Bi-lstm-sa low complexity otfs channel estimation method and system based on basis expansion model

Abstract

The application relates to a Bi-LSTM-SA low-complexity OTFS channel estimation method and system based on a basis expansion model and belongs to the technical field of wireless communication and deep learning. In view of the problems of low channel estimation accuracy and high equalization complexity in a high-speed mobile scene, the application converts time-domain channel estimation into low-dimensional basis coefficient estimation through a basis expansion model, extracts basis coefficient time sequence features by using a self-attention enhanced bidirectional long short-term memory network, and realizes high-precision channel estimation. Meanwhile, a two-stage equalizer is adopted, single-tap equalization is carried out in a time-frequency domain, and residual interference is suppressed through iterative interference cancellation in a delay-Doppler domain. The application effectively balances estimation accuracy and calculation complexity, and improves the anti-Doppler spread capability and spectral utilization efficiency of a system.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and deep learning technology, and relates to a low-complexity OTFS channel estimation method and system based on the base extension model Bi-LSTM-SA. Background Technology

[0002] With the development of sixth-generation mobile communication technology, reliable communication in high-speed mobile scenarios has become a core technical requirement. Orthogonal Time Frequency Space (OTFS) modulation, as a novel modulation technique, transforms the time-varying channel into a delayed Doppler domain for processing. This converts the rapidly varying and diffused channel response in the traditional time and frequency domain into a channel representation with slowly varying and sparse characteristics, fundamentally overcoming the negative impacts of channel time-varying and Doppler spread in high-speed scenarios. This provides an effective solution for high-speed mobile communication scenarios such as high-speed rail and vehicle-to-everything (V2X) communication.

[0003] To address the channel estimation problem in OTFS systems, existing technologies mainly follow three technical routes. The first category is traditional correlation or threshold-based algorithms. Correlation Channel Estimation (CCE) algorithms assume that the channel remains constant within one symbol period and achieve channel estimation by estimating the cross-correlation function of elements in the time-delayed Doppler domain. However, in high-speed mobile scenarios, the channel coherence time is much shorter than the symbol duration, and this assumption no longer holds, leading to a rapid decrease in estimation accuracy. Threshold Channel Estimation (TCE) algorithms have a simple structure, but they also suffer from low channel estimation accuracy and difficulty in tracking rapid channel changes in high-speed mobile scenarios.

[0004] The second category is channel estimation algorithms based on the Basis Expansion Model (BEM). These algorithms use the Generalized Complex Exponential-BEM (GCE-BEM) model to transform the estimation problem of the time-domain channel impulse response (CIR) into a basis coefficient estimation problem. They utilize the linear minimum mean square error (LMMSE) basis coefficient estimates at the pilots and the basis coefficients estimated at the data points using Lagrange interpolation. While this algorithm has a simple structure, in high-speed scenarios, the interpolation results struggle to accurately track the fast time-varying characteristics of the channel, leading to a significant increase in estimation error. Due to the sparsity of the BEM basis coefficients, an improved regularized orthogonal matching pursuit (iROMP) iterative sparse channel estimation algorithm based on BEM has emerged. This algorithm improves estimation accuracy through iterative feedback, but it relies on predefined sparsity parameters and is sensitive to noise and model mismatch.

[0005] The third category is deep learning algorithms. Deep Neural Networks (DNNs), Long Short-Term Memory (LSTM) networks, and Gated Recurrent Units (GRUs), among others, possess powerful learning capabilities for temporal features, effectively capturing the structured characteristics of the channel in different domains, thus resisting Doppler spread and multipath effects. Existing work has applied LSTM to OTFS channel estimation, but the unidirectional LSTM structure used can only utilize pilot information from past moments and cannot incorporate pilot information from future moments. This results in the lack of temporal correlation contained in subsequent pilots when predicting Channel State Information (CSI) at data symbol positions. Therefore, a denser configuration of pilots is required to ensure estimation accuracy.

[0006] After channel estimation, equalizer design becomes another critical issue affecting system performance. The OTFS system employs minimum mean square error (MMSE) equalizers in both the time-frequency and delay-Doppler domains, involving high-dimensional matrix inversion operations, which are too complex to implement in practical systems. In contrast, while single-tap equalizers in the time-frequency domain have lower complexity, they suffer significant performance degradation in high-speed mobile scenarios. Therefore, designing a low-complexity equalizer while maintaining channel estimation accuracy is a key challenge for improving the practicality of the OTFS system.

[0007] In summary, traditional correlation or thresholding algorithms suffer from low estimation accuracy in high-speed scenarios, BEM-based interpolation algorithms struggle to track rapid channel changes, and BEM-based sparse reconstruction algorithms are highly sensitive to noise. In deep learning algorithms, unidirectional LSTM cannot utilize backward information and model global temporal correlations, resulting in significant pilot overhead. Furthermore, existing equalization schemes cannot simultaneously meet the requirements of low complexity and high performance. Therefore, there is an urgent need for an OTFS system technology that can achieve high-precision channel estimation and match low-complexity equalization in high-speed mobile scenarios. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a low-complexity OTFS channel estimation method and system based on the base extension model Bi-LSTM-SA.

[0009] To achieve the above objectives, the present invention provides the following technical solution: A low-complexity orthogonal time-frequency spatial channel estimation method based on a basis extension model includes the following steps: The delay-Doppler domain transmission symbol matrix of the orthogonal time-frequency space system transmitter is converted into a time-frequency domain transmission symbol matrix through symplectic finite Fourier inverse transform. After inserting a cyclic prefix, a time-domain transmission symbol matrix is ​​generated. After transmission through the wireless channel, the receiver removes the cyclic prefix and obtains the time-frequency domain receiver symbol matrix through discrete Fourier transform. The basis extension model is used to represent the time-domain channel impulse response as a linear combination of the basis function matrix and basis coefficients, thus transforming the time-domain channel estimation problem into a basis coefficient estimation problem, where the basis coefficient vector... basis function matrix , , Q As the order of the base extended model, M For the number of subcarriers, R For resolution parameters; By receiving symbols in the time-frequency domain using the pilot positions, the pilot position basis coefficient vector is estimated using the linear minimum mean square error algorithm, and the real and imaginary parts are separated and recombined into a real-valued input matrix. ,in Here is the basic coefficient matrix to be estimated; The real-valued input matrix is ​​fed into a bidirectional long short-term memory network to extract forward and backward temporal features in parallel, outputting a hidden state sequence. , In a positive hidden state, This is a reverse hidden state; Calculation via self-attention mechanism query vector Key vector Sum value vector Attention weights are obtained by Softmax normalization. Output global features , For learnable weight matrix, For feature dimensions; Will Input a shallow neural network with 2QL neurons, and use the loss function... To optimize the objective, an adaptive moment estimation optimizer is used to iteratively update the weights. Output base coefficient estimates , For optimal weights, These are bias parameters; Channel state information is obtained by reconstructing the time-domain channel impulse response based on the basis coefficient estimates and the basis function matrix.

[0010] Furthermore, in the bidirectional long short-term memory network, the first... t Hidden state at each time step Through the Gate of Oblivion Input gate Output gate and candidate memory cells The calculation yielded, where For time step t Input, To modify the activation function of the linear unit, For the input weight matrix, This is a cyclic weight matrix. This is the bias parameter.

[0011] Furthermore, when the linear minimum mean square error algorithm estimates the pilot position basis coefficient vector, the mapped autocorrelation matrix... The mapped noise covariance matrix ,in , B For the basis function matrix, It is the identity matrix. L For the number of multipath channels, The time-domain channel impulse response autocorrelation matrix is... For frequency domain noise variance, This indicates the conjugate transpose. It represents the Kronecker product.

[0012] A low-complexity two-level equilibrium method includes the following steps: The basis coefficients of the data location are estimated using the method described above, and the time-domain channel impulse response matrix is ​​reconstructed. ,pass The estimated value of the time-frequency domain channel matrix is ​​obtained, where It is the discrete Fourier transform matrix; First-level equilibrium: Extraction The diagonal elements are used as the time-frequency domain channel vector. Calculate the equilibrium coefficient , For conjugate operations, For noise power, a coarse estimate of the soft symbol vector is obtained through single-tap equalization. , To receive the data symbol vector, This is a dot product operation; Will The data is converted to a time-delay-Doppler domain soft symbol input via a symplectic finite Fourier transform. ; Second-level equalization: Based on the time-delay-Doppler domain equivalent channel matrix estimate An iterative interference cancellation algorithm based on the log-likelihood ratio is adopted, with an initial log-likelihood ratio of... Initial data soft sign mean , This is a matrix vectorization operation; in the k-th iteration, the interference cancellation output... , The time-delay-Doppler domain channel autocorrelation matrix is ​​obtained through the damping factor. Update log-likelihood ratio Update the soft sign mean of the data. iteration K The equalization result will be output after this step.

[0013] Furthermore, the damping factor =0.7, used to control the weight distribution of the current calculated value and the historical value in the iterative update, and to suppress error propagation and oscillation.

[0014] Furthermore, the time-frequency domain received symbol matrix is ​​obtained in the following manner: after removing the cyclic prefix of the time-domain received symbol matrix at the receiver, each column is processed... M Point Discrete Fourier Transform, i.e. ,Y This is the time-domain received symbol matrix.

[0015] A low-complexity orthogonal time-frequency spatial channel estimation system based on a basis extension model includes: The transformation module is used to convert the delay-Doppler domain transmission symbol matrix of the transmitter of the orthogonal time-frequency space system into a time-frequency domain transmission symbol matrix through symplectic finite Fourier inverse transform. After inserting a cyclic prefix, a time-domain transmission symbol matrix is ​​generated. After transmission through the wireless channel, the receiver removes the cyclic prefix and obtains the time-frequency domain receiver symbol matrix through discrete Fourier transform. The basis extension model module is used to represent the time-domain channel impulse response as a linear combination of basis function matrices and basis coefficients, thus transforming the time-domain channel estimation problem into a basis coefficient estimation problem. The pilot estimation module is used to receive symbols in the time-frequency domain at the pilot position, estimate the pilot position basis coefficient vector through the linear minimum mean square error algorithm, and separate and reassemble the real and imaginary parts into a real-valued input matrix. The bidirectional long short-term memory network module is used to extract forward and backward temporal features from the real-valued input matrix in parallel and output the hidden state sequence. The self-attention module is used to model the global dependencies of the hidden state sequence and output a feature vector that integrates local and temporal features. The shallow neural network module is used to perform nonlinear calibration on the feature vectors and output the estimated basis coefficients. The reconstruction module is used to reconstruct the time-domain channel impulse response based on the basis coefficient estimates and the basis function matrix to obtain channel state information.

[0016] Furthermore, in the basis extension model module, the elements of the basis function matrix B , , , Q As the base extended model order, M For the number of subcarriers, R This refers to the resolution parameter.

[0017] A low-complexity two-level equilibrium system includes: The channel reconstruction module is used to reconstruct the time-domain channel impulse response matrix and the estimated value of the time-frequency domain channel matrix by using the basis coefficients of the data location estimated by the system. The first-level equalization module is used to extract the diagonal elements of the time-frequency domain channel matrix, calculate the equalization coefficients, and perform single-tap equalization on the received data symbol vector to obtain a coarse estimate of the soft symbol vector. The domain transformation module is used to convert the coarsely estimated data soft symbol vector into the time-delayed-Doppler domain data soft symbol input through a symplectic finite Fourier transform; The second-level equalization module is used to output the equalization result by using an iterative interference cancellation algorithm based on the log-likelihood ratio, which is based on the estimated value of the time-delay-Doppler domain equivalent channel matrix and controls the iterative update process through the damping factor.

[0018] Furthermore, in the second-level equalization module, the maximum number of iterations of the iterative interference cancellation algorithm is... K Satisfying the residual norm reduced to Below, and the damping factor =0.7.

[0019] The beneficial effects of this invention are as follows: (1) This invention transforms the high-dimensional time-domain channel estimation problem into a low-dimensional basis coefficient estimation problem through a basis extension model, which significantly reduces the number of parameters to be estimated and fundamentally reduces the computational complexity of channel estimation. The bidirectional long short-term memory network structure adopted can utilize both forward and backward time-series information simultaneously, overcoming the limitation of unidirectional networks that can only rely on historical information, realizing comprehensive modeling of the dynamic characteristics of fast time-varying channels, and significantly improving the accuracy of basis coefficient estimation.

[0020] (2) The self-attention mechanism introduced in this invention can dynamically focus on key features in the basic coefficient sequence, effectively capture long-term global dependencies within the sequence, complement the local feature extraction capability of the bidirectional long short-term memory network, and further enhance the model's representation capability in complex channel environments.

[0021] (3) This invention transforms the estimation of the basis coefficients in the complex field into neural network processing in the real field, avoiding the extra overhead caused by complex numerical operations, and speeding up the training and inference of the model while ensuring the estimation accuracy.

[0022] (4) The low-complexity two-stage equalization architecture proposed in this invention cleverly combines the low-complexity advantage of time-frequency domain single-tap equalization with the high-performance advantage of delay-Doppler domain iterative interference elimination. The first-stage equalization utilizes the channel's approximate diagonal characteristics to quickly eliminate multipath effects, while the second-stage equalization utilizes the channel's sparsity characteristics to deeply suppress residual interference, achieving a good trade-off between performance and complexity. In the second-stage equalization, a damping factor is introduced to smoothly control the iterative process, effectively suppressing error propagation and iterative oscillation phenomena, ensuring the algorithm's rapid convergence and stable operation under different signal-to-noise ratio conditions.

[0023] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 The transmission model for the OTFS system; Figure 2 This is a Bi-LSTM-SA network model based on BEM; Figure 3 The NMSE performance of different channel estimation algorithms at a moving speed of 100 km / h; Figure 4 The NMSE performance of different channel estimation algorithms at a moving speed of 500 km / h; Figure 5 The NMSE performance of different channel estimation algorithms at a moving speed of 1000 km / h; Figure 6 BER performance for different scenarios at a moving speed of 100km / h; Figure 7 BER performance for different scenarios at a moving speed of 500 km / h; Figure 8 BER performance for different scenarios at a moving speed of 1000 km / h; Figure 9 NMSE performance of different channel estimation algorithms at different speeds with SNR=7dB; Figure 10 NMSE performance of different channel estimation algorithms at different speeds with SNR=23dB; Figure 11 BER performance for different schemes at different speeds with SNR=7dB; Figure 12 BER performance of different schemes at different speeds with SNR=23dB; Figure 13 BER performance for different equilibrium schemes at a moving speed of 100km / h; Figure 14 BER performance for different equilibrium schemes at a moving speed of 500 km / h; Figure 15 BER performance for different equilibrium schemes at a moving speed of 1000 km / h; Figure 16 This describes the iterative convergence process of the LLR-IIC algorithm. Figure 17 Comparison of spectral efficiency at a moving speed of 500 km / h; Figure 18 A comparison of spectral efficiency at different frame lengths. Detailed Implementation

[0025] 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.

[0026] 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.

[0027] 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.

[0028] Example 1: Bi-LSTM-SA Channel Estimation Method and System Based on Basis Extension Model Reference Figure 1 As shown in Table 1, the transmitter constructs a delayed Doppler domain transmit symbol matrix. The system carrier frequency is 5.9 GHz, the subcarrier spacing is 156.25 kHz, the number of subcarriers is 64, and the cyclic prefix length is 1.6 microseconds. The length is... The quadrature amplitude modulation data symbols are arranged as follows Through the symplectic finite Fourier inverse transform, i.e., the formula... This is then converted into a time-frequency domain transmitted symbol matrix. (Refer to...) Figure 1 The frame structure inserts a preamble sequence and pilot symbols into the symbols, generates a time-domain transmit symbol matrix through inverse discrete Fourier transform, and adds a cyclic prefix.

[0029] Table 1 System Simulation Parameters

[0030] After removing the cyclic prefix at the receiver, the time-domain received symbol vector is obtained. for:

[0031] in , For the first n The OFDM symbol in the first l The time-domain channel impulse response vector in the path, It is an additive white Gaussian noise vector. This is the time-domain channel impulse response matrix.

[0032] Reference Figure 2 (Bi-LSTM-SA network model based on BEM), modeled using a basal extension model. The time-domain channel impulse response is... Represented as a basis function matrix B with basis coefficient vector Combinations:

[0033] Where basis functions The m The elements are This allows the parameters to be estimated to be derived from... ML Reduced to QL. At this point, the time-domain channel vector can be represented as... ,in , It represents the Kronecker product.

[0034] Receiving symbols using the time-frequency domain of pilot positions The pilot position basis coefficients are estimated using a linear minimum mean square error algorithm. Observation matrix The formula for calculating the mapped autocorrelation matrix is:

[0035] in The mapped noise covariance matrix is: The estimated value of the pilot position fundamental coefficient is:

[0036] Among them, least squares estimation .

[0037] The real and imaginary parts of the aforementioned basis coefficients are separated and recombined into a real-valued input matrix. .

[0038] The matrix is ​​input into a bidirectional long short-term memory network. The network extracts features in parallel through forward and backward LSTM units. The information flow within each LSTM unit is adjusted using the following formula:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] in To modify the activation function of the linear unit, For the input weight matrix, This is a cyclic weight matrix. This is the bias parameter.

[0045] Then, the forward and reverse hidden states are concatenated as follows: Input to the self-attention layer. The self-attention layer computes the query vector. Key vector AND value vector Output Attention weights .

[0046] Finally, a shallow neural network with 2QL neurons is used to perform non-linear calibration of the features. The loss function is... To optimize the objective, an adaptive moment estimation optimizer is used to update the weights and output the estimated base coefficients. .

[0047] Example 2: Low-complexity two-level equilibrium method and system The first-level equilibrium is referenced. Figure 1 The time-frequency domain is shown. The time-domain channel impulse response matrix reconstructed using Example 1 is also described. ,pass The time-frequency domain channel matrix is ​​obtained. Its diagonal elements are extracted as the time-frequency domain channel vector. Calculate the equilibrium coefficient A single-tap equalizer is used to eliminate multipath effects and output a coarse-estimated soft symbol vector for the data. .

[0048] The second-stage equalization is performed in the time-delayed Doppler domain. The first-stage output is then subjected to a symplectic finite Fourier transform. Transform to the time-delayed Doppler domain. Based on the equivalent channel matrix in the time-delayed Doppler domain. An iterative interference cancellation algorithm based on the log-likelihood ratio is executed.

[0049] Initialize the log-likelihood ratio With the soft sign mean of the data .

[0050] Reference Figure 16 (Iterative convergence process of the LLR-IIC algorithm): In the k-th iteration, reconstruct the residual disturbance:

[0051] Introducing damping factor =0.7 for smoothing the log-likelihood ratio update:

[0052] Update data soft sign mean After K iterations, the final equilibrium result is output.

[0053] Example 3: Simulation Verification and Complexity Analysis This embodiment uses Tables 1, 2, 3 and 4 for simulation verification and quantitative analysis.

[0054] Table 2 Parameter Definition Table for Training Phase

[0055] Table 3. Comparison of Time Complexity and FLOPS of Different Channel Estimation Algorithms

[0056] Table 4 Comparison of Time Complexity of Different Equalizers

[0057] The dataset consists of samples from an extended vehicle channel model, with speeds ranging from 0 km / h to 990 km / h. Referring to Table 2, the batch size was set to 128, the number of training epochs to 500, the learning rate to 0.001, and the hidden layer size of the bidirectional LSTM layer to be... The hidden layer size of the shallow neural network is 2QL.

[0058] Reference Figures 3 to 5 The performance of normalized mean square error was compared at different moving speeds. (Refer to...) Figures 6 to 8 Compare the bit error rate performance of different schemes. (Refer to...) Figures 9 to 12 This verifies the model's generalization ability in speed scenarios outside the training set. (Refer to...) Figures 13 to 15 The bit error rate performance of different equalization schemes was compared. (Refer to...) Figure 17 and Figure 18 We analyzed the spectral efficiency at different speeds and frame lengths.

[0059] Regarding the complexity analysis, referring to Table 3, the total complexity of the channel estimation algorithm proposed in this invention is:

[0060] in , , , Its floating-point operations per second are at... to Magnitude.

[0061] Referring to Table 4, the complexity of the low-complexity two-stage equalizer proposed in this invention is: Far lower than the minimum mean square error equalizer in the time-delay Doppler domain. This avoids the problem of high-dimensional matrix inversion in time-frequency domain minimum mean square error equalizers, achieving a good trade-off between performance and complexity.

[0062] 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 low-complexity orthogonal time-frequency spatial channel estimation method based on a basis extension model, characterized in that: Includes the following steps: The delay-Doppler domain transmission symbol matrix of the orthogonal time-frequency space system transmitter is converted into a time-frequency domain transmission symbol matrix through symplectic finite Fourier inverse transform. After inserting a cyclic prefix, a time-domain transmission symbol matrix is ​​generated. After transmission through the wireless channel, the receiver removes the cyclic prefix and obtains the time-frequency domain receiver symbol matrix through discrete Fourier transform. The basis extension model is used to represent the time-domain channel impulse response as a linear combination of the basis function matrix and basis coefficients, thus transforming the time-domain channel estimation problem into a basis coefficient estimation problem, where the basis coefficient vector... basis function matrix , , Q As the order of the base extended model, M For the number of subcarriers, R For resolution parameters; By receiving symbols in the time-frequency domain using the pilot positions, the pilot position basis coefficient vector is estimated using the linear minimum mean square error algorithm, and the real and imaginary parts are separated and recombined into a real-valued input matrix. ,in Here is the basic coefficient matrix to be estimated; The real-valued input matrix is ​​fed into a bidirectional long short-term memory network to extract forward and backward temporal features in parallel, outputting a hidden state sequence. , In a positive hidden state, This is a reverse hidden state; Calculation via self-attention mechanism query vector Key vector Sum value vector Attention weights are obtained by Softmax normalization. Output global features , For learnable weight matrix, For feature dimensions; Will Input a shallow neural network with 2QL neurons, and use the loss function... To optimize the objective, an adaptive moment estimation optimizer is used to iteratively update the weights. Output base coefficient estimates , For optimal weights, These are bias parameters; Channel state information is obtained by reconstructing the time-domain channel impulse response based on the basis coefficient estimates and the basis function matrix.

2. The low-complexity orthogonal time-frequency spatial channel estimation method based on the basis extension model according to claim 1, characterized in that: In the bidirectional long short-term memory network, the first... t Hidden state at each time step Through the Gate of Oblivion Input gate Output gate and candidate memory cells The calculation yielded, where For time step t Input, To modify the activation function of the linear unit, For the input weight matrix, This is a cyclic weight matrix. This is the bias parameter.

3. The low-complexity orthogonal time-frequency spatial channel estimation method based on the basis extension model according to claim 1, characterized in that: When the linear minimum mean square error algorithm estimates the pilot position basis coefficient vector, the mapped autocorrelation matrix... The mapped noise covariance matrix ,in , B For the basis function matrix, It is the identity matrix. L For the number of multipath channels, The time-domain channel impulse response autocorrelation matrix is... For frequency domain noise variance, This indicates the conjugate transpose. It represents the Kronecker product.

4. A low-complexity two-level equilibrium method, characterized in that: Includes the following steps: The basis coefficients of the data location are estimated using the method described in any one of claims 1-3, and the time-domain channel impulse response matrix is ​​reconstructed. ,pass The estimated value of the time-frequency domain channel matrix is ​​obtained, where It is the discrete Fourier transform matrix; First-level equilibrium: Extraction The diagonal elements are used as the time-frequency domain channel vector. Calculate the equilibrium coefficient , For conjugate operations, For noise power, a coarse estimate of the soft symbol vector is obtained through single-tap equalization. , To receive the data symbol vector, This is a dot product operation; Will The data is converted to a time-delay-Doppler domain soft symbol input via a symplectic finite Fourier transform. ; Second-level equalization: Based on the time-delay-Doppler domain equivalent channel matrix estimate An iterative interference cancellation algorithm based on the log-likelihood ratio is adopted, with an initial log-likelihood ratio of... Initial data soft sign mean , This is a matrix vectorization operation; in the k-th iteration, the interference cancellation output... , The time-delay-Doppler domain channel autocorrelation matrix is ​​obtained through the damping factor. Update log-likelihood ratio Update the soft sign mean of the data. iteration K The equalization result will be output after this step.

5. The low-complexity two-level equilibrium method according to claim 4, characterized in that: The damping factor =0.7, used to control the weight distribution of the current calculated value and the historical value in the iterative update, and to suppress error propagation and oscillation.

6. The low-complexity two-level equilibrium method according to claim 4, characterized in that: The time-frequency domain received symbol matrix is ​​obtained as follows: after removing the cyclic prefix from the time-domain received symbol matrix at the receiver, each column is processed... M Point-based discrete Fourier transform, i.e. , Y This is the time-domain received symbol matrix.

7. A low-complexity orthogonal time-frequency spatial channel estimation system based on a basis extension model, characterized in that: include: The transformation module is used to convert the delay-Doppler domain transmission symbol matrix of the transmitter of the orthogonal time-frequency space system into a time-frequency domain transmission symbol matrix through symplectic finite Fourier inverse transform. After inserting a cyclic prefix, a time-domain transmission symbol matrix is ​​generated. After transmission through the wireless channel, the receiver removes the cyclic prefix and obtains the time-frequency domain receiver symbol matrix through discrete Fourier transform. The basis extension model module is used to represent the time-domain channel impulse response as a linear combination of basis function matrices and basis coefficients, thus transforming the time-domain channel estimation problem into a basis coefficient estimation problem. The pilot estimation module is used to receive symbols in the time-frequency domain at the pilot position, estimate the pilot position basis coefficient vector through the linear minimum mean square error algorithm, and separate and reassemble the real and imaginary parts into a real-valued input matrix. The bidirectional long short-term memory network module is used to extract forward and backward temporal features from the real-valued input matrix in parallel and output the hidden state sequence. The self-attention module is used to perform global dependency modeling on the hidden state sequence and output a feature vector that integrates local and temporal features. The shallow neural network module is used to perform nonlinear calibration on the feature vectors and output the estimated basis coefficients. The reconstruction module is used to reconstruct the time-domain channel impulse response based on the basis coefficient estimates and the basis function matrix to obtain channel state information.

8. The low-complexity orthogonal time-frequency spatial channel estimation system based on the basis extension model according to claim 7, characterized in that: In the basis extension model module, the elements of the basis function matrix B , , , Q As the order of the base extended model, M For the number of subcarriers, R This refers to the resolution parameter.

9. A low-complexity two-stage equilibrium system, characterized in that: include: The channel reconstruction module is used to reconstruct the time-domain channel impulse response matrix and the estimated value of the time-frequency domain channel matrix by using the basis coefficients of the data location estimated by the system according to any one of claims 7-8. The first-level equalization module is used to extract the diagonal elements of the time-frequency domain channel matrix, calculate the equalization coefficients, and perform single-tap equalization on the received data symbol vector to obtain a coarse estimate of the soft symbol vector. The domain transformation module is used to convert the coarsely estimated data soft symbol vector into the time-delayed-Doppler domain data soft symbol input through a symplectic finite Fourier transform. The second-level equalization module is used to output the equalization result by using an iterative interference cancellation algorithm based on the log-likelihood ratio, which is based on the estimated value of the time-delay-Doppler domain equivalent channel matrix and controls the iterative update process through the damping factor.

10. The low-complexity two-stage equilibrium system according to claim 9, characterized in that: In the second-level equalization module, the maximum number of iterations of the iterative interference cancellation algorithm. K Satisfying the residual norm reduced to Below, and the damping factor =0.7.

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