FBMC channel estimation method based on CNN interpolation algorithm optimization

Abstract

The invention discloses an FBMC channel estimation method based on CNN interpolation algorithm optimization. The method comprises the following steps: 1) pilot frequency structure design; 2) calculating a channel estimation value at a data symbol position; and 3) performing channel interpolation and performance estimation. According to the method, the pilot frequency data estimation value of the receiving end of the FBMC system is input into the constructed convolutional neural network model for processing, noise reduction and feature extraction are carried out on time-varying channel information through the CNN model, and the performance limitations of high calculation complexity, insufficient estimation precision and the like of a traditional channel estimation interpolation method under the complex channel condition are overcome; therefore, the channel estimation precision of the FBMC system in the low SNR and complex fading environment is improved.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a filter bank multi-carrier FBMC (Filter Bank Multi Carrier, FBMC for short) channel estimation method based on optimization of a convolutional neural network (CNN) interpolation algorithm. Background Art

[0002] With the development of 5G and future wireless communication technologies, the demand for efficient channel estimation algorithms continues to increase. Traditional channel estimation methods usually use pilot symbol-based interpolation techniques, such as the least squares method (LS) and constant interpolation, linear interpolation, spline interpolation and other algorithms. These traditional interpolation algorithms are usually less adaptable to scenarios with rapidly changing channels, especially in time-varying and frequency-selective channels. Their performance is easily affected by noise and multipath effects, resulting in large errors in interpolation accuracy and system bit error rate (BER) compared with the ideal channel state.

[0003] In FBMC systems, due to its efficient use of spectrum and strong anti-interference ability, more and more studies tend to use FBMC for channel estimation. For FBMC systems, due to the lack of protection intervals (such as cyclic prefixes in orthogonal frequency division multiplexing OFDM), higher requirements are placed on channel estimation. In addition, the FBMC channel estimation process relies on the accurate interpolation of pilot symbols, so traditional interpolation methods have certain limitations. In recent years, with the continuous research of deep learning technology, especially convolutional neural networks (CNN), excellent performance has been shown in channel estimation. CNN can effectively capture the complex nonlinear characteristics in channel response, deeply model channel features through multi-layer convolution and nonlinear activation functions, and significantly improve the estimation accuracy of time-varying channels and non-stationary channels. In addition, CNN can automatically learn the complex characteristics of the channel and restore the lost channel information through interpolation algorithms. Summary of the invention

[0004] The purpose of the present invention is to provide a FBMC channel estimation method based on CNN interpolation algorithm optimization in view of the shortcomings of the prior art. This method can reduce noise and extract features of time-varying channel information by constructing a CNN model, overcome the defects of high computational complexity and insufficient estimation accuracy of traditional channel estimation interpolation methods under complex channel conditions, and thus improve communication quality.

[0005] The technical solution for achieving the purpose of the present invention is:

[0006] A FBMC channel estimation method based on CNN interpolation algorithm optimization includes the following steps:

[0007] 1) Pilot structure design: The pilot structure of this technical solution inserts pilot symbols in an interval manner on a two-dimensional time-frequency plane. Two auxiliary pilot symbols are introduced to cooperatively cancel the inherent non-orthogonal interference of the pilot in the first-order field. The pilot structure defines the time-frequency point where the auxiliary pilot is located as (m, n), and the time-frequency point where the pilot is located as (p, q). When (m, n) = (p, q ± 1), the inherent interference of the auxiliary pilot to the pilot point is the largest, thereby minimizing the power of the auxiliary pilot. Suppose the pilot is a p,q ,but That is, the total interference received at the pilot point (p, q), and the calculation formula is as shown in formula (1):

[0008]

[0009] Where Ω is the time-frequency point set of the auxiliary pilot, and the time-frequency point set contains the locations of all auxiliary pilots. is the interference coefficient of the filter bank, which represents the interference of the auxiliary pilot time-frequency point (m,n) to the pilot point (p,q). Finally, the interference values ​​at all auxiliary pilot time-frequency points are accumulated to obtain the total interference. According to the symmetry of the prototype filter interference coefficient, when the inherent interference in the first-order neighborhood is completely eliminated, When , the channel estimation value at the pilot can be calculated, and the power consumed by the auxiliary pilot is as shown in formula (2):

[0010] p=|a m,n 2 (2)

[0011] Specifically include:

[0012] 1-1) After the pilot structure design is completed, the precoding method is introduced: that is, taking the time-frequency point where the pilot is located as the center, the surrounding n adjacent symbols are precoded, and the inherent non-orthogonal interference of the pilot is eliminated by designing the coding matrix. Take n=16. At this time, the coded symbols are exactly 16 data symbols in the first-order neighborhood of the pilot. The overall coding layout is in a diamond shape. Let the symbol vector before coding be s=[s 1 ,s 2 ,...,s n-1 ] T , the symbol vector after encoding mapping is s coded , the encoding matrix is ​​ω=[ω 1 ,ω 2 ,...,ω n-1 ], then the relationship between the symbols is s coded =ω·s, where the dimension of the encoding matrix ω is n×n, the symbol vector s before encoding and the symbol vector s after encoding mapping coded Is a column vector of dimension n. At the receiving end, the inverse encoding matrix ω is used.-1 The original symbol vector can be restored: s = ω -1 ·s coded , encoding matrix ω and inverse encoding matrix ω -1 Satisfies the following relationship: ω·ω -1 =I, where I is the unit matrix. This relationship ensures that the energy of the symbols before and after coding remains constant and does not introduce noise amplification effect. Let vector ζ be the interference coefficient corresponding to the pilot position. Vector ζ represents a column vector with dimension n. In order to eliminate interference, the inherent interference at the pilot position must be set to zero. The coding matrix ω constructed in the above manner can completely eliminate interference. The constraint relationship between the two is shown in formula (3):

[0013]

[0014] According to ω·ω -1 =I, the encoding matrix ω is set so that ζ·ω=0, where 0 represents a full zero vector of the corresponding dimension;

[0015] 1-2) Step 1-1) completes the interference elimination of the coded symbol position, and the inherent interference elimination process of the uncoded symbol to the pilot position is:

[0016] Define the uncoded symbol vector around the pilot point as s u ,s u The corresponding interference coefficient vector is ζ u , then the inherent interference caused by these uncoded symbols to the pilot is expressed as In order to eliminate interference, an auxiliary vector α is introduced, and the symbol to be transmitted after encoding is expressed as s coded =s u +α, the constraint relationship for eliminating the interference caused by the coded symbol to the pilot position is shown in formula (4):

[0017] ζ u ·s coded =ζ u ·(s u +α)=0 (4),

[0018] The Lagrange multiplier method is used to solve the correction vector and solve the auxiliary vector α with the minimum norm. * , expressed as shown in formula (5):

[0019]

[0020] 2) Calculate the channel estimation value at the data symbol position: After estimating the channel response at the pilot position, the CNN interpolation algorithm is used to calculate the channel estimation value at the data symbol position. CNN includes a data input layer, a convolution layer, a RELU excitation layer, a pooling layer, and an output layer. The CNN model is trained using a back propagation algorithm, using the known channel response and pilot symbols as training data. The specific process is as follows:

[0021] 2-1) Data preparation and pilot design: According to the pilot structure designed in step 1), in the FBMC system, the input channel is modulated and the pilot symbol is inserted, and the generated signal is represented as shown in formula (6):

[0022]

[0023] where a k is the modulation symbol, g[n] is the impulse response of the FBMC filter, T is the symbol interval, N is the number of subcarriers, and after the pilot is inserted, the received signal through the channel is expressed as shown in formula (7):

[0024] y[n]=h[n]*x[n]+w[n] (7),

[0025] Where h[n] is the channel impulse response, w[n] is Gaussian white noise, and the two-dimensional frequency domain formed by the pilot symbol distribution is expressed as shown in formula (8):

[0026] Y[f]=P[f]*H[f]+W[f] (8),

[0027] Wherein, P[f] is the frequency domain distribution of the pilot symbol, and H[f] is the channel frequency response;

[0028] 2-2) CNN channel estimation model design: The input of the CNN model is the frequency domain characteristics of the pilot symbol, and the output is the estimated complete channel response, as follows:

[0029] 2-2-1) Input layer: The pilot structure diagram is input into the network as a two-dimensional matrix with a size of M×N, where M is the time dimension and N is the frequency dimension, representing the two-dimensional matrix extracted from the receiving end pilot. The input pilot structure diagram is normalized to reduce the impact of the numerical range on model training. The normalization result is shown in formula (9):

[0030]

[0031] Among them, Y input [m,n] represents the value of the input signal at the two-dimensional index, σ is the standard deviation of the input data, μ is the mean of the input data, and the calculation formula of the parameter μ is shown in formula (10):

[0032]

[0033] 2-2-2) Convolutional layer: The convolutional layer is the core of CNN. It uses multiple convolutional kernel filters to slide the input data and extract local features. For the input Y, the operation formula of each convolution kernel is shown in formula (11):

[0034]

[0035] in, is the output of the kth convolution kernel at position (i, j), x (i,j) is the value of the input matrix, w (i,j) is the weight matrix of the kth convolution kernel, with size h×v, b (k) is the bias, σ is the activation function, and the ReLU function is selected: σ(x) = max(0,x). The size of the convolution result is calculated as follows: Assuming that the size of the input matrix is ​​(M, N), the size of the convolution kernel is (h, w), the sliding step is s, and the padding is p, the output matrix size is as shown in formula (12):

[0036]

[0037] 2-2-3) Pooling layer: The pooling layer performs dimensionality reduction on the output of the convolutional layer, using maximum pooling or average pooling. The formula of the maximum pooling layer is shown in formula (13):

[0038] p i,j =max{z m,n :m∈[i·s,i·s+k-1], n∈[j·s, j·s+k-1]} (13),

[0039] Where s is the step size of the pooling window, k is the size of the pooling window, and the output size after pooling is as shown in formula (14):

[0040]

[0041] 2-2-4) Fully connected layer: The feature map output by the pooling layer is flattened and then input into the fully connected layer. For the input vector V∈R d , the output of the fully connected layer is o = σ(Wv+b), where is the weight function, is the bias vector, d out is the dimension of the output vector;

[0042] 2-2-5) Output layer: The complete channel estimate generated by the output layer is output as the result. The final output layer is a linear regression layer used to generate the estimated complete channel response matrix The formula of the output layer is Where W out and b out are the parameters of the linear regression layer;

[0043] 3) Channel interpolation and performance estimation: After step 2), the CNN model completes channel interpolation and estimates the result of the complete channel response: Then the MMSE equalization algorithm is used to perform channel compensation and data recovery, and the result is: in The original data symbol is estimated. Finally, the algorithm performance is verified by simulation. The evaluation indicators include mean square error (MSE) and bit error rate (BER). The MSE calculation formula is shown in formula (15):

[0044]

[0045] The bit error rate BER is: number of erroneous bits / total number of bits, and the values ​​of the two change with the SNR.

[0046] This technical solution aims to address the performance limitations of traditional interpolation methods for channel estimation, such as high computational complexity and insufficient estimation accuracy under complex channel conditions. By building a CNN network model and using CNN to extract nonlinear channel features, the accuracy and robustness of channel estimation can be effectively improved. This method improves the performance of the FBMC system under low signal-to-noise ratio (SNR) conditions and can adapt to complex channel environments such as multipath fading and frequency selective channel environments. In addition, CNN has strong generalization capabilities and can be applied to a variety of pilot design schemes based on the system computational complexity and the requirements of different channel environments.

[0047] This method can reduce noise and extract features of time-varying channel information by constructing a CNN model, overcome the defects of high computational complexity and insufficient estimation accuracy of traditional channel estimation methods under complex channel conditions, and thus improve communication quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a schematic diagram of the auxiliary pilot structure;

[0049] Figure 2 Schematic diagram of pilot symbols using the precoding method;

[0050] Figure 3 This is a schematic diagram of the basic structure of CNN;

[0051] Figure 4 This is the structural block diagram of the CNN channel estimation model;

[0052] Figure 5 It is the block diagram of FBMC system;

[0053] Figure 6 Schematic diagram of the channel estimation system model. DETAILED DESCRIPTION

[0054] The content of the present invention is further described below in conjunction with the drawings and embodiments, but the present invention is not limited thereto.

[0055] Example:

[0056] A FBMC channel estimation method based on CNN interpolation algorithm optimization includes the following steps:

[0057] 1) Pilot structure design: Figure 1 As shown, the pilot structure in this example inserts pilot symbols in an interval manner on a two-dimensional time-frequency plane. Two auxiliary pilot symbols are introduced to cooperatively cancel the inherent non-orthogonal interference of the pilot in the first-order domain. The pilot structure defines the time-frequency point where the auxiliary pilot is located as (m, n), and the time-frequency point where the pilot is located as (p, q). When (m, n) = (p, q ± 1), the inherent interference of the auxiliary pilot to the pilot point is the largest, thereby minimizing the power of the auxiliary pilot. Suppose the pilot is a p,q ,but That is, the total interference received at the pilot point (p, q), and the calculation formula is as shown in formula (1):

[0058]

[0059] Where Ω is the time-frequency point set of the auxiliary pilot, and the time-frequency point set contains the locations of all auxiliary pilots.

[0060] is the interference coefficient of the filter bank, which represents the interference of the auxiliary pilot time-frequency point (m,n) to the pilot point (p,q). Finally, the interference values ​​at all auxiliary pilot time-frequency points are accumulated to obtain the total interference. According to the symmetry of the prototype filter interference coefficient, when the inherent interference in the first-order neighborhood is completely eliminated, When , the channel estimation value at the pilot can be calculated, and the power consumed by the auxiliary pilot is as shown in formula (2):

[0061] p=|a m,n 2 (2)

[0062] Specifically include:

[0063] 1-1) After the pilot structure design is completed, the precoding method is introduced: that is, taking the time-frequency point where the pilot is located as the center, the surrounding n adjacent symbols are precoded, and the inherent non-orthogonal interference of the pilot is eliminated by designing the coding matrix. In this example, n=16 is taken. At this time, the coding symbols are exactly 16 data symbols in the first-order neighborhood of the pilot. The overall coding layout is in a diamond shape. The coding schematic diagram is shown as follows Figure 2 As shown, let the symbol vector before encoding be s=[s 1 ,s 2 ,...,s n-1 ] T , the symbol vector after encoding mapping is s coded , the encoding matrix is ​​ω=[ω 1 ,ω 2 ,...,ω n-1 ], then the relationship between the symbols is s coded =ω·s, where the dimension of the encoding matrix ω is n×n, the symbol vector s before encoding and the symbol vector s after encoding mapping coded Is a column vector of dimension n. At the receiving end, the inverse encoding matrix ω is used. -1 The original symbol vector can be restored: s = ω -1 ·s coded , encoding matrix ω and inverse encoding matrix ω -1 Satisfies the following relationship: ω·ω -1 =I, where I is the unit matrix. This relationship ensures that the energy of the symbols before and after coding remains constant and does not introduce noise amplification effect. Let vector ζ be the interference coefficient corresponding to the pilot position. Vector ζ represents a column vector with dimension n. In order to eliminate interference, the inherent interference at the pilot position must be set to zero. The coding matrix ω constructed in the above manner can completely eliminate interference. The constraint relationship between the two is shown in formula (3):

[0064]

[0065] According to ω·ω -1 =I, the encoding matrix ω is set so that ζ·ω=0, where 0 represents a full zero vector of the corresponding dimension;

[0066] 1-2) Step 1-1) completes the interference elimination of the coded symbol position, and the inherent interference elimination process of the uncoded symbol to the pilot position is:

[0067] Define the uncoded symbol vector around the pilot point as s u ,s u The corresponding interference coefficient vector is ζ u , then the inherent interference caused by these uncoded symbols to the pilot is expressed as In order to eliminate interference, an auxiliary vector α is introduced, and the symbol to be transmitted after encoding is expressed as scoded =s u +α, the constraint relationship for eliminating the interference caused by the coded symbol to the pilot position is shown in formula (4):

[0068] ζ u ·s coded =ζ u ·(s u +α)=0 (4),

[0069] The Lagrange multiplier method is used to solve the correction vector and solve the auxiliary vector α with the minimum norm. * , expressed as shown in formula (5):

[0070]

[0071] 2) Calculate the channel estimation value at the data symbol position: After estimating the channel response at the pilot position, the CNN interpolation algorithm is used to calculate the channel estimation value at the data symbol position. The basic structure of CNN is as follows: Figure 3 As shown in the figure, it includes data input layer, convolution layer, RELU excitation layer, pooling layer and output layer. The CNN model is trained using the back propagation algorithm, with known channel responses and pilot symbols as training data. The specific process is as follows:

[0072] 2-1) Data preparation and pilot design: According to the pilot structure designed in step 1), in the FBMC system, the input channel is modulated and the pilot symbol is inserted, and the generated signal is represented as shown in formula (6):

[0073]

[0074] where a k is the modulation symbol, g[n] is the impulse response of the FBMC filter, T is the symbol interval, N is the number of subcarriers, and after the pilot is inserted, the received signal through the channel is expressed as shown in formula (7):

[0075] y[n]=h[n]*x[n]+w[n] (7),

[0076] Where h[n] is the channel impulse response, w[n] is Gaussian white noise, and the two-dimensional frequency domain formed by the pilot symbol distribution is expressed as shown in formula (8):

[0077] Y[f]=P[f]*H[f]+W[f] (8),

[0078] Wherein, P[f] is the frequency domain distribution of the pilot symbol, and H[f] is the channel frequency response;

[0079] 2-2) CNN channel estimation model design: The input of the CNN model is the frequency domain characteristics of the pilot symbol, and the output is the estimated complete channel response, as follows:

[0080] 2-2-1) Input layer: The pilot structure diagram is input into the network as a two-dimensional matrix with a size of M×N, where M is the time dimension and N is the frequency dimension, representing the two-dimensional matrix extracted from the receiving end pilot. The input pilot structure diagram is normalized to reduce the impact of the numerical range on model training. The normalization result is shown in formula (9):

[0081]

[0082] Among them, Y input [m,n] represents the value of the input signal at the two-dimensional index, σ is the standard deviation of the input data, μ is the mean of the input data, and the calculation formula of the parameter μ is shown in formula (10):

[0083]

[0084] 2-2-2) Convolutional layer: The convolutional layer is the core of CNN. It uses multiple convolutional kernel filters to slide the input data and extract local features. For the input Y, the operation formula of each convolution kernel is shown in formula (11):

[0085]

[0086] in, is the output of the kth convolution kernel at position (i, j), x (i,j) is the value of the input matrix, w (i,j) is the weight matrix of the kth convolution kernel, with size h×v, b (k) is the bias, σ is the activation function, and the ReLU function is selected: σ(x) = max(0,x). The size of the convolution result is calculated as follows: Assuming that the size of the input matrix is ​​(M, N), the size of the convolution kernel is (h, w), the sliding step is s, and the padding is p, the output matrix size is as shown in formula (12):

[0087]

[0088] 2-2-3) Pooling layer: The pooling layer performs dimensionality reduction on the output of the convolutional layer, using maximum pooling or average pooling. The formula of the maximum pooling layer is shown in formula (13):

[0089] p i,j =max{z m,n :m∈[i·s,i·s+k-1], n∈[j·s, j·s+k-1]} (13),

[0090] Where s is the step size of the pooling window, k is the size of the pooling window, and the output size after pooling is as shown in formula (14):

[0091]

[0092] 2-2-4) Fully connected layer: The feature map output by the pooling layer is flattened and then input into the fully connected layer. For the input vector V∈R d , the output of the fully connected layer is o = σ(Wv+b), where is the weight function, is the bias vector, d out is the dimension of the output vector;

[0093] 2-2-5) Output layer: The complete channel estimate generated by the output layer is output as the result. The final output layer is a linear regression layer used to generate the estimated complete channel response matrix The formula of the output layer is Where W out and b out are the parameters of the linear regression layer;

[0094] 3) Channel interpolation and performance estimation: After step 2), the CNN model completes channel interpolation and estimates the result of the complete channel response: Then the MMSE equalization algorithm is used to perform channel compensation and data recovery, and the result is: in The original data symbol is estimated. Finally, the algorithm performance is verified by simulation. The evaluation indicators include mean square error (MSE) and bit error rate (BER). The MSE calculation formula is shown in formula (15):

[0095]

[0096] The bit error rate BER is: number of erroneous bits / total number of bits, and the values ​​of the two change with the SNR.

[0097] In this example, if Figure 4 As shown, each module of the CNN model processes the received signal and noise in an orderly manner during the FBMC channel estimation process;

[0098] In this example, if Figure 5As shown in the figure, the FBMC system consists of four parts: OQAM preprocessing, integrated filter, analysis filter and OQAM post-processing. The OQAM preprocessing separates the real and imaginary parts of the transmitted signal after constellation mapping, ensuring the real orthogonality of the system. The integrated filter is composed of inverse Fourier transform (IFFT) and polyphase structure (PPN). It mainly modulates the output signal after OQAM preprocessing to subcarriers on different frequency bands respectively, and then adds them together to merge them into a broadband signal. The analysis filter is the inverse process of the integrated filter. It is composed of polyphase structure and Fourier transform (FFT) to demodulate the subcarrier signal in the broadband signal. The OQAM post-processing is to first take the real part of the subcarrier signal, and then reconstruct the real signal into a complex signal through real-complex conversion to restore the original signal. P / S and S / P represent parallel-to-serial conversion and serial-to-parallel conversion respectively.

[0099] In this example, if Figure 6 As shown in the figure, the FBMC system first provides the original bit stream (binary data) from the data source, transmits the data to the channel coding module, encodes the original bit stream data to increase the redundancy of the data, thereby enhancing the ability to resist noise and interference, and then converts the encoded data into a signal waveform through digital modulation and transmits it through the wireless channel. Since the channel will introduce noise, multipath fading, phase shift and other influences, time, frequency and phase synchronization processing are required at the receiving end. Finally, a convolutional neural network is used to estimate the channel and output data.

Claims

1. A FBMC channel estimation method based on CNN interpolation algorithm optimization, characterized in that: The steps include: 1) Pilot structure design: The pilot structure inserts pilot symbols in an interval manner on the two-dimensional time-frequency plane, and introduces two auxiliary pilot symbols to cooperatively offset the inherent non-orthogonal interference of the pilot in the first-order domain. The pilot structure defines the time-frequency point where the auxiliary pilot is located as (m,n), and the time-frequency point where the pilot is located as (p,q). When (m,n) = (p,q±1), the inherent interference of the auxiliary pilot to the pilot point is the largest, making the power of the auxiliary pilot minimum. Suppose the pilot is a p,q ,but That is, the total interference received at the pilot point (p, q), and the calculation formula is as shown in formula (1): Where Ω is the time-frequency point set of the auxiliary pilot, and the time-frequency point set contains the locations of all auxiliary pilots. is the interference coefficient of the filter bank, which represents the interference of the auxiliary pilot time-frequency point (m,n) to the pilot point (p,q). The interference values ​​at all auxiliary pilot time-frequency points are accumulated to obtain the total interference. According to the symmetry of the prototype filter interference coefficient, when the inherent interference in the first-order neighborhood is completely eliminated, When , the channel estimation value at the pilot can be calculated, and the power consumed by the auxiliary pilot is as shown in formula (2): p=|a m,n 2 (2), Specifically include: 1-1) After the pilot structure design is completed, the precoding method is introduced: that is, taking the time-frequency point where the pilot is located as the center, the surrounding n adjacent symbols are precoded, and the coding matrix is ​​designed to help eliminate the inherent non-orthogonal interference suffered by the pilot. Take n = 16. At this time, the coded symbols are exactly the 16 data symbols in the first-order neighborhood of the pilot. The overall coding layout is in a diamond shape. Let the symbol vector before coding be s = [s1, s2, ..., s n-1 ] T , the symbol vector after encoding mapping is s coded , the encoding matrix is ​​ω=[ω1,ω2,...,ω n-1 ], then the relationship between the symbols is s coded =ω·s, where the dimension of the encoding matrix ω is n×n, the symbol vector s before encoding and the symbol vector s after encoding mapping coded Is a column vector of dimension n. At the receiving end, the inverse encoding matrix ω is used. -1 Restore the original symbol vector: s = ω -1 ·s coded , encoding matrix ω and inverse encoding matrix ω -1 The following relationship is satisfied: ω·ω -1 =I, where I is the unit matrix. Let vector ζ be the interference coefficient corresponding to the pilot position. Vector ζ represents a column vector with dimension n. Let the inherent interference at the pilot be zero. The coding matrix ω constructed in the above manner can completely eliminate the interference. The constraint relationship between the two is shown in formula (3): According to ω·ω -1 =I, the encoding matrix ω is set so that ζ·ω=0, where 0 represents a full zero vector of the corresponding dimension; 1-2) Step 1-1) completes the interference elimination of the coded symbol position, and the inherent interference elimination process of the uncoded symbol to the pilot position is: Define the uncoded symbol vector around the pilot point as s u ,s u The corresponding interference coefficient vector is ζ u , then the inherent interference caused by these uncoded symbols to the pilot is expressed as Introducing the auxiliary vector α, the symbol to be sent after encoding is represented as s coded =s u +α, the constraint relationship for eliminating the interference caused by the coded symbol to the pilot position is shown in formula (4): g u ·s coded =ζ u ·(s u +a)=0(4), The Lagrange multiplier method is used to solve the correction vector and solve the auxiliary vector α with the minimum norm. * , expressed as shown in formula (5): 2) Calculate the channel estimation value at the data symbol position: After estimating the channel response at the pilot position, the CNN interpolation algorithm is used to calculate the channel estimation value at the data symbol position. CNN includes a data input layer, a convolution layer, a RELU excitation layer, a pooling layer, and an output layer. The CNN model is trained using a back propagation algorithm, using the known channel response and pilot symbols as training data. The specific process is as follows: 2-1) Data preparation and pilot design: According to the pilot structure designed in step 1), in the FBMC system, the input channel is modulated and the pilot symbol is inserted, and the generated signal is represented as shown in formula (6): where a k is the modulation symbol, g[n] is the impulse response of the FBMC filter, T is the symbol interval, N is the number of subcarriers, and after the pilot is inserted, the received signal through the channel is expressed as shown in formula (7): y[n]=h[n]*x[n]+w[n](7), Where h[n] is the channel impulse response, w[n] is Gaussian white noise, and the two-dimensional frequency domain formed by the pilot symbol distribution is expressed as shown in formula (8): Y[f]=P[f]*H[f]+W[f](8), Wherein, P[f] is the frequency domain distribution of the pilot symbol, and H[f] is the channel frequency response; 2-2) CNN channel estimation model design: The input of the CNN model is the frequency domain characteristics of the pilot symbol, and the output is the estimated complete channel response, as follows: 2-2-1) Input layer: The pilot structure diagram is input into the network as a two-dimensional matrix with a size of M×N, where M is the time dimension and N is the frequency dimension, representing the two-dimensional matrix extracted from the receiving end pilot. The input pilot structure diagram is normalized, and the normalization result is shown in formula (9): Among them, Y input [m,n] represents the value of the input signal at the two-dimensional index, σ is the standard deviation of the input data, μ is the mean of the input data, and the calculation formula of the parameter μ is shown in formula (10): 2-2-2) Convolution layer: Use multiple convolution kernel filters to slide the input data to extract local features. For input Y, the operation formula of each convolution kernel is shown in formula (11): in, is the output of the kth convolution kernel at position (i, j), x (i,j) is the value of the input matrix, w (i,j) is the weight matrix of the kth convolution kernel, with size h×v, b (k) is the bias, σ is the activation function, and the ReLU function is selected: σ(x) = max(0,x). The size of the convolution result is calculated as follows: Assuming that the size of the input matrix is ​​(M, N), the size of the convolution kernel is (h, w), the sliding step is s, and the padding is p, the output matrix size is as shown in formula (12): 2-2-3) Pooling layer: Use Max Pooling or Average Pooling. The formula of the Max Pooling layer is as shown in formula (13): p i,j =max{z m,n :m∈[i·s,i·s+k-1]、n∈[j·s,j·s+k-1]}(13), Where s is the step size of the pooling window, k is the size of the pooling window, and the output size after pooling is as shown in formula (14): 2-2-4) Fully connected layer: The feature map output by the pooling layer is flattened and then input into the fully connected layer. For the input vector V∈R d , the output of the fully connected layer is o = σ(Wv+b), where is the weight function, is the bias vector, d out is the dimension of the output vector; 2-2-5) Output layer: The complete channel estimate generated by the output layer is output as the result. The final output layer is a linear regression layer used to generate the estimated complete channel response matrix The formula of the output layer is Where W out and b out are the parameters of the linear regression layer; 3) Channel interpolation and performance estimation: After step 2), the CNN model completes channel interpolation and estimates the result of the complete channel response: Then the MMSE equalization algorithm is used to perform channel compensation and data recovery, and the result is: in The original data symbol is estimated. Finally, the algorithm performance is verified by simulation. The evaluation indicators include mean square error (MSE) and bit error rate (BER). The MSE calculation formula is shown in formula (15): The bit error rate BER is: number of erroneous bits / total number of bits, and the values ​​of the two change with the SNR.

Images