Manifold optimization-based multi-user hybrid beam forming method for very low earth orbit satellites

Abstract

The invention relates to a multi-user hybrid beam forming method for a very low orbit satellite based on manifold optimization. The method comprises the following steps: establishing a satellite-ground communication system comprising a VLEO satellite and K user terminals with the same parameters; modeling is carried out on the multi-user hybrid beam forming problem of the very low orbit satellite; designing a digital beam forming matrix; designing an analog beam forming matrix; performing power distribution on each user, and designing a power distribution matrix; solving a final hybrid beam forming matrix; and performing complete link simulation and performance analysis. According to the multi-user hybrid beamforming method for the very low orbit satellite based on manifold optimization, the actual feasibility and accuracy of a hybrid beamforming algorithm are remarkably enhanced by establishing a VLEO satellite communication system channel model close to the reality; compared with other hybrid beam forming algorithms, the method has higher user total reachable rate performance.

Description

Technical Field

[0001] The present invention relates to the field of satellite communication technology, and in particular to a very low orbit satellite multi-user hybrid beamforming method based on manifold optimization. Background Art

[0002] In the field of satellite communications, especially for very low earth orbit (VLEO) satellite networks, high-performance beamforming methods are the key to increasing beam energy, reducing interference between users, and enhancing data transmission rates. With the rapid development of space technology, VLEO satellites can provide lower communication delays and stronger signal strength due to their low orbit characteristics, and beamforming technology suitable for VLEO satellites is urgently needed.

[0003] At present, the mainstream solution for beamforming technology of VLEO satellite networks is to determine the location of user terminals and then adjust the beam to point to the user for data transmission. For beamforming methods with known channel matrices, the full digital beamforming algorithm consumes too much power, so the number of RF links can be reduced, and a hybrid beamforming algorithm can be designed to reduce power consumption. For the selection of optimization targets, the mainstream solution is to use the total achievable rate as the optimization target, so the complexity of formula derivation is very high and it is difficult to allocate power.

[0004] The prior art has the following problems:

[0005] 1. Excessive power consumption: For all-digital satellite antenna arrays, equipping each antenna with an RF link will greatly increase the power consumption. Therefore, the number of RF links can be reduced and a hybrid beamforming algorithm can be designed to reduce power consumption.

[0006] 2. Complex derivation of the optimization process: The mainstream beamforming algorithm takes the total achievable rate of users as the optimization target. In a multi-user scenario, the expression of the signal-to-interference-noise ratio is complex, so the optimization of the optimization target and the power allocation solution process are complex.

[0007] 3. Feasibility issues in actual scenarios: The channel models used in the current design of beamforming algorithms are mostly ideal channel models, which cannot simulate the actual satellite-to-ground channel environment and have feasibility issues in actual scenarios.

[0008] 4. Performance enhancement issue: For the existing beamforming technology, its performance still has room for improvement, and a better beamforming algorithm can be designed to improve performance.

[0009] In summary, the existing technology has shortcomings in dealing with multi-user beamforming in VLEO satellite networks, and there is an urgent need for a low-power, easy-to-derive beamforming method suitable for real scenarios. Summary of the invention

[0010] The present invention aims to solve the technical problems of excessively high power consumption, complex derivation of the optimization process, poor feasibility in actual scenarios and the need to continue to enhance performance in the multi-user hybrid beamforming method in a very low earth orbit (VLEO) satellite network in the prior art, and provide a very low earth orbit satellite multi-user hybrid beamforming method based on manifold optimization.

[0011] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0012] A very low earth orbit satellite multi-user hybrid beamforming method based on manifold optimization comprises the following steps:

[0013] Step S1: establishing a satellite-to-ground communication system including a VLEO satellite and K user terminals with the same parameters;

[0014] Step S2: Modeling the VLO satellite multi-user hybrid beamforming problem;

[0015] Step S3: designing a digital beamforming matrix;

[0016] Step S4: designing an analog beamforming matrix;

[0017] Step S5: Allocate power to each user and design a power allocation matrix;

[0018] Step S6: solving the final hybrid beamforming matrix;

[0019] Step S7: Complete link simulation and performance analysis.

[0020] In the above technical solution, step S1 is specifically as follows: in the established satellite-to-ground communication system, the VLEO satellite is a multi-antenna satellite with M antennas, the antennas are uniform array antennas, and the satellite is in a very low orbit hkm above the ground; the K user terminals are single-antenna terminals, which are evenly distributed within the range of rkm, and the weights of the K user terminals are recorded as {α1, α2, ..., α i ,...,α K The communication scenario is selected as a line-of-sight propagation scenario in a non-terrestrial network urban area scenario.

[0021] In the above technical solution, step S2 is specifically:

[0022] The data stream transmitted by the VLEO satellite for K user terminals is K signals, and the number of RF links carried by the VLEO satellite antenna is N. RF , the hybrid beamforming matrix contains the analog beamforming matrix and digital beamforming matrix

[0023] The signals received by K user terminals Expressed as: y = HV RF V B s+n;

[0024] in, is the channel matrix, is the simulated beamforming matrix, is the digital beamforming matrix, To send a signal to K users, is additive Gaussian white noise, subject to distributed;

[0025] The expression of the hybrid beamforming matrix is:

[0026]

[0027] Where β is a scalar factor, MSE is the mean square error, σ is the standard deviation of Gaussian white noise, and I K is the identity matrix of size K.

[0028] In the above technical solution, step S3 is specifically:

[0029] First, the power constraint is weakened and the total power constraint is normalized. The optimization problem is expressed as:

[0030]

[0031] Where tr(·) represents the trace of the matrix;

[0032] Next, introduce a scalar factor and let V B =βV U , put it into the expression of mean square error MSE, and get:

[0033]

[0034] Solving for the scalar factor β is:

[0035]

[0036] Next, the Lagrange multiplier method is used to solve the optimization problem. The optimal solution satisfies the KKT condition. According to the KKT condition, V is solved. U The closed-form solution is:

[0037]

[0038] Finally, according to V B =βV U Get the digital beamforming matrix V B .

[0039] In the above technical solution, step S4 is specifically as follows:

[0040] First, the obtained β and V U Substituted into the expression of mean square error MSE, the objective function J(V RF ) is expressed as:

[0041]

[0042] Next, the simulated beamforming matrix V is solved using the manifold optimization algorithm RF , define J(V RF ) About the simulated beamforming matrix V RF The conjugate gradient of get:

[0043]

[0044] in, Indicates V RF conjugation of;

[0045] Next, using the manifold optimization algorithm, all feasible solutions that satisfy the constant modulus constraint are represented as a manifold and searched in the tangent space along the Riemann gradient, and the step size is determined using the Armijo-Goldstein condition;

[0046] Finally, the search points are mapped back to the manifold, and the simulated beamforming matrix V is determined through repeated iterations of the manifold algorithm. RF The optimal solution of .

[0047] In the above technical solution, step S5 is specifically as follows:

[0048] First, the hybrid beamforming matrix vectors of K users are normalized, and the hybrid beamforming vector of the kth user is expressed as:

[0049]

[0050] remember The total power is P, and the power allocation matrix is ​​P = diag (p1, ... p K ), where diag(·) means diagonalizing the vector, and the total power of the user satisfies Then the digital beamforming matrix after power allocation is The hybrid beamforming matrix is:

[0051]

[0052] Next, the received signal to interference and noise ratio of the kth user is expressed as:

[0053]

[0054] The kth user rate is expressed as:

[0055] R k =log2(1+SINR k )

[0056] in, is the kth row of H, v B,k V B The kth column of

[0057] because The power allocation problem is simplified to:

[0058]

[0059] Among them, α k is the weight of the kth user;

[0060] The optimal solution is obtained using the water injection algorithm:

[0061]

[0062] Among them, q k,k is the kth main diagonal element of Q, and the selection of λ satisfies:

[0063]

[0064] In the above technical solution, step S6 is specifically: multiplying the digital beamforming matrix, the analog beamforming matrix and the power allocation matrix obtained in steps S3, S4 and S5 to obtain the final result of the hybrid beamforming matrix:

[0065] V=V RF V B P.

[0066] In the above technical solution, step 7 is specifically as follows:

[0067] The satellite side generates a signal vector to be sent to K user terminals, maps it to M antennas using the hybrid beamforming matrix obtained in step S6 for transmission, and receives it by the user terminal after passing through the channel frequency response matrix and adding Gaussian white noise;

[0068] Perform performance analysis and calculate the total achievable rate of K user terminals under different signal-to-noise ratios.

[0069] The present invention has the following beneficial effects:

[0070] The VLEO satellite multi-user hybrid beamforming method based on manifold optimization of the present invention significantly enhances the practical feasibility and accuracy of the hybrid beamforming algorithm by establishing a VLEO satellite communication system channel model close to reality.

[0071] The very low orbit satellite multi-user hybrid beamforming method based on manifold optimization of the present invention has higher user total achievable rate performance compared with other hybrid beamforming algorithms.

[0072] The VLO satellite multi-user hybrid beamforming method based on manifold optimization of the present invention is designed with mean square error as the optimization target. Compared with taking the total achievable rate as the optimization variable, the complexity of formula derivation can be reduced. At the same time, the optimization target can also greatly reduce the interference between users, thereby decoupling the process of solving the beamforming vector from the power allocation process and simplifying the difficulty of solving.

[0073] The multi-user hybrid beamforming method for very low-orbit satellites based on manifold optimization of the present invention improves the scalability and maintainability of the system. As the number of satellite antennas and the number of users increase, the multi-user hybrid beamforming method for very low-orbit satellites based on manifold optimization of the present invention can easily cope with the expansion of the number of antennas and the number of users without large-scale modification of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0075] Figure 1 The present invention is a flow chart of a very low orbit satellite multi-user hybrid beamforming method based on manifold optimization.

[0076] Figure 2 Schematic diagram of the model of multi-user link of VLE satellite communication system.

[0077] Figure 3 Schematic diagram of the channel model scenario.

[0078] Figure 4 Schematic diagram of simulation results of total achievable rate versus signal-to-noise ratio.

[0079] Figure 5 Schematic diagram of simulation results of bit error rate versus signal-to-noise ratio. DETAILED DESCRIPTION

[0080] The present invention is described in detail below with reference to the accompanying drawings.

[0081] like Figure 1 As shown, the VLO satellite multi-user hybrid beamforming method based on manifold optimization of the present invention comprises the following steps:

[0082] Step S1: Establish a satellite-to-ground communication system including a VLEO satellite and K user terminals with the same parameters, wherein the VLEO satellite is a multi-antenna satellite with M antennas, the antennas are uniform array antennas, and the satellite is in a very low orbit hkm above the ground; the K user terminals are single-antenna terminals, which are evenly distributed within the range of rkm, and the weights of the K user terminals are recorded as {α1, α2, ..., α i ,...,α K The communication scenario is selected as the line-of-sight propagation scenario in the non-terrestrial network urban area scenario. In this satellite-to-ground communication system scenario, the channel frequency response matrix between the M antennas of the VLEO satellite and the K single-antenna users is generated.

[0083] like Figure 2 As shown, Figure 2 The VLEO satellite in the upper left corner is a multi-antenna satellite with M antennas. The antennas are uniform array antennas and the satellite is in a very low orbit h km above the ground. Figure 2 The K user terminals in the lower right corner are single-antenna terminals and are evenly distributed within the range of rkm. The weights of the K user terminals are recorded as {α1,α2,...,α i ,...,α K}.

[0084] like Figure 3 As shown, the communication scenario is selected as a line-of-sight propagation scenario in a non-terrestrial network urban area scenario. In this satellite-to-ground communication system scenario, the channel frequency response matrix between the M antennas of the VLEO satellite and the K single-antenna users is generated.

[0085] All parameters for channel modeling of the satellite-to-ground communication system are as follows: the center frequency is 20 GHz; all user terminals are evenly distributed in a circle with a radius of 10 km, and the height of all user terminals is consistent, which is 1.5 m; the satellite antenna is a "3gpp-3d" array antenna, the number of antennas is set to 64, and the arrangement is 8 rows and 8 columns; the satellite orbit altitude is 300 km, the satellite initial position latitude is 52.3 degrees, and the longitude is 29.7 degrees; the user terminal uses a single antenna, and the number of user terminals is set to 4.

[0086] Step S2: Modeling the VLO satellite multi-user hybrid beamforming problem.

[0087] Assume that the number of satellite antennas is M, and it serves K single-antenna users at the same time. The satellite uses hybrid beamforming technology, including analog beamforming matrix design and digital beamforming matrix design, and the number of RF links is N. RF , find the signal received by K users Next, find the optimization target: mean square error MSE.

[0088] Hybrid beamforming includes two parts: analog beamforming and digital beamforming. Analog beamforming operates on signals in the analog domain. The mainstream structure uses a phase shifter, which can only change the phase of the signal. Digital beamforming processes the signal in the digital domain and can adjust the amplitude and phase of the signal arbitrarily.

[0089] The data stream transmitted by the VLEO satellite for K user terminals is K signals, and the number of RF links carried by the VLEO satellite antenna is N. RF , the hybrid beamforming matrix to be designed includes the analog beamforming matrix and digital beamforming matrix The signals received by K user terminals It can be expressed as:

[0090] y=HV RF V B s+n (1.1)

[0091] in, is the channel matrix, is the simulated beamforming matrix, is the digital beamforming matrix, To send a signal to K users, is additive Gaussian white noise, subject to distributed.

[0092] The designed hybrid beamforming matrix takes the mean square error as the optimization target. Its purpose is to make the signal received by the user terminal as close as possible to the signal sent by the VLEO satellite through hybrid beamforming. Its expression is:

[0093]

[0094] Where β is a scalar factor, MSE is the mean square error, σ is the standard deviation of Gaussian white noise, and I K is the identity matrix of size K.

[0095] The next step is to decouple the problem. The hybrid beamforming algorithm is derived and designed according to the mean square error criterion in step S2, and the hybrid beamforming design is abstracted into a mathematical problem and derived and optimized. Since the required hybrid beamforming matrix contains the analog beamforming matrix and the digital beamforming matrix, it is necessary to decouple the algorithm design. First, the digital beamforming matrix is ​​designed, and then the analog beamforming matrix is ​​optimized according to the digital beamforming matrix. In the process of solving the beamforming matrix, since the optimization target is the mean square error, it is impossible to perform multi-user power allocation while solving the beamforming matrix. Therefore, the hybrid beamforming design and power allocation process must also be decoupled. In the hybrid beamforming design process, it is assumed that the beamforming matrix adopts a normalized power constraint.

[0096] Step S3: Design the digital beamforming matrix.

[0097] First, the power constraint is weakened and the total power constraint is normalized to express the optimization problem. Then, a scalar factor is introduced and substituted into the expression of the mean square error MSE to solve the expression of the scalar factor. Finally, the Lagrange multiplier method is used to solve the above optimization problem. The optimal solution satisfies the KKT condition, and a closed-form solution can be obtained according to the KKT condition.

[0098] Specifically:

[0099] First, the power constraint is weakened and the total power constraint is normalized. The optimization problem can be expressed as:

[0100]

[0101] Here, tr(·) represents the trace of the matrix, i.e., the sum of the main diagonal elements. Next, we introduce a scalar factor, V B =βV U , put it into the expression of mean square error MSE, we can get:

[0102]

[0103] Since the optimal solution is satisfied when the total transmit power reaches the maximum, the expression of the scalar factor β can be solved, and it can be obtained:

[0104]

[0105] Next, the Lagrange multiplier method is used to solve the above optimization problem. The optimal solution satisfies the KKT condition. According to the KKT condition, V can be solved. U The closed-form solution is:

[0106]

[0107] Finally, according to VB =βV U Get the digital beamforming matrix V B .

[0108] Step S4: Designing the analog beamforming matrix.

[0109] First, the obtained β and V U Substituted into the expression of mean square error MSE, the objective function becomes only with the simulated beamforming matrix V RF Next, the manifold optimization algorithm is used to obtain the simulated beamforming matrix.

[0110] Specifically:

[0111] First, the obtained β and V U Substituted into the expression of mean square error MSE, the objective function becomes only with the simulated beamforming matrix V RF The function of the change, the objective function J(V RF ) is expressed as:

[0112]

[0113] Next, the simulated beamforming matrix V is solved using the manifold optimization algorithm RF , define J(V RF ) About the simulated beamforming matrix V RF The conjugate gradient of You can get:

[0114]

[0115] in, Indicates V RF The conjugation of.

[0116] Next, using the manifold optimization algorithm, all feasible solutions that satisfy the constant modulus constraint are represented as a manifold and searched in the tangent space along the Riemann gradient, and the step size is determined using the Armijo-Goldstein condition;

[0117] Finally, the search points are mapped back to the manifold, and the simulated beamforming matrix V is determined through repeated iterations of the manifold algorithm. RF The optimal solution of .

[0118] Step S5: Allocate power to each user and design a power allocation matrix.

[0119] First, the hybrid beamforming matrix vector of K users is normalized. The total power is P, which is the noise power multiplied by the signal-to-noise ratio. The power allocation matrix is ​​P = diag (p1, ... p K), where diag(·) means diagonalizing the vector, and the total power of the user satisfies Therefore, the digital beamforming matrix after power allocation can be expressed, and the received signal-to-interference-noise ratio and achievable rate of the kth user can be expressed. Then, the power allocation problem is simplified by approximating the inter-user interference to 0, and the solution is obtained by the water injection method.

[0120] After obtaining the analog beamforming matrix and the digital beamforming matrix, the power of the K user terminals is allocated according to their weights. The power allocated to the K user terminals is {p1, p2, …, p i ,...,p k}, the total power is P, and the power allocation adopts the water injection algorithm.

[0121] First, the hybrid beamforming matrix vectors of K users are normalized, and the hybrid beamforming vector of the kth user can be expressed as:

[0122]

[0123] remember The total power is P, and the power allocation matrix is ​​P = diag (p1, ... p K ), where diag(·) means diagonalizing the vector, and the total power of the user satisfies Then the digital beamforming matrix after power allocation is The hybrid beamforming matrix is:

[0124]

[0125] Next, the received signal to interference and noise ratio of the kth user is expressed as:

[0126]

[0127] The kth user rate can be expressed as:

[0128] R k =log2(1+SINR k )(1.12)

[0129] in, is the kth row of H, v B,k V B The kth column of .

[0130] Since the design criterion of the beamforming matrix is ​​the minimum mean square error (MSE), the advantage of this optimization objective is that each user receives only the signal sent to itself as much as possible, which greatly reduces the interference between users. The interference between users can be approximated to 0, that is, Therefore, the power allocation problem can be simplified to:

[0131]

[0132] Among them, α k is the weight of the kth user.

[0133] The optimal solution to this problem can be obtained using the water injection algorithm:

[0134]

[0135] Among them, q k,k is the kth main diagonal element of Q, and the selection of λ satisfies:

[0136]

[0137] Step S6: Solve the final hybrid beamforming matrix.

[0138] The digital beamforming matrix, the analog beamforming matrix and the power allocation matrix obtained in step S3, step S4 and step S5 are multiplied to obtain the final result of the hybrid beamforming matrix, that is:

[0139] V=V RF V B P (1.15)

[0140] Step S7: Complete link simulation and performance analysis.

[0141] Perform complete link simulation including:

[0142] The real channel frequency response matrix between the satellite and the ground is used to generate the signal vectors sent to K user terminals on the satellite side, which are mapped to M antennas for transmission using the hybrid beamforming matrix obtained in step S6. After passing through the channel frequency response matrix and adding Gaussian white noise, the signal vectors are received by the user terminals.

[0143] Perform performance analysis, calculate the total achievable rate of K user terminals under different signal-to-noise ratios, and compare and analyze with other algorithms. The signal-to-noise ratio is selected to be -10dB to 30dB. Figure 4 and 5 As shown, the sum rate obtained by the method of the present invention is 17 bits / s / Hz at a 20 dB signal-to-noise ratio and 24.6 bits / s / Hz at a 30 dB signal-to-noise ratio.

[0144] The VLEO satellite multi-user hybrid beamforming method based on manifold optimization of the present invention significantly enhances the practical feasibility and accuracy of the hybrid beamforming algorithm by establishing a VLEO satellite communication system channel model close to reality.

[0145] The very low orbit satellite multi-user hybrid beamforming method based on manifold optimization of the present invention has higher user total achievable rate performance compared with other hybrid beamforming algorithms.

[0146] The VLO satellite multi-user hybrid beamforming method based on manifold optimization of the present invention is designed with mean square error as the optimization target. Compared with taking the total achievable rate as the optimization variable, the complexity of formula derivation can be reduced. At the same time, the optimization target can also greatly reduce the interference between users, thereby decoupling the process of solving the beamforming vector from the power allocation process and simplifying the difficulty of solving.

[0147] The multi-user hybrid beamforming method for very low-orbit satellites based on manifold optimization of the present invention improves the scalability and maintainability of the system. As the number of satellite antennas and the number of users increase, the multi-user hybrid beamforming method for very low-orbit satellites based on manifold optimization of the present invention can easily cope with the expansion of the number of antennas and the number of users without large-scale modification of the algorithm.

[0148] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

Claims

1. A very low earth orbit satellite multi-user hybrid beamforming method based on manifold optimization, characterized in that: The following steps are involved: Step S1: establishing a satellite-to-ground communication system including a VLEO satellite and K user terminals with the same parameters; Step S2: Modeling the VLO satellite multi-user hybrid beamforming problem; Step S3: designing a digital beamforming matrix; Step S4: designing an analog beamforming matrix; Step S5: Allocate power to each user and design a power allocation matrix; Step S6: solving the final hybrid beamforming matrix; Step S7: Complete link simulation and performance analysis.

2. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 1, characterized in that: Step S1 is specifically as follows: in the established satellite-to-ground communication system, the VLEO satellite is a multi-antenna satellite with M antennas, the antennas are uniform array antennas, and the satellite is in a very low orbit hkm above the ground; K user terminals are single-antenna terminals, which are evenly distributed within the range of rkm, and the weights of the K user terminals are recorded as {α1, α2, ..., α i ,...,α K The communication scenario is selected as a line-of-sight propagation scenario in a non-terrestrial network urban area scenario.

3. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 1, characterized in that: Step S2 is specifically as follows: The data stream transmitted by the VLEO satellite for K user terminals is K signals, and the number of RF links carried by the VLEO satellite antenna is N. RF , the hybrid beamforming matrix contains the analog beamforming matrix and digital beamforming matrix The signals received by K user terminals Expressed as: y = HV RF V B s+n; in, is the channel matrix, is the simulated beamforming matrix, is the digital beamforming matrix, To send a signal to K users, is additive Gaussian white noise, subject to distributed; The expression of the hybrid beamforming matrix is: Where β is a scalar factor, MSE is the mean square error, σ is the standard deviation of Gaussian white noise, and I K is the identity matrix of size K.

4. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 3, characterized in that: Step S3 is specifically as follows: First, the power constraint is weakened and the total power constraint is normalized. The optimization problem is expressed as: Where tr(·) represents the trace of the matrix; Next, introduce a scalar factor and let V B =βV U , put it into the expression of mean square error MSE, and get: Solving for the scalar factor β is: Next, the Lagrange multiplier method is used to solve the optimization problem. The optimal solution satisfies the KKT condition. According to the KKT condition, V is solved. U The closed-form solution is: Finally, according to V B =βV U Get the digital beamforming matrix V B .

5. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 4, characterized in that: Step S4 is specifically as follows: First, the obtained β and V U Substituted into the expression of mean square error MSE, the objective function J(V RF ) is expressed as: Next, the simulated beamforming matrix V is solved using the manifold optimization algorithm RF , define J(V RF ) About the simulated beamforming matrix V RF The conjugate gradient of get: in, Indicates V RF conjugation of; Next, using the manifold optimization algorithm, all feasible solutions that satisfy the constant modulus constraint are represented as a manifold and searched in the tangent space along the Riemann gradient, and the step size is determined using the Armijo-Goldstein condition; Finally, the search points are mapped back to the manifold, and the simulated beamforming matrix V is determined through repeated iterations of the manifold algorithm. RF The optimal solution of .

6. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 5, characterized in that: Step S5 is specifically as follows: First, the hybrid beamforming matrix vectors of K users are normalized, and the hybrid beamforming vector of the kth user is expressed as: remember The total power is P, and the power allocation matrix is ​​P = diag (p1, ... p K ), where diag(·) means diagonalizing the vector, and the total power of the user satisfies Then the digital beamforming matrix after power allocation is The hybrid beamforming matrix is: Next, the received signal to interference and noise ratio of the kth user is expressed as: The kth user rate is expressed as: R k =log2(1+SINR k ) in, is the kth row of H, v B,k V B The kth column of because The power allocation problem is simplified to: Among them, α k is the weight of the kth user; The optimal solution is obtained using the water injection algorithm: Among them, q k,k is the kth main diagonal element of Q, and the selection of λ satisfies:

7. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 6, characterized in that: Step S6 is specifically as follows: The digital beamforming matrix, the analog beamforming matrix and the power allocation matrix obtained in step S3, step S4 and step S5 are multiplied to obtain the final result of the hybrid beamforming matrix: V=V RF V B P。 8. The VLE satellite multi-user hybrid beamforming method based on manifold optimization according to claim 7, characterized in that: Step 7 is as follows: The satellite side generates a signal vector to be sent to K user terminals, maps it to M antennas using the hybrid beamforming matrix obtained in step S6 for transmission, and receives it by the user terminal after passing through the channel frequency response matrix and adding Gaussian white noise; Perform performance analysis and calculate the total achievable rate of K user terminals under different signal-to-noise ratios.

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