A multi-gateway precoding method in a multi-beam satellite system

Abstract

The application discloses a multi-gateway precoding method in a multi-beam satellite system, comprising the following steps: constructing a user side receiving signal model; establishing an optimization problem with total transmission power as a constraint and weighted sum rate maximization as an objective; establishing an optimization problem with total transmission power as a constraint and MSE minimization as an objective; establishing equivalence between the weighted sum rate maximization problem and the matrix weighted sum MSE minimization problem in the sense of the same global optimal solution, and integrating the constraint condition into the weighted sum MSE minimization objective to transform into an unconstrained weighted sum MSE minimization problem; solving the unconstrained weighted sum MSE minimization problem, fixing the solution precoding matrix and the weight matrix, updating the precoding matrix to minimize the MSE cost function, and cyclically iterating to update the three matrices until the system sum rate performance converges, and scaling the precoding matrix to meet the power limit. The method can effectively improve the system sum rate of the multi-beam satellite system.

Description

Technical Field

[0001] This invention belongs to the field of multi-beam satellite technology, specifically relating to a multi-gateway precoding method in a multi-beam satellite system. Background Technology

[0002] Multi-beam satellites utilize multiple point beams to achieve coverage of the entire service area, effectively increasing satellite system throughput through frequency reuse. However, this technology also faces severe co-channel interference problems. Precoding technology is a key technique that can effectively suppress inter-beam interference in multi-beam satellite systems. The satellite transmitter performs preprocessing operations before signal transmission based on pre-obtained CSI (Channel State Information) to overcome inter-beam interference; however, when the number of beams is large, the feeder link cannot support all beam signals.

[0003] Therefore, when the number of beams is huge, how to improve the speed of multi-beam satellite systems has become an urgent problem to be solved. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention provides a multi-gateway precoding method for multi-beam satellite systems. A multi-gateway precoding method for a multi-beam satellite system, the multi-gateway precoding method comprising: Construct a received signal model on the user side; An estimated signal is obtained based on the received signal model, wherein the estimated signal is obtained from the precoding matrix and the deprecoding matrix; Based on the precoding matrix, a first optimization problem is established with the total transmit power as a constraint and the weighted sum rate as the objective. Based on the precoding matrix and the deprecoding matrix, a second optimization problem is established with the total transmit power as a constraint and the MSE as the objective. Let the global optimal solutions of the first optimization problem and the second optimization problem be the same, establish the equivalence between the weighted sum rate maximization problem and the matrix weighted sum MSE minimization problem, and integrate the constraints into the MSE minimization objective to transform it into an unconstrained weighted sum MSE minimization problem; Update the weight matrix and the deprecoding matrix, and fix the weight matrix and the deprecoding matrix to update the precoding matrix according to the unconstrained weighted sum and MSE minimization problem until a preset condition is met to complete the precoding of the multi-gateway system.

[0005] Optionally, the received signal model is represented as:

[0006] in, For the first The first beam cluster i Users in each beam The received signal, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, , User The number of receiving antennas, for 3D complex matrix For the first One gateway is used to transmit signals. Send to user The precoding matrix, , To send to user The number of symbols, For the first A gateway is used to transmit signals. Send to user The precoding matrix, , To send to user The number of symbols, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, , For the first One gateway is used to transmit signals. Send to user The precoding matrix, To obey Distributed additive white Gaussian noise, It follows a complex normal distribution. For users The average noise variance at that location, For the set of all users, , The total number of gateways. For the first The total number of beams in a beam cluster For the first The total number of beams in a beam cluster It can be any value.

[0007] Optionally, the estimated signal is represented as:

[0008] in, For signal The estimated signal, For the first One gateway is used to transmit signals. Send to user The solution precoding matrix, This is the conjugate transpose of the matrix.

[0009] Optionally, the first optimization problem can be expressed as:

[0010] in, To find the optimal precoding matrix that maximizes the objective function, For users The weight, For users rate, , The base-2 logarithm of the absolute value of a determinant. As constraints, For trace operation, For the first k Each gateway manages the total transmit power of the feed.

[0011] Optionally, the second optimization problem can be expressed as:

[0012]

[0013] in, To find the optimal solution precoding matrix and precoding matrix that minimize the objective function, For trace operation, As constraints, For the first k Each gateway manages the total transmit power of the feed source. For the equivalent of, This is the expected operation.

[0014] Optionally, after establishing a second optimization problem with total transmit power as a constraint and MSE as the objective, the following steps are also included: By fixing all precoding matrices and minimizing the sum of MSE, the MMSE deprecoding matrix is ​​obtained, which is expressed as:

[0015] in, For the first One gateway is used to transmit signals. Send to user The MMSE deprecoding matrix, ; The MMSE matrix is ​​obtained from the MMSE decoding precoding matrix, and the MMSE matrix is ​​represented as follows:

[0016] in, For the first The minimum mean square error matrix of the received signals for each user.

[0017] Optionally, establish the equivalence between the weighted sum rate maximization problem and the matrix-weighted sum MSE minimization problem, and integrate the constraints into the MSE minimization objective to transform it into an unconstrained weighted sum MSE minimization problem, including: The matrix weighted sum MSE minimization problem is obtained, which is expressed as:

[0018] in, To find the optimal weight matrix, solution precoding matrix, and precoding matrix that minimize the objective function, For users The weight, For the first The weight matrix of each receiver. ; test The first-order optimality condition yields the optimal... ,in, , The optimal ; The matrix weighted sum MSE minimization problem and Replace with and This makes the matrix-weighted sum MSE minimization problem equivalent to a weighted sum rate maximization problem, thus integrating power constraints into the matrix-weighted sum MSE minimization problem and transforming it into an unconstrained weighted sum MSE minimization problem. The weighted sum rate maximization problem is expressed as:

[0019] in, To find the optimal precoding matrix that maximizes the objective function.

[0020] Optionally, the unconstrained weighted sum MSE minimization problem is expressed as:

[0021] in, To find the optimal weight matrix, solution precoding matrix, and precoding matrix that minimize the objective function, .

[0022] Optionally, updating the weight matrix and the deprecoding matrix, and fixing the weight matrix and the deprecoding matrix, to update the precoding matrix according to the unconstrained weighted sum MSE minimization problem, includes: The weight matrix is ​​updated using a closed-form approach; The deprecoding matrix is ​​updated, and the update formula for the deprecoding matrix is ​​expressed as follows:

[0023] in, For the updated solution precoding matrix, ; The updated weight matrix and the updated deprecoding matrix are fixed, and the precoding matrix is ​​updated according to the unconstrained weighted sum MSE minimization problem.

[0024] Optionally, the update formula for the precoding matrix is:

[0025] in, For the updated precoding matrix, For the first User priority For the first The user's deprecation precoding matrix, For the first User weight matrix For the first k The gateway to the first The user's channel matrix.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows: The multi-gateway precoding method provided by this invention first constructs a user-side received signal model. Then, it establishes two optimization problems: one with total transmit power as a constraint and aiming to maximize the weighted sum rate, and the other with total transmit power as a constraint and aiming to minimize the mean squared error (MSE). Since the global optimal solutions to both problems are identical, the equivalence between the weighted sum rate maximization problem and the matrix-weighted sum MSE minimization problem is established. The constraints are integrated into the MSE minimization objective, transforming it into an unconstrained weighted sum MSE minimization problem. Finally, the block coordinate descent method is used to solve the objective function. By fixing the solution precoding matrix and weight matrix, the precoding matrix is ​​updated to minimize the weighted sum MSE objective function. Using this method, the rate of multi-beam satellite systems can be effectively improved.

[0027] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating a multi-gateway precoding method in a multi-beam satellite system provided by an embodiment of the present invention. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0030] Example 1 Please see Figure 1 , Figure 1 This is a flowchart illustrating a multi-gateway precoding method in a multi-beam satellite system according to an embodiment of the present invention. The present invention provides a multi-gateway precoding method in a multi-beam satellite system, the multi-gateway precoding method comprising: Step 1: Construct the received signal model on the user side.

[0031] Specifically, consider One gateway, among which gateway ( Gateway On the management satellite root transmitting antenna and for the first Provide services to users within a beam cluster. Assuming time-division multiplexing, each beam in the same time slot provides service to only one user within the beam area, define... It is the first The first beam cluster i Users in each beam User The number of receiving antennas is defined. It is the set of all users, that is:

[0032] in, The total number of gateways. For the first The total number of beams in a beam cluster.

[0033] make Indicates the first One gateway is used to transmit signals. Send to user The precoding matrix, i.e.:

[0034] in, For the first k Each gateway sends a pair to the user The vector after precoding the signal To send to user The signal , , It is a complex matrix. For the first The total number of transmitting antennas on satellites managed by each gateway. To send to user The number of symbols.

[0035] Assumption , For the expected operation, This is the conjugate transpose of the matrix. Due to satellite transmission power limitations, the following must be satisfied:

[0036] in, For trace operation, The total transmit power of the feed managed by the k-th gateway.

[0037] Assuming full-frequency multiplexing between beams, the user-side received signal model is represented as follows:

[0038] in, For the first The first beam cluster i Users in each beam The received signal, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, , For the first One gateway is used to transmit signals. Send to user The precoding matrix, To send to user The signal , To send to user The number of symbols, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, , For the first j The total number of transmitting antennas on satellites managed by each gateway. For the first One gateway is used to transmit signals. Send to user The precoding matrix, To send to user The signal is defined. It is the first The first beam cluster l Users in each beam To obey Distributed additive white Gaussian noise, It follows a complex normal distribution. For users The average noise variance at that location, For users The number of receiving antennas, , For the first The total number of beams in a beam cluster It can be any value.

[0039] The interference experienced by each user during signal transmission comes not only from other user signals within the same cluster, but also from interference generated by user signals within other clusters.

[0040] Step 2: Obtain the estimated signal based on the received signal model, wherein the estimated signal is obtained from the precoding matrix and the deprecoding matrix.

[0041] Specifically, we assume that the signals from different users are independent of each other and unrelated to receiver noise. Treating interference as noise and considering a linear decoding strategy, the estimated signal is thus expressed as:

[0042] in, For signal The estimated signal, For the first One gateway is used to transmit signals. Send to user The solution precoding matrix.

[0043] Step 3: Based on the precoding matrix, establish the first optimization problem with the total transmit power as a constraint and the weighted sum rate as the objective.

[0044] Here, the first optimization problem is expressed as:

[0045] in, To solve for the optimal precoding matrix To maximize the objective function For users The weight of the user in the system Priority level, For users rate, , The base-2 logarithm of the absolute value of a determinant. As constraints, For trace operation, For the first k Each gateway manages the total transmit power of the feed.

[0046] Step 4: Based on the precoding matrix and the deprecoding matrix, establish a second optimization problem with the total transmit power as a constraint and the MSE (mean square error) as the objective.

[0047] Specifically, in and Under the independence assumption, the MSE matrix It can be written as:

[0048] in, For users The mean square error matrix of the received and transmitted symbols after de-precoding. For the equivalent of, To Seeking expectations.

[0049] The second optimization problem is expressed as:

[0050] in, To find the optimal solution, the precoding matrix and the precoding matrix ( Minimize the objective function.

[0051] Step 5: Obtain the MMSE decoding precoding matrix and the MMSE matrix.

[0052] Step 5.1: Fix all precoding matrices and minimize the sum of MSE to obtain the MMSE deprecoding matrix. The MMSE deprecoding matrix is ​​expressed as:

[0053] in, For the first One gateway is used to transmit signals. Send to user The MMSE deprecoding matrix, , is the covariance matrix of the total received signal at the user's location.

[0054] Step 5.2: Obtain the MMSE matrix from the MMSE decoding precoding matrix. The MMSE matrix is ​​represented as:

[0055] in, For the first The minimum mean square error matrix of the received signals for each user.

[0056] Step 6: Make the global optimal solutions of the first optimization problem and the second optimization problem the same, establish the equivalence between the weighted sum rate maximization problem and the matrix weighted sum MSE minimization problem, and integrate the constraints into the MSE minimization objective to transform it into an unconstrained weighted sum MSE minimization problem.

[0057] Step 6.1: Obtain the matrix weighted sum MSE minimization problem, which is expressed as:

[0058] in, To solve for the optimal weight matrix, solution precoding matrix, and precoding matrix ( To minimize the objective function, For the first The weight matrix of each receiver. .

[0059] Step 6.2, Inspection The first-order optimality condition yields the optimal... .

[0060] Specifically, minimizing the optimal solution to the above problem It can be obtained from the MMSE decoding precoding matrix. Furthermore, with other variables fixed, the objective function relative to... It is convex, therefore, by inspection The first-order optimality condition is obtained. , The optimal .

[0061] Step 6.3: Minimize the weighted sum of matrices in the MSE problem. and Replace with and This makes the matrix-weighted sum MSE minimization problem equivalent to the weighted sum rate maximization problem, thus integrating the power constraint into the matrix-weighted sum MSE minimization problem and transforming it into an unconstrained weighted sum MSE minimization problem.

[0062] Specifically, in the matrix weighted sum and MSE minimization problem and Replace with and For all The following are equivalent optimization problems:

[0063] in, To solve for the optimal precoding matrix This maximizes the objective function.

[0064] definition Expanding the weighted sum rate maximization problem, we obtain the expanded weighted sum rate maximization problem, which is expressed as: .

[0065] In the global optimal solution In the same sense, it is equivalent to a weighted sum rate maximization problem. Integrating the power constraint into the matrix-weighted sum MSE minimization problem transforms it into an unconstrained weighted sum MSE minimization problem.

[0066] Here, the unconstrained weighted sum MSE minimization problem is expressed as:

[0067] in, To solve for the optimal weight matrix, solution precoding matrix, and precoding matrix ( To minimize the objective function, .

[0068] Step 7: Update the weight matrix and the deprecoding matrix, and fix the weight matrix and the deprecoding matrix to update the precoding matrix according to the unconstrained weighting and MSE minimization problem until the preset conditions are met, thus completing the precoding of the multi-gateway system.

[0069] Specifically, the block coordinate descent method is used to solve the unconstrained weighted summation and MSE minimization problem. By fixing the solution precoding matrix and weight matrix, the precoding matrix is ​​updated to minimize the MSE cost function. The three variables are updated iteratively until the preset conditions are met (i.e., the system and rate performance converge). The precoding matrix is ​​then scaled to meet the power constraint.

[0070] In other words, each optimization variable Since all variables are convex, the block coordinate descent method is used to solve for the objective function. Specifically, the weighted sum MSE objective function is minimized by fixing two of the three variables in sequence and updating the third.

[0071] Step 7.1: Initialize the weight matrix and decompose the precoding matrix into a zero matrix. The precoding matrix is ​​initialized using the ZF method and calculated. :

[0072] Calculate the power scaling factor Multiply by the precoding matrix This is the initialized precoding matrix.

[0073] Step 7.2: Update the optimal weight matrix using a closed-form formula. The update formula for the weight matrix is ​​as follows: , This is the updated weight matrix, which is also the optimal weight matrix.

[0074] Step 7.3: Update the deprecoding matrix. The update formula for the deprecoding matrix is ​​expressed as:

[0075] in, The updated MMSE deprecoding matrix, i.e., the updated deprecoding matrix, When the calculation begins, here All are initialized precoding matrices.

[0076] Step 7.4: Fix the updated weight matrix and the updated deprecoding matrix, and update the precoding matrix according to the unconstrained weighted summation and MSE minimization problem.

[0077] Specifically, after fixing the updated deprecoding matrix and the updated sum weight matrix, relative to The first-order optimality condition yields the updated precoding matrix, and the update formula for the precoding matrix is:

[0078] in, For the updated precoding matrix, For the first Priority for individual users For the first The solution precoding matrix for each user For the first Weight matrix of each user For the first k The gateway to the first Channel matrix for each user.

[0079] Step 7.5: Repeat steps 7.2-7.5 to determine whether the preset conditions have been met. If so (i.e., when the sum rate performance of the system converges), then scale the precoding matrix to meet the power constraint. If not, then iteratively update the precoding matrix, weight matrix, and precoding matrix using the above formula based on the updated deprecoding matrix, updated weight matrix, and updated precoding matrix until the preset conditions are met.

[0080] Here, the preset condition is that the sum rate of the next iteration minus the sum rate of the previous iteration is less than or equal to a preset value. The preset condition is expressed as:

[0081] in, This is the current updated weight matrix. This is the weight matrix after the last update. This is a preset value, for example, a value of 10. -3 .

[0082] Here, the specific operation of scaling the precoding matrix is: calculating the power scaling factor. Multiply the power scaling factor with the updated precoding matrix. To meet power constraints, precoding of multiple gateways is completed.

[0083] The multi-gateway precoding method provided by this invention first constructs a user-side received signal model. Then, it establishes two optimization problems: one with total transmit power as a constraint and aiming to maximize the weighted sum rate, and the other with total transmit power as a constraint and aiming to minimize the mean squared error (MSE). Since the global optimal solutions to both problems are identical, the equivalence between the weighted sum rate maximization problem and the matrix-weighted sum MSE minimization problem is established. The constraints are integrated into the MSE minimization objective, transforming it into an unconstrained weighted sum MSE minimization problem. Finally, the block coordinate descent method is used to solve the objective function. By fixing the solution precoding matrix and weight matrix, the precoding matrix is ​​updated to minimize the weighted sum MSE objective function. Using this method, the rate of multi-beam satellite systems can be effectively improved.

[0084] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0085] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0086] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0087] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A multi-gateway precoding method in a multi-beam satellite system, characterized in that, Multiple gateway precoding methods include: Construct a received signal model on the user side; An estimated signal is obtained based on the received signal model, wherein the estimated signal is obtained from the precoding matrix and the deprecoding matrix; Based on the precoding matrix, a first optimization problem is established with the total transmit power as a constraint and the weighted sum rate as the objective. Based on the precoding matrix and the deprecoding matrix, a second optimization problem is established with the total transmit power as a constraint and the MSE as the objective. Let the global optimal solutions of the first optimization problem and the second optimization problem be the same, establish the equivalence between the weighted sum rate maximization problem and the matrix weighted sum MSE minimization problem, and integrate the constraints into the MSE minimization objective to transform it into an unconstrained weighted sum MSE minimization problem; The weight matrix and the deprecoding matrix are updated, and the weight matrix and the deprecoding matrix are fixed. The precoding matrix is ​​then updated according to the unconstrained weighted sum MSE minimization problem until a preset condition is met, thus completing the precoding of the multi-gateway system. The unconstrained weighted sum MSE minimization problem is expressed as: in, To find the optimal weight matrix, solution precoding matrix, and precoding matrix that minimize the objective function, The total number of gateways. For the first The total number of beams in a beam cluster; For users The weight, For trace operation, For the first The weight matrix of each receiver. ; The base-2 logarithm of the absolute value of a determinant. ， in, For users The mean square error matrix of the received and transmitted symbols after de-precoding. For the equivalent of, For the set of all users, For the first One gateway is used to transmit signals. Send to user The solution precoding matrix, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, For the first One gateway is used to transmit signals. Send to user The precoding matrix, This is the conjugate transpose of the matrix; For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, For the first One gateway is used to transmit signals. Send to user The precoding matrix, For the first k Each gateway manages the total transmit power of the feed.

2. The multi-gateway precoding method according to claim 1, characterized in that, The received signal model is represented as follows: in, For the first The first beam cluster i Users in each beam The received signal, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, , User The number of receiving antennas, for 3D complex matrix For the first One gateway is used to transmit signals. Send to user The precoding matrix, , To send to user The number of symbols, For the first One gateway is used to transmit signals. Send to user The precoding matrix, , To send to user The number of symbols, For from the first On satellites managed by a gateway root transmitting antenna to user The channel matrix, , For the first One gateway is used to transmit signals. Send to user The precoding matrix, To obey Distributed additive white Gaussian noise, It follows a complex normal distribution. For users The average noise variance at that location, For the set of all users, , The total number of gateways. For the first The total number of beams in a beam cluster For the first The total number of beams in a beam cluster It can be any value.

3. The multi-gateway precoding method according to claim 2, characterized in that, The estimated signal is represented as: in, For signal The estimated signal, For the first One gateway is used to transmit signals. Send to user The solution precoding matrix, This is the conjugate transpose of the matrix.

4. The multi-gateway precoding method according to claim 2, characterized in that, The first optimization problem is expressed as: in, To find the optimal precoding matrix that maximizes the objective function, For users The weight, For users rate, , The base-2 logarithm of the absolute value of a determinant. As constraints, For trace operation, For the first k Each gateway manages the total transmit power of the feed.

5. The multi-gateway precoding method according to claim 3, characterized in that, The second optimization problem is expressed as: in, To find the optimal solution precoding matrix and precoding matrix that minimize the objective function, For trace operation, As constraints, For the first k Each gateway manages the total transmit power of the feed source. For the equivalent of, This is the expected operation.

6. The multi-gateway precoding method according to claim 5, characterized in that, After establishing the second optimization problem with total transmit power as the constraint and MSE as the objective, it also includes: By fixing all precoding matrices and minimizing the sum of MSE, the MMSE deprecoding matrix is ​​obtained, which is expressed as: in, For the first One gateway is used to transmit signals. Send to user The MMSE deprecoding matrix, ; The MMSE matrix is ​​obtained from the MMSE decoding precoding matrix, and the MMSE matrix is ​​represented as follows: in, For the first The minimum mean square error matrix of the received signals for each user.

7. The multi-gateway precoding method according to claim 6, characterized in that, Establish the equivalence between the weighted sum rate maximization problem and the matrix-weighted sum MSE minimization problem, and integrate the constraints into the MSE minimization objective to transform it into an unconstrained weighted sum MSE minimization problem, including: Obtain the matrix weighted sum MSE minimization problem, which is expressed as: in, To find the optimal weight matrix, solution precoding matrix, and precoding matrix that minimize the objective function, For users The weight, For the first The weight matrix of each receiver. ; test The first-order optimality condition yields the optimal... ,in, , For optimal ; The problem of minimizing the weighted sum of the matrices in the MSE and Replace with and This makes the matrix-weighted sum MSE minimization problem equivalent to a weighted sum rate maximization problem, thus integrating the power constraint into the matrix-weighted sum MSE minimization problem and transforming it into an unconstrained weighted sum MSE minimization problem, which is expressed as: in, To find the optimal precoding matrix that maximizes the objective function.

8. The multi-gateway precoding method according to claim 7, characterized in that, Updating the weight matrix and the solution precoding matrix, and fixing the weight matrix and the solution precoding matrix, to update the precoding matrix according to the unconstrained weighted sum MSE minimization problem, includes: The weight matrix is ​​updated using a closed-form approach; The deprecoding matrix is ​​updated, and the update formula for the deprecoding matrix is ​​expressed as follows: in, For the updated solution precoding matrix, ; The updated weight matrix and the updated deprecoding matrix are fixed, and the precoding matrix is ​​updated according to the unconstrained weighted sum MSE minimization problem.

9. The multi-gateway precoding method according to claim 8, characterized in that, The update formula for the precoding matrix is: in, For the updated precoding matrix, For the first User priority For the first The user's deprecation precoding matrix, For the first User weight matrix For the first k The gateway to the first The user's channel matrix.

Images