OTFS channel estimation method based on dynamic sparse Bayesian under low earth orbit satellite

Abstract

The invention relates to the field of digital information transmission, in particular to an OTFS channel estimation method based on dynamic sparse Bayesian under a low earth orbit satellite, which comprises the following steps of: converting an information symbol and a pilot symbol into a time delay Doppler domain sending matrix; sending the time delay Doppler domain sending matrix to a receiving end; dividing a pilot signal of a receiving end into a channel vector and a verification pilot signal; modeling a channel vector into a compressed sensing problem based on an OTFS system, and solving the compressed sensing problem by adopting dynamic sparse Bayesian channel estimation to obtain a posterior channel vector; iteratively updating the hyper-parameter of the posterior channel vector to obtain an optimal channel estimation result; performing iterative optimization on a channel estimation result by adopting a verification pilot signal to obtain an estimated channel vector; the OTFS channel estimation method designed by the invention has relatively strong anti-noise and anti-interference capabilities, and the estimation precision is remarkably superior to that of a traditional sparse Bayesian learning method.

Description

Technical Field

[0001] This invention relates to the field of digital information transmission, and specifically to an OTFS channel estimation method based on dynamic sparse Bayes under low Earth orbit satellites. Background Technology

[0002] Orthogonal Time-Frequency-Space (OTFS) modulation, due to its channel modeling, uniform diversity, and time-invariant properties in the Doppler-Delay (DD) domain, has become one of the key technologies in highly dynamic communication environments. In OTFS systems, obtaining accurate DD domain channel state information (CSI) is a prerequisite for reliable demodulation.

[0003] In existing technologies, mainstream OTFS channel estimation methods mainly include pilot-based compressed sensing estimation and deep learning-based end-to-end estimation. The former offers flexible deployment but suffers from insufficient spectral efficiency; the latter requires no pilots but relies heavily on a large amount of labeled data, limiting its generalization ability. Especially in LEO satellite communication scenarios, most existing OTFS channel estimation methods fail to consider the Doppler squint effect and cannot fully utilize the temporal correlation of the channel, resulting in insufficient estimation accuracy and robustness.

[0004] Therefore, there is an urgent need to design a channel estimation method that balances spectral efficiency and dynamic modeling capabilities to improve the overall performance of the OTFS communication system under LEO satellites. Summary of the Invention

[0005] In view of this, this application discloses an OTFS channel estimation method based on dynamic sparse Bayesian methods for low-Earth orbit satellites to solve the above problems; including:

[0006] S1. Convert the information symbols and pilot symbols into a time-delayed Doppler domain transmission matrix;

[0007] S2. Send the time-delayed Doppler domain transmission matrix to the receiving end;

[0008] S3. Divide the pilot signal at the receiving end into a channel vector and a verification pilot signal;

[0009] S4. Based on the OTFS system, the channel vector is modeled as a compressed sensing problem. Dynamic sparse Bayesian channel estimation is used to solve the compressed sensing problem to obtain the posterior channel vector. During the solution process, the channel vector of the current frame is regarded as following a Gaussian distribution with the channel estimation of the historical frames as the mean.

[0010] S5. Iteratively update the hyperparameters of the posterior channel vector to obtain the optimal channel estimation result; the hyperparameters include noise accuracy and channel correlation coefficient; the update adopts the expectation-maximization algorithm;

[0011] S6. Using the verification pilot signal, the channel estimation result is iteratively optimized to obtain the estimated channel vector; the iterative optimization includes: performing path verification and sparsity refinement on the initially estimated channel vector, and eliminating redundant paths through reconstruction error analysis.

[0012] The beneficial effects of this application include:

[0013] A dynamic sparse Bayesian channel estimation method is designed. This method assumes that the channel prior follows the mean of the previous frame's channel, using historical frame channel estimates as prior information. It explicitly models the temporal correlation of the channel and introduces a channel correlation coefficient. By controlling the degree of memory between the current channel and the previous channel, the current estimation cannot rely too much on past values, thus adaptively adjusting the dependence of the current frame channel on the historical channel. This results in significantly better estimation accuracy than traditional sparse Bayesian learning methods under low signal-to-noise ratio conditions.

[0014] Based on the idea of ​​machine learning algorithm, the receiver pilot is divided into two parts: preliminary estimation and verification optimization. A path verification mechanism is designed to perform path verification and sparsity refinement on the preliminary estimated channel vector. Redundant paths are eliminated through reconstruction error analysis, and iterative optimization is performed to improve the physical reliability of the channel estimation and enhance the anti-noise and anti-interference capabilities of the channel estimation.

[0015] This paper presents an OTFS channel estimation method based on dynamic sparse Bayesian methods for low-Earth orbit satellites. The method employs the expectation-maximization algorithm and an iterative optimization strategy to solve the dynamic sparse Bayesian channel estimation problem, providing a new design approach for those skilled in the art. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites in this application.

[0017] Figure 2 This is a schematic diagram of the pilot arrangement at the transmitting end in an embodiment of this application;

[0018] Figure 3 This is a schematic diagram of the channel vector and verification pilot signal in the embodiments of this application;

[0019] Figure 4 The simulation parameters are set in the embodiments of this application;

[0020] Figure 5 This is a comparison chart of NMSE for each OTFS channel estimation method in the embodiments of this application under different signal-to-noise ratios;

[0021] Figure 6 This is a comparison chart of the bit error rates of various OTFS channel estimation methods in the embodiments of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, features, and advantages of this application clearer and to enable those skilled in the art to better understand the technical solutions of this application, the following detailed description of this application is provided in conjunction with the accompanying drawings and embodiments.

[0023] S1. Convert the information symbols and pilot symbols into a time-delayed Doppler domain transmission matrix.

[0024] S2. Send the time-delayed Doppler domain transmission matrix to the receiving end.

[0025] Specifically, the transmitting end places the information symbols on an M×N time-delay Doppler domain grid to form a transmission signal matrix; the matrix is ​​vectorized and converted into a time-frequency domain signal through a Synthys Fourier transform, and then converted into a time-domain signal through a Heisenberg transform before being transmitted.

[0026] like Figure 1 The diagram shows the pilot scheme used in this embodiment. Unlike the common scheme of embedding pilots with a guard interval, the transmitter in this application does not require a guard interval, and the pilot power is the same as the symbol power. , representing the intermediate coordinate on the delay axis, Indicates the number of subcarriers. This indicates the index corresponding to the maximum delay on the delay axis, which is determined by adjusting the boundary parameters of the pilot arrangement. This allows for control over the number of pilots, improving spectrum utilization. The specific expression for pilot arrangement is:

[0027]

[0028] in, Indicates pilot symbol, Represents data symbols.

[0029] S3. Divide the pilot signal at the receiving end into the channel vector and the verification pilot signal.

[0030] Specifically, such as Figure 3 As shown, based on the training and validation concepts in machine learning, this application divides the symbols available for channel estimation at the receiver into two parts: a channel vector and a validation pilot signal. Figure 3 In the diagram, the rhombus represents the channel vector, used for dynamic sparse Bayesian channel estimation, and the hexagon represents the verification pilot signal, used for further processing of the estimated channel to obtain a more accurate channel estimate.

[0031] S4. Based on the OTFS system, the channel vector is modeled as a compressed sensing problem. Dynamic sparse Bayesian channel estimation is used to solve the compressed sensing problem to obtain the posterior channel vector. During the solution process, the channel vector of the current frame is regarded as following a Gaussian distribution with the channel estimation of the historical frames as the mean.

[0032] Specifically, considering a rectangular pulse, the input-output relationship of OTFS in the delayed Doppler domain is as follows:

[0033]

[0034] in, This represents the input to OTFS. For system noise, and These represent modulo operations with respect to M and N, respectively. The number of propagation paths can be represented by an appropriate Q value, which can approximate the effect of fractional Doppler. Existing research, including literature, indicates that when... The channel can be approximated at this time. and The specific form is as follows:

[0035]

[0036]

[0037] like Figure 2 The diagram shows the pilot arrangement in this embodiment. Based on the input-output relationship of the OTFS system, the matrix form formula for the input and output of the OTFS system is obtained:

[0038]

[0039] in, This represents the received signal used for preliminary channel estimation. ,correspond Figure 3 The receiving symbol corresponding to the diamond symbol; Indicates and The matrix formed by the corresponding pilot signals; This represents the Hadamard product; the rectangular pulse function affects the phase of the pilot symbol, therefore the pilot signal is multiplied by... Phase compensation is performed using the conjugate of the matrix. Represents the phase compensation matrix. yes The vector form of the pilot signal multiplied by Phase compensation is performed using the conjugate of the sparse vector; This represents the time-delay-Doppler domain channel impulse response, i.e., the current channel vector. , representing the total possible propagation paths, Indicates the maximum delay index. Indicates the maximum Doppler index; Indicates Gaussian noise; Representation of the perception matrix

[0040] noise Modeling with a mean of 0 and a precision (the reciprocal of the variance) of 0. Gaussian white noise, the formula is:

[0041]

[0042] Will The model is based on a gamma distribution controlled by hyperparameters a and b, with the following formula:

[0043]

[0044] Due to noise It is a Gaussian distribution, and the linear combination in the Gaussian additive noise model still follows a Gaussian distribution, therefore In a given and Under the given conditions, it also conforms to a Gaussian distribution, and the likelihood function of the received signal is obtained as follows:

[0045]

[0046] This application will use channel vectors The prior is considered to be the mean. A Gaussian distribution, assigning a distinct variance to each delay-Doppler tap, can "simulate" sparsity while maintaining the algorithm's low complexity and tractability. The accuracy is... ,in This represents the channel vector estimated in the previous frame, and its physical meaning is the current channel vector. The estimated value of the previous frame Fluctuation around the center. Vector The channel correlation coefficient controls the degree of memory between the current channel and the previous channel. A larger coefficient indicates a more stable channel change, while a smaller coefficient indicates a faster channel change. This prevents the current estimate from relying too much on past values. This modeling method can adaptively adjust the degree of dependence of the current frame channel on historical channels.

[0047] make , yes variance, channel vector The prior representation is:

[0048]

[0049] This application adopts parameters that are 1 and Gamma distribution description accuracy According to the conjugate prior, the posterior distribution also follows a Gaussian distribution, in the case of hyperparameters. and It is known that and Given the information, the channel vector is solved using the maximum a posteriori probability criterion; the formula is:

[0050]

[0051]

[0052]

[0053] in, express gamma distribution, express The posterior distribution. After further derivation and simplification, the final expression for the posterior channel vector is obtained:

[0054]

[0055]

[0056]

[0057] in, Represents the posterior channel vector. Represents the current channel vector. This represents the received signal used for preliminary channel estimation. Indicates the distribution precision. This represents the channel vector estimated in the previous frame. Represents the channel correlation coefficient. Indicates the accuracy of noise distribution. , representing the total possible propagation paths, Indicates the maximum delay index. Indicates the maximum Doppler index. This represents the mean. Represents variance. This represents the perception matrix.

[0058] Specifically, the further derivation and organization include:

[0059] Step 1: Substitute Bayes' theorem into... The posterior distribution is then simplified and rearranged.

[0060] because In the known Under the condition of only relying , and It is control The prior knowledge does not affect the observation. Only by and Control, and Irrelevant, substituting Bayes' theorem into The posterior distribution, after simplification and rearrangement, is obtained as follows:

[0061]

[0062]

[0063] Step 2: Substitute the likelihood function formula into the prior distribution.

[0064]

[0065]

[0066]

[0067] in, The formula for the likelihood function is given.

[0068] Step 3: Decompose the posterior expression. Since the numerator of the posterior expression is the product of two Gaussian probability density functions, it will still be a Gaussian function after decomposition:

[0069]

[0070]

[0071] Step 4: Rewrite the posterior expression in integral form.

[0072] because The posterior expression of is in denominator the observed marginal distributions, and therefore can be written in integral form, where represents all possible marginal distributions. The summation of values ​​results in a total probability density that satisfies normalization in the posterior:

[0073]

[0074] Step 5: Integrate the a posteriori expression in integral form.

[0075] Specifically, the definition of the integral term includes The part is:

[0076]

[0077] Expanding the exponents and merging them yields:

[0078]

[0079] in, , , , respectively, represent intermediate parameters.

[0080] Rearranging the exponential function into perfect square form yields:

[0081]

[0082] in ,right Integrating, we finally obtain:

[0083]

[0084] Step 6: Substitute the integral result back into the posterior expression to end the derivation and simplification.

[0085] Specifically, will be for Substitute the integral result The denominator of the posterior expression is obtained as follows:

[0086]

[0087] Will and Substituting the value will give you The final closed expression:

[0088]

[0089] The final posterior expression is obtained by simplification.

[0090] S5. Iteratively update the hyperparameters of the posterior channel vector to obtain the optimal channel estimation result; the hyperparameters include noise accuracy and channel correlation coefficient; the update adopts the expectation-maximization algorithm.

[0091] Specifically, due to Since the hyperparameters cannot be calculated analytically, this application employs the Expectation-Maximization (EM) algorithm to solve for them. Sparse Bayesian learning uses the Type-II maximum likelihood method to estimate the hyperparameters by maximizing the marginal log-likelihood, as shown in the formula:

[0092]

[0093] The EM algorithm equates the log-likelihood in the above equation to an expectation optimization problem, and uses an iterative optimization strategy to transform the log-marginal likelihood into an expectation function:

[0094]

[0095] Solving the expectation function yields the update formulas for the hyperparameters; specifically, the update formulas for the hyperparameters include:

[0096] Step 1: Extract information from the original Q function regarding... Part of it is denoted as ,according to The formula yields:

[0097]

[0098]

[0099] Step 2, right Taking the derivative, we get Update format:

[0100]

[0101] Step 3: Add information about the Q function. Part of it is denoted as :

[0102]

[0103]

[0104] in, express The main diagonal element.

[0105] Step 4, for Taking the derivative and setting it to zero, we obtain the formula for updating the noise accuracy:

[0106]

[0107] in, For use in describing precision The parameters.

[0108] Step 5: To obtain the optimal channel correlation coefficient This application uses the Type-II maximum likelihood method for updating within the EM framework, incorporating channel priors into maximizing the expected log likelihood function, to obtain... about The following parts were compiled:

[0109]

[0110]

[0111]

[0112] Step 6, for By taking the derivative and setting it to zero, we obtain the update formula for the channel correlation coefficient.

[0113]

[0114] Furthermore, the hyperparameters are updated using an update formula, and the hyperparameters are substituted back into the posterior channel vector to obtain the optimal channel estimation result.

[0115] S6. Using the verification pilot signal, the channel estimation result is iteratively optimized to obtain the estimated channel vector; the iterative optimization includes: performing path verification and sparsity refinement on the initially estimated channel vector, and eliminating redundant paths through reconstruction error analysis.

[0116] Specifically, by performing structural verification and sparsity refinement on the initial estimate, the influence of redundant paths caused by prior bias or sample perturbation is eliminated. This is based on the initially estimated channel vector. Using the corresponding perception matrix Construct the signal reconstruction expression: ,in, This represents the verification signal obtained based on the current channel estimation. In order to improve the sparsity and accuracy of the channel vector, the impact of non-zero path coefficients on the signal reconstruction error is examined.

[0117] This application designs a path verification mechanism, which is used for iterative optimization to examine the impact of each non-zero path coefficient in the channel estimation vector on the signal reconstruction error. The path verification mechanism includes:

[0118] S601, Set the current estimated channel vector as... , It contains multiple non-zero paths.

[0119] S602. For each non-zero path i, construct a channel zeroing vector. The channel zeroing vector is used to set the i-th path to zero, while the rest remain unchanged.

[0120] S603. Calculate the reconstruction error between the reconstructed signal after removing path i and the actual received signal. The formula used to calculate the error is:

[0121]

[0122] in, Indicates the reconstruction error. Represents the perception matrix, Represents the channel zeroing vector. This represents the verification signal obtained based on the current channel estimation.

[0123] S604. If the reconstruction error is less than the original error, that is, the reconstruction effect is better after removing the path, then the path is determined to be a pseudo path caused by the estimation error and is removed from the final channel estimation; otherwise, the path is retained.

[0124] S605, repeat S601~S604 until all paths have been verified, and obtain the estimated channel vector.

[0125] This path verification mechanism can improve the physical reliability of channel estimation and enhance the robustness of the model when pilot resources are limited.

[0126] Furthermore, the OTFS channel estimation method based on dynamic sparse Bayes under low-Earth orbit satellites in this embodiment is simulated, with parameter settings as follows: Figure 4 As shown, the simulation uses a single-input single-output system, with 4-QAM modulation at the transmitting end and the 3GPP NTN-TDL-B channel model.

[0127] To evaluate system performance through numerical verification, the Normalized Mean Square Error (NMSE) is used to assess system performance in the OTFS system channel estimation. The NMSE calculation formula is as follows:

[0128]

[0129] like Figure 5 The figure shows a comparison of NMSE values ​​for various OTFS channel estimation methods under different signal-to-noise ratios (SNRs). It can be seen that the performance of the sparse Bayesian estimation method is superior to the traditional OMP and LS algorithms. This is because the sparse Bayesian channel estimation method utilizes prior information about the channel. The channel estimation method based on dynamic sparse Bayesian proposed in this application significantly outperforms the traditional sparse Bayesian method at low SNRs, demonstrating the robustness of the proposed scheme in low SNR scenarios, as this invention incorporates prior information from historical frames. As the SNR increases, the gap with the traditional sparse Bayesian algorithm gradually decreases, but it still outperforms the traditional sparse Bayesian algorithm. Figure 6 The figure shows a comparison of the bit error rates of various channel estimation algorithms. It can be seen that, under any SNR, the D-SBL algorithm based on the OTFS channel estimation method designed in this application has a better bit error rate than other algorithms.

[0130] Finally, it should be noted that the above description only depicts some embodiments of this application. For those skilled in the art, various changes, modifications, substitutions, and variations can be conceived of these embodiments without departing from the principles and spirit of this application. The scope of protection of this application is defined by the appended claims and their equivalents, and all the above-mentioned behaviors should be covered within the scope of protection of this application.

Claims

1. A channel estimation method for low-Earth orbit satellites based on dynamic sparse Bayesian methods, characterized in that, include: S1. Convert the information symbols and pilot symbols into a time-delayed Doppler domain transmission matrix; S2. Send the time-delayed Doppler domain transmission matrix to the receiving end; S3. Divide the pilot signal at the receiving end into a channel vector and a verification pilot signal; S4. Based on the OTFS system, the channel vector is modeled as a compressed sensing problem. Dynamic sparse Bayesian channel estimation is used to solve the compressed sensing problem to obtain the posterior channel vector. During the solution process, the channel vector of the current frame is regarded as following a Gaussian distribution with the channel estimation of the historical frames as the mean. S5. Iteratively update the hyperparameters of the posterior channel vector to obtain the optimal channel estimation result; the hyperparameters include noise accuracy. Channel correlation coefficient The update employs the expectation-maximization algorithm. S6. Using the verification pilot signal, iteratively optimize the channel estimation results to obtain the estimated channel vector; The iterative optimization includes: performing path verification and sparsity refinement on the initially estimated channel vector, and eliminating redundant paths through reconstruction error analysis.

2. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 1, characterized in that, The process involves sending the time-delay Doppler domain transmission matrix to the receiving end, where the transmitting end places information symbols on an M×N time-delay Doppler domain grid to form a transmission signal matrix; the transmission signal matrix is ​​vectorized, converted into a time-frequency domain signal through a symmetric Fourier transform, and then converted into a time-domain signal through a Heisenberg transform before being transmitted.

3. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 2, characterized in that, The transmitting end does not require a guard interval, and the pilot power is the same as the symbol power.

4. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 1, characterized in that, The OTFS system has the following input / output matrix formula: ； in, This represents the received signal used for preliminary channel estimation; Indicates and The matrix formed by the corresponding pilot signals; Hadamard product; matrix Represents the phase compensation matrix. yes The vector form of the pilot signal multiplied by The conjugate is used for phase compensation; This represents the time-delay-Doppler domain channel impulse response, i.e., the current channel vector; Indicates Gaussian noise; This represents the perception matrix.

5. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 1, characterized in that, The dynamic sparse Bayesian channel estimation will use the channel vector The prior is considered to be the mean. Gaussian distribution, with a distribution precision of ,in, This represents the channel vector estimated in the previous frame, and its physical meaning is the current channel vector. The estimated value of the previous frame Fluctuation around the center The channel correlation coefficient controls the degree of memory between the current channel and the previous channel. A larger coefficient indicates a more stable channel change, while a smaller coefficient indicates a faster channel change.

6. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 1, characterized in that, The posterior channel vector is formulated as follows: ； ； ； in, Represents the posterior channel vector. Represents the current channel vector. This represents the received signal used for preliminary channel estimation. express Distribution accuracy, This represents the channel vector estimated in the previous frame. , Indicates the maximum delay index. Indicates the maximum Doppler index. This represents the mean. Represents variance. Represents the perception matrix, , express The variance.

7. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 1, characterized in that, The iterative update includes: estimating the hyperparameters by maximizing the marginal log-likelihood using the Type-II maximum likelihood method, as shown in the formula: ； An iterative optimization strategy is used to transform the log-marginal likelihood into an expectation function: ； Solving the expectation function yields the update formula for the hyperparameters; The hyperparameters are updated using an update formula, and the hyperparameters are substituted back into the posterior channel vector to obtain the optimal channel estimation result.

8. The OTFS channel estimation method based on dynamic sparse Bayes for low-Earth orbit satellites according to claim 1, characterized in that, The iterative optimization of the channel estimation results is performed using this path verification mechanism. The path verification mechanism includes: S601, Set the current estimated channel vector as... , Contains multiple non-zero paths; S602. For each non-zero path i, construct a channel zeroing vector; the channel zeroing vector is used to set the i-th path to zero, while the rest remain unchanged. S603. Calculate the reconstruction error between the reconstructed signal after removing path i and the actual received signal; the formula used to calculate the error is: ； in, Indicates the reconstruction error. Represents the perception matrix, Represents the channel zeroing vector. This represents the verification signal obtained based on the current channel estimation. S604. If the reconstruction error is less than the original error, that is, the reconstruction effect is better after removing the path, then the path is determined to be a pseudo path caused by the estimation error and is removed from the final channel estimation; otherwise, the path is retained. S605, repeat S601~S604 until all paths have been verified, and obtain the estimated channel vector.

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