A Sum-Rate Maximization Multi-User MISO Beamforming Method Based on CG Depth Expansion

Abstract

The present invention discloses a sum-rate maximization multi-user MISO beamforming method based on CG depth unfolding. This method is applicable to a downlink multi-user MISO wireless communication system and includes the following steps: 1. Construct an initial optimization problem for maximizing the system sum-rate under the total transmit power constraint; 2. Utilize strong duality and KKT conditions to obtain the optimal structure of the transmit beamforming vector; 3. Use the conjugate gradient iteration algorithm to calculate the inverse matrix in the transmit beamforming vector; 4. Generate a training data set required for training a neural network, and use depth unfolding to build an unsupervised neural network based on the conjugate gradient algorithm; 5. The base station configures the network with the training parameters obtained by offline training in step 4 and performs online calculation to obtain the optimal transmit beamforming vector. Compared with the traditional WMMSE iteration method, the present invention can significantly reduce the online calculation complexity of the algorithm while ensuring performance, which is conducive to engineering implementation.

Description

Technical Field

[0001] The present invention relates to a downlink multi-user MISO wireless communication system, and in particular to a multi-user MISO beamforming method for sum-rate maximization based on CG deep unfolding. Background Art

[0002] Transmit beamforming technology is the key to improving the spectral efficiency of next-generation wireless networks. It is used to transmit signals from an antenna array to one or more users. The design goal is to maximize the signal power of the target user as much as possible and reduce the interference to non-target users. In a wireless communication system, the multi-user transmit beamforming optimization problem under sum-rate maximization is a non-convex problem and is not easy to solve. Moreover, existing calculation methods such as the traditional minimum mean square error (MMSE) algorithm have certain losses in sum-rate performance, while the WMMSE iterative algorithm aiming at maximizing the sum-rate has a high computational complexity and is not easy to be implemented in engineering.

[0003] In recent years, deep learning methods have been widely applied in the field of communication. It can train a neural network offline and then use the trained neural network for online deployment. Compared with traditional methods, the methods based on deep learning have the advantages of low computational complexity and strong robustness.

[0004] Existing multi-user beamforming design methods based on deep learning generally have problems such as more training parameters, inconvenient implementation in actual systems, and still too high complexity, and it is difficult to achieve a good balance between performance and complexity. Summary of the Invention

[0005] Aiming at the defects existing in the above-mentioned existing technologies, the purpose of the present invention is to provide a multi-user MISO beamforming method for sum-rate maximization based on CG deep unfolding, so as to solve the technical problems that existing methods generally have more training parameters, inconvenient implementation in actual systems, and still too high complexity, and it is difficult to achieve a good balance between performance and complexity.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A multi-user MISO beamforming method for sum-rate maximization based on CG deep unfolding includes the following steps:

[0008] Step 1, construct an initial optimization problem P1. In this optimization problem, the transmit beamforming vectors configured for each user at the base station are used as optimization variables, the optimization goal is to maximize the system information transmission rate, and the total antenna transmit power constraint is satisfied;

[0009] Step 2, utilize strong duality and KKT conditions to obtain the general form of the optimal structure of the downlink transmit beamforming vectors;

[0010] Step 3: Calculate the transmit beamforming vector using the conjugate gradient iteration algorithm for the inverse matrix in

[0011] Step 4: Generate the training data set required for training the neural network, build an unsupervised neural network based on the conjugate gradient algorithm using deep unfolding, and perform offline training with the maximization of the sum rate as the training objective to obtain the training parameter values;

[0012] Step 5: The base station configures the network with the training parameters obtained from the offline training in Step 4 and performs online calculation to obtain the optimal transmit beamforming vector configured for each user respectively.

[0013] In the above Step 1, the optimization objective of the initial optimization problem P1 is:

[0014] Maximize

[0015] The constraint conditions of the optimization problem are:

[0016] In formulas (1) and (2), log2(·) represents the logarithmic function with base 2, |·| represents the modulus value of a complex number, ||·|| represents the vector 2-norm, (·) H represents the conjugate transpose of a vector, the optimization variable w k ∈C N×1 represents the transmit beamforming vector configured by the base station for the k-th user, h k ∈C N×1 is the channel between the base station and the k-th user, w k ∈C N×1 represents the transmit beamforming vector configured by the base station for the k-th user, i represents the i-th user, N represents the number of transmit antennas at the base station, K represents the number of users, P represents the total transmit power of the base station, σ 2 is the noise power, represents the transmit power constraint at the base station side.

[0017] In the above Step 2, according to the strong duality and KKT conditions, the general form of the optimal structure of the transmit beamforming vector for the optimization problem P1 is:

[0018]

[0019] where λ i >0 represents the Lagrange multiplier and satisfies the constraint represents the transmit power of the k-th user and satisfies the constraint h i ∈C N×1 is the channel between the base station and the i-th user, I NDenotes the N-dimensional identity matrix.

[0020] In step 3, the conjugate gradient algorithm is used to solve for the transmit beamforming vector The inverse matrix in. The conjugate gradient (CG) algorithm is an effective iterative method for solving linear equations. Compared with direct inversion, the CG algorithm significantly reduces the computational complexity in each iteration and can solve problems in the form of

[0021]

[0022] where A ∈ C K×K is a positive definite matrix, b ∈ C K

[0023] Write the formula (3) to be determined in the present invention as a CG algorithm optimization problem:

[0024]

[0025] That is b = h k , Denotes the optimal result obtained by using the CG algorithm to solve formula (3),

[0026] In step 4, the input of the unsupervised network is the channel G = [h1, h2, h3... h k ∈ C N×K between the base station and the user and the noise power σ 2 , and the output is the optimal transmit beamforming vector configured by the base station for each user m Take the step size α m in the conjugate gradient algorithm, β i (λ i > 0 and satisfies the constraint ) in formula (3), and p k (p k > 0 and satisfies the constraint ) as the training parameters of the unsupervised network. Use deep unfolding to build a model-driven unsupervised neural network. Each layer of this network corresponds to an iteration of the conjugate gradient algorithm, and a normalization processing layer is added to meet the constraint conditions and Train this neural network using the following training objective.

[0027] The training objective is: maximize

[0028] where

[0029] In step 5, the base station configures the network with the training parameters obtained from the offline training in step 4 and performs online calculation to obtain the optimal transmit beamforming vectors configured for each user respectively.

[0030] Advantages: Compared with the prior art, the multi-user MISO beamforming method for sum-rate maximization based on CG deep unfolding of the present invention has the following advantages:

[0031] 1. The neural network of the present invention combines the internal structure of the transmit beamforming vector that maximizes the sum rate with an advanced DNN network, and uses deep unfolding to construct a model-driven unsupervised neural network. Compared with the data-driven "black box" DNN network, this network has better generalization ability and interpretability.

[0032] 2. Compared with the traditional WMMSE algorithm, the present invention significantly reduces the computational complexity while ensuring the system performance, which is convenient for engineering implementation. Description of the Drawings

[0033] Figure 1 is the flowchart of the method of the present invention.

[0034] Figure 2 is the network structure diagram corresponding to each iteration of the CG algorithm of the present invention.

[0035] Figure 3 is the simulation experiment result diagram of the present invention. Detailed Embodiments

[0036] The present invention will be described in detail below with reference to the drawings and embodiments.

[0037] A typical application scenario of the present invention is the communication between a multi-antenna base station and multiple single-antenna users in a wireless communication system, and the goal is to maximize the system sum rate.

[0038] As Figure 1 shown, a multi-user MISO beamforming method for sum-rate maximization based on CG deep unfolding of the present invention includes the following steps:

[0039] Step 1, construct an initial optimization problem P1. In this optimization problem, the transmit beamforming vectors configured for each user at the base station are used as optimization variables, the optimization goal is to maximize the system information transmission rate, and the total antenna transmit power constraint is satisfied;

[0040] That is, the optimization goal of the initial optimization problem P1 is to maximize

[0041] The constraint condition is:

[0042] In equations (1) and (2), log2(·) represents the logarithmic function with base 2, |·| represents the modulus of a complex number, ||·|| represents the vector 2-norm, and (·) H represents the conjugate transpose of a vector, and the optimization variable w k ∈C N×1 represents the transmit beamforming vector configured by the base station for the k-th user, h k ∈C N×1 is the channel between the base station and the k-th user, w k ∈C N×1 represents the transmit beamforming vector configured by the base station for the k-th user, i represents the i-th user, N represents the number of transmit antennas at the base station, K represents the number of users, P represents the total transmit power of the base station, σ 2 is the noise power, represents the transmit power constraint at the base station.

[0043] Step 2: Utilize strong duality and the KKT conditions to obtain the optimal structure of the downlink transmit beamforming vector;

[0044] Using strong duality and the KKT conditions, the general form of the optimal transmit beamforming vector for the optimization problem P1 can be obtained as

[0045]

[0046] where λ i >0 represents the Lagrange multiplier and satisfies the constraint p k >0 represents the transmit power of the k-th user and satisfies the constraint h i ∈C N×1 is the channel between the base station and the i-th user, I N represents the N-dimensional identity matrix.

[0047] Step 3: Use the conjugate gradient iteration algorithm to calculate the inverse matrix in the transmit beamforming vector ;

[0048] The conjugate gradient (CG) algorithm is an effective iterative method for solving linear equations. Compared with directly finding the inverse, the CG algorithm significantly reduces the computational complexity in each iteration and can solve problems in the form of

[0049]

[0050] where A ∈ C K×K is a positive definite matrix, b ∈ C K

[0051] Write the formula (3) to be determined in the present invention as the CG algorithm optimization problem:

[0052]

[0053] That is Solve The specific iteration process of the original conjugate gradient (CG) algorithm is as follows:

[0054]

[0055]

[0056] where α m , β m are the step length parameters in the m-th iteration of the CG algorithm.

[0057] One of the key features of this algorithm is that it can converge after K iterations, and when a v close to the exact result m is obtained, the iteration step can easily terminate after m iterations. When the number of iterations m is equal to the number of users K, the exact result can be obtained.

[0058] Step 4: Generate the training data set required for training the neural network. Use deep unfolding to build an unsupervised neural network based on the conjugate gradient algorithm, and perform offline training with the maximization of the sum rate as the training objective to obtain the training parameter values;

[0059] The input of the unsupervised network is the channel G = [h1, h2, h3... h k ∈ C N×K between the base station and the users and the noise power σ 2 , and the output is the optimal transmit beamforming vector configured by the base station for each user. The original conjugate gradient algorithm is iterative and parameterized by trainable variables. The step lengths α m , β m in the conjugate gradient algorithm and λ i in formula (3) (λ i > 0 and satisfies the constraint ), p k (p k > 0 and satisfies the constraint ) are used as the training parameters of the unsupervised network. Use deep unfolding to build a model-driven unsupervised neural network. Each layer of this network corresponds to an iteration of the conjugate gradient algorithm, and a normalization processing layer is added to satisfy the constraint conditions and Train this neural network with the following training objective.

[0060] The training objective is: Maximize

[0061] wherein

[0062] Step 5: The base station configures the network with the training parameters obtained by offline training in Step 4 and performs online calculation to obtain the optimal transmit beamforming vectors configured for each user respectively.

[0063] In order to verify the technical effects of the present invention, simulation experiments were carried out. The parameters involved in the simulation experiments are shown in the following table:

[0064] Table 1 Simulation Experiment Parameter Table

[0065] Parameter Value Number of base station transmitting antennas 32 Number of user receiving antennas 1 Number of users 16 Base station transmitting power 30 dBm Channel model Rayleigh channel Modulation method QPSK Fixed number of CG iterations 5 Number of training sets 10000 Number of test sets 1000

[0066] Table 2 Comparison Table of Computational Complexity

[0067]

[0068] In order to further illustrate the effects of the present invention, the present invention also performed performance simulations on two existing technical solutions and compared them with the performance of the present invention. The two existing technical solutions are the weighted minimum mean square error (WMMSE) method and the traditional minimum mean square error (MMSE) method respectively.

[0069] Specifically, Table 1 is the simulation experiment parameter table, and Table 2 is the comparison table of the WMMSE method and the method of the present invention in terms of computational complexity. The calculation method of complexity is to calculate the number of real number multiplications. represents the number of iterations of the WMMSE algorithm. represents the number of iterations of the CG algorithm. Figure 3 is the comparison result of the simulation experiment, where the abscissa is the signal-to-noise ratio (dB) and the ordinate is the system sum rate (bps / Hz). The simulation results show that the method of this embodiment has better performance than the traditional MMSE method and can achieve the same performance as the WMMSE method, and significantly reduces its computational complexity.

[0070] Where the present invention is not described in detail, it is all well-known techniques to those skilled in the art.

[0071] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations according to the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the existing technology should be within the protection scope determined by the claims.

Claims

1. A sum-rate maximization multi-user MISO beamforming method based on CG depth unfolding, characterized in that: It includes the following steps: Step 1, construct the initial optimization problem P1. In this optimization problem, the transmit beamforming vectors configured for each user at the base station are used as the optimization variables, and the optimization objective is to maximize the system information transmission rate, and it satisfies the total antenna transmit power constraint; Step 2, utilize strong duality and KKT conditions to obtain the general form of the optimal structure of the downlink transmit beamforming vectors; Step 3: Calculate the transmit beamforming vector by using the conjugate gradient iteration algorithm The inverse matrix in Step 4, generate the training data set required for training the neural network, use deep unfolding to build an unsupervised neural network based on the conjugate gradient algorithm, and perform offline training with maximizing the sum rate as the training objective to obtain the training parameter values; Step 5, the base station configures the network with the training parameters obtained from the offline training in Step 4 and performs online calculation to obtain the optimal transmit beamforming vectors configured for each user respectively.

2. The sum-rate maximization multi-user MISO beamforming method based on CG depth unfolding according to claim 1, characterized in that: In the said Step 1, the optimization objective of the initial optimization problem P1 is: Maximize The constraints of the optimization problem are as follows: In formulas (1) and (2), log2(·) represents the logarithmic function with base 2, |·| represents the modulus value of a complex number, ||·|| represents the vector 2-norm, and (·) H represents the conjugate transpose of a vector, and the optimization variable w k ∈C N×1 represents the transmit beamforming vector configured by the base station for the k-th user, h k ∈C N×1 is the channel between the base station and the k-th user, w k ∈C N×1 represents the transmit beamforming vector configured by the base station for the k-th user, i represents the i-th user, N represents the number of transmit antennas at the base station, K represents the number of users, P represents the total transmit power of the base station, σ 2 is the noise power, represents the transmit power constraint at the base station side.

3. A sum-rate maximization multi-user MISO beamforming method based on CG depth unfolding according to claim 2, characterized in that: In the said Step 2, according to the strong duality and KKT conditions, the general form of the optimal structure of the transmit beamforming vectors of the optimization problem P1 is: where λ i > 0 represents the Lagrange multiplier and satisfies the constraint represents the transmit power of the k-th user and satisfies the constraint is the channel between the base station and the i-th user, and I N represents the N-dimensional identity matrix.

4. A sum-rate maximization multi-user MISO beamforming method based on CG depth unfolding according to claim 3, characterized in that: In step 3, the conjugate gradient iteration algorithm is used to calculate the transmit beamforming vector The specific steps for the inverse matrix in Write formula (3) as a problem solved by the CG algorithm: wherein represents the best result obtained by solving formula (3) using the CG algorithm, and calculates 5. A sum-rate maximization multi-user MISO beamforming method based on CG depth unfolding according to claim 4, characterized in that: In step 4, the input of the unsupervised network is the channel between the base station and the user and the noise power σ 2 , and the output is the optimal transmit beamforming vector configured by the base station for each user Take the step size in the conjugate gradient algorithm and λ in formula (3) i , p k as the training parameters of the unsupervised network, where λ i > 0 and satisfies the constraint and satisfies the constraint Build an unsupervised neural network based on model-driven using deep unfolding. Each layer of this network corresponds to an iteration of the conjugate gradient algorithm, and a normalization layer is added to meet the constraint conditions and Train this neural network with the following training objective: The training objective is: to maximize Among them

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