each individual in the population; The individuals in the existing population are selected, mutated and crossed to obtain new individuals. When the number of new individuals is equal to the population size PO, the new population replaces the old population and one iteration is completed. The iterative operation is repeated until the maximum number of iterations is reached. When the maximum number of iterations is reached, the iteration stops. At this time, the individual with the largest utility function in the population is the optimal beam allocation variable. The beam allocation variable is fixed. The value of is the value of the individual and the optimal beamforming vector at this time can be calculated.

2. The secure beamforming method based on dynamic beam allocation according to claim 1, wherein: In a large-scale multi-beam low-orbit satellite constellation, satellite users and eavesdroppers are all single-antenna users. A single satellite can generate N beams. The total area served by these N beams constitutes the communication range of a single satellite. The diameter of each beam is D. The distance between the eavesdropper and the legitimate user is εD, 0.15≤ε<1. In this system, there are K users randomly distributed in a circular area. The users in the circular area are located in the communication coverage of multiple LEO satellites in this constellation. The minimum elevation angle at which a satellite in this constellation can communicate with a user is α. When the elevation angle of the satellite relative to the user is greater than α, the satellite can transmit signals to the user. The set of satellites whose communication range can cover any of the K users is expressed as gather Contains the numbers of J satellites, that is, User k is also in Q k The satellite set is represented as The set of satellites whose elevation angle relative to user k is greater than 0 is expressed as When user k is within the communication range of satellite j, the beam directly covering user k and the adjacent beams of the beam can provide a higher signal-to-noise ratio for user k. The number of beams that a single satellite can provide services to users is not less than one. The set of beams that satellite j can provide services to user k is expressed as The constellation system can utilize up to A beam transmits useful signals for user k; All LEO satellites in the constellation can share the user's transmission information. The same beam of the satellite can serve multiple users, and a user can also receive signals from multiple beams. All satellites in the constellation operate on the same frequency band. Different beams of the same satellite use full-frequency multiplexing. Communications between different users will interfere with each other. Satellite users' communications may be eavesdropped by a nearby eavesdropper. All beam resources in the network need to be dynamically allocated in real time and combined with beamforming technology to achieve secure transmission for users. The maximum number of beams that can be processed by the satellite system for single-user transmission is O. k , the communication of user k must be completed by at least one beam, and the number of beams does not exceed U k =min{I k ,O k }.

3. The secure beamforming method based on dynamic beam allocation according to claim 1, wherein: During the solution process, the satellite downlink channel is obtained based on the fact that the satellite links in the large-scale multi-beam low-orbit satellite constellation are all static slow-fading channels and the channels between different beams are independent.

4. The secure beamforming method based on dynamic beam allocation according to claim 1, wherein: The received signal at each user is used to calculate the received signal-to-interference-noise ratio at the user, and the eavesdropper e who eavesdrops on user k is used to calculate the received signal-to-interference-noise ratio at the user. k For example, the received signal to noise ratio at user k and eavesdropper e k Received signal-to-interference-and-noise ratio at and Finally, the receiving security rate C at user k can be k for:

5. The secure beamforming method based on dynamic beam allocation according to claim 1, wherein: The optimization problem of minimizing the total transmit power of the satellite constellation is: Where, Indicates whether the i-th beam from satellite j carries the useful signal of user k, represents the beamforming coefficient of beam i from satellite j transmitting the useful signal to user k, represents the beam set that satellite j can provide service to user k, C k represents the receiving security rate at user k, Indicates the minimum security rate required for user k to achieve communication security; Represents a collection of users: Represents user k and eavesdropper e k The received signal-to-interference-and-noise ratio at represents the minimum SINR required for user k to successfully decode the signal; P th Indicates the maximum transmission power of each satellite, Represents the set of satellites in the system, U k Q represents the maximum number of beams that the satellite system can handle for single-user transmission. k represents the number of satellites within the visible range of user k; constraint (9b) represents the communication security rate constraint for each user; constraint (9c) represents the reception SINR constraint for each user; constraint (9d) represents the power constraint for each satellite; constraint (9e) represents the constraint on the sum of the number of beams used by the satellite to transmit signals to user k; constraint (9f) represents the beam allocation criterion constraint for transmitting useful signals to the user.

6. A secure beamforming system based on dynamic beam allocation, characterized in that: A method for implementing the secure beamforming method based on dynamic beam allocation according to any one of claims 1 to 5, comprising a secure rate solving module, an optimization problem building module, and an optimization problem solving module; The safe rate calculation module is based on a large-scale multi-beam low-orbit satellite constellation system. It models and analyzes the signal transmission model in this system, calculates the received signal-to-interference-and-noise ratio (SINR) from the received signal at each satellite user, and thus calculates the safe rate for each user. The optimization problem construction module is to ensure that the safe rate of each user in the large-scale multi-beam low-orbit satellite constellation system is not less than the minimum safe rate. The signal-to-interference-and-noise ratio of each user is not less than the minimum signal-to-interference-and-noise ratio Satellite transmission power is limited by P th , the number of beams provided by the satellite constellation to provide services to users is less than U k As a constraint, an optimization problem is established to minimize the total transmit power of the satellite constellation; The optimization problem solving module fixes the beam allocation variables. The original optimization problem can be converted into a convex second-order cone programming problem, which can be solved to obtain the satellite's transmit beamforming vector. The beam allocation variables will be searched for the optimal solution through a genetic algorithm. This optimal solution will be used as the basis for the satellite to perform beam allocation and beamforming to complete data transmission.

7. A computer device, characterized in that: The invention comprises a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the security beamforming method based on dynamic beam allocation according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that A computer program is stored in a computer-readable storage medium. When the computer program is executed by a processor, the secure beamforming method based on dynamic beam allocation according to any one of claims 1 to 5 can be implemented.

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