Channel estimation and symbol-level precoding joint design method based on machine learning

Abstract

The invention discloses a machine learning assisted symbol-level precoding and channel estimation joint design method. The method comprises the following steps: generating a data set containing a plurality of user receiving signals; processing a received signal by using a convolutional neural network by taking minimization of a mean square error between a real channel and an estimated channel as a criterion to obtain an estimated channel matrix; combining the estimated channel matrix with user symbol information, and constructing channel data containing virtual and real parts; carrying out joint processing on the channel matrix and the user symbol information by using a Transform neural network, and calculating a key low-dimensional variable of symbol-level precoding optimization; and in combination with the estimated channel information and the key low-dimensional variable, calculating a symbol-level precoding closed form to obtain a sending signal. According to the method, joint optimization of channel estimation and symbol-level precoding can be realized, and the system performance is remarkably improved with relatively low calculation complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of large-scale MIMO communication, and particularly relates to a joint design method for channel estimation and symbol-level precoding based on machine learning. Background Art

[0002] In recent years, mobile communication technology has developed rapidly, posing higher requirements for the spectral efficiency and energy efficiency of communication systems. As a key technology for cellular wireless communication, large-scale MIMO technology significantly improves system performance through spatial multiplexing and diversity gain, and has become a core technology for the new generation of mobile communication standards.

[0003] Precoding, as a key signal processing technology in wireless communication systems, can effectively improve the reliability and spectral efficiency of signal transmission by performing complex transformations on data at the transmitter. Precoding techniques are mainly divided into two categories: linear precoding and nonlinear precoding.

[0004] Linear precoding uses a linear transformation matrix to accurately map the transmitted signal to a multi-antenna array, achieving spatial diversity gain. This type of method effectively suppresses multi-user interference in multi-antenna systems through algebraic transformations, improving system capacity and communication reliability.

[0005] Nonlinear precoding has significant advantages over linear precoding. Its core feature is the ability to break through the constraints of linear transformation and perform more complex signal processing through nonlinear mapping. This technology can more flexibly adjust the power and phase distribution of the transmitted signal, significantly improving system performance. Symbol-level precoding, as a representative method of nonlinear precoding, innovatively realizes the exploitation of beneficial interference in multi-user systems by specially processing data symbols.

[0006] The core feature of symbol-level precoding is the exploitation of beneficial interference. Instead of simply suppressing interference like traditional precoding, this method actively utilizes the interference signals in multi-user systems. Through a carefully designed symbol mapping strategy, the originally harmful interference is transformed into exploitable signal resources, thus breaking through the performance limit of traditional precoding. The key lies in the innovative reconstruction of the spatial structure of the transmitted signal, enabling the signals of different users to have beneficial interactions during transmission.

[0007] The accurate acquisition of channel state information is the key to optimizing the performance of wireless communication systems. Traditional channel estimation methods insert pilot signals at the transmitter and estimate channel characteristics based on the pilot signals at the receiver. However, multipath fading, time-varying channels, and complex noise environments pose great challenges to channel estimation.

[0008] Deep learning provides an innovative technical paradigm for wireless communication systems. Through massive data training and adaptive network structures, machine learning algorithms can accurately model complex non-linear channel characteristics, breaking through the limitations of traditional signal processing methods. Especially in the fields of symbol-level precoding and channel estimation, deep learning demonstrates powerful modeling and optimization potential.

[0009] However, existing symbol-level precoding and channel estimation methods still face many challenges. Traditional channel estimation techniques mainly rely on pilot signals and linear estimation models, making it difficult to accurately capture the non-linear characteristics and time-variability of complex wireless channels. Most existing precoding methods are limited to linear transformations and cannot fully utilize interference information in multi-user systems. In addition, traditional methods usually adopt iterative algorithms for channel estimation and precoding design, with high computational complexity and severely restricted real-time performance. In scenarios with limited pilot resources, it is even more difficult for existing technologies to accurately estimate the channel state and perform effective symbol-level precoding, resulting in a significant decline in system performance. Summary of the Invention

[0010] Object of the Invention: This invention focuses on analyzing the impact of imperfect channel state information errors in channel estimation on the performance of symbol-level precoding in large-scale MIMO systems. Based on this, a joint design of symbol-level precoding and channel estimation based on deep learning is proposed to jointly optimize the two to improve the downlink transmission performance and solve the problems that occur in the above background technology.

[0011] Technical Solution: To achieve the above object of the invention, the technical solution adopted in this invention is as follows:

[0012] A joint design method of channel estimation and symbol-level precoding based on machine learning, comprising the following steps:

[0013] Generate a data set containing received signals of multiple users;

[0014] Using a convolutional neural network to process the received signals with the criterion of minimizing the mean square error between the true channel and the estimated channel, to obtain the estimated channel matrix;

[0015] Combine the estimated channel matrix with user symbol information to construct channel data including real and imaginary parts;

[0016] Use a Transformer neural network to jointly process the channel matrix and user symbol information to calculate the key low-dimensional variable for symbol-level precoding optimization, that is, the normal vector of the favorable interference region of user symbols;

[0017] Combine the estimated channel information and the key low-dimensional variable to calculate the symbol-level precoding closed form to obtain the transmitted signal.

[0018] Further, in the dataset, the K channel vectors are jointly represented as The received signals of all users can be jointly represented as where K is the number of users and N is the number of base station antennas.

[0019] Further, the input layer of the convolutional neural network inputs the received signals to be processed, separates the received signals into real and imaginary parts and normalizes them. The normalized data samples enter the neural network from the input layer; afterwards, the input information undergoes repeated convolution, pooling, and activation multiple times to extract the frequency-domain and spatial features in the received signals; after completing multiple convolutions, poolings, and activations, the extracted feature data is input into the fully connected layer to map the extracted features into an estimated channel matrix; at the same time, the signal-to-noise ratio also participates in the fully connected as a node to adjust the training result; finally, two groups of real number matrices are output from the output layer, and after merging, a complex number matrix is obtained, representing the estimated channel state information.

[0020] Further, the estimated channel matrix and the K user symbol information matrices in the dataset are put together to obtain an intermediate matrix The real and imaginary parts of M are expanded and concatenated along the column direction to obtain

[0021] Further, through the Transformer neural network for dimensionality reduction, a key low-dimensional variable

[0022] Further, the input encoding layer of the Transformer neural network first preprocesses the complex number matrix M, separates and concatenates its real and imaginary parts to form a real number matrix Subsequently, position encoding is performed to retain the spatial relationship information of the matrix elements; the Transformer encoder extracts the key features in the matrix by stacking L layers of structures, each layer containing multi-head self-attention, layer normalization, and a feed-forward network, and the output mapping layer uses a fully connected network to compress the output of the Transformer encoder to the target dimension 2K×1 to obtain the low-dimensional variable δ.

[0023] Further, in the training stage, the Transformer neural network calculates the predicted low-dimensional variable δ through forward propagation, and then uses the loss function to evaluate the quality of the current δ and :

[0024]

[0025] where

[0026]

[0027] respectively represent taking the real part and the imaginary part, Λ represents the diagonal matrix of the normal boundary parameters of the user symbol beneficial interference region, and σ 2 represents the noise power, and P T represents the transmission signal constraint, and x represents the single-user transmission signal.

[0028] Furthermore, the diagonal matrix Λ is calculated through the user symbol information matrix s in the dataset, and is substituted into the transmission vector expression without power limitation together with the key low-dimensional variable δ and the estimated channel matrix to obtain the optimal transmission vector without power limitation with the real and imaginary parts separated

[0029]

[0030] wherein,

[0031]

[0032] Furthermore, according to the obtained optimal transmission vector without power limitation the separated real and imaginary parts are reconstructed into the complex form x through the mapping relationship * , and the vector is normalized using the power scaling factor to obtain the optimal transmission signal satisfying the power constraint

[0033] The present invention also provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the steps of the above-mentioned joint design method of channel estimation and symbol-level precoding based on machine learning.

[0034] Beneficial effects: The joint design method of channel estimation and symbol-level precoding based on machine learning proposed by the present invention has the following advantages compared with the prior art:

[0035] 1. Compared with the traditional optimization-based symbol-level precoding scheme, the neural network-based symbol-level precoding scheme can maintain good downlink transmission performance while greatly reducing the computational complexity required for symbol-level updates based on the data-driven method and the characteristic of no iterative calculation. At the same time, the data-driven characteristic of the neural network greatly simplifies the design of symbol-level precoding under imperfect state information.

[0036] 2. Compared with the traditional channel estimation scheme based on the compressed sensing algorithm, the neural network-based channel estimation method makes up for the possible performance loss caused by the channel model mismatch in a data-driven manner, thereby improving the performance of the channel estimation algorithm while reducing the computational complexity.

[0037] 3. Under the neural network-based joint design framework, the neural network-based channel estimation method will optimize the results of channel estimation in the scenario of limited pilots in the direction of enhancing the performance of symbol-level precoding, and the symbol-level precoding will adapt to the errors in channel estimation and thus have strong robustness. Description of the Drawings

[0038] Figure 1 It is the overall flowchart of the method of the present invention;

[0039] Figure 2 It is the detailed method flowchart of the embodiment of the present invention. Detailed Embodiments

[0040] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0041] The embodiment of the present invention provides a joint design method for channel estimation and symbol-level precoding based on machine learning. By designing a received signal model and generating a data set containing multiple user received signals, it supports the optimization of channel estimation and symbol-level precoding. On this basis, a convolutional neural network is used to process the received signals, aiming to minimize the mean square error between the true channel and its estimated channel, so as to obtain an accurate channel estimation matrix. The estimated channel matrix is then combined with the user symbol information, and the Transformer is relied on to reduce the dimension of the channel matrix and user symbol information and extract effective symbol representations. Based on the dimensionality reduction results, an optimization problem is constructed, aiming to minimize the error between the received signal and the target symbol, and the closed-form solution of symbol-level precoding is calculated to obtain the transmitted signal, thus realizing the effective joint design of channel estimation and symbol-level precoding.

[0042] Specifically, as Figure 1 shown, a joint design method for channel estimation and symbol-level precoding based on machine learning described in this embodiment specifically includes the following steps:

[0043] (1) Design a received signal model and generate a data set containing multiple user received signals for subsequent neural network training.

[0044] In this step, a received signal model is established using real channel data and unit pilot data. Exemplarily, consider a large-scale MIMO uplink pilot transmission link in a single-cell multi-user scenario, where the number of base station antennas is N, the number of users is K, and each user is equipped with 1 antenna. Let the received signal of the k-th user be y k , and sends a pilot sequence of length N to the base station in its own cell The channel vector is The noise n k is additive white Gaussian noise with zero mean and variance σ 2 . The received signal model can be expressed as

[0045]

[0046] The K channel vectors are jointly represented as The received signals of all users can be jointly represented as

[0047] (2) Using a convolutional neural network to process the received signal with the criterion of minimizing the mean square error between the real channel and the estimated channel, an estimated channel matrix is obtained

[0048] In this step, the criterion for channel estimation is to minimize the mean square error between the real channel and the estimated channel. Since the channel estimation process based on deep learning needs to perform separate channel estimations for each object, through a convolutional neural network, using the received signal the estimated channel is obtained

[0049] In this embodiment, the convolutional neural network includes an input layer, a convolutional layer, a pooling layer, an activation layer, a fully connected layer, and an output layer. The input layer inputs the received signal to be processed. Considering that the received signal is complex while the convolutional neural network processes real numbers, the received signal needs to be first separated into real and imaginary parts and normalized. The normalized data samples enter the neural network from the input layer. Then, the input information undergoes repeated convolution, pooling, and activation operations. The convolutional layer performs convolution operations on the input samples to extract the frequency domain and spatial features in the K×N×M-dimensional received signal. To minimize the complexity of the network as much as possible, the number of convolutional kernels is minimized without affecting the performance. The pooling layer can reduce the number of features extracted by the convolutional layer and eliminate redundant features through pooling operations. The role of the activation layer is to introduce non-linearity, and the ReLU(·) function is used for activation after each pooling layer

[0050] After multiple convolutions, poolings, and activations, the extracted feature data is input into the fully connected layer, and the extracted features are mapped to the estimated channel matrix. At the same time, the signal-to-noise ratio also participates in the full connection as a node to adjust the training result and improve the accuracy of channel estimation. Finally, two groups of K×N-dimensional real number matrices are output from the output layer, corresponding to the real part and the imaginary part of the estimated channel respectively. After merging, a K×N-dimensional complex number matrix is obtained. Represents the estimated channel state information.

[0051] (3) Combine the estimated channel matrix with the user's symbol information to construct channel data including real and imaginary parts.

[0052] In this step, the estimated channel matrix and the K user symbol information matrices in the dataset are put together to obtain the intermediate matrix Expand the real and imaginary parts of M and concatenate them along the column direction to obtain

[0053] (4) Use the Transformer neural network to jointly process the channel matrix and user symbol information, and calculate the key low-dimensional variables for symbol-level precoding optimization, that is, the normal vector of the favorable interference region of the user symbol.

[0054] In this step, through the Transformer neural network for dimensionality reduction to obtain the key low-dimensional variables

[0055] This Transformer neural network mainly includes an input encoding layer, a multi-head self-attention layer, a feed-forward neural network layer, and an output mapping layer.

[0056] The input encoding layer first preprocesses the complex matrix M, separates and concatenates its real and imaginary parts to form a real matrix Subsequently, positional encoding is performed to retain the spatial relationship information of the matrix elements. The positional encoding adds the positional embedding vector generated by the sine and cosine functions to the input features, enabling the network to perceive the relative positions of the elements in the matrix.

[0057] The multi-head self-attention mechanism is the core component of the Transformer. For the i-th attention head, the query matrix Q is generated through a linear projection layer i , the key matrix K i and the value matrix V i :

[0058]

[0059] where is a learnable projection matrix. The attention calculation formula for the i-th attention head is:

[0060]

[0061] where calculates the dot product between the query and the key to measure the relevance, and d i is the dimension of the query and the key, and head i represents the feature representation matrix after attention weighting. The multi-head mechanism calculates H independent attention heads in parallel. Each attention head extracts information in different feature subspaces. The output Z of the multi-head attention is obtained by concatenating the results of each head and performing a linear transformation:

[0062] Z = Concat(head1, head2, …, head H )W o

[0063] where W o is the projection matrix, and the output is passed to the next layer after residual connection and layer normalization.

[0064] The feed-forward neural network layer receives the output matrix Z from the self-attention layer and consists of two fully connected layers. The first layer maps the input to a hidden layer of a higher dimension and introduces a non-linear transformation using the ReLU(·) activation function. The second layer maps the hidden layer back to the original dimension. The expression for this layer is:

[0065] FFN(Z) = max(0, ZW1 + b1)W2 + b2

[0066] where W1 and W2 are weight matrices, and b1 and b2 are bias vectors. The output of the feed-forward network also undergoes layer normalization.

[0067] The Transformer encoder extracts the key features in the matrix by stacking L layers of the above structure (each layer contains multi-head self-attention, layer normalization, and a feed-forward network). The output mapping layer uses a fully connected network to compress the output of the Transformer encoder to the target dimension 2K×1 to obtain the low-dimensional variable δ.

[0068] In the training phase, the network calculates the predicted low-dimensional variable δ through forward propagation, and then uses the loss function to evaluate the quality of the current δ and

[0069]

[0070] where

[0071]

[0072] ​ respectively represent taking the real part and the imaginary part, Λ represents the diagonal matrix of the normal boundary parameters of the user symbol beneficial interference region, and σ 2 represents the noise power, and P T represents the transmission signal constraint, x represents the single-user transmission signal, and ||·||2 represents taking the two-norm of the vector.

[0073] This loss function comprehensively considers the signal transmission error and the power constraint. The first term measures the error between the transmitted signal and the target symbol, and the second term represents the power regularization term. Based on the calculated loss value, the gradients of the loss function with respect to the parameters of each layer of the network are calculated by the backpropagation algorithm, and the weight matrix and bias vector of the Transformer are updated using the gradient descent method, enabling the network to gradually learn the optimal dimensionality reduction mapping relationship.

[0074] After sufficient training, in the actual application stage, in the face of a new input matrix the network no longer needs to optimize the loss function and update the parameters, but directly outputs the optimal low-dimensional variable δ through the forward calculation process.

[0075] (5) Combine the estimated channel information and the key low-dimensional variables to calculate the closed-form symbol-level precoding to obtain the transmission signal.

[0076] In this step, first perform symbol feature extraction on the extended vector to generate the symbol matrix

[0077]

[0078] where the sign(·) function maps the elements to {-1, 0, 1} according to the positivity and negativity of the vector elements.

[0079] By judging whether the vector elements satisfy the modulation order threshold condition, an indication vector w for judging whether the symbol belongs to the beneficial interference region is obtained

[0080]

[0081] where |·| is to find the absolute value of the vector elements, and θ min and θ max represent the lower and upper threshold values of the symbol beneficial interference region respectively.

[0082] The diagonal matrix of the normal boundary parameters of the user symbol information beneficial interference region is obtained through element-by-element multiplication

[0083]

[0084] Among them, ⊙ represents the element-wise product calculation of two vectors, and diag(·) means forming a diagonal matrix with the elements inside the parentheses as diagonal elements.

[0085] The calculated diagonal matrix A, the vector δ obtained in step (4), and the estimated channel matrix obtained in step (2) are substituted into the expression of the transmit vector without power constraint, and the optimal transmit vector without power constraint with real and imaginary parts separated is obtained

[0086]

[0087] Among them,

[0088]

[0089] According to the obtained optimal transmit vector without power constraint it is reconstructed into the complex form x by separating the real and imaginary parts through the mapping relationship * , and the vector is normalized using the power scaling factor to obtain the optimal transmit signal satisfying the power constraint

[0090] This embodiment takes advantage of the superiority of deep learning in the fields of channel estimation and symbol-level precoding, and innovatively solves the limitations of traditional channel parameter estimation methods. Machine learning methods can significantly improve the accuracy and robustness of channel estimation through nonlinear feature extraction and deep representation.

[0091] In a multi-user massive MIMO communication system, the deep learning model can effectively capture complex channel characteristics and has stronger signal processing capabilities compared with traditional linear estimation methods. The introduction of advanced technologies such as convolutional neural networks and Transformer has transformed channel parameter estimation from linear mapping to nonlinear feature extraction.

[0092] Channel estimation is a key technology in modern communication systems, which directly affects the communication performance and spectrum efficiency of the system. This solution breaks through the performance bottleneck of traditional channel estimation in complex channel environments through machine learning methods, providing a new technical path for efficient and accurate signal processing.

[0093] As a key signal processing technology in multi-antenna communication systems, the core goal of precoding technology is to effectively combat channel fading and interference through signal preprocessing at the transmitter end and improve the communication performance of the system. This solution realizes the end-to-end optimization of signal processing through the joint design of channel estimation and symbol-level precoding, providing an innovative solution for future intelligent communication systems.

[0094] An embodiment of the present invention also provides a computer program product, including a computer program which, when executed by a processor, implements the steps of the method for jointly designing channel estimation and symbol-level precoding based on machine learning. The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to the processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing devices, so that when the program codes are executed by the processor or controller, the steps of the method of the present invention are implemented. The program codes can be executed entirely on the machine, partially on the machine, executed partially on the machine as an independent software package and partially on a remote machine, or executed entirely on a remote machine or server. Where the present invention is not elaborated, it is all well-known techniques to those skilled in the art.

[0095] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A joint design method for channel estimation and symbol-level precoding based on machine learning, characterized in that: It includes the following steps: Generate a data set containing multiple user received signals; Taking the minimization of the mean square error between the true channel and the estimated channel as the criterion, use a convolutional neural network to process the received signals to obtain an estimated channel matrix; Combine the estimated channel matrix with the user symbol information to construct channel data containing real and imaginary parts; Use a Transformer neural network to jointly process the channel matrix and the user symbol information, and calculate the key low-dimensional variables optimized by symbol-level precoding, that is, the normal vector of the favorable interference region of the user symbols; Combine the estimated channel information and the key low-dimensional variables to calculate the symbol-level precoding closed form to obtain the transmitted signal.

2. The joint design method of channel estimation and symbol-level precoding based on machine learning according to claim 1, characterized in that: In the dataset, the K channel vectors are jointly represented as The received signals of all users are jointly represented as where K is the number of users and N is the number of base station antennas.

3. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 1, characterized in that: The input layer of the convolutional neural network inputs the received signals to be processed, separates the received signals into real and imaginary parts and normalizes them, and the normalized data samples enter the neural network from the input layer; then, the input information undergoes repeated convolution, pooling, and activation to extract the frequency domain and spatial features in the received signals; After completing multiple convolutions, poolings, and activations, the extracted feature data is input into the fully connected layer, and the extracted features are mapped to the estimated channel matrix; at the same time, the signal-to-noise ratio also participates in the fully connected as a node to adjust the training results; finally, two sets of real number matrices are output from the output layer, and after merging, a complex matrix is obtained, representing the estimated channel state information.

4. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 2, characterized in that: The estimated channel matrix and the K user symbol information matrices in the dataset are combined to obtain an intermediate matrix The real and imaginary parts of M are expanded and cascaded along the column direction to obtain where K is the number of users and N is the number of antennas at the base station side.

5. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 4, characterized in that: Reduce the dimension through the Transformer neural network to obtain the key low-dimensional variables 6. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 1, characterized in that: The input encoding layer of the Transformer neural network first preprocesses the complex matrix M, separates its real and imaginary parts and concatenates them to form a real matrix Subsequently, positional encoding is performed to retain the spatial relationship information of the matrix elements; The Transformer encoder extracts key features from the matrix by stacking L layers, each layer containing multi-head self-attention, layer normalization, and a feed-forward network. The output mapping layer uses a fully-connected network to compress the output of the Transformer encoder to the target dimension 2K×1, obtaining the low-dimensional variable δ, where K is the number of users. The key features in the matrix are extracted, and the output mapping layer uses a fully-connected network to compress the output of the Transformer encoder to the target dimension 2K×1, obtaining the low-dimensional variable δ, where K is the number of users.

7. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 4, characterized in that: During the training phase, the Transformer neural network calculates the predicted low-dimensional variable δ through forward propagation, and then uses the loss function to evaluate the quality of the current δ and : Among them, respectively represent taking the real part and the imaginary part, Λ represents the diagonal matrix of the normal boundary parameters of the user symbol favorable interference region, σ 2 represents the noise power, P T represents the transmission signal constraint, and x represents the single-user transmission signal.

8. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 1, characterized in that: Calculate the diagonal matrix Λ from the user symbol information matrix s in the dataset, and combine it with the key low-dimensional variable δ and the estimated channel matrix Substitute it into the expression of the transmit vector without power constraint to obtain the optimal transmit vector without power constraint with real and imaginary parts separated Among them, respectively represent taking the real part and the imaginary part, Λ represents the diagonal matrix of the normal boundary parameters of the user symbol beneficial interference region, and σ 2 represents the noise power, P T represents the transmission signal constraint, I 2K represents the unit vector.

9. A joint design method for channel estimation and symbol-level precoding based on machine learning according to claim 8, characterized in that: According to the obtained optimal transmission vector without power constraint The real and imaginary parts are separated and represented through the mapping relationship to reconstruct the complex form x * , and using the power scaling factor normalize the vector to obtain the optimal transmission signal u that satisfies the power constraint * = γx * .

10. A computer program product comprising a computer program, characterized in that, When the computer program is executed by a processor, it realizes the steps of a joint design method for channel estimation and symbol-level precoding based on machine learning according to any one of claims 1-9.

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