Large-scale MIMO low-orbit satellite-ground cooperation robust precoding method

Abstract

The invention discloses a large-scale MIMO (Multiple Input Multiple Output) low-orbit satellite-ground cooperation robust precoding method, which considers potential service interruption of a base station to a user terminal, introduces a low-orbit satellite to cooperate with the base station to serve a user, and guarantees the communication performance of the user. Considering that a satellite end can only obtain inaccurate launching angle information, the invention provides a low-orbit satellite-ground cooperation robust precoding method based on angle error distribution information. According to the method, the problems of system traversal reachability and rate maximization under respective energy consumption constraints of a low earth orbit satellite and a ground base station are established, the optimization problem is rewritten by using positive semidefinite relaxation and rate approximation, and an autocorrelation matrix of a channel is deduced based on angle error information of a launching angle of the low earth orbit satellite and is used for robust precoding. And then a robust precoder is designed by using a CCCP algorithm. According to the large-scale MIMO low-orbit satellite-ground cooperation robust precoding method provided by the invention, the complexity of solving the optimization problem is remarkably reduced, a robust effect can be realized under the condition of an angle error of a transmitting angle, and the communication rate of a user is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of satellite and ground collaborative communication, and in particular to a large-scale MIMO low-orbit satellite-ground collaborative robust precoding method taking into account inaccurate user transmission angles obtained by a low-orbit satellite end. Background Art

[0002] With the continuous growth of device connections and data traffic, the development of the sixth generation (6G) wireless network has become an inevitable trend. In addition to achieving higher communication capacity, 6G networks must also ensure ubiquitous coverage. Traditional terrestrial networks are mainly deployed in densely populated and developed areas, covering only about 6% of the earth's surface. As a result, users in remote areas often lack reliable communication services. In contrast, satellite networks can effectively supplement terrestrial networks, provide wide coverage, and have higher anti-interference capabilities when dealing with geographical obstacles. The orbital altitude of low-orbit satellites is generally 200-2000 kilometers, so they have lower latency and path loss than geosynchronous orbit satellites and medium-earth orbit satellites. Massive MIMO technology has the advantage of significantly improving the degrees of freedom in the spatial domain and has been widely used in terrestrial networks. Extending massive MIMO technology to low-orbit satellite communication systems has great potential to improve spectrum efficiency and anti-interference capabilities. In low-orbit satellite communication systems, the effect of downlink precoding depends largely on the accuracy of channel state information based on the transmission angle. However, due to the long distance between low-orbit satellites and ground user terminals, the system has significant propagation delay. Therefore, it is difficult to obtain the user's accurate transmission angle, so it is a challenging task to use the estimated transmission angle for precoding design in massive MIMO satellite communication systems. Therefore, it is necessary to consider the imperfect channel state information of the satellite downlink channel and perform robust precoding design based on this. Integrated satellite-ground networks combine the advantages of ground networks and satellite networks and have become a hot research area in recent years. Satellite-ground collaborative networks can expand the coverage of ground networks and enhance the service performance of user terminals. However, under the same spectrum service range, satellite networks and ground networks interfere with each other. If a joint precoding design is not performed to control the mutual interference between networks, the user's communication performance will suffer a huge attenuation. Therefore, it is necessary to consider the collaborative precoder design of satellites and ground in satellite-ground collaborative networks. Summary of the invention

[0003] Purpose of the invention: In view of the shortcomings of the prior art, the purpose of the present invention is to provide a large-scale MIMO low-orbit satellite-ground collaborative robust precoding method that takes into account the inaccuracy of the satellite downlink channel transmission angle, which can optimize the system's sum and rate performance and reduce the complexity of implementing this optimization process, making it easy to implement.

[0004] Technical solution: To achieve the above-mentioned invention object, the present invention provides a method for robust precoding of large-scale MIMO low-orbit satellite-ground collaboration, wherein the low-orbit satellite is equipped with a large-scale MIMO antenna array, and uses the same spectrum resources with multiple ground base stations to collaboratively serve multiple users; the low-orbit satellite can only obtain rough prior position angle information of the user; the robust precoding is a precoding scheme based on inaccurate estimated angle and angle error distribution information; the robust precoding method comprises the following steps:

[0005] The system traversal reachability and rate maximization problem under the energy consumption constraints of low-orbit satellites and ground base stations is established; the link status of the base station downlink channel is introduced, and the path gain factor of the base station downlink channel to the user is considered to be affected by the link status. The inaccuracy of the satellite downlink channel transmission angle is considered, and the angle error model is introduced;

[0006] Rewrite the optimization problem using semidefinite relaxation and rate approximation;

[0007] The autocorrelation matrix of the channel vector is derived based on the transmission angle error model of the low-orbit satellite for robust precoding, and the CCCP algorithm is used to solve the optimization problem. The steps of deriving the autocorrelation matrix of the channel vector are as follows:

[0008] A channel vector representing the user, and determining the representation of each element in the vector, the channel vector combining the satellite downlink channel and the downlink channels of all ground base stations;

[0009] The channel autocorrelation matrix is ​​the result of finding the expectation of the outer product of the channel vector and its conjugate transpose. In various cases, the random variables in each element of the channel autocorrelation matrix are the transmission angle errors of the satellite channel. Finding the expectation is to process the angle errors based on the known error distribution information.

[0010] Derive the elements of the channel autocorrelation matrix that are only affected by the satellite channel;

[0011] The elements in the channel autocorrelation matrix that are jointly affected by the satellite channel and the base station channel are derived, and the expectation of the error angle is gradually solved using the approximate relationship of trigonometric functions.

[0012] Furthermore, the base station downlink channel link state sta∈{los,nlos,out} is introduced to model the impact of the link state on the channel, which is specifically expressed as:

[0013]

[0014] In the formula, h i,j represents the downlink channel from the i-th base station to the j-th user, L i,j represents the number of multipaths, is the array response vector of the base station downlink channel, θ i,j,l and correspond to the vertical angle and horizontal angle associated with the lth path, respectively, is the path gain factor affected by the link status. sta∈{los,nlos,out} represents the link status. When sta∈{los,nlos}, Otherwise, it decays to the preset value.

[0015] Furthermore, the signal-to-interference-to-noise ratio of the user received signal is modeled as:

[0016]

[0017] In the formula, w i,j represents the full digital precoding vector of the i-th base station for the j-th user, b j represents the full digital precoding vector of the low-orbit satellite for the jth user, g j represents the downlink channel of the low-orbit satellite to the jth user, K u is the number of user terminals, N B is the number of base stations, is the noise variance, and the superscript H denotes the conjugate transpose.

[0018] Furthermore, the optimization problem of maximizing the system traversal reachability and rate under the energy constraints of low-orbit satellites and ground base stations is expressed as:

[0019]

[0020] In the formula, represents the traversal reachable rate, represents the expectation, P B,max is the maximum transmission power of the base station, P S,max is the maximum transmission power of the low-orbit satellite, ‖·‖ 2 Represents the square of the magnitude of a vector.

[0021] Further, let and Re-order and Yes||w j || 2 =Tr(W j )and Tr(·) represents the matrix trace, and the variable to be optimized is w i,j With b j Became W j , the energy consumption constraint is rewritten as:

[0022]

[0023] In the formula, A B,i and A SIt is a diagonal matrix, where the elements on the diagonal correspond to the position of the low-orbit satellite or any ground base station, and the elements at other positions are 0. Using semi-positive definite relaxation and rate approximation, the optimization problem is rewritten as:

[0024]

[0025] In the formula,

[0026]

[0027] Represents a variable collection τ is the iteration index, the matrix is the autocorrelation matrix of the channel vector derived based on the channel angle error.

[0028] Furthermore, the massive MIMO low-orbit satellite transmission angle error model is expressed as:

[0029]

[0030] In the formula, and represents the estimated value of the transmission angle of the low-orbit satellite to the jth user, and the angle estimation error and is introduced as a random variable, and It represents the common angle deviation of all users caused by satellite attitude jitter, which can be ignored. For the jth user, its angle error is and Follows uniform distribution.

[0031] Furthermore, the channel h of the jth user j The structure is: Front M t The elements are generated by the satellite downlink channel, and then every N t Elements are generated by the base station downlink channel; M t is the number of antennas of the LEO satellite, N t is the number of antennas of each ground base station; the matrix H j The (m,n)th element of is represented as:

[0032]

[0033] In the formula, g j is the downlink channel gain from the low-orbit satellite to the jth user, v j is the array response vector, As the label of the current base station,

[0034] Indicates the i m 、i n The downlink channel of a base station to the jth user.

[0035] Furthermore, when m≤M t ,n≤M t , the autocorrelation matrix of the channel The results are as follows:

[0036]

[0037] In the formula,

[0038]

[0039] M 1 、M 2 are the number of antennas in the x and y directions of the satellite respectively.

[0040] Furthermore, when m≤M t ,n>M t When the channel autocorrelation matrix The result is:

[0041]

[0042] In the formula, γ m Yes j The mean value of B 1 and B 2 They are:

[0043]

[0044] The present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the large-scale MIMO low-orbit satellite-to-ground collaborative robust precoding method.

[0045] Beneficial effects: The present invention models a large-scale MIMO low-orbit satellite-ground cooperative system, derives the signal-to-interference-to-noise ratio of the user's received signal, and on this basis establishes the system traversal reachability and rate maximization problem under the energy consumption constraints of the low-orbit satellite and the ground base station, uses semi-positive definite relaxation and rate approximation to rewrite the optimization problem, and derives the channel autocorrelation matrix for robust precoding based on the transmission angle error information of the low-orbit satellite. Then, the CCCP algorithm is used to design a robust precoder, which can achieve a robust effect when there is an error in the transmission angle of the low-orbit satellite, reduce the impact of the angle error, and improve the user's communication rate. It also reduces the complexity of solving the optimization problem and the physical layer implementation, and speeds up the calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The figure is a flow chart of the overall method of an embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, the technical solutions are clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. It should be noted that the embodiments are only examples of some of the present invention, not all embodiments. Based on these embodiments, all other implementation methods obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0048] The invention discloses a large-scale MIMO low-orbit satellite-ground collaborative robust precoding method, which takes into account that ground obstacles may affect the communication performance of ground users and even cause the downlink of base stations to be interrupted. In order to avoid affecting the communication performance of ground users, the invention introduces low-orbit satellites to provide top-down communication services for ground users and ensure the communication needs of users. The method is equipped with a large-scale MIMO antenna array at the low-orbit satellite end, and the satellite and multiple ground base stations use the same spectrum resources to collaboratively serve multiple users. The low-orbit satellite end can only obtain rough prior position angle information of the user, and the ground base station end can obtain accurate channel state information of the user. Based on this, the ground gateway manages the downlink transmission of the satellite and the ground base station, so that the low-orbit satellite and the ground base station send the precoded information to each user. Robust precoding is a precoding scheme based on inaccurate estimated angles and angle error distribution information. Each antenna unit of the antenna array of the low-orbit satellite and the base station independently sends a signal, and the precoding of the low-orbit satellite and the ground base station is updated as the position of the satellite and each user terminal changes.

[0049] like Figure 1 As shown, a large-scale MIMO low-orbit satellite-ground collaborative robust precoding method disclosed in an embodiment of the present invention first establishes a low-orbit satellite and ground channel model, and introduces an angle error model to characterize the inaccuracy of the satellite downlink channel transmission angle. Then, based on the user's received signal, the energy consumption constraints of the satellite and the base station are considered to characterize the optimization problem of maximizing the traversal reachability and rate. The optimization objectives and constraints are rewritten using semi-positive definite relaxation and rate approximation. Then, based on the angle error model, the autocorrelation matrix of the channel vector is derived for robust precoding to reduce the impact of the angle error. Finally, the CCCP algorithm is used to solve the optimization problem.

[0050] Specifically, the steps of deriving the autocorrelation matrix of the channel vector include: characterizing the channel vector of the user, determining the representation of each element in the vector, and the channel vector combines the satellite downlink channel and the downlink channels of all ground base stations; the channel autocorrelation matrix is ​​the expected result of the outer product of the channel vector and its conjugate transpose, and in various cases, represents each element in the channel autocorrelation matrix, and the random variable in each element is the angular error of the satellite channel. The expectation is to process the angular error of the satellite downlink channel according to the known angular error distribution information; derive the elements in the channel autocorrelation matrix that are only affected by the satellite channel; derive the elements in the channel autocorrelation matrix that are jointly affected by the satellite channel and the base station channel. Since the angular error value is usually small, the approximate relationship of trigonometric functions can be used to gradually solve the expected result of the error angle.

[0051] The method of this embodiment is described in more detail below with reference to a specific scenario.

[0052] Part 1: Constructing low-orbit satellite channel model and angle error model

[0053] Specifically, consider a low-orbit satellite equipped with a massive MIMO uniform planar array with M antennas. t =M 1 M 2 , where M 1 and M 2 Represent the number of antennas uniformly distributed along the x-axis and y-axis respectively. Based on the ray tracing model, the downlink spatial domain channel response of the low-orbit satellite to the jth user at time t and frequency f is:

[0054]

[0055] In the formula, Represents the Doppler shift caused by satellite movement. represents the minimum path delay, τ j,l is the delay of the lth path from the low-orbit satellite to user j. j (t,f) represents the channel gain, where L s,j is the multipath number, g j,l represents the complex gain of the lth path. is the Doppler shift caused by user movement, It is assumed that the delay and Doppler shift caused by the LEO satellite can be compensated at each user. It should be noted that LEO satellite communication systems usually operate under line-of-sight conditions, so the channel can be modeled using the Rician channel model. j (t,f) is assumed to follow a Rician distribution, and its Rician factor is κ m , the average power is γ, where

[0056] Uniform planar array response vector v j as follows:

[0057]

[0058] Among them, θ j and Represents the angle relative to the x-axis and y-axis respectively. and v y (θ j ) represent the array response vectors corresponding to the x-axis and y-axis, respectively, and are defined as follows:

[0059]

[0060] In the actual low-orbit satellite downlink scenario, the high-speed movement of the low-orbit satellite often leads to inaccurate launch angles. The actual launch angle can be modeled as:

[0061]

[0062] in, and represents the estimated angle of the jth user. Angle estimation error and is introduced as a random variable. and represents the common angle deviation of all users caused by satellite attitude jitter, and its value is very small and can be ignored. Although the incomplete channel state information of each user is considered in the low-Earth orbit satellite communication system, the distribution information of the transmission angle error can be considered to be known. Assume that the angle error of the jth user is and It obeys uniform distribution within a certain range.

[0063] Part II: Building Ground Channel Model and Link State Model

[0064] Assume that each ground base station is equipped with a size N t =N 1 N 2 The uniform planar array response vector, where N 1 and N 2 They correspond to the number of array elements arranged along the x and z axes respectively. The downlink channel between the i-th base station and the j-th user can be simulated as:

[0065]

[0066] Among them, sta∈{los,nlos,out} represents the link status, α i,j,lis the complex gain of each path. When sta∈{los,nlos}, each path follows an independent and identical distribution (iid) On the contrary, when the link is in the out state, the link will be greatly attenuated, and the diameter gain in this embodiment will be attenuated by 40dB. i,j,l and Corresponding to the vertical angle and horizontal angle associated with the lth path respectively. The horizontal direction vector and the perpendicular vector a v (θ i,j,l ) are:

[0067]

[0068] Part III: Constructing the Optimization Problem

[0069] let represents the precoding vector from the i-th base station to the j-th user, ‖w i,j ‖ 2 =P i,j is the signal transmission power. The signal x sent by the i-th base station to the j-th user b,i,j satisfy Likewise, let represents the precoding vector of the satellite for the jth user. The signal x sent by the satellite to the jth user s,j Also satisfied Then, the received signal of the jth user is:

[0070]

[0071] in, The variance is The noise variance is given by Given as , where κ represents the Boltzmann constant, B represents the bandwidth, and T refers to the noise temperature.

[0072] In the above formula, the first two terms represent the signal, and the third and fourth terms represent the interference. Then, the signal-to-interference-to-noise ratio of the signal received by the jth user is:

[0073]

[0074] Taking into account the angle estimation error in the satellite downlink channel, the ergodic rate is used here to define the achievable rate for the jth user, as shown below:

[0075]

[0076] The goal is to maximize the sum rate of the satellite-ground cooperative network through precoding design. We consider setting power thresholds for low-orbit satellites and each base station. Therefore, the entire optimization problem can be expressed as follows:

[0077]

[0078] Part IV: Designing Robust Precoders

[0079] Step 1: Order and The superscript H represents the conjugate transpose. and Therefore, ||w j || 2 =Tr(W j )and Tr(·) represents the matrix trace. In this way, the variables to be optimized are w i,j With b j Became W j , the above energy consumption constraint can be rewritten as:

[0080]

[0081] In the formula, A B,i and A S It is a diagonal matrix, where the elements on the diagonal corresponding to the position of a low-orbit satellite or any ground base station are 1, and the elements at other positions are 0. At this time, the matrix variable to be optimized W j Should satisfy rank(W j )=1, rank(·) indicates the matrix rank.

[0082] Step 2: The above traversal achievable rate has high computational complexity, so use a tight upper bound function Replace the original R j , rewrite the original optimization goal traversal reachability and rate as follows:

[0083]

[0084] In the formula,

[0085]

[0086] The matrix in the formula It is the channel autocorrelation matrix derived based on the channel angle error.

[0087] Step 3: Use the concave-convex process to further process the above optimization objectives. Specifically, g j (W) Use the first-order Taylor expansion to transform the original optimization problem Rewritten as:

[0088]

[0089] In the formula,

[0090]

[0091] Represents a variable collection τ is the iteration index. The current problem It is convex and can be solved using convex optimization tools. Usually, the matrix variables obtained will satisfy the rank constraint, that is, rank(W j )=1, then the actual precoding vectors of the low-orbit satellite and the ground base station can be obtained by the eigenvalue decomposition method. If the obtained matrix variable does not satisfy the rank 1 constraint, the precoding vector can be obtained by the Gaussian randomization method.

[0092] Step 4: Use the known distribution information of satellite transmission angle error to solve the channel autocorrelation matrix This is used to design robust precoding. Specifically, it includes:

[0093] Step 4.1: Characterize the user's channel vector and determine the representation of each element in the vector, which combines the satellite downlink channel and the downlink channels of all ground base stations.

[0094] Specifically, first, H j Elements in the matrix. h j The structure is: Front M t The elements are generated by the satellite downlink channel, and then every N t The elements are generated by the base station downlink channel. t is the number of antennas of the LEO satellite, N t is the number of antennas at each ground base station.

[0095] Using m to represent h j The element index in, when m≤M t When , this element is generated by the satellite downlink channel. It can be expressed as:

[0096]

[0097] Where, m = 0, ..., M t -1, g j is the downlink channel gain from the low-orbit satellite to the jth user, g j It follows a Rician distribution, and its Rician factor is κ m , the average power is γ, where v j is the array response vector. M 2 is the number of antennas in the y direction of the satellite, Indicates rounding up.

[0098] When M t <m, let As the label of the current base station, let k be the index of the downlink channel element of this base station. Therefore, k is expressed as a function of the index m as follows:

[0099]

[0100] Matrix H j The (m,n)th element of can be expressed as:

[0101]

[0102] Step 4.2: Calculate the

[0103] When m≤M t ,n≤M t , The results are as follows:

[0104]

[0105] In the formula,

[0106]

[0107]

[0108] When m≤M t ,n>M t , you need to calculate the result of the following expression:

[0109]

[0110] Among them, γ m Yes j Next, we first use the known angle error distribution information to calculate Find the integral. Specifically, we need to consider result. The value is small, so there is and Furthermore, the following approximate results can be obtained:

[0111]

[0112] therefore,

[0113]

[0114] If t 1 =0, m≠1, then the integral as follows:

[0115]

[0116] When t 1 =0 and m=1, The result is 1. If t 1 ≠0, It becomes impossible to integrate directly. So we have:

[0117]

[0118] There are also Re-order About The integral part of is:

[0119]

[0120] in,

[0121]

[0122] In summary, the results of the channel autocorrelation matrix in the second case are as follows:

[0123]

[0124] The third case is similar to the second case, so no further discussion is needed. As for the fourth case, since it does not involve a random variable, its mean is equal to itself.

[0125] During the dynamic movement of the satellite and each user terminal, as the satellite's estimated transmission angle for each user terminal changes and the ground base station's instantaneous channel state information for each user terminal changes, the aforementioned robust precoding process is dynamically implemented to form an updated collaborative robust precoding method.

[0126] An embodiment of the present invention further discloses a computer program product, including a computer program, which, when executed by a processor, implements the steps of the massive MIMO low-orbit satellite-to-ground collaborative robust precoding method.

[0127] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0128] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for robust precoding of large-scale MIMO low-orbit satellite-ground collaboration, characterized in that: The low-orbit satellite is equipped with a large-scale MIMO antenna array, which uses the same spectrum resources as multiple ground base stations to collaboratively serve multiple users; the low-orbit satellite can only obtain rough prior position angle information of the user; the robust precoding is a precoding scheme based on inaccurate estimated angle and angle error distribution information; the robust precoding method comprises the following steps: Establish the system traversal reachability and rate maximization problem under the energy consumption constraints of low-orbit satellites and ground base stations; The link status of the base station downlink channel is introduced, and the path gain factor of the base station downlink channel to the user is considered to be affected by the link status. The inaccuracy of the satellite downlink channel transmission angle is considered, and the angle error model is introduced; Rewrite the optimization problem using semidefinite relaxation and rate approximation; The autocorrelation matrix of the channel vector is derived based on the transmission angle error model of the low-orbit satellite for robust precoding, and the CCCP algorithm is used to solve the optimization problem. The steps of deriving the autocorrelation matrix of the channel vector are as follows: A channel vector representing the user, and determining the representation of each element in the vector, the channel vector combining the satellite downlink channel and the downlink channels of all ground base stations; The channel autocorrelation matrix is ​​the result of finding the expectation of the outer product of the channel vector and its conjugate transpose. In various cases, it represents each element in the channel autocorrelation matrix. The random variable in each element is the transmission angle error of the satellite channel. Finding the expectation is to process the angle error according to the known error distribution information. Derive the elements of the channel autocorrelation matrix that are only affected by the satellite channel; The elements in the channel autocorrelation matrix that are jointly affected by the satellite channel and the base station channel are derived, and the expectation of the error angle is gradually solved using the approximate relationship of trigonometric functions.

2. The method for robust precoding of large-scale MIMO low-orbit satellite-ground collaboration according to claim 1, characterized in that: The base station downlink channel link state sta∈{los,nlos,out} is introduced to model the impact of the link state on the channel, which is specifically expressed as: In the formula, h i,j represents the downlink channel from the i-th base station to the j-th user, L i,j represents the number of multipaths, is the array response vector of the base station downlink channel, θ i,j,l and correspond to the vertical angle and horizontal angle associated with the lth path, respectively, is the path gain factor affected by the link status. sta∈{los,nlos,out} represents the link status. When sta∈{los,nlos}, Otherwise, it decays to the preset value.

3. The method for robust precoding for low-orbit satellite-ground collaboration of massive MIMO according to claim 2, characterized in that: The signal-to-interference-to-noise ratio of the user received signal is modeled as: In the formula, w i,j represents the full digital precoding vector of the i-th base station for the j-th user, b j represents the full digital precoding vector of the low-orbit satellite for the jth user, g j represents the downlink channel of the low-orbit satellite to the jth user, K u is the number of user terminals, N B is the number of base stations, is the noise variance, and the superscript H denotes the conjugate transpose.

4. The method for robust precoding for low-orbit satellite-ground collaboration of massive MIMO according to claim 3, characterized in that: The optimization problem of maximizing the system traversal reachability and rate under the energy constraints of low-orbit satellites and ground base stations is expressed as: In the formula, represents the traversal reachable rate, represents the expectation, P B,max is the maximum transmission power of the base station, P S,max is the maximum transmission power of the low-orbit satellite, ‖·‖ 2 Represents the square of the magnitude of a vector.

5. The method for robust precoding for low-orbit satellite-ground collaboration of massive MIMO according to claim 4, characterized in that: make and Re-order and Yes||w j || 2 =Tr(W j )and Tr(·) represents the matrix trace, and the variable to be optimized is w i,j With b j Became W j , the energy consumption constraint is rewritten as: In the formula, A B,i and A S It is a diagonal matrix, where the elements on the diagonal correspond to the position of the low-orbit satellite or any ground base station, and the elements at other positions are 0. Using semi-positive definite relaxation and rate approximation, the optimization problem is rewritten as: In the formula, Represents a variable collection τ is the iteration index, the matrix is the autocorrelation matrix of the channel vector derived based on the channel angle error.

6. The method for robust precoding of massive MIMO low-orbit satellite-ground collaboration according to claim 1, characterized in that: The massive MIMO low-orbit satellite transmission angle error model is expressed as: In the formula, and represents the estimated value of the transmission angle of the low-orbit satellite to the jth user, and the angle estimation error and is introduced as a random variable, and represents the common angle deviation of all users caused by satellite attitude jitter, which can be ignored; for the jth user, its angle error and Follows uniform distribution.

7. The method for robust precoding for low-orbit satellite-ground collaboration of massive MIMO according to claim 6, characterized in that: The channel h of the jth user j The structure is: Front M t The elements are generated by the satellite downlink channel, and then every N t Elements are generated by the base station downlink channel; M t is the number of antennas of the LEO satellite, N t is the number of antennas of each ground base station; the matrix H j The (m,n)th element of is represented as: In the formula, g j is the downlink channel gain from the low-orbit satellite to the jth user on the ground, v j is the satellite’s antenna array response vector, As the label of the current base station, Indicates the i m 、i n The downlink channel of a base station to the jth user.

8. The method for robust precoding for low-orbit satellite-ground collaboration of massive MIMO according to claim 7, characterized in that: When m≤M t ,n≤M t , the channel autocorrelation matrix The results are as follows: In the formula, M1 and M2 are the number of antennas in the x and y directions of the satellite respectively.

9. The method for robust precoding for low-orbit satellite-ground collaboration of massive MIMO according to claim 7, characterized in that: When m≤M t ,n>M t When the channel autocorrelation matrix The result is: In the formula, γ m Yes j The mean of B1 and B2 are: M1 and M2 are the number of antennas in the x and y directions of the satellite respectively.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the massive MIMO low-orbit satellite-to-ground collaborative robust precoding method are implemented according to any one of claims 1 to 9.

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