Extensible MU-MIMO precoding method based on homographical neural network

Abstract

The invention provides an extensible MU-MIMO precoding method based on a homomorphic neural network. The method comprises the following steps: S1, constructing a communication system model; s2, the MU-MIMO cellular network is constructed into a wireless virtual isomorphic directed graph; and S3, designing an information carrying graph neural network (ICGNN) precoding algorithm suitable for dynamic changes of the number of users and the number of user antennas in a cellular network, and completing extensible MU-MIMO precoding based on the same composition neural network. According to the method, the performance of the ICGNN method under different user numbers is displayed through training in a basic scene of K = 5 users, when a graph with a larger size is extrapolated, the ICGNN performance is better and is always superior to WMMSE, and compared with WMMSE, the performance of the ICGNN method provided by the invention is always improved by more than or equal to 95%.

Description

Technical Field

[0001] The invention relates to a scalable MU-MIMO precoding method based on a homogeneous graph neural network, and belongs to the technical field of communications. Background Art

[0002] MU-MIMO downlink precoding technology can effectively suppress interference between users and is a promising solution to enhance the capacity of wireless communication systems. However, the downlink precoding problem usually needs to be modeled as a non-convex NP-hard problem, such as the weighted sum rate (WSR) maximization problem, which makes it very difficult to solve. The weighted minimum mean square error (WMMSE) algorithm provides a closed expression for finding the local optimal solution to the WSR maximization problem and achieves excellent performance. Therefore, it is widely used as a standard comparison scheme. However, the algorithm's iterative solution process and high-dimensional matrix inversion operations have high computational complexity, resulting in significant computational delays and cannot meet the needs of actual scenarios.

[0003] Existing deep learning technology (DL) provides a new solution for balancing algorithm performance and complexity. Its core idea is to use deep neural network (DNN) or convolutional neural network (CNN) to replace the calculation process of WMMSE algorithm, realize the mapping relationship between input channel matrix and output precoding matrix, and thus reduce complexity. However, DL-based algorithms generally have the defect of poor generalization ability. When the number of access users or the number of user antennas in the cellular network changes, the neural network needs to be redesigned and trained, and it still cannot meet the real-time requirements. Therefore, designing a low-complexity and scalable universal precoding algorithm has become a research hotspot. Summary of the invention

[0004] The present invention aims to solve the calculation delay in the MU-MIMO downlink precoding process and the technical problem that the neural network cannot adaptively complete precoding according to the number of access users, and further proposes a scalable MU-MIMO precoding method based on a homogeneous graph neural network.

[0005] The technical solution adopted by the present invention to solve the above problems is: the present invention proposes a scalable MU-MIMO precoding method based on a homogeneous graph neural network, comprising:

[0006] Step 1: Construct a wireless virtual homogeneous directed graph;

[0007] Step 2: Use prior knowledge to assign features to nodes and edges in the wireless virtual homogeneous directed graph;

[0008] Step 3: Map the node features and edge features to the real number domain for realization;

[0009] Step 4: Input the node features of the target node's neighbor nodes and the edge features pointing to the target node into the message passing network M(·) to obtain the aggregate features of the neighbor node information;

[0010] Step 5: Update the network U(·) based on the node features, and perform a secondary update on the target features of the target node by combining the aggregated features of the neighbor node information;

[0011] Step 6: Update the power factor (p) of the target feature after the second update of the node feature update network U(·) output k,i (Θ),λ k,i (Θ)) is constrained to complete the scalable MU-MIMO precoding of homogeneous graph neural networks.

[0012] Optionally, the step of constructing a wireless virtual homogeneous directed graph in step 1 includes:

[0013] Step 1.1: Treat all multi-antenna users as multiple single-antenna receivers;

[0014] Step 1.2: Virtualize the base station into multiple virtual base station nodes, where the virtual base station nodes are identical to the single-antenna receiver being served;

[0015] Step 1.3: Treat the virtual base station node and the single-antenna receiver served by the corresponding virtual base station node as a whole virtual node, and construct a virtual node set Among them, V is the set of virtual nodes, v k,i is the virtual node of the i-th antenna of user k, v k,i The index is ((k-1)N r +i);

[0016] Step 1.4: According to the interference relationship between all single-antenna receivers, connect any two virtual nodes to construct a virtual directed edge, and construct a wireless virtual isomorphic directed graph G = (V, E), where V is the set of virtual nodes and E is the set of directed edges.

[0017] Optionally, in step 2, using prior knowledge to assign features to nodes and edges in the wireless virtual homogeneous directed graph specifically includes:

[0018] Assign the channel state information as a feature to the edge and obtain the edge feature tensor

[0019] The target feature is concatenated with the channel feature and assigned to the node as a feature to obtain the node feature matrix Among them, node v k,i The channel characteristics are Node v k,i The target feature is pk,i and λ k,i The initial value of is equal power allocation;

[0020] The expression of the edge-specific matrix is:

[0021]

[0022] In formula (1), is a zero vector and H is a three-dimensional tensor.

[0023] Optional, the node v after the real number in step 3 k,i The node characteristics are The real number of slave nodes v k,i To the adjacent node v m,j The edge proof is in, To obtain the real part, To take the imaginary part.

[0024] Optionally, the step of obtaining aggregate features of neighbor node information in step 4 includes:

[0025] Step 4.1: Let the i-th virtual node in the wireless virtual isomorphic directed graph be v i , v i The initial characteristics are in, Indicates v i The lth update of the target feature;

[0026] Step 4.2: Set node v i Neighbor node v j Node features and points to node v i The edge feature H (j,i,:) After concatenation, they are input into the message passing network M(·);

[0027] Step 4.3: Set all neighbor nodes v j ,j∈N(i) is input into the maximum value MAX function of the output feature in the message passing network M(·) to obtain the aggregated features of the neighbor node information.

[0028] Optionally, the step of performing a secondary update on the target feature of the target node in step 5 includes:

[0029] Step 5.1: Set node v i Node features After being concatenated with the aggregated features of neighbor node information, it is input into the node update network U(·) to obtain the node v i The target features obtained by the first update And keep the channel characteristics constant;

[0030] Step 5.2: Target features obtained based on the first update Get the updated features of all nodes Repeat steps 4.2, 4.3 and 5.1 to get node v i Target features after secondary update

[0031] Node v i The target features obtained by the first update The expression is:

[0032]

[0033] In formula (2), is the aggregated feature of neighbor node information;

[0034] Node v i The target features obtained by the second update The expression is:

[0035]

[0036] In formula (3), It is the aggregated feature of the neighbor node information after the first update.

[0037] Optionally, the step of completing scalable MU-MIMO precoding of the homogeneous graph neural network in step 6 includes:

[0038] Step 6.1: Update the power factor (p) of the target feature output by the network U(·) for the node k,i (Θ),λ k,i (Θ)) is constrained, where Θ is the weight of the ICGNN network;

[0039] Step 6.2: Calculate p k,i (Θ) and λ k,i (Θ) Recovered precoding matrix Through the precoding matrix V k (Θ) calculating the signal-to-noise ratio between the virtual base station node and the single-antenna receiver;

[0040] Step 6.3: Calculate the loss function of the ICGNN network during training based on the signal-to-noise ratio between the virtual base station node and the single-antenna receiver, and iterate the ICGNN network using an unsupervised method until convergence, completing the scalable MU-MIMO precoding of the homogeneous graph neural network;

[0041] The expression for recovering the precoding matrix is:

[0042]

[0043] In formula (4), p k,i ≥0, p k,i is the downlink power allocation factor of the ith antenna of user k, λ k,i ≥0,λ k,i is the equivalent uplink power allocation factor;

[0044] The calculation formula of the signal-to-noise ratio between the virtual base station node and the single-antenna receiver is:

[0045]

[0046] The calculation formula of the loss function of the ICGNN network is:

[0047]

[0048] In formula (6), E(·) is the average value of the desired realization of all channels;

[0049] Constrained power factor (p k,i (Θ),λ k,i The expression of (θ) is:

[0050]

[0051] In formula (7), Θ is the weight of the ICGNN network.

[0052] The beneficial effects of the present invention are:

[0053] 1. The present invention demonstrates the performance of the ICGNN method under different numbers of users by training in a basic scenario of K=5 users. When extrapolated to a larger graph, the performance of ICGNN is better and is always better than WMMSE. Compared with WMMSE, the performance improvement of the ICGNN method proposed in the present invention is always ≥95%.

[0054] 2. When the present invention processes antennas of different numbers of users, no adjustment is required. Each user is equipped with N r =2 antennas scenario training model, and tested the performance under different antenna configurations. The results show that ICGNN can still show good performance under various configurations, proving that the present invention has strong generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 A flowchart of a scalable MU-MIMO precoding method based on a homogeneous graph neural network provided by the present invention;

[0056] Figure 2A schematic diagram of constructing a wireless virtual homogeneous directed graph provided by the present invention;

[0057] Figure 3 This is a schematic diagram of performance comparison under different user number scenarios provided by the present invention;

[0058] Figure 4 A schematic diagram of the comparison of the operating time provided by the present invention;

[0059] Figure 5 This is a schematic diagram of performance comparison under different user antenna number scenarios provided by the present invention. DETAILED DESCRIPTION

[0060] Combination Figure 1-2 This embodiment is described.

[0061] like Figure 1 As shown, the steps of the scalable MU-MIMO precoding method based on the homogeneous graph neural network described in this embodiment include:

[0062] S1: Build a communication system model;

[0063] S101: This embodiment considers a single-cell downlink MU-MIMO system, in which the base station (BS) is equipped with N t transmit antennas and provide services to K users, each of which is equipped with N r The channel between user k and BS is expressed as BS uses precoding matrix To preprocess the signal sent to user k, where d k represents the number of data streams received by user k;

[0064] The signal received by the kth user is expressed as:

[0065]

[0066] In formula (1), is the data sent to user k, is additive Gaussian white noise, assuming

[0067] S102: Describe the specific form of the signal received by user k on any receiving antenna i and establish the WSR maximization problem P 3 ;

[0068] Formula (1) can be expressed as follows:

[0069]

[0070] In formula (2), is the channel between the ith antenna of user k and the BS, Indicates m The i-th data stream s i,m The precoding vector of

[0071] The signal received by the i-th antenna of user k is:

[0072]

[0073] In formula (3), is the noise on the i-th receiving antenna;

[0074] The spectral efficiency (SE) of the i-th antenna of user k is denoted by R i,k , establish the WSR maximization problem P 3 :

[0075]

[0076] S103: By observing the problem P 3 Find the precoding vector v i,k The optimal solution structure of MISO beamforming can be used to solve:

[0077]

[0078] In formula (6), p k,i ≥0 represents the downlink power allocation factor of the ith antenna of user k. Considering the uplink and downlink duality, λ k,i ≥0 can be understood as an equivalent uplink power allocation factor, satisfying

[0079] S2: Construct the MU-MIMO cellular network as a wireless virtual homogeneous directed graph;

[0080] S201: Consider each multi-antenna user as multiple single-antenna receivers;

[0081] S202: Virtualizing the BS into multiple virtual BS nodes, the number of which is the same as the number of single-antenna receivers served by the BS;

[0082] S203: These virtual BSs and their served single-antenna receivers are regarded as a whole virtual node (VN), and V is used to represent the set of VNs. Since each VN includes a single-antenna receiver, for the convenience of representation, the VN corresponding to the i-th antenna of user k is denoted as v k,i The set V of VN can be expressed as And the cardinality of set V is |V|=KN r Therefore, the node v in the set k,i The index is ((k-1)Nr +i).

[0083] S204: Connect these virtual nodes to construct virtual directed edges according to the interference relationship between all single-antenna receivers. In this embodiment, E represents a set of directed edges, and the wireless virtual graph can be represented as G = (V, E). The reason for setting it as a directed edge is that there are differences in the interference links between any two single-antenna receivers.

[0084] like Figure 2 As shown, in combination with S201-S204, a wireless virtual homogeneous directed graph is constructed, and the interference of single antenna receiver 1 to single antenna receiver 2 comes from the data sent by the BS to single antenna receiver 1, which is received by single antenna receiver 2 through the channel from the BS to single antenna receiver 2. Similarly, the interference of single antenna receiver 2 to single antenna receiver 1 is received by single antenna receiver 1 through the channel from the BS to single antenna receiver 1. In summary, the edge between any two nodes is set as a directed edge.

[0085] S3: Design an Information Carrying Graph Neural Network (ICGNN) precoding algorithm suitable for the dynamic change of the number of users and user antennas in cellular networks;

[0086] S301: Assign features to nodes and edges using prior knowledge;

[0087] S30101: In wireless communication networks, the precoding matrix is ​​directly determined by the channel state information (CSI). This embodiment assigns CSI as a feature to nodes and edges, which is called the channel feature. In addition, this embodiment introduces a feature that is related to the solution of the optimization problem, which is called the target feature. The target feature is concatenated with the channel feature and used as the node feature, while the edge feature is only composed of the channel feature. k,i The channel characteristics can be expressed as in v k,i The target feature is defined as in p k,i and λ k,i The initial value of is set to equal power distribution, that is The overall node feature matrix can be expressed as Edge feature tensor It is expressed as:

[0088]

[0089] In formula (7), is a zero vector, because there is no self-connected edge on each VN, H is a three-dimensional tensor, and according to formula (3), v k,iThe received interference signal and the desired signal both reach the receiver through the same channel. Therefore, the signal directed to node v k,i The directed edges of are characterized by the channel vector h i,k Representation.

[0090] S302: Both M(·) and U(·) consist of fully connected layers. The specific network structures of M(·) and U(·) are shown in Table 1 and Table 2, respectively. Sigmoid is used to ensure the output power factor (p k,i ,λ k,i ) is positive. Since neural networks do not support complex number operations, the node features and edge features are mapped to the real number domain for realization. In the MU-MIMO wireless virtual graph, the realized node v k,i The node characteristics are The real number of slave nodes v k,i To the adjacent node v m,j The edge proof is in, To obtain the real part, To take the imaginary part;

[0091] Table 1

[0092]

[0093] Table 2

[0094]

[0095] S303: Record the i-th VN in the wireless virtual graph as v i , v i The initial features are recorded as v i The lth update of the target feature: v i Neighbor node v j Node features With pointing v i The edge feature H (j,i,:) After concatenation, input into the message passing network M(·);

[0096] S304: All neighbor nodes v j ,j∈N(i) is the output feature in step 6, which is input into the maximum value MAX function to obtain the aggregated features of the neighbor node information;

[0097] S305: Set the node v i Features The sum is concatenated with the aggregated features output from step 7 and input into the node feature update network U(·), and the node v is obtained. i The target feature of the first update And keep the channel characteristics constant;

[0098] S306: Target features obtained based on the first update Get the updated features of all nodes Execute S303-S305 again to get node v i Secondary update of target features

[0099] Node v i The target features obtained by the first update The expression is:

[0100]

[0101] In formula (8), is the aggregated feature of neighbor node information;

[0102] Node v i The target features obtained by the second update The expression is:

[0103]

[0104] In formula (9), It is the aggregated feature of the neighbor node information after the first update.

[0105] S307: Power factor (p k,i (Θ),λ k,i (Θ)) to ensure that they meet the power constraint, which is achieved through the following transformation:

[0106]

[0107] In formula (10), Θ represents the network weight of ICGNN.

[0108] S308: ICGNN is trained using an unsupervised learning method until convergence to complete the scalable MU-MIMO precoding of the homogeneous graph neural network. The loss function is defined as follows:

[0109]

[0110] In formulas (11) and (12), Indicates that through p k,i (Θ) and λ k,i (Θ) According to the precoding matrix recovered by equation (6), it is expected that E(·) represents the average of all channel realizations. Since neural networks do not support complex value operations, it is necessary to map complex value operations to the real number domain, using the following decomposition method:

[0111] Example

[0112] Combination Figure 3-5 This example is explained in detail. This example uses Python 3.8 and Pytorch 11.2 to implement the ICGNN architecture on a GeForce GTX3080Ti. During network training, the Adam optimizer is used with a learning rate of 0.001 and a batch size of 100. User priority weights All results are taken from 10 4 Average value achieved by the sub-channel.

[0113] This embodiment considers a cellular network scenario, in which the BS is equipped with N t = 16 antennas, and users are equipped with multiple antennas, randomly distributed in a circular area within 500 meters from the BS. The transmission power of the base station is P t =10dBm, the total system bandwidth is 20MHz, the receiver noise power spectral density is -174dBm / Hz, and the channel between the base station and the user adopts a circularly symmetric standard complex normal distribution with path loss, and the path loss is set to -30.5-36.7log 10 (d) [dB], where d represents the distance between the BS and the user (in meters).

[0114] This embodiment considers the following comparative schemes for comparison: WMMSE[1]: WMMSE is based on the results after 100 iterations. In addition, the initial precoding matrix of the WMMSE algorithm is generated using the MRT[2] technology. MRT[2]: A heuristic precoding scheme with low computational complexity; WCGCN[3]: A GNN-based beamforming method originally designed for adhoc networks and modified for MU-MIMO scenarios.

[0115] This example first shows the performance of each solution under different user number scenarios. r = 2 antennas, such as Figure 3 As shown in the figure, the results show that the ICGNN method can achieve spectral efficiency (SE) comparable to WMMSE and outperforms MRT and WCGCN regardless of the configuration, which highlights the versatility and effectiveness of ICGNN. Figure 4 The paper also shows the running time comparison between the WMMSE algorithm and ICGNN. ICGNN uses simple forward reasoning and GPU parallel computing to significantly reduce the running time to about one second.

[0116] In Table 3, this example verifies the generalization ability of ICGNN. The percentage in the table represents the performance ratio of the ICGNN algorithm relative to WMMSE. This example demonstrates the performance of the ICGNN method under different numbers of users by training in the basic scenario of K=5 users. The results show that when extrapolated to larger-sized graphs, ICGNN performs better and is always better than WMMSE. The performance on smaller-sized graphs decreases slightly, but the performance is still over 95%.

[0117] Table 3

[0118]

[0119] This embodiment further compares the performance of ICGNN when users are equipped with different numbers of antennas. This embodiment considers a scenario where the number of users K = 3. The reason for choosing this specific configuration is that Figure 3 In the example, when the number of users is K = 3, the performance advantage of the proposed algorithm compared with WMMSE is not prominent enough. It will be more convincing to study its generalization ability under this scenario configuration. Figure 5 As shown in the figure, when users are equipped with different numbers of antennas, ICGNN always outperforms WCGCN and is comparable to the performance of WMMSE, demonstrating the strong versatility of the network model because no adjustment is required when dealing with different numbers of user antennas.

[0120] In Table 4, this embodiment is based on each user being equipped with N r =2 antennas scenario and tested its performance under different antenna configurations. The results showed that ICGNN can still show good performance under various configurations, thus confirming its strong generalization ability.

[0121] Table 4

[0122]

[0123] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. A scalable MU-MIMO precoding method based on homogeneous graph neural network, characterized in that: The steps of the scalable MU-MIMO precoding method based on homogeneous graph neural network include: Step 1: Construct a wireless virtual homogeneous directed graph; Step 2: Use prior knowledge to assign features to nodes and edges in the wireless virtual homogeneous directed graph; Step 3: Map the node features and edge features to the real number domain for realization; Step 4: Input the node features of the neighbor nodes of the target node and the edge features pointing to the target node into the message passing network M(·) to obtain the aggregate features of the neighbor node information; Step 5: Update the network U(·) based on the node features, and perform a secondary update on the target features of the target node by combining the aggregated features of the neighbor node information; Step 6: Update the power factor (p) of the target feature after the second update of the node feature update network U(·) output k,i (Θ),λ k,i (Θ)) is constrained to complete the scalable MU-MIMO precoding of homogeneous graph neural networks.

2. The scalable MU-MIMO precoding method based on homogeneous graph neural network according to claim 1, characterized in that: The steps of constructing a wireless virtual homogeneous directed graph in step 1 include: Step 1.1: Treat all multi-antenna users as multiple single-antenna receivers; Step 1.2: Virtualize the base station into multiple virtual base station nodes, where the virtual base station nodes are identical to the single-antenna receiver being served; Step 1.3: Treat the virtual base station node and the single-antenna receiver served by the corresponding virtual base station node as a whole virtual node, and construct a virtual node set Among them, V is the set of virtual nodes, v k,i is the virtual node of the i-th antenna of user k, v k,i The index is ((k-1)N r +i); Step 1.4: According to the interference relationship between all single-antenna receivers, connect any two virtual nodes to construct a virtual directed edge, and construct a wireless virtual isomorphic directed graph G = (V, E), where V is the set of virtual nodes and E is the set of directed edges.

3. The scalable MU-MIMO precoding method based on homogeneous graph neural network according to claim 1, characterized in that: In step 2, the prior knowledge is used to assign features to nodes and edges in the wireless virtual homogeneous directed graph, including: Assign the channel state information as a feature to the edge and obtain the edge feature tensor The target feature is concatenated with the channel feature and assigned to the node as a feature to obtain the node feature matrix Among them, node v k,i The channel characteristics are Node v k,i The target feature is p k,i and λ k,i The initial value of is equal power allocation; The expression of the edge-specific matrix is: In formula (1), is a zero vector and H is a three-dimensional tensor.

4. The scalable MU-MIMO precoding method based on homogeneous graph neural network according to claim 1, characterized in that: The node v after real numbering in step 3 k,i The node characteristics are The real number of slave nodes v k,i To the adjacent node v m,j The edge proof is in, To obtain the real part, To take the imaginary part.

5. The scalable MU-MIMO precoding method based on homogeneous graph neural network according to claim 1, characterized in that: The steps of obtaining the aggregate features of neighbor node information in step 4 include: Step 4.1: Let the i-th virtual node in the wireless virtual isomorphic directed graph be v i , v i The initial characteristics are in, Indicates v i The lth update of the target feature; Step 4.2: Set node v i Neighbor node v j Node features and points to node v i The edge feature H (j,i,:) After concatenation, they are input into the message passing network M(·); Step 4.3: Set all neighbor nodes v j ,j∈N(i) is input into the maximum value MAX function of the output feature in the message passing network M(·) to obtain the aggregated features of the neighbor node information.

6. The scalable MU-MIMO precoding method based on homogeneous graph neural network according to claim 1, characterized in that: The step of performing a secondary update on the target feature of the target node in step 5 includes: Step 5.1: Set node v i Node features After being concatenated with the aggregated features of the neighbor node information, it is input into the node update network U(·) to obtain the node v i The target features obtained by the first update And maintain the channel characteristics constant; Step 5.2: Target features obtained based on the first update Get the updated features of all nodes Repeat steps 4.2, 4.3 and 5.1 to get node v i Target features after secondary update Node v i The target features obtained by the first update The expression is: In formula (2), is the aggregated feature of neighbor node information; Node v i The target features obtained by the second update The expression is: In formula (3), It is the aggregated feature of the neighbor node information after the first update.

7. The scalable MU-MIMO precoding method based on homogeneous graph neural network according to claim 1, characterized in that: The steps of completing the scalable MU-MIMO precoding of the homogeneous graph neural network in step 6 include: Step 6.1: Update the power factor (p) of the target feature output by the network U(·) for the node k,i (Θ),λ k,i (Θ)) is constrained, where Θ is the weight of the ICGNN network; Step 6.2: Calculate p k,i (Θ) and λ k,i (Θ) Recovered precoding matrix By precoding matrix V k (Θ) calculating the signal-to-noise ratio between the virtual base station node and the single-antenna receiver; Step 6.3: Calculate the loss function of the ICGNN network during training based on the signal-to-noise ratio between the virtual base station node and the single-antenna receiver, and iterate the ICGNN network using an unsupervised method until convergence, completing the scalable MU-MIMO precoding of the homogeneous graph neural network; The expression for recovering the precoding matrix is: In formula (4), p k,i ≥0, p k,i is the downlink power allocation factor of the ith antenna of user k, λ k,i ≥0,λ k,i is the equivalent uplink power allocation factor; The calculation formula of the signal-to-noise ratio between the virtual base station node and the single-antenna receiver is: The calculation formula of the loss function of the ICGNN network is: In formula (6), E(·) is the average value of the desired realization of all channels; Constrained power factor (p k,i (Θ),λ k,i The expression of (θ) is: In formula (7), Θ is the weight of the ICGNN network.

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