A hybrid beamforming design method for OFDM-based broadband millimeter wave relay systems

Abstract

The application relates to a kind of OFDM-based broadband millimeter wave relay system hybrid beamforming design method, comprising: calculating the receiving signal of target node under the condition that each node is all digital processor;The receiving signal is processed using minimum mean square error criterion in target node, and MMSE matrix is calculated;Using the equivalence between maximizing sum rate and minimum weighted mean square error algorithm, the maximum sum rate problem is converted into minimum weighted mean square error problem according to MMSE matrix;Deep unfolding neural network is used to solve the minimum weighted mean square error problem, and all digital processor of each node is obtained;Each node's all digital processor is decomposed based on least square decomposition algorithm, and hybrid beamforming matrix of each node is calculated, the complexity of the algorithm is greatly reduced, and the running time of the system can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a hybrid beamforming design method for a broadband millimeter-wave relay system based on OFDM. Background Technology

[0002] Millimeter-wave communication with massively multi-input multiple-output (MIMO) capabilities has been recognized as a key technology to meet the ever-increasing data rate demands of fifth-generation and later systems. Traditional all-digital beamforming architectures are unsuitable for massively multi-MIMO systems because they require a dedicated RF link for each antenna, resulting in significant hardware costs and power consumption. To address this issue, hybrid beamforming design is considered the optimal solution for balancing system performance and power consumption. Hybrid beamforming design consists of two parts: a high-dimensional analog beamformer and a low-dimensional digital beamformer. This approach significantly reduces hardware costs and power consumption while maintaining high system performance.

[0003] Taking advantage of the large bandwidth of millimeter-wave signals, hybrid beamforming design in broadband systems achieves higher system performance and can provide higher data rates. Another characteristic of millimeter waves is their high frequency, short wavelength, and significant path loss in free space, which limits their propagation to line-of-sight channels. However, with the help of relay nodes, the propagation distance can be greatly increased. Therefore, research on hybrid beamforming for millimeter-wave broadband systems has significant practical implications.

[0004] For broadband systems, Orthogonal Frequency Division Multiplexing (OFDM) technology is typically used to overcome multipath fading. In millimeter-wave OFDM systems, the digital processor is designed individually for each subcarrier, while the analog precoder is universal for all subcarrier signals. This is a key difference between broadband and narrowband systems, and it also explains why hybrid beamforming designs for narrowband systems cannot be directly applied to broadband systems. Currently, broadband systems mainly use algorithms that directly maximize the system and rate to design the optimal hybrid beamforming solution. While this algorithm can guarantee finding a local optimum, it suffers from high complexity due to matrix inversion operations involved in the iterative optimization process.

[0005] To address the drawbacks of high complexity described above, which makes it difficult to apply in real-time systems, the low-complexity hybrid beamforming design method for millimeter-wave broadband relay systems based on depth unfolding researched in this invention is of great significance. Summary of the Invention

[0006] To address the problems existing in the background art, this invention provides a smart design method for hybrid beamforming in broadband millimeter-wave relay systems, comprising:

[0007] S1: Calculate the received signal of the target node when each node is a fully digital processor;

[0008] S2: At the target node, the received signal is processed using the minimum mean square error criterion to calculate the MMSE matrix;

[0009] S3: Utilizing the equivalence between the maximum sum rate and minimum weighted mean square error algorithms, the maximum sum rate problem is transformed into the minimum weighted mean square error problem based on the MMSE matrix;

[0010] S4: Solve the minimum weighted mean square error problem based on a deep unfolded neural network to obtain a fully digital processor for each node;

[0011] S5: The least squares decomposition algorithm decomposes the all-digital processor of each node and calculates the hybrid beamforming matrix of each node.

[0012] Preferably, the received signal of the target node includes:

[0013] y[k]=W fd [k]H2[k]G fd [k]H1[k]F fd [k]s[k]+W fd [k]H2[k]G fd [k]n1[k]+W fd [k]n2[k]

[0014] Where y[k] represents the received signal of the target node to the k-th subcarrier, s[k] represents the input data stream of the k-th subcarrier, and F fd [k] represents the all-digital processor of the transmitting node, G fd [k] represents the all-digital processor of the relay node, W fd [k] represents the all-digital processor of the target node; H1[k] represents the channel matrix from the transmitting node to the relay node on the k-th subcarrier; H2[k] represents the channel matrix from the relay node to the target node on the k-th subcarrier; n1[k] represents the additive white Gaussian noise from the transmitting node to the relay node on the k-th subcarrier, with a mean of 0 and a variance of . n2[k] represents the additive white Gaussian noise on each of the kth subcarriers from the relay node to the target node, with a mean of 0 and a variance of .

[0015] Preferably, the calculation of the MMSE matrix includes:

[0016] W fd [k]=(H2[k]G fd [k]H1[k]F fd [k]) H [H2[k]G fd [k]H1[k]F fd [k](H2[k]G fd [k]H1[k]F fd [k]) H +Φ[k]] -1

[0017]

[0018]

[0019] Among them, R H Let R denote the conjugate transpose of matrix R. Then the MMSE matrix is ​​expressed as:

[0020] E MMSE [k]=(IW fd [k]H2[k]G fd [k]H1[k]F fd [k])(IW fd [k]H2[k]G fd [k]H1[k]F fd [k]) H +W fd [k]Φ[k]W fd H [k]

[0021] =[I+(H2[k]G fd [k]H1[k]F fd [k]) H Φ -1 [k]H2[k]G fd [k]H1[k]F fd [k] -1

[0022] Among them, E MMSE [k] represents the MMSE matrix corresponding to the k-th subcarrier, R -1 Let R be the inverse matrix.

[0023] Preferably, the minimum weighted mean square error problem includes:

[0024]

[0025]

[0026]

[0027] Where V[k] represents the weight matrix corresponding to the k-th subcarrier, and K represents the number of subcarriers. Denotes the Frobenius norm, E t E represents the maximum transmit power of the transmitting node. r This indicates the maximum transmit power of the relay node, when At this time, the minimum weighted mean square error problem and the maximum sum rate problem have the same KKT conditions, and Tr() represents finding the trace of the matrix. It represents the statistical expectation.

[0028] Preferably, step S4 includes:

[0029] S41: Fix V[k] and F fd [k] will be about G fd Substituting the power constraint term of [k] into the minimum weighted mean square error problem transforms the minimum weighted mean square error problem into an unconstrained problem, calculating G. fd The closed-form solution expression for [k];

[0030] S42: Fixed G fd [k] and V[k] will be related to F fd Substituting the power constraint term of [k] into the minimum weighted mean square error problem transforms the minimum weighted mean square error problem into an unconstrained problem, and calculates F. fd The closed-form solution expression for [k];

[0031] S43: Fixed F fd [k] and G fd [k], solve for the closed-form expression of V[k] using the expression of V[k]:

[0032] S44: G fd The closed-form solution expression for [k], F fd The closed-form solution expression of [k] and the closed-form solution expression of V[k] are expanded into the layer structure of a deep neural network, and a power constraint normalization function is added after each layer in the deep expanded neural network to construct the deep expanded neural network.

[0033] S45: Use the channel matrices H1[k] and H2[k] as inputs to the deep unfolded neural network for forward propagation, and use the minimum weighted mean square error problem as the loss function. The deep unfolded neural network is trained using the automatic differentiation structure in the PyTorch platform in an unsupervised manner until the minimum weighted mean square error problem converges, resulting in a fully digital processor for each node.

[0034] Preferably, step S5 includes:

[0035] S51: Construct matrix G using the least squares method fd The decomposition optimization problem model of [k] will use matrix G. fd The decomposition optimization problem model of [k] is transformed into a problem about G. trf G rrf and G bb The unconstrained problem of [k] can be solved by fixing G. trf G rrf and G bb The two variables in [k] are updated alternately to solve for G. trf G rrf and G bb The closed-form solution of [k] will give matrix G trf and G rrf The closed-form solution is normalized under constant modulus constraints to obtain the analog part processor of the relay node, for G. bb The closed-form solution of [k] is normalized by power constraints to obtain the digital part processor of the relay node, until matrix G is obtained. fd The decomposition optimization problem model of [k] converges, based on the simulated partial processor G of the relay node. trf Analog Part Processor G rrf and digital part processor G bb [k] The hybrid beamforming matrix G = G of the relay node is calculated. trf ×G bb [k]×G rrf ;

[0036] S52: Construct matrix F using the least squares method fd The decomposition optimization problem model of [k] will use matrix F fd The decomposition optimization problem model of [k] is transformed into a problem about F. rf and F bb The unconstrained problem of [k] can be solved by fixing F. rf and F bb A variable in [k] is used to alternately update and solve for F. rf and F bb The closed-form solution of [k] will F rf The closed-form solution is normalized under constant modulus constraints to obtain the analog part of the processor of the launch node; F bb The closed-form solution of [k] is normalized by power constraints to obtain the digital part processor of the transmitter node; based on the analog processor F of the transmitter node... rf and the digital processor F of the launch node bb [k] The hybrid beamforming matrix F = F of the transmitting node is calculated. rf ×F bb [k];

[0037] S53: Construct matrix W using the least squares method fd The decomposition optimization problem model of [k] will use matrix W fd The decomposition and optimization problem model of [k] is transformed into a problem about W. bb [k] and W rf The unconstrained problem is solved by fixing W. bb [k] and W rf One of the variables, W is updated alternately to solve the problem. bb [k] and W rf The closed-form solution, W rf The closed-form solution is normalized under constant modulus constraints to obtain the simulation part processor of the target node; based on the simulation part processor W of the target node... rf and the digital part processor W of the target node bb [k] The hybrid beamforming matrix W = W of the target node is calculated. bb [k]×W rf .

[0038] The present invention has at least the following beneficial effects

[0039] First, this invention addresses the complexity of traditional iterative algorithms by employing a deep unfolded neural network to replace the iterative steps in traditional networks, significantly reducing algorithm complexity and effectively improving system runtime, making its application in real-time systems possible. Second, it addresses the performance degradation caused by the difficult-to-interpret underlying structure of current deep neural networks (DNNs). Unlike the black-box structure of DNNs, the deep unfolded neural network of this invention leverages domain knowledge from traditional communications and is built based on a mathematical model. Its underlying architecture is clear, exhibiting good generalization ability while maintaining the same system performance as traditional algorithms. Finally, the analog processor matrix and digital processor matrix of each node are combined to form a new processor matrix, which is the hybrid processor matrix designed for each node in this invention. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0041] Figure 2 This is a schematic diagram of the broadband relay system model structure of the present invention;

[0042] Figure 3 This is a schematic diagram of the deep unfolding process of the present invention;

[0043] Figure 4 This is a schematic diagram of the decomposition algorithm proposed in this invention. Detailed Implementation

[0044] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0045] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0046] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0047] High-frequency wireless channels exhibit frequency selectivity. OFDM technology decomposes them into a series of narrowband channels with flat fading. For hybrid digital-analog transceivers using OFDM, Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) operations need to be added between the digital and analog processors. A cyclic prefix (CP) also needs to be added to avoid inter-symbol interference. This means that each subcarrier channel needs to share the analog processor, while the digital processor needs to be designed independently for each subcarrier channel. Broadband relay systems, such as... Figure 2 As shown: Input data stream of the k∈Kth subcarrier in the communication system First, the digital portion (baseband pre-encoder) of the transmitting node F bb [k] processing, followed by Inverse Fast Fourier Transform (IFFT) operation, adding a cyclic prefix (CP), and then passing through the analog section (RF pre-encoder) of the transmit node. rfAfter processing, the signal is sent to the relay node; the relay node first processes the received signal through the first analog section (relay RF combiner) G. rrf After processing, the cyclic prefix (CP) is removed, followed by Fast Fourier Transform (FFT) processing, and then processed by the digital part (baseband pre-encoder) of the relay node. bb [k] is processed, then subjected to an Inverse Fast Fourier Transform (IFFT) operation, and after adding the cyclic prefix (CP), it is processed by the second analog part (relay RF precoding) of the relay node G. trf After processing, the signal is sent to the target node; the target node first processes the received signal through its analog section (RF combiner) W. rf After processing and removing the cyclic prefix (CP), the data is then subjected to a Fast Fourier Transform (FFT) before being input into the digital part (baseband pre-encoder) of the target node. bb [k] receives the received signal; where the data stream vector s[k] satisfies Meanwhile, the information transmission process is affected by noise. n1[k] and n2[k] represent the additive white Gaussian noise vectors of the SR link (the link from the transmitting node to the relay node) and the RD link (the link from the relay node to the transmitting node), respectively, with a mean of 0 and variances of 0 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ... and

[0048] Please see Figure 1 In this invention, a fully digital precoder corresponding to the subcarrier signal of each node is first designed. Then, the proposed decomposition algorithm is used to decompose the fully digital processor matrix into a hybrid processor matrix. The specific process is as follows:

[0049] S1: Calculate the received signal of the target node when each node is a fully digital processor;

[0050] The received signal at the target node can be described as follows:

[0051] y[k]=W fd [k]H2[k]G fd [k]H1[k]F fd [k]s[k]+W fd [k]H2[k]G fd [k]n1[k]+W fd [k]n2[k]

[0052] Where y[k] represents the received signal of the target node to the k-th subcarrier, s[k] represents the input data stream of the k-th subcarrier, and F fd [k] represents the all-digital processor of the transmitting node, G fd [k] represents the all-digital processor of the relay node, W fd[k] represents the all-digital processor of the target node; H1[k] represents the channel matrix from the transmitting node to the relay node on the k-th subcarrier; H2[k] represents the channel matrix from the relay node to the target node on the k-th subcarrier; n1[k] represents the additive white Gaussian noise from the transmitting node to the relay node on the k-th subcarrier, with a mean of 0 and a variance of . n2[k] represents the additive white Gaussian noise on each of the kth subcarriers from the relay node to the target node, with a mean of 0 and a variance of .

[0053] S2: At the target node, the received signal is processed using the minimum mean square error criterion to calculate the MMSE matrix;

[0054] The calculated MMSE matrix includes:

[0055] W fd [k]=(H2[k]G fd [k]H1[k]F fd [k]) H [H2[k]G fd [k]H1[k]F fd [k](H2[k]G fd [k]H1[k]F fd [k]) H +Φ[k]] -1

[0056]

[0057]

[0058] Among them, R H Let R denote the conjugate transpose of matrix R. Then the MMSE matrix is ​​expressed as:

[0059] E MMSE [k]=(IW fd [k]H2[k]G fd [k]H1[k]F fd [k])(IW fd [k]H2[k]G fd [k]H1[k]F fd [k]) H +W fd [k]Φ[k]W fd H [k]

[0060] =[I+(H2[k]G fd [k]H1[k]F fd [k]) H Φ -1[k]H2[k]G fd [k]H1[k]F fd [k] -1

[0061] Among them, E MMSE [k] represents the MMSE matrix corresponding to the k-th subcarrier, R -1 Let R be the inverse matrix.

[0062] S3: Utilizing the equivalence between the maximum sum rate and minimum weighted mean square error algorithms, the maximum sum rate problem is transformed into the minimum weighted mean square error problem based on the MMSE matrix;

[0063]

[0064]

[0065]

[0066] Where V[k] represents the weight matrix corresponding to the k-th subcarrier, and K represents the number of subcarriers. Denotes the Frobenius norm, E t E represents the maximum transmit power of the transmitting node. r This indicates the maximum transmit power of the relay node, when At this time, the minimum weighted mean square error problem and the maximum sum rate problem have the same KKT conditions, and Tr() represents finding the trace of the matrix. It represents the statistical expectation.

[0067] S4: Solve the minimum weighted mean square error problem based on a deep unfolded neural network to obtain a fully digital processor for each node;

[0068] Traditional methods for minimizing the WMMSE problem typically employ an iterative optimization approach, where two variables are alternately fixed while the Lagrange multiplier is used to solve for the third variable until the objective function falls below a predefined threshold. However, this approach requires numerous iterations and a complex solution process, significantly increasing the algorithm's computational complexity. To avoid this problem, this invention uses a deep unfolded neural network to replace extensive iterative operations, effectively reducing computational complexity.

[0069] The idea behind deep unrolling is as follows: For a model-based method that requires iterative inference, the iteration is unrolled into a hierarchical structure similar to a neural network. Then, the model parameters are decomposed across layers to obtain a new neural network-like structure. This new structure can be easily trained using gradient-based methods. The resulting network combines the expressive power of traditional deep neural networks while allowing inference to be performed in a fixed number of layers. These layers can be optimized for optimal performance. The general process of deep unrolling can be described as follows: Figure 3 As shown.

[0070] Please see Figure 4 In the embodiments of the present invention, the specific method for expanding the iterative algorithm into a neural network is as follows:

[0071] S41: Fix V[k] and F fd [k] will be about G fd Substituting the power constraint term of [k] into the minimum weighted mean square error problem transforms the minimum weighted mean square error problem into an unconstrained problem, calculating G. fd The closed-form solution expression for [k];

[0072] In step S41, the minimum weighted mean square error problem is transformed into an unconstrained problem as follows:

[0073]

[0074]

[0075] Then, in the unconstrained problem G fd The closed-form solution expression for [k] is:

[0076]

[0077] S42: Fixed G fd [k] and V[k] will be related to F fd Substituting the power constraint term of [k] into the minimum weighted mean square error problem transforms the minimum weighted mean square error problem into an unconstrained problem, and calculates F. fd The closed-form solution expression for [k];

[0078] In step S42, the minimum weighted mean square error problem is transformed into an unconstrained problem as follows:

[0079]

[0080] β=Tr(F fd [k](F fd [k]) H )×K / E t

[0081] Then, in the unconstrained problem F fdThe closed-form solution expression for [k] is:

[0082]

[0083] S43: Fixed F fd [k] and G fd The closed-form solution of V[k], obtained by solving the expression of V[k], is as follows:

[0084]

[0085] By observation, we can see that the above expression contains a matrix inversion operation, which has high computational complexity. Therefore, we propose an alternative structure for matrix inversion, defining the expression for matrix inversion as follows:

[0086] A -1 =A + X+AY+Z

[0087] Among them, A- 1 Let X represent the inverse of matrix A; X, Y, and Z represent trainable parameters; A + This means taking the reciprocal of each element on the diagonal of matrix A, while setting the off-diagonal elements to 0;

[0088] S44: G fd The closed-form solution expression for [k], F fd The closed-form solution expression of [k] and the closed-form solution expression of V[k] are expanded into the layer structure of a deep neural network, and a power constraint normalization function is added after each layer in the deep expanded neural network to construct the deep expanded neural network.

[0089] In the (l+1)th layer of a deep unfolded neural network, G fd The structure of [k] can be represented as:

[0090]

[0091]

[0092]

[0093] in, and Represents trainable parameters, O (g ,l+1) This represents the bias parameters of the (l+1)th layer of the deep neural network, relative to V[k] and F. bb The structure of [k] can be implemented in the same way:

[0094]

[0095]

[0096]

[0097]

[0098] In order to ensure that the output G of each layer fd [k] and F fd [k] satisfies the power constraint condition. An activation function is added after each layer of the network, and this activation function is set as the power constraint normalization function.

[0099]

[0100]

[0101] G is obtained through deep unfolded neural networks fd [k] and F fd [k] is the output of the last layer of the deep unfolded neural network. and L is the total number of layers in the deep network), according to the formula, W fd [k]=(H2[k]G fd [k]H1[k]F fd [k]) H [H2[k]G fd [k]H1[k]F fd [k](H2[k]G fd [k]H1[k]F fd [k]) H +Φ[k]] -1 W was calculated fd [k], the above method can ensure that the final output of the network conforms to the power constraint, and f1() and f2() represent the power constraint normalization function.

[0102] S45: Use the channel matrices H1[k] and H2[k] as inputs to the deep unfolded neural network for forward propagation, and use the minimum weighted mean square error problem as the loss function. The deep unfolded neural network is trained using the automatic differentiation structure in the PyTorch platform in an unsupervised manner until the minimum weighted mean square error problem converges, resulting in a fully digital processor for each node.

[0103] S5: The all-digital processor of each node is decomposed based on the least squares decomposition algorithm to calculate the hybrid beamforming matrix of each node:

[0104] S51: Construct matrix G using the least squares method fdThe decomposition optimization problem model of [k] will use matrix G. fd The decomposition optimization problem model of [k] is transformed into a problem about G. trf G rrf and G bb The unconstrained problem of [k] can be solved by fixing G. trf G rrf and G bb The two variables in [k] are updated alternately to solve for G. trf G rrf and G bb The closed-form solution of [k] will give matrix G trf and G rrf The closed-form solution is normalized under constant modulus constraints to obtain the analog part processor of the relay node, for G. bb The closed-form solution of [k] is normalized by power constraints to obtain the digital part processor of the relay node, until matrix G is obtained. fd The decomposition optimization problem model of [k] converges, based on the simulated partial processor G of the relay node. trf Analog Part Processor G rrf and digital part processor G bb The hybrid beamforming matrix G = G of the relay node is calculated. trf ×G bb ×G rrf ;

[0105] Matrix G fd The decomposition optimization problem model for [k] is as follows:

[0106]

[0107]

[0108]

[0109] in, and The relay analog pre-encoder matrix G is respectively trf and relay analog combiner matrix G rrf The set of feasible solutions, matrix G fd The decomposition optimization problem model of [k] is transformed into a problem about G. trf G rrf and G bb Unconstrained problems:

[0110]

[0111]

[0112]

[0113] By fixing G trf G rrf and G bb The two variables in the solution are updated alternately to solve for G. trf G rrf and G bb Closed-form solution:

[0114]

[0115]

[0116]

[0117] Where n represents the number of iterations, matrix G trf and G rrf The closed-form solution is normalized under constant modulus constraints;

[0118]

[0119]

[0120] Among them, G rrf (i,j) and G trf (i,j) represent matrix G respectively. rrf And matrix G trf The element in the i-th row and j-th column;

[0121] For G bb Power constraint normalization is performed on the closed-form solution:

[0122]

[0123] Until matrix G fd The decomposition optimization problem model of [k] converges, based on the simulated partial processor G of the relay node. trf Analog Part Processor G rrf and digital part processor G bb [k] The hybrid beamforming matrix G = G of the relay node is calculated. trf ×G bb [k]×G rrf ;

[0124] S52: Construct matrix F using the least squares method fd The decomposition optimization problem model of [k] will use matrix F fd The decomposition optimization problem model of [k] is transformed into a problem about F. rf and F bb The unconstrained problem of [k] can be solved by fixing F. rf and F bbA variable in [k] is used to alternately update and solve for F. rf and F bb The closed-form solution of [k] will F rf The closed-form solution is normalized under constant modulus constraints to obtain the analog part of the processor of the launch node; F bb The closed-form solution of [k] is normalized by power constraints to obtain the digital part processor of the transmitter node; based on the analog part processor F of the transmitter node... rf and the digital part processor F of the launch node bb [k] The hybrid beamforming matrix F = F of the transmitting node is calculated. rf ×F bb [k];

[0125] Matrix F fd The decomposition optimization problem model for [k] is as follows:

[0126]

[0127]

[0128]

[0129] in, Simulate the pre-encoder matrix F for the transmitting node rf The set of feasible solutions:

[0130] matrix F fd The decomposition optimization problem model of [k] is transformed into a problem about F. rf and F bb Unconstrained problems of [k]:

[0131]

[0132]

[0133] By fixing F rf and F bb A variable in [k] is used to alternately update and solve for F. rf and F bb Closed-form solution for [k]:

[0134]

[0135]

[0136] Where n represents the number of iterations, F rf Normalize the closed-form solution using constant modulus constraints:

[0137]

[0138] Among them, F rf (i,j) represents the element in the i-th row and j-th column of the matrix; F fd [k] will F fd Power constraint normalization is performed on the closed-form solution of [k]:

[0139]

[0140] According to the analog part of the launch node processor F rf and the digital part processor F of the launch node bb [k] The hybrid beamforming matrix F = F of the transmitting node is calculated. rf ×F bb [k];

[0141] S53: Construct matrix W using the least squares method fd The decomposition optimization problem model of [k] will use matrix W fd The decomposition and optimization problem model of [k] is transformed into a problem about W. bb [k] and W rf The unconstrained problem is solved by fixing W. bb [k] and W rf One of the variables, W is updated alternately to solve the problem. bb [k] and W rf The closed-form solution, W rf The closed-form solution is normalized under constant modulus constraints to obtain the digital part processor of the target node; based on the analog part processor W of the target node... rf and the digital part processor W of the target node bb [k] The hybrid beamforming matrix W = W of the target node is calculated. bb [k]×W rf ;

[0142] Construct matrix W fd The decomposition and optimization problem model of [k]:

[0143]

[0144]

[0145] in, The target node simulates the pre-encoder matrix W. rf The set of feasible solutions:

[0146] matrix W fd The decomposition and optimization problem model of [k] is transformed into a problem about W. bb [k] and W rf Unconstrained problems:

[0147]

[0148]

[0149] By fixing W bb [k] and W rf One of the variables, W is updated alternately to solve the problem. bb [k] and W rf Closed-form solution:

[0150]

[0151]

[0152] W rf Normalize the closed-form solution using constant modulus constraints:

[0153]

[0154] Among them, W rf (i,j) represents matrix W rf The element in the i-th row and i-th column will be W bb [k] is the receiver processor matrix of the target node (receiving node), so no power constraint is needed; based on the analog processor W of the target node... rf and the target node's digital processor W bb [k] The hybrid beamforming matrix W = W of the target node is calculated. bb [k]×W rf .

[0155] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0156] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A hybrid beamforming design method for a broadband millimeter-wave relay system based on OFDM, characterized in that, include: S1: Calculate the received signal of the target node when each node is a fully digital processor; S2: At the target node, the received signal is processed using the minimum mean square error criterion to calculate the MMSE matrix; S3: Utilizing the equivalence between the maximum sum rate and minimum weighted mean square error algorithms, the maximum sum rate problem is transformed into the minimum weighted mean square error problem based on the MMSE matrix; The minimum weighted mean square error problem includes: in, Indicates the first The weight matrix corresponding to each subcarrier Indicates the number of subcarriers. Denotes the Frobenius norm. This indicates the maximum transmit power of the transmitting node. This indicates the maximum transmit power of the relay node, when At that time, the minimum weighted mean square error problem and the maximum sum rate problem have the same KKT conditions. This indicates finding the trace of a matrix. Indicates statistical expectation; Indicates the first The MMSE matrix corresponding to each subcarrier; The fully digital processor representing the transmitting node; This refers to the all-digital processor of the relay node; This indicates the distance from the transmitting node to the relay node at the [number]th ... Channel matrix of subcarriers; Indicates the first The input data stream of each subcarrier; This indicates the distance from the transmitting node to the relay node at the [number]th ... Additive white Gaussian noise for each subcarrier, with a mean of 0 and a variance of . ; S4: Solve the minimum weighted mean square error problem based on a deep unfolded neural network to obtain a fully digital processor for each node; Step S4 includes: S41: Fixed and , regarding Substituting the power constraint term into the minimum weighted mean square error problem transforms the minimum weighted mean square error problem into an unconstrained problem, and then calculating... The closed-form solution expression; S42: Fixed and , regarding Substituting the power constraint term into the minimum weighted mean square error problem transforms the minimum weighted mean square error problem into an unconstrained problem, and then calculating... The closed-form solution expression; S43: Fixed and ,pass Solving the expression The closed-form solution expression; S44: Will Closed-form solution expression, Closed-form solution expression and The closed-form solution expression is expanded into a layer structure of a deep neural network, and a power constraint normalization function is added after each layer in the deep expanded neural network to construct the deep expanded neural network. S45: Channel matrix and The input to the deep unfolded neural network is used for forward propagation, and the minimum weighted mean square error problem is used as the loss function. The deep unfolded neural network is trained using the automatic differentiation structure in the PyTorch platform in an unsupervised manner until the minimum weighted mean square error problem converges, resulting in a fully digital processor for each node. S5: The least squares decomposition algorithm decomposes the all-digital processor of each node and calculates the hybrid beamforming matrix of each node.

2. The hybrid beamforming design method for a broadband millimeter-wave relay system based on OFDM according to claim 1, characterized in that, The received signals of the target node include: in, Indicates the target node to the first The received signal of each subcarrier, Indicates the first The input data stream of each subcarrier, This indicates the all-digital processor of the transmitting node. This refers to the all-digital processor of the relay node. This refers to the all-digital processor of the target node. This indicates the distance from the transmitting node to the relay node at the [number]th ... Channel matrix of subcarriers; This indicates that the relay node is at the 1st digit from the target node. Channel matrix of subcarriers; This indicates the distance from the transmitting node to the relay node at the [number]th ... Additive white Gaussian noise for each subcarrier, with a mean of 0 and a variance of . ; This indicates that the relay node is at the 1st digit from the target node. Additive white Gaussian noise for each subcarrier, with a mean of 0 and a variance of . .

3. The hybrid beamforming design method for a broadband millimeter-wave relay system based on OFDM according to claim 2, characterized in that, The calculated MMSE matrix includes: The MMSE matrix is ​​then represented as: in, Indicates the first The MMSE matrix corresponding to each subcarrier.

4. The hybrid beamforming design method for a broadband millimeter-wave relay system based on OFDM according to claim 1, characterized in that, Step S5 includes: S51: Constructing a matrix using the least squares method The decomposition and optimization problem model will use the matrix The decomposition and optimization problem model is transformed into a model about , and The unconstrained problem, through fixed , and The two variables in the solution are updated alternately. , and The closed-form solution will be the matrix and The closed-form solution is normalized under constant modulus constraints to obtain the analog part processor of the relay node. The closed-form solution is normalized by power constraints to obtain the digital part processor of the relay node, until the matrix... The decomposition and optimization problem model converged, based on the simulated processor of the relay node. Analog processor and digital part processor The hybrid beamforming matrix of the relay node is calculated. ; S52: Constructing a matrix using the least squares method The decomposition and optimization problem model will use the matrix The decomposition and optimization problem model is transformed into a model about and The unconstrained problem, through fixed and One of the variables is updated alternately to solve the problem. and The closed-form solution will The closed-form solution is normalized under constant modulus constraints to obtain the analog part of the processor of the launch node; The closed-form solution is normalized with power constraints to obtain the digital processor of the transmitter node; based on the analog processor of the transmitter node... and digital processors of the launch node The hybrid beamforming matrix of the transmitting node is calculated. ; S53: Constructing a matrix using the least squares method The decomposition and optimization problem model will use the matrix The decomposition and optimization problem model is transformed into a model about and The unconstrained problem, through fixed and One of the variables is updated alternately to solve the problem. and The closed-form solution will The closed-form solution is normalized under constant modulus constraints to obtain the simulation part processor of the target node; based on the simulation part processor of the target node... and the digital part processor of the target node The hybrid beamforming matrix of the target node is calculated. .

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