Depth expansion large-scale MIMO LEO satellite precoding method based on GNN

Abstract

The invention relates to the technical field of low earth orbit (LEO) satellite communication, in particular to a deep expansion large-scale MIMO LEO satellite precoding method based on a graph neural network (GNN). The method comprises the following steps: firstly, constructing a power-limited energy efficiency maximization precoding problem of large-scale MIMO LEO satellite communication; secondly, converting an original problem into a series of iterative solution sub-problems through a Dinkelbach algorithm, and converting the sub-problems into convex problems by using a weighted minimum mean square error (WMMSE) method to obtain an iterative update expression of a user precoding vector; the GNN is constructed for the complex matrix inversion in the user precoding vector updating process to perform depth expansion, and the Taylor expansion is applied to approach the matrix inversion operation in the GNN framework, so that the calculation efficiency is further improved. According to the method, higher energy efficiency of the system can be realized, the complexity of solving the optimization problem is remarkably reduced, and the operation speed is increased.

Description

Technical Field

[0001] The present invention relates to the field of satellite communication technology, and in particular to precoding technology in massive multiple-input multiple-output (MIMO) low earth orbit (LEO) satellite communications. Background Art

[0002] The rapid growth of data traffic, driven by the increasing popularity of smart devices, highlights the need to evolve communication networks toward the sixth generation (6G) technology. However, the limitations of traditional terrestrial networks, such as unevenly distributed infrastructure and unstable wireless environment, hinder their ability to handle the growing data demand. 6G is envisioned as a fully interconnected and autonomous network that provides seamless coverage and ubiquitous services by integrating terrestrial networks with satellite systems. Positioned at altitudes between 500 km and 2000 km, LEO satellites have received significant attention due to their advantages over geostationary orbit (GEO) satellites, such as reduced round-trip delay, lower path loss, and lower launch costs. Despite advances, optimizing LEO satellite systems remains a challenging task. Traditional approaches often lack real-time adaptability and computational efficiency, especially for improving energy efficiency (EE) under power constraints. Artificial intelligence (AI) offers promising solutions to optimize precoding techniques in real time and enhance system adaptability. Machine learning, especially deep learning, can predict interference, optimize power allocation, and manage satellite resources. These AI-driven approaches have the potential to reduce computational load, improve network performance, and enhance EE, coverage, and bandwidth utilization to meet the needs of future communication technologies. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a GNN-based deep expansion massive MIMO LEO satellite precoding method, which can optimize the energy efficiency of the system for the downlink communication scenario of the massive MIMO LEO satellite communication system, and reduce the complexity of implementing this optimization process, making it easy to implement.

[0004] Technical solution: In order to achieve the above purpose, the present invention adopts the following technical solution:

[0005] In a first aspect, the present invention provides a deep unfolding massive MIMO LEO satellite precoding method based on GNN, comprising the following steps:

[0006] Constructing the power-limited energy-efficiency maximization precoding problem for massive MIMO LEO satellite communications;

[0007] The original problem is transformed into a series of iterative sub-problems by using the Dinkelbach algorithm, and the sub-problems are transformed into a convex problem by using the weighted minimum mean square error (WMMSE) method, and the update expressions of the user precoding vector and the auxiliary variables introduced to represent the user receiving matrix and the weight matrix are obtained; the update process of the user precoding vector involves the matrix inversion problem;

[0008] For the N in the user precoding vector update process t ×N t The complex matrix of is inverted to construct the graph neural network GNN for deep expansion, where N t is the number of satellite antennas; each antenna on the satellite is defined as a vertex, and the connection between antenna vertices is defined as an edge. The hidden representation of each edge is updated by aggregating the information of adjacent vertices connected by the edge; at the same time, based on the result of Taylor expansion approximate matrix inversion, a one-dimensional feature vector of the edge feature is added;

[0009] The precoding result is obtained by normalizing the precoding vector obtained by combining Dinkelbach, WMMSE and GNN.

[0010] Furthermore, during the nth iteration, the weight matrix u of the kth user is k , receiving matrix ω k and the precoding vector b k The update expression is as follows:

[0011]

[0012] where γ k represents the average channel gain of the kth user, v k represents the array response vector between the satellite and the kth user, N0 represents the noise variance, K represents the number of users, (·) H represents the conjugate transpose of a matrix, |·| represents the modulus of a complex number, (·) * represents the conjugate of a complex number, B w represents the system bandwidth, ρ represents the auxiliary variable at the nth iteration, 1 / ξ represents the efficiency of the transmit power amplifier, a opt represents the optimal Lagrange multiplier, and I represents the identity matrix.

[0013] Furthermore, let the precoding vector b of the kth user be k Update the N that needs to be inverted in the expression t =N t The complex matrix is ​​M k , use GNN to calculate the matrix M k Inverse, in the lth layer of GNN, connect the vth iAntenna vertex and v j The edge of the antenna vertex (v i ,v j ) for:

[0014]

[0015] Where σ(·) represents the activation function, P s (·) and P d (·) represents the pooling function, They represent the edges in layer l-1 (v i ,v j )、(i,v j )、(v i ,j)’s hidden representation, c=[c0,c1] T s=[s0,s1] T and d = [d0, d1] T is a trainable parameter, Respectively represent M k Multiply it by the value of the corresponding index position of the matrix concatenated from all (l-1) layers of edge features.

[0016] Furthermore, the output precoding vector is normalized by the following formula:

[0017]

[0018] where b k represents the precoding vector of the kth user, P max represents the transmission power budget, K represents the number of users, and b represents the power budget of k The matrix is ​​composed of ‖·‖, ‖·‖ represents the Frobenius norm of the matrix, ‖·‖2 represents the 2-norm of the vector, and Π{·} represents the normalization processing of the precoding vector.

[0019] Furthermore, the loss function of the GNN network used for matrix inversion is the upper bound of the system energy efficiency.

[0020] In a second aspect, the present invention provides a deep unfolding massive MIMO LEO satellite precoding system based on GNN, comprising:

[0021] The problem construction and transformation module is used to construct the power-limited energy-efficiency maximization precoding problem of massive MIMO LEO satellite communications; and to transform the original problem into a series of iterative sub-problems through the Dinkelbach algorithm, and to transform the sub-problems into a convex problem using the weighted minimum mean square error (WMMSE) method, and obtain the update expression of the user precoding vector and the auxiliary variables introduced to represent the user receiving matrix and the weight matrix; the user precoding vector update process involves the matrix inversion problem;

[0022] The deep expansion and solution module is used to update the N t ×N t The complex matrix of is inverted to construct the graph neural network GNN for deep expansion, where N t is the number of satellite antennas; each antenna on the satellite is defined as a vertex, and the connection between antenna vertices is defined as an edge. The hidden representation of each edge is updated by aggregating the information of adjacent vertices connected by the edge; at the same time, based on the result of Taylor expansion approximate matrix inversion, the one-dimensional feature vector of the edge feature is added; and the precoding result is obtained by normalizing the precoding vector obtained by combining Dinkelbach, WMMSE and GNN.

[0023] In a third aspect, the present invention provides a computer system comprising a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein the computer program / instruction, when executed by the processor, implements the steps of the GNN-based deep expansion massive MIMO LEO satellite precoding method.

[0024] In a fourth aspect, the present invention provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the GNN-based deep expansion massive MIMO LEO satellite precoding method.

[0025] Beneficial effects: The present invention utilizes Dinkelbach and WMMSE iterations to solve the energy efficiency maximization precoding problem, and then uses a graph neural network to deeply expand the matrix inversion process therein, which can achieve higher energy efficiency of the system, significantly reduce the complexity of solving the optimization problem, and speed up the calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0027] Figure 2 Schematic diagram of the update process of specific parameters in an embodiment of the present invention;

[0028] Figure 3Schematic diagram of a specific update process of GNN in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] like Figure 1 As shown, the deep expansion massive MIMO LEO satellite precoding method based on GNN disclosed in the embodiment of the present invention is used for low-orbit satellites to provide communication services for multiple single-antenna users. First, a power-limited energy efficiency maximization precoding problem is constructed, and then the original problem is converted into multiple sub-problems through the Dinkelbach algorithm. Then, the WMMSE method is used to convert these sub-problems into convex problems for solution. However, the matrix inversion problem is involved in the process of solving the precoding vector. Since the complexity of calculating the matrix inversion is extremely high, it is considered to introduce GNN for deep expansion. In addition, since Taylor expansion can approximate the matrix inversion, the one-dimensional feature vector that can increase the edge feature is derived, so as to more accurately approximate the inverse of the matrix, thereby reducing the complexity and obtaining a more ideal performance. Specifically, after the WMMSE method converts the sub-problem into a convex problem, the update expression of the user precoding vector and the auxiliary variables introduced to represent the user receiving matrix and the weight matrix can be obtained; wherein the matrix inversion problem is involved in the process of updating the user precoding vector; for N in the process of updating the user precoding vector t ×N t The complex matrix of is inverted to construct the graph neural network GNN for deep expansion, where N t is the number of satellite antennas; each antenna on the satellite is defined as a vertex, and the connection between antenna vertices is defined as an edge. The hidden representation of each edge is updated by aggregating the information of adjacent vertices connected by the edge; at the same time, based on the result of Taylor expansion approximate matrix inversion, the one-dimensional feature vector of the edge feature is added; finally, the precoding vector obtained by combining Dinkelbach, WMMSE and GNN is normalized to obtain the precoding result.

[0031] The method of this embodiment is described in more detail below with reference to a specific scenario.

[0032] Part 1: Building a target massive MIMO LEO satellite communication energy efficiency optimization model

[0033] Specifically, consider a downlink communication system involving a low-orbit satellite and K user terminals (UTs), each equipped with a single antenna. Mounted on the satellite is a large uniform planar array (UPA) consisting of elements arranged at half-wavelength intervals along the x-axis and y-axis. This configuration includes unit and along the y-axis Unit. The total number of antennas on the satellite is expressed as Set the number of user paths of the kth UT to L k At time t, the frequency response of the complex baseband channel at frequency f can be expressed as:

[0034]

[0035] in and represent the channel gain, Doppler shift, propagation delay and array response vector, respectively. v k,l It is mainly determined by the Doppler frequency shift caused by satellite movement and UT, and can be expressed as in and are the Doppler shifts caused by the motion of the LEO satellite and the UT, respectively. Considering the relatively high altitude of the LEO satellite, it is reasonable to assume that the Doppler shift caused by the satellite motion under different propagation paths l for the same UT is These Doppler shifts vary from one UT to another, especially In addition, due to the relatively long distance between the LEO satellite and the UT, the propagation delay τ corresponding to the kth UT path l k,l It is much larger than the terrestrial wireless channel. The propagation delay is expressed as in represents the shortest delay among all k-th propagation paths, represents the delay caused by the lth path of the kth UT. For satellite communication channels, since the satellite is at a high altitude relative to the scatterers near the UT, it can be assumed that all propagation paths related to the same UT have the same angle, and the array response vector can be rewritten as v k,l =v k . Therefore, the channel response can be converted to:

[0036]

[0037] where g k (t,f) is the channel gain of the kth UT, that is:

[0038]

[0039] The signal received by the kth UT can be expressed as:

[0040]

[0041] In the formula Indicates that The shorthand expression of n k represents the complex Gaussian additive white noise at the kth UT, with mean 0 and variance N0. It is assumed that the noise variance of all UTs is equal. represents the precoding vector of the kth UT. The signal transmitted from the satellite to the kth UT is s k , its power spectrum is set to 1, that is

[0042] Considering the total power consumption of the transmitter of the low-orbit satellite communication system, it can be modeled as:

[0043]

[0044] where 1 / ξ and P t They represent the efficiency of the transmit power amplifier and the power consumed by the transmitter on the satellite. For a fully digital transmitter on a low-orbit satellite, the total power consumption can be expressed as:

[0045] P t =N t P RFC +P LO +P BB

[0046] Where P BB is the power consumed by the baseband digital precoder, P LO is the power consumed by the local oscillator. RFC =P DAC +P mixer +P LPF +P BBA , where P DAC , P mixer , P LPF and P BBA They represent the power used by the digital-to-analog converter, mixer, low-pass filter, and baseband amplifier respectively.

[0047] Part II: Problem Formulation and Precoding Design

[0048] Step S1: Establish EE optimization problem:

[0049] Based on the received signal, the signal-to-noise ratio (SINR) of the kth UT in downlink transmission can be defined as:

[0050]

[0051] The average data rate of the kth UT at the transmitter is given by Given, the average rate achievable for:

[0052]

[0053] Average rate The lack of clear analytical expressions often makes it difficult to optimize. Monte Carlo methods can be used to estimate the required values; however, they have a high computational complexity. Replace with an upper bound, such as:

[0054]

[0055] where g k It is for g k A shorthand representation of (t,f).

[0056] In order to maximize the total achievable system EE of digital precoding in low-orbit satellite communication systems, the following maximization problem can be formulated:

[0057]

[0058] Step S2, solving the EE maximization precoding problem:

[0059] By using the Dinkelbach algorithm, we solve the problem iteratively through a series of subproblems These subproblems converge to the solution of the original problem. After that, n is assigned as the index and ρ is n is represented as an auxiliary variable during the nth iteration. Then, the nth subproblem can be expressed as:

[0060]

[0061] variable and ρ n In the sub-problem More specifically, for a given Subsequent sub-questions The values ​​are:

[0062]

[0063] Considering that the process is the same for each sub-problem, the index n is omitted. The weighted minimum mean square error (WMMSE) problem is equivalent to The maximization problem in are the same. Then the problem can be transformed into:

[0064]

[0065] where ω k and u k is an auxiliary variable, ω k represents the receiving matrix of user k, u k represents the weight matrix of user k, e k It is expressed as:

[0066]

[0067] question The three variables are closely interdependent. BCD can be used to solve the problem In this approach, two of the three variables are fixed while the remaining one is updated. k and u k The expression is:

[0068]

[0069] ω k and u k If the value remains unchanged, it can be ignored by k Irrelevant terms to simplify the problem The resulting simplified problem is a convex quadratic optimization problem that can be solved directly using standard convex optimization algorithms. Specifically, the third variable can be updated by fixing two of the three variables. k 、u k and b k The update expression is as follows:

[0070]

[0071]

[0072] where a opt It represents the optimal Lagrange multiplier. By introducing the Lagrange multiplier, the constraints are integrated into the objective function, turning it into an unconstrained optimization problem.

[0073] Figure 2 The whole process of WMMSE algorithm is shown

[0074]

[0075] Among them U e , W l and B l It is a simplified expression of the above formula.

[0076] The inverse of a matrix has very high complexity and it is necessary to examine alternative methods with lower complexity. Then we can get:

[0077]

[0078] Step S3: Use GNN to simplify the precoding problem:

[0079] GNN is introduced to implement the end-to-end matrix inversion process to solve this problem. Define a graph as G = (V, E, s, t), where V is the set of points and E is the set of edges. Map nodes to their features, where d1 is the feature dimension of the point, Map edges to their features, where d2 is the feature dimension of the edge.

[0080] For N t Antenna Satellite, M k is of size N t ×N t Therefore, each antenna on the satellite is defined as a vertex. The connection between antenna vertices is defined as an edge. i The antenna vertex (denoted as ) and v j The antenna vertex (denoted as ) is defined as (v i ,v j ). The precoding strategy is learned using edge-updated GNNs. This involves updating the hidden representation of each edge by aggregating information about neighboring vertices connected by these edges. Specifically, a k 、e k and M k Find the inverse, where a k and e k It is a scalar inversion, just take the reciprocal, M k YesN t ×N t dimensional matrix, its inversion requires extremely high complexity. To this end, GNN is used to calculate the matrix M k In layer l, the edge (v i ,v j ) It is expressed as:

[0081]

[0082] Items (a) and (b) are the edges (v i ,v j )arrive and Aggregate information of adjacent edges. s (·) and P d(·) represents the pooling function, which is used to aggregate the edges (v i ,v j )The hidden representation of the adjacent edges. and Respectively represent no antenna v i and without antenna v j A collection of. s (·,s (l) ) and Q d (·,d (l) ) represent the trainable parameters s (l) and d (l) The processing functions are used to and From the edge (v i ,v j ) extracts valuable information from adjacent edges. C(·) represents a combination function c with trainable parameters (l) When Q s (·,s (l) ) and Q d (·,d (l) ) is a linear function, C(·) is a linear function cascaded with the activation function σ(·), the edge (v i ,v j ) is transformed into the update equation:

[0083]

[0084] Taylor expansion provides a feasible method for solving the inverse of the matrix. The inverse matrix P -1 It can be approximated by a first-order Taylor expansion around P0:

[0085]

[0086] Taylor expansion can be used to approximate P using P0 -1 . A first-order Taylor expansion is used iteratively to obtain a more accurate approximation. Observe that this iterative equation is similar to the update equation for edge updates in GNNs. Definition F (l -1) Represents the matrix formed by concatenating the edge features of all (l-1) layers, and the initial value of P0 is M k .but (v i ,v j ) elements can be expressed as

[0087]

[0088] The above formula can be regarded as the edge (v i ,v j), The edge (v) in the representation layer (l) i ,v j ) is a hidden representation. First, it passes through the (l-1) layer AN vi For adjacent edges (v i ,v j ) is aggregated and then combined with the edge (v i ,v j ) is combined with the hidden representation of . The above formula has no trainable parameters. It is just similar to the update method of the edge and cannot be considered as the update equation of the edge update. However, it can still be embedded in the update equation of . Specifically, Add to edge (v i ,v j ) in the update equation. In the (l) layer, the edge (v i ,v j )’s hidden representation:

[0089] For the edge (v i ,v j ), select from the input Two-term connected vector

[0090] Edge (v i ,v j ) is hidden by Replace with renew:

[0091]

[0092] Where c = [c0, c1] T s=[s0,s1] T and d = [d0, d1] T are trainable parameters. Substituting all parameters can be rewritten as:

[0093]

[0094] in and

[0095] (a), (b) and (c) correspond to trainable parameters, c is Replaced by Replaced by As for (d), this is an additional term. Since the information from non-adjacent edges can be aggregated after multiple layers are stacked, (d) is omitted to reduce the computational complexity without affecting the expression ability of GNN. Then the edge (v i ,vj )The update equation is:

[0096]

[0097] The output is obtained by concatenating the results of a single-layer MLP of all edge features in layer l By calculating b k , but it may not meet the transmission power constraint, so it needs to be normalized by the following formula:

[0098]

[0099] The network is trained in an unsupervised manner. Since the optimal precoder is still unknown, only channel-related samples are needed, and there is no need to obtain the optimal precoder. The loss function of the network is the upper bound of the system EE, as the problem The upper bound of the objective function. Therefore, the loss function is defined as follows:

[0100]

[0101] in is the size of the training batch, represents the dth training batch

[0102] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0103] Based on the same inventive concept, an embodiment of the present invention discloses a GNN-based deep expansion massive MIMO LEO satellite precoding system, including: a problem construction and transformation module, used to construct a power-limited energy-efficiency maximization precoding problem for massive MIMO LEO satellite communications; and converting the original problem into a series of iteratively solved sub-problems through the Dinkelbach algorithm, and using the WMMSE method to convert the sub-problems into a convex problem, to obtain the user precoding vector and the update expression of the auxiliary variables introduced to represent the user receiving matrix and the weight matrix; wherein the user precoding vector update process involves a matrix inversion problem; a deep expansion and solution module, used for N in the user precoding vector update process t ×N t The complex matrix of is inverted to construct the graph neural network GNN for deep expansion, where N tis the number of satellite antennas; each antenna on the satellite is defined as a vertex, and the connection between antenna vertices is defined as an edge. The hidden representation of each edge is updated by aggregating the information of adjacent vertices connected by the edge; at the same time, based on the result of Taylor expansion approximate matrix inversion, the one-dimensional feature vector of the edge feature is added; and the precoding result is obtained by normalizing the precoding vector obtained by combining Dinkelbach, WMMSE and GNN.

[0104] An embodiment of the present invention also discloses a computer system, including a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein when the computer program / instruction is executed by the processor, the steps of the GNN-based deep expansion massive MIMO LEO satellite precoding method are implemented.

[0105] An embodiment of the present invention also discloses a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the GNN-based deep expansion massive MIMO LEO satellite precoding method.

[0106] 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 deep unfolding massive MIMO LEO satellite precoding method based on GNN, characterized in that: The steps include: Constructing the power-limited energy-efficiency maximization precoding problem for massive MIMO LEO satellite communications; The original problem is transformed into a series of iterative sub-problems by using the Dinkelbach algorithm, and the sub-problems are transformed into a convex problem by using the weighted minimum mean square error (WMMSE) method, and the update expressions of the user precoding vector and the auxiliary variables introduced to represent the user receiving matrix and the weight matrix are obtained; The process of updating the user precoding vector involves the matrix inversion problem; For the N in the user precoding vector update process t ×N t The complex matrix of is inverted to construct the graph neural network GNN for deep expansion, where N t is the number of satellite antennas; each antenna on the satellite is defined as a vertex, and the connection between antenna vertices is defined as an edge. The hidden representation of each edge is updated by aggregating the information of adjacent vertices connected by the edge; at the same time, based on the result of Taylor expansion approximate matrix inversion, a one-dimensional feature vector of the edge feature is added; The precoding result is obtained by normalizing the precoding vector obtained by combining Dinkelbach, WMMSE and GNN.

2. The GNN-based deep unfolding massive MIMO LEO satellite precoding method according to claim 1, characterized in that: During the nth iteration, the weight matrix u of the kth user is k , receiving matrix ω k and the precoding vector b k The update expression is as follows: where γ k represents the average channel gain of the kth user, v k represents the array response vector between the satellite and the kth user, N0 represents the noise variance, K represents the number of users, (·) H represents the conjugate transpose of a matrix, |·| represents the modulus of a complex number, (·) * represents the conjugate of a complex number, B w represents the system bandwidth, ρ represents the auxiliary variable at the nth iteration, 1 / ξ represents the efficiency of the transmit power amplifier, a opt represents the optimal Lagrange multiplier, and I represents the identity matrix.

3. The GNN-based deep unfolding massive MIMO LEO satellite precoding method according to claim 1, characterized in that: The precoding vector b of the kth user is k Update the N that needs to be inverted in the expression t ×N t The complex matrix is ​​M k , use GNN to calculate the matrix M k The inverse of In the layer, connect the vth i Antenna vertex and v j The edge of the antenna vertex (v i ,v j ) for: Where σ(·) represents the activation function, P s (·) and P d (·) represents the pooling function, Respectively Layer mid-edge (v i ,v j )、(i,v j )、(v i ,j)’s hidden representation, c=[c0,c1] T s=[s0,s1] T and d = [d0, d1] T is a trainable parameter, Respectively represent M k Multiply all The matrix formed by concatenating the layer edge features corresponds to the value of the subscript position.

4. The GNN-based deep unfolding massive MIMO LEO satellite precoding method according to claim 1, characterized in that: The output precoding vector is normalized by the following formula: where b k represents the precoding vector of the kth user, P max represents the transmission power budget, K represents the number of users, and b represents the power budget of k The matrix is ​​composed of ‖·‖, ‖·‖ represents the Frobenius norm of the matrix, ‖·‖2 represents the 2-norm of the vector, and Π{·} represents the normalization processing of the precoding vector.

5. The GNN-based deep unfolding massive MIMO LEO satellite precoding method according to claim 1, characterized in that: The loss function of the GNN network used for matrix inversion is the upper bound of the system energy efficiency.

6. A deep unfolding massive MIMO LEO satellite precoding system based on GNN, characterized by: include: Problem construction and transformation module, which is used to construct the power-limited energy-efficiency maximization precoding problem for massive MIMO LEO satellite communications; The original problem is transformed into a series of iterative sub-problems by using the Dinkelbach algorithm, and the sub-problems are transformed into a convex problem by using the weighted minimum mean square error (WMMSE) method, so as to obtain the update expressions of the user precoding vector and the auxiliary variables introduced to represent the user receiving matrix and the weight matrix; The process of updating the user precoding vector involves the matrix inversion problem; The deep expansion and solution module is used to update the N t ×N t The complex matrix of is inverted to construct the graph neural network GNN for deep expansion, where N t is the number of satellite antennas; each antenna on the satellite is defined as a vertex, and the connection between antenna vertices is defined as an edge. The hidden representation of each edge is updated by aggregating the information of adjacent vertices connected by the edge; at the same time, based on the result of Taylor expansion approximate matrix inversion, the one-dimensional feature vector of the edge feature is added; and the precoding result is obtained by normalizing the precoding vector obtained by combining Dinkelbach, WMMSE and GNN.

7. The GNN-based deep unfolding massive MIMO LEO satellite precoding system according to claim 6, characterized in that: In the problem construction and transformation module, during the nth iteration, during the transformation of the convex problem, the weight matrix u of the kth user is k , receiving matrix ω k and the precoding vector b k The update expression is as follows: where γ k represents the average channel gain of the kth user, v k represents the array response vector between the satellite and the kth user, N0 represents the noise variance, K represents the number of users, (·) H represents the conjugate transpose of a matrix, |·| represents the modulus of a complex number, (·) * represents the conjugate of a complex number, B w represents the system bandwidth, ρ represents the auxiliary variable at the nth iteration, 1 / ξ represents the efficiency of the transmit power amplifier, a opt represents the optimal Lagrange multiplier, and I represents the identity matrix.

8. The GNN-based deep unfolding massive MIMO LEO satellite precoding system according to claim 6, characterized in that: In the depth expansion and solution module, the precoding vector b of the kth user is recorded as k Update the N that needs to be inverted in the expression t ×N t The complex matrix is ​​M k , use GNN to calculate the matrix M k The inverse of In the layer, connect the vth i Antenna vertex and v j The edge of the antenna vertex (v i ,v j ) for: Where σ(·) represents the activation function, P s (·) and P d (·) represents the pooling function, Respectively Layer mid-edge (v i ,v j )、(i,v j )、(v i ,j)’s hidden representation, c=[c0,c1] T s=[s0,s1] T and d = [d0, d1] T is a trainable parameter, Respectively represent M k Multiply all The matrix formed by concatenating the layer edge features corresponds to the value of the subscript position.

9. A computer system comprising a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, characterized in that: When the computer program / instructions are executed by a processor, the steps of the GNN-based deep unfolding massive MIMO LEO satellite precoding method are implemented according to any one of claims 1-5.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the GNN-based deep unfolding massive MIMO LEO satellite precoding method are implemented according to any one of claims 1-5.

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