A channel estimation method for an OTFS system combining distributed compressive sensing and deep learning

Abstract

The application provides a channel estimation method for an OTFS system combining distributed compressed sensing and deep learning, and belongs to the technical field of channel estimation, and comprises the following steps: first, receiving a delay Doppler signal and pre-processing the same; determining a non-zero item position through a Bi-LSTM neural network to capture the correlation between each column, and updating a support set in combination with a measurement matrix; updating sparsity through the support set; obtaining a residual r after iteration, and stopping the loop when the number of iterations or the residual reaches a requirement, and outputting a channel estimation result. Compared with an OMP algorithm and an SBL algorithm, the algorithm provided by the application has better performance in a low signal-to-noise ratio condition, and has stronger robustness when the number of paths increases or the non-zero item position changes. Meanwhile, since the algorithm inherits the low complexity of a greedy algorithm, the calculation time is also much smaller than that of the SBL algorithm, thereby guaranteeing the real-time performance of the algorithm. Therefore, the algorithm has certain development potential in a complex communication environment, and is helpful to promote the development of the field of channel estimation of the OTFS system.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel estimation, and in particular relates to a method for estimating an OTFS delay-Doppler channel by using a Bi-LSTM-CS algorithm that combines a greedy algorithm with deep learning. Background Art

[0002] As 5G matures and becomes increasingly widespread, it's been discovered that while 5G has achieved lower latency and increased communication capacity, capacity bottlenecks still exist in areas such as high-density urban centers. Furthermore, current latency still cannot guarantee the maturity of technologies with extremely high latency requirements, such as telemedicine and autonomous driving. Furthermore, due to the high attenuation of high-frequency bands, a large number of base stations and fiber optic networks are required to meet coverage requirements, which in turn increases construction costs. To address these issues, sixth-generation mobile communications (6G) satellite-to-ground communications have emerged. However, due to the rapid movement of satellites relative to the ground, ensuring reliable and efficient communication in high-speed mobile scenarios has become a key challenge in achieving satellite-to-ground communications. Orthogonal frequency division multiplexing (OFDM), the dominant modulation technology in current mobile systems, is highly sensitive to Doppler spreading and, therefore, suffers from severe inter-carrier interference (ICI) under high-mobility communication conditions. To maintain reliable communication in high-mobility scenarios, the orthogonal time-frequency space (OTFS) system has been proposed. OTFS represents signals in the delay-Doppler domain, converting the traditional time-varying selective channel in the time-frequency domain into a constant sparse channel in the delay-Doppler domain. This allows all symbols to experience a nearly constant fading channel gain, enabling OTFS to outperform OFDM in high-mobility environments. Furthermore, OTFS can be viewed as an extension of OFDM, adding pre-processing and post-processing modules at both the transmitter and receiver, ensuring sufficient compatibility with existing communication architectures. Furthermore, it is crucial to note that in real-world communication scenarios, effective scatterers are typically limited, and the channel can be modeled as a sparse model in the delay-Doppler domain. Therefore, its sparse nature enables more accurate estimation of channel state information. Summary of the Invention

[0003] To address the above-mentioned deficiencies in the prior art, the present invention proposes a channel estimation method for OTFS systems that combines distributed compressed sensing and deep learning. This method has better performance under low signal-to-noise ratio conditions, is more robust when paths increase or the positions of non-zero items change, and ensures the real-time performance of the algorithm.

[0004] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0005] This solution provides a method for estimating OTFS delay-Doppler channels using a Bi-LSTM-CS algorithm that combines a greedy algorithm with deep learning, and is characterized by comprising the following steps:

[0006] S1, receiving the delay Doppler signal and preprocessing it;

[0007] S2, using the Bi-LSTM neural network to capture the correlation between each column and determine the location of non-zero items;

[0008] S3, joint measurement matrix to update support set;

[0009] S4. Update the sparsity through the support set to obtain the residual r after iteration. When the number of iterations or the residual reaches the requirement, stop the loop and output the channel estimation result.

[0010] Furthermore, the step S1 includes the following steps:

[0011] S101. The signal undergoes OTFS modulation and passes through SFFT to obtain the received signal in the delay-Doppler domain. OTFS (Orthogonal Time Frequency Space) is a modulation technique that uses a time-frequency lattice to represent data, overcome multipath interference, and improve spectrum utilization and system performance. The SFFT (Symplectic Finite Fourier Transform) is a mathematical tool used to process signals and data in a finite-dimensional symplectic phase space. It is similar to the traditional Fourier transform, but is applicable to symplectic phase spaces. In the symplectic finite Fourier transform, a signal or system is represented as a symplectic structure and converted from the time domain to the frequency domain via a Fourier transform.

[0012] S102: The received signal in the delay-Doppler domain is saved and channel estimation is performed using the Bi-LSTM-CS algorithm, which combines distributed compressed sensing with deep learning. Bi-LSTM-CS is an application of a bidirectional long short-term memory (LSTM) network in a compressed sensing scenario, leveraging compressed sensing technology to improve the efficiency and performance of neural network training.

[0013] Furthermore, step S2 includes the following steps:

[0014] S201. Build forward LSTM and backward LSTM architectures, and combine them into a Bi-LSTM neural network architecture.

[0015] S202. Use the Bi-LSTM neural network architecture to find p for each input vector r, and then use p to determine entries with higher non-zero probabilities, where p is the probability that each element in the vector is non-zero.

[0016] S203, where i(t), f(t), o(t), and c(t) are the input gate, forget gate, output gate, and unit state vector, respectively. W pi , (i=1, 2, 3) is the peephole connection, W reci and W i , (i = 1, 2, 3, 4) are the recurrent connection and input connection, g(·) is the tanh(·) function, and σ(·) is the sigmoid function. We use this architecture to find p for each input vector r and then use p to determine the entries with higher non-zero probability. The relationship between the various vectors is as follows:

[0017] i(t)=σ(W2r(t)+W rec1 p(t-1)+W p2 c(t-1))

[0018] f(t)=σ(W1r(t)+W rec2 P(t-1)+W p1 c(t-1))

[0019] o(t)=σ(W4r(t)+W rec3 p(t-1)+W p3 c(t))

[0020] a(t)=g(W3r(t)+W rec4 p(t-1))

[0021] c(t)=f(t)⊙c(t-1)+i(t)⊙a(t)

[0022] p(t)=o(t)⊙g(c(t))

[0023] where ⊙ represents the Hadamard product. The Hadamard product is an element-by-element multiplication operation performed on two matrices or vectors of the same dimension, generating a new matrix or vector where each element is the product of the elements of the two inputs at the corresponding position.

[0024] S204. The residual r of each channel is the received signal vector y, and then these residual vectors are input into the neural network.

[0025] S205, using the input weight matrix W in formula (8) with the help of each Bi-LSTM model in the network i , (i = 1, 2, 3, 4) to capture the characteristics of the input content, and then through the cyclic weight matrix W recand the cell state vector c to capture the correlation between the residual vectors, and finally the output P∈C of the Bi-LSTM is transformed into a sparse vector space v∈C by a transformation matrix U. ncell×1 transformed into a sparse vector space v∈C P×1 where ncell is the number of cells in the model, and P is the length of the sparse vector.

[0026] S206, After transforming into a sparse vector space, softmax is used to determine the probability that each entry of the output vector is not zero. The jth entry of the ith channel output vector is denoted as:

[0027]

[0028] where the softmax function maps a vector to a probability distribution by exponentiating each element to a positive number and then normalizing to get a probability distribution, commonly used in the output layer of multi-classification problems.

[0029] Further, the step S3 comprises the following steps:

[0030] S301, In order to calculate the specific parameters of each weight matrix and transformation matrix in the model, we need to minimize the cross-entropy cost function of the training set.

[0031] S302, By calculation, the parameter calculation can be converted to solving the following optimization problem:

[0032]

[0033] L k，l，i，j (j)log(s 0，k，l，i (j)) k，l，i (j))

[0034] where M and N are the number of training set small batch segmentation and the corresponding size, L is the number of neural network channels, P is the length of the sparse vector, i.e. the number of columns and rows of the input signal matrix. Λ represents the set of model parameters, s0 is the one-hot vector in each iteration, whose non-zero entries are 1 and the rest are 0.

[0035] S303, In order to solve the optimization problem of the above formula, we use the backpropagation through time algorithm combined with Nesterov momentum:

[0036] ΔΛ k =Λ k -Λ k-1

[0037]

[0038] Where Nesterov momentum is an optimization algorithm that predicts the next parameter forward, then adjusts in the gradient descent direction, which enhances convergence and stability. Epsilon is the learning rate, mu k is the momentum parameter determined by the training scheme, is the gradient of the cost function:

[0039]

[0040] S304, in order to derive the calculation formula We get according to the known quantity:

[0041]

[0042]

[0043] Where v i is Figure 5 The output vector of the ith channel in Because s0 is a one-hot vector, beta is always equal to 1. And from v i = UP i We get:

[0044]

[0045] S305, finally, the calculation formula Can be expressed as

[0046] Further, the step S4 comprises the following steps:

[0047] S401, after determining the probability of each position being non-zero, the position with the maximum probability is selected and the support set is updated jointly with the measurement matrix.

[0048] S402, the specific estimation result of the sparse vector in the current iteration is determined by the least square method Get the residual vector in the next iteration:

[0049]

[0050]

[0051] S403, when the number of loop iterations reaches the length P of the sparse vector or is less than the preset residual ResMin, the algorithm stops the loop and outputs the estimation result obtained last time.

[0052] Compared with the prior art, the beneficial effects of the present application are:

[0053] In this paper, a channel estimation method for OTFS system is proposed by combining distributed compressed sensing and deep learning. For the received signal, the scheme firstly performs data preprocessing, and extracts the pilot symbols of multiple data frames to form a received signal matrix, which converts the channel estimation into the sparse vector reconstruction of the MMV problem. Then, the Bi-LSTM neural network is used to capture the time correlation between the column vectors of the matrix, and the number and position of the non-zero entries in the sparse vector are determined through this dependence. Finally, the specific values of these non-zero entries are determined by the least square method, and the channel estimation is completed. Compared with the OMP algorithm and the SBL algorithm, the proposed algorithm has better performance in the case of low signal-to-noise ratio, and has stronger robustness when the path increases or the position of the non-zero entry changes. At the same time, since it inherits the low complexity of the greedy algorithm, the calculation time is also much smaller than the SBL algorithm, which ensures the real-time performance of the algorithm. Therefore, the algorithm has certain development potential in complex communication environment, and helps to promote the development of OTFS system channel estimation field. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 A flowchart of the method of the present application.

[0055] Figure 2 A process diagram of the present application.

[0056] Figure 3 A flowchart of the Bi-LSTM neural network architecture.

[0057] Figure 4 An error diagram of the system bit error rate simulation result of the algorithm of the present application under the JSM-1 and JSM-2 models in the embodiment.

[0058] Figure 5 A schematic diagram of the channel estimation normalized mean square error simulation result of the algorithm of the present application under the JSM-1 and JSM-2 models in the embodiment. DETAILED DESCRIPTION

[0059] The specific embodiments of the present application are described below to facilitate the understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0060] EMBODIMENT

[0061] The present application proposes a channel estimation method for OTFS system by combining distributed compressed sensing and deep learning. Figure 1 AND Figure 2is the best embodiment of the present application, and the following will be described in detail Figure 1 and Figure 2 The present application is described in detail. The flow chart of the method of the present application is shown in Figure 1 , comprising the following steps:

[0062] S1, receiving the time delay Doppler signal and preprocessing it, the implementation method is as follows:

[0063] S101, the signal is modulated by OTFS, and the time delay-Doppler domain received signal is obtained after SFFT.

[0064] Where OTFS is an orthogonal time-frequency space (Orthogonal Time Frequency Space) that uses time-frequency lattice to represent data, overcome multipath interference, improve spectrum utilization and system performance; SFFT is a symplectic finite Fourier transform (Symplectic Finite Fourier Transform) that is a mathematical tool for processing signals and data in finite-dimensional symplectic phase space. It is similar to the traditional Fourier transform, but it is suitable for symplectic phase space, and in the symplectic finite Fourier transform, the signal or system is represented as a symplectic structure and converted from time domain to frequency domain by Fourier transform.

[0065] S102, save the obtained time delay-Doppler domain received signal, and use the Bi-LSTM-CS algorithm combining distributed compressed sensing and deep learning for channel estimation. Where Bi-LSTM-CS is the application of bidirectional long short-term memory (Bidirectional Long Short-Term Memory) in the compressed sensing scenario, which uses compressed sensing technology to improve the efficiency and performance of neural network training.

[0066] S2, determine the position of non-zero items by capturing the correlation between each column through the Bi-LSTM neural network, and update the support set with the measurement matrix, the implementation method is as follows:

[0067] S201, build a forward LSTM and a backward LSTM architecture, and combine them into a Bi-LSTM neural network architecture.

[0068] S202, find p for each input vector r through the Bi-LSTM neural network architecture, and then determine the entry with higher non-zero probability through p. Where p is the probability that each element in the vector is not zero.

[0069] S203, where i(t), f(t), o(t), c(t) are input gate, forget gate, output gate and cell state vector respectively, W pi , (i=1, 2, 3) is a peephole connection, W reciand W i , (i = 1, 2, 3, 4) are the recurrent connection and input connection, g(·) is the tanh(·) function, and σ(·) is the sigmoid function. We use this architecture to find p for each input vector r and then use p to determine the entries with higher non-zero probability. The relationship between the various vectors is as follows:

[0070] i(t)=σ(W2r(t)+W rec1 p(t-1)+W p2 c(t-1))

[0071] f(t)=σ(W1r(t)+W rec2 p(t-1)+W p1 c(t-1))

[0072] o(t)=σ(W4r(t)+W rec3 p(t-1)+W p3 c(t))

[0073] a(t)=g(W3r(t)+W rec4 p(t-1))

[0074] c(t)=f(t)⊙c(t-1)+i(t)⊙a(t)

[0075] p(t)=o(t)⊙g(c(t))

[0076] where ⊙ represents the Hadamard product. The Hadamard product is an element-by-element multiplication operation performed on two matrices or vectors of the same dimension, generating a new matrix or vector where each element is the product of the elements of the two inputs at the corresponding position.

[0077] S204. The residual r of each channel is the received signal vector y, and then these residual vectors are input into the neural network.

[0078] S205, using the input weight matrix W in formula (8) with the help of each Bi-LSTM model in the network i , (i = 1, 2, 3, 4) to capture the characteristics of the input content, and then through the cyclic weight matrix W rec and the unit state vector c to capture the correlation between the residual vectors, and finally transform the Bi-LSTM output P∈C ncell×1 Convert to sparse vector space v∈C P×1 Where ncell is the number of units in the model and P is the length of the sparse vector.

[0079] S206, After converting to sparse vector space, softmax is used to determine the probability that each entry of the output vector is not zero. The jth entry of the ith channel output vector is denoted as follows:

[0080]

[0081] The softmax function maps a vector to a probability distribution by exponentiating each element to make it positive and then normalizing to get a probability distribution, which is commonly used in the output layer of multi-classification problems.

[0082] S3, Update sparsity by support set, the implementation method is as follows:

[0083] S301, In order to calculate the specific parameters of each weight matrix and transformation matrix in the model, we need to minimize the cross-entropy cost function of the training set.

[0084] S302, Through calculation, the parameter calculation can be converted into solving the following optimization problem:

[0085]

[0086] L k，l，i，j (Λ)=-s 0，k，l，i (j)log(s k，l，i (j))

[0087] Where M and N are the number of training set small batch segmentation and the corresponding size, L is the number of neural network channels, P is the length of sparse vector, that is, the number of columns and rows of input signal matrix. Λ represents the set of model parameters, s0 is the one-hot vector in each iteration, whose non-zero entries are 1 and the rest are 0.

[0088] S303, In order to solve the optimization problem of the above formula, we use the backpropagation algorithm with time combined with Nesterov momentum:

[0089] ΔΛ k =Λ k -Λ k-1

[0090]

[0091] Where Nesterov momentum is an optimization algorithm that first predicts the next step parameter, then adjusts in the gradient descent direction, enhancing convergence and stability. ε is the learning rate, μ k is the momentum parameter determined by the training scheme, is the gradient of the cost function:

[0092]

[0093] S304, in order to obtain the calculation formula Based on the known quantities we get:

[0094]

[0095]

[0096] where v i for Figure 5 The output vector of the i-th channel in, Since s0 is a one-hot vector, β is always equal to 1. And from v i =UP i have to:

[0097]

[0098] S305, finally, the calculation formula It can be expressed as

[0099] S4. Obtain the residual r after iteration. When the number of iterations or the residual reaches the requirement, stop the loop and output the channel estimation result. The implementation method is as follows:

[0100] S401: After determining the non-zero probability of each position, select the position with the maximum probability and update the support set in conjunction with the measurement matrix.

[0101] S402: Determine the specific estimation result of the sparse vector in the current iteration by the least squares method Get the residual vector in the next iteration:

[0102]

[0103]

[0104] S403: When the number of loop iterations reaches the length P of the sparse vector or is less than the preset residual ResMin, the algorithm stops looping and outputs the last obtained estimation result.

[0105] Since the channel response is considered a time-correlated joint sparse structure in the proposed scheme, we set the channel response to a joint sparse model (JSM) in our experiments. We first used the JSM-2 model for experimental simulation. Under this model, the positions of the non-zero elements of the channel response experienced by each symbol, i.e., the support set, remain consistent. The non-zero elements are random complex numbers that follow a Rayleigh distribution. In each experiment, the positions of the non-zero elements in the channel taps vary randomly within the channel length, but the corresponding elements still follow a Rayleigh distribution, and the support set of the channel response for each symbol remains consistent. The final result is the average of multiple simulation experiments.

[0106] The simulation results show that when different algorithms use the same pilot overhead for channel estimation, when the signal-to-noise ratio is small, the bit error rate performance of the Bi-LSTM-CS channel estimation algorithm is close to that of the orthogonal matching pursuit (OMP) algorithm and the SBL algorithm. However, when the SNR is 16 dB, the bit error rate of the Bi-LSTM-CS channel estimation algorithm is 3.98×10 -5 , closer to the bit error rate under ideal channel state information (assuming the channel state information is known at the receiver). In the NMSE results, the performance of the embedded pilot-assisted channel estimation method is most affected by noise compared to other algorithms. While the OMP algorithm reduces computational complexity, its performance also deteriorates compared to the SBL algorithm. The Bi-LSTM-CS algorithm proposed in this paper performs similarly to the SBL algorithm in good communication environments, but benefits from capturing the temporal correlation between multiple symbols and performs better in low signal-to-noise ratio environments.

[0107] Next, we conducted experimental simulations using the JSM-1 model. Unlike JSM-2, in this model, the nonzero tap positions of the channel response experienced by each symbol are divided into shared and unique components. In the experiment, we set the first seven nonzero tap positions to be identical, while the remaining two nonzero tap positions were different. The nonzero elements were random complex numbers following a Rayleigh distribution. As a control, we added a case where the number of common supports was known at the receiver (i.e., no common support was estimated; the OMP algorithm was used only under the unique support).

[0108] Simulation results show that under the JSM-1 model, the performance of the OMP and SBL algorithms degrades more significantly. This is because the presence of separate sparse components makes the algorithms more likely to make errors when searching for the location of non-zero elements. The Bi-LSTM-CS algorithm, on the other hand, takes advantage of the fact that consecutive symbols have partially identical support sets, improving the accuracy of support set estimation. Compared with the JSM-2 model, the bit error rate is less affected and can still reach 4.86×10- -5, second only to the bit error rate when the common support set is known and the channel state information is ideal. Furthermore, because the Bi-LSTM-CS algorithm only requires a single training run for the neural network, its computation time for channel estimation on received signals is almost as fast as that of the greedy algorithm. Therefore, Bi-LSTM-CS offers a significant advantage in real-time performance.

[0109] When the signal-to-noise ratio is fixed at 8dB and the frequency shift of each path is a randomly generated integer multiple of the Doppler value, the Bi-LSTM-CS algorithm is more robust than other algorithms. This means that when the communication environment is complex and changing and the data rate increases, the algorithm proposed in this paper is more reliable.

Claims

1. A method for channel estimation algorithm for OTFS system combining distributed compressed sensing and deep learning, characterized in that: The following steps are involved: S1. Receive a delay Doppler signal and pre-process it. Step S1 includes: S101. The signal is modulated by OTFS and passed through SFFT to obtain the delay-Doppler domain received signal. OTFS (Orthogonal Time Frequency Space) is a modulation technique that uses a time-frequency lattice to represent data, overcome multipath interference, and improve spectrum utilization and system performance. SFFT (Symplectic Finite Fourier Transform) is a mathematical tool used to process signals and data in a finite-dimensional symplectic phase space. It is similar to the traditional Fourier transform, but is applicable to symplectic phase spaces. In the symplectic finite Fourier transform, a signal or system is represented as a symplectic structure and converted from the time domain to the frequency domain through the Fourier transform. S102. The delay-Doppler domain received signal is saved and channel estimation is performed using a Bi-LSTM-CS algorithm that combines distributed compressed sensing and deep learning. The Bi-LSTM-CS is an application of a bidirectional long short-term memory network in a compressed sensing scenario, which uses compressed sensing technology to improve the efficiency and performance of neural network training. S2. Capturing the correlation between each column by a Bi-LSTM neural network to determine the position of the non-zero item, wherein step S2 includes the following steps: S201. Build forward LSTM and backward LSTM architectures, and combine them into a Bi-LSTM neural network architecture. S202. Find p for each input vector r using a Bi-LSTM neural network architecture, and then determine entries with higher non-zero probabilities using p, where p is the probability that each element in the vector is non-zero; S203, where i(t), f(t), o(t), and c(t) are the input gate, forget gate, output gate, and unit state vector, respectively. W pi , (i=1,2,3) is the peephole connection, W reci and W i , (i=1,2,3,4) are the recurrent connection and input connection respectively, g(·) is the tanh(·) function, σ(·) is the sigmoid function. We use this architecture to find p for each input vector r, and then use p to determine the entry with a higher non-zero probability. The relationship between the various vectors is as follows: i(t)=σ(W2r(t)+W rec1 p(t-1)+W p2 c(t-1)) f(t)=σ(W1r(t)+W rec2 p(t-1)+W p1 c(t-1)) o(t)=σ(W4r(t)+W rec3 p(t-1)+W p3 c(t)) a(t)=g(W3r(t)+W rec4 p(t-1)) c(t)=f(t)⊙c(t-1)+i(t)⊙a(t) p(t)=o(t)⊙g(c(t)) Where ⊙ represents the Hadamard product, which is an element-by-element multiplication operation used for two matrices or vectors of the same dimension to generate a new matrix or vector whose each element is the result of multiplying the elements of the two inputs at the corresponding position; S204, the residual r of each channel is the received signal vector y, and then these residual vectors are input into the neural network; S205, using the input weight matrix W with the help of each Bi-LSTM model in the network i , (i=1,2,3,4) to capture the characteristics of the input content, and then through the cyclic weight matrix W rec and the unit state vector c to capture the correlation between the residual vectors, and finally transform the Bi-LSTM output P∈C ncell×1 Convert to sparse vector space v∈C P×1 , where ncell is the number of units in the model and P is the length of the sparse vector; S206. After conversion to the sparse vector space, softmax is used to determine the probability that each entry of the output vector is non-zero, as shown in the following formula. The j-th entry of the output vector of the i-th channel is expressed as: The softmax function maps the vector to a probability distribution, converts each element into a positive number through an exponential function, and then normalizes it to obtain a probability distribution. It is often used in the output layer of multi-classification problems. S3. Update the support set by combining the measurement matrix, wherein step S3 includes the following steps: S301. In order to calculate the specific parameters of each weight matrix and transformation matrix in the model, we need to minimize the cross entropy cost function of the training set; S302. Through calculation, the parameter calculation can be converted into solving the following optimization problem: L k,l,i,j (Λ)=-S 0,k,l,i (j)log(s k,l,i (j)) Where M and N are the number and size of mini-batch splits of the training set, respectively; L is the number of neural network channels; P is the length of the sparse vector, i.e., the number of columns and rows of the input signal matrix; Λ represents the set of model parameters; and s0 is a one-hot vector whose non-zero entries are 1 and the rest are 0 in each iteration. S303. In order to solve the optimization problem of the above formula, we use the back-propagation over time algorithm combined with Nesterov momentum: DL k =L k -L k-1 Nesterov momentum is an optimization algorithm that first predicts the next step parameters and then adjusts them in the direction of gradient descent, which enhances convergence and stability. ε is the learning rate, μ is the learning rate, and k is the momentum parameter determined by the training regimen, is the gradient of the cost function: S304, in order to obtain the calculation formula Based on the known quantities we get: where v i is the output vector of the i-th channel, Because s0 is a one-hot vector, β is always equal to 1, and v i =UP i have to: S305, finally, the calculation formula It can be expressed as ; S4. Update the sparsity through the support set to obtain the residual r after iteration. When the number of iterations or the residual reaches the requirement, stop the loop and output the channel estimation result. The step S4 includes the following steps: S401, after determining the non-zero probability of each position, select the position with the maximum probability and update the support set in conjunction with the measurement matrix; S402: Determine the specific estimation result of the sparse vector in the current iteration by the least squares method Get the residual vector in the next iteration: S403: When the number of loop iterations reaches the length P of the sparse vector or is less than the preset residual ResMin, the algorithm stops looping and outputs the last obtained estimation result.

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