Non-ground network channel estimation method and system based on packet preselection sparse Bayesian

Abstract

The invention discloses a non-ground network channel estimation method and system based on packet preselection sparse Bayesian. The method comprises the following steps: acquiring a received signal of an AFDM symbol at a receiving end; the method comprises the following steps: constructing a channel estimation problem into a sparse recovery model based on sparse characteristics and received signals of a satellite channel in a time delay-Doppler domain; constructing a sensing matrix based on the AFDM modulation parameters and a preset time delay-Doppler grid; based on the sparse recovery model and the sensing matrix, sparse Bayesian learning based on a grouping pre-selection mechanism is adopted to solve a sparse channel vector in the sparse recovery model; comprising the following steps: grouping sensing matrixes according to time delay dimensions, and performing two-stage screening based on received signals to obtain a simplified dictionary matrix; and based on the simplified dictionary matrix and the received signal, iteratively estimating a sparse channel vector by adopting an SBL-EM algorithm, and further mapping to obtain a channel parameter. According to the invention, on the premise that the estimation precision is almost not lost, the problem of too high calculation complexity is fundamentally solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication, in particular to a non-terrestrial network channel estimation method and system based on a group pre-selected sparse Bayesian. BACKGROUND

[0002] Space-ground integrated network is the core architecture of the sixth generation mobile communication, aiming to realize global seamless coverage through the integration of satellite and ground network. However, the orthogonal frequency division multiplexing OFDM (Orthogonal Frequency Division Multiplexing) waveform adopted by the existing fifth generation mobile communication system faces the technical bottleneck of serious degradation of subcarrier orthogonality under the large Doppler frequency offset generated by satellite high-speed movement, and it is difficult to meet the demand of high reliability and high bandwidth for future satellite communication.

[0003] This technical bottleneck has led to the exploration of new waveform technology. Affine frequency division multiplexing AFDM (Affine Frequency Division Multiplexing) as a new multi-carrier scheme has become a potential choice to solve the communication problem in high-speed moving scene due to its strong robustness to Doppler spread. Although AFDM shows superior performance in theory, its application in actual system still faces challenges, especially in accurate and efficient channel estimation under fractional Doppler effect, and the existing methods have obvious shortcomings, which restricts the practical process of AFDM in non-terrestrial network.

[0004] The effectiveness of most existing technologies is limited to ideal channel conditions or integer Doppler assumption, resulting in serious performance limitation in real fractional Doppler scenarios. The method based on approximate maximum likelihood criterion needs prior information of the number of paths, and its practicability is limited. The method based on compressed sensing utilizes the channel sparsity, which is an effective way to solve this problem. Among them, the sparse Bayesian learning SBL (Sparse Bayesian Learning) framework is concerned due to its advantages such as no need to preset sparsity, high estimation accuracy and strong noise resistance. However, in order to accurately capture the fractional Doppler effect caused by satellite high-speed movement, a high-resolution time-delay-Doppler virtual grid needs to be constructed, resulting in a sharp increase in the dimension of the sensing matrix (dictionary). The matrix inversion operation involved in the standard SBL algorithm has a cubic relationship with the number of dictionary atoms, so that the calculation overhead of applying AFDM in non-terrestrial network becomes unbearable, which becomes the main bottleneck of its actual deployment.

[0005] Therefore, there is an urgent need for a channel estimation method that can significantly reduce the computational complexity while maintaining the high precision of SBL, in order to promote the practical process of AFDM in space-ground integrated communication. SUMMARY

[0006] Therefore, the application provides a non-terrestrial network channel estimation method and system based on grouping pre-selection sparse Bayesian.

[0007] The first object of the application is to provide a non-terrestrial network channel estimation method based on grouping pre-selection sparse Bayesian.

[0008] The second object of the application is to provide a non-terrestrial network channel estimation system based on grouping pre-selection sparse Bayesian.

[0009] The first object of the application can be achieved by adopting the following technical solutions:

[0010] A non-terrestrial network channel estimation method based on grouping pre-selection sparse Bayesian, the method comprises:

[0011] acquiring a received signal of a single AFDM symbol at a receiving end;

[0012] Based on the sparse characteristics of the satellite channel in the delay-Doppler domain and the received signal, the channel estimation problem is constructed as a sparse recovery model;

[0013] Based on the AFDM modulation parameters and the preset delay-Doppler grid, a sensing matrix is constructed;

[0014] Based on the sparse recovery model and the sensing matrix, a sparse Bayesian learning based on a grouping pre-selection mechanism is used to solve the sparse channel vector in the sparse recovery model; including: grouping the sensing matrix according to the delay dimension, performing two-stage screening at the group level and within the group based on the received signal, and adding the screened atoms to the simplified candidate atom set; based on the simplified candidate atom set, a corresponding simplified dictionary matrix is obtained; based on the simplified dictionary matrix and the received signal, the SBL-EM algorithm is used to iteratively estimate the sparse channel vector;

[0015] Based on the sparse channel vector, the delay, Doppler and gain parameters of the channel are mapped.

[0016] Optionally, a non-terrestrial network channel estimation method based on grouping pre-selection sparse Bayesian, the method comprises:

[0017] acquiring a received signal of a plurality of continuous AFDM symbols at a receiving end;

[0018] Based on the sparse characteristics of the satellite channel in the delay-Doppler domain and the received signal, the channel estimation problem is constructed as a sparse recovery model;

[0019] constructing a sensing matrix based on the AFDM modulation parameters and a preset delay-Doppler grid;

[0020] Based on the sparse recovery model and the sensing matrix, a sparse Bayesian learning based on grouping pre-selection mechanism is used to solve the sparse channel vector matrix in the sparse recovery model; including: grouping the sensing matrix according to the delay dimension, performing two-stage screening at the group level and within the group based on the received signal, and adding the screened atoms to the simplified candidate atom set; based on the simplified candidate atom set, a corresponding simplified dictionary matrix is obtained; based on the simplified dictionary matrix and the received signal, the SBL-EM algorithm is used to iteratively estimate the sparse channel vector matrix;

[0021] Based on the sparse channel vector matrix, the delay, Doppler and gain parameters of the channel are mapped.

[0022] The second object of the application can be achieved by adopting the following technical solutions:

[0023] A non-ground network channel estimation system based on grouping pre-selection sparse Bayesian, the system is used for any of the above non-ground network channel estimation methods.

[0024] The present application has the following beneficial effects relative to the prior art:

[0025] (1) The core contradiction of high complexity and high precision cannot be achieved: the application introduces a grouping correlation pre-selection mechanism, which introduces an intelligent screening step before the sparse Bayesian learning framework, reduces the computational complexity by 1-2 orders of magnitude without losing the estimation accuracy, and solves the fundamental problem that the standard SBL algorithm cannot be applied in NTN-AFDM system due to the large virtual grid.

[0026] (2) Provide a complete and flexible solution for space-air-ground integration: the application not only forms a core method of "high-efficiency pre-selection-high-precision estimation" under single symbol, but also further constructs a multi-symbol joint estimation expansion scheme using channel short-time stationary characteristics, forming a hierarchical technology system that can be flexibly configured according to actual needs, taking into account real-time and ultimate performance, and providing key support for practical deployment of space-air-ground integrated communication system. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the application, and those skilled in the art can obtain other drawings from the structures shown in the drawings without creative labor.

[0028] Figure 1 Schematic diagram of a non-terrestrial network AFDM system transceiver structure of embodiment 1 of the present application;

[0029] Figure 2 Schematic diagram of an embedded pilot structure adopted by the AFDM system of embodiment 1 of the present application;

[0030] Figure 3 General flowchart of a non-terrestrial network channel estimation method based on packet pre-selection sparse Bayesian of embodiment 1 of the present application;

[0031] Figure 4 Bit error rate performance comparison chart of the SBL algorithm based on packet pre-selection of embodiment 1 of the present application and various comparative algorithms under the NTNTDL-A channel;

[0032] Figure 5 Normalized mean square error performance comparison chart of the SBL algorithm based on packet pre-selection of embodiment 1 of the present application and various comparative algorithms under the NTNTDL-A channel;

[0033] Figure 6 Bit error rate performance comparison chart of the SBL algorithm based on packet pre-selection in the single observation vector mode of embodiment 1 of the present application and various comparative algorithms under the NTNTDL-B channel;

[0034] Figure 7 Normalized mean square error performance comparison chart of the SBL algorithm based on packet pre-selection in the single observation vector mode of embodiment 1 of the present application and various comparative algorithms under the NTNTDL-B channel;

[0035] Figure 8 Bit error rate performance comparison chart of multi-symbol joint processing (pre-selection MSBL) and single-symbol processing (pre-selection SBL) in the multi-observation vector mode of embodiment 2 of the present application under the NTNTDL-B channel. DETAILED DESCRIPTION

[0036] In order to make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application. It should be understood that the described specific embodiments are only used to explain the present application, and are not used to limit the present application.

[0037] Embodiment 1:

[0038] For the convenience of understanding the subsequent receiving method, the signal model of the communication system is briefly described as follows: the channel estimation method of the AFDM system of the non-terrestrial network based on compressed sensing, the transceiver structure of the communication system where the method is located is referred to Figure 1 The randomly generated information bits are first subjected to quadrature phase shift keying (QPSK) baseband modulation to generate a transmission symbol vector Known pilot symbols are inserted at specific positions of the symbol, and a guard interval is added according to the embedded pilot structure to form a complete transmission AFDM symbol, the pilot structure of the transmission symbol is referred to Figure 2 The modulation symbol is subjected to affine frequency division multiplexing modulation to generate a time domain transmission signal , and the modulation formula is , wherein is the conjugate of the fast Fourier transform matrix , and and are the conjugates of the matrix , and , the parameter is set to , represents a non-zero positive integer used to approximate the original channel response in the case of fractional Doppler; is a parameter set according to the channel condition, representing the maximum normalized Doppler shift; is an arbitrary irrational number. The transmission signal is subjected to AFDM demodulation after passing through the non-terrestrial network channel to obtain a received signal y.

[0039] The channel model in this embodiment is based on the non-terrestrial network channel model defined in the 3GPP TR 38.811 standard, specifically the NTN-TDL-A and NTN-TDL-B channel models, which can effectively simulate the multipath delay and high Doppler frequency offset existing in satellite communication, especially the fractional Doppler effect to be solved. The received signal is subjected to AFDM demodulation to obtain a received signal and channel estimation (a core step) is performed to estimate the equivalent channel , and the minimum mean square error equalization is performed on the received data symbol part to compensate for channel distortion.

[0040] As shown in Figure 3 , the embodiment provides a non-terrestrial network channel estimation method based on grouping pre-selected sparse Bayesian, comprising the following steps:

[0041] S301, signal receiving: acquiring a received signal of an AFDM symbol at a receiving end.

[0042] The AFDM symbol in the embodiment is a single AFDM symbol, i.e., a single observation vector mode.

[0043] S302, problem modeling: based on the sparse characteristics of the satellite channel in the delay-Doppler domain and the received signal, the channel estimation problem is constructed as a sparse recovery model.

[0044] Based on the sparse characteristics of the satellite channel in the delay-Doppler domain, the channel estimation problem is constructed as a sparse signal recovery problem, i.e., the mathematical model is where y is a received signal vector, is a sensing matrix, is a sparse channel vector to be estimated, is a noise vector.

[0045] S303, sensing matrix construction: based on the AFDM modulation parameters and the preset delay-Doppler grid, the sensing matrix is constructed.

[0046] Specifically, step S303 includes:

[0047] (1) Determine the virtual grid parameters, and divide the Doppler delay grid.

[0048] According to the characteristics of the non-terrestrial network channel, the maximum delay spread and the maximum Doppler spread are determined; then, the delay-Doppler domain is discretely grid divided: the delay range is divided into grid points, and the delay vector can be expressed as ; the Doppler range is divided into grid points, and the Doppler grid interval (resolution) is , and the Doppler vector can be expressed as ; wherein the grid resolution is a tunable parameter, which determines the accuracy of estimating the fractional Doppler effect, and is usually set to a fraction of the subcarrier interval (e.g. ), and the value should ensure that the grid can cover all possible Doppler values of the channel.

[0049] (2) Calculate the equivalent channel matrix of each grid point.

[0050] The matrix corresponds to the equivalent channel of the AFDM modulation of a specific virtual grid point path, wherein represents the i-th element of the vector τ, represents the j-th element of the vector v. In the presence of fractional Doppler, the response of a single path will spread in the delay-Doppler domain, and the matrix It is just for capturing this fractional Doppler effect that the structure is built, which is a nearly banded matrix, and the calculation formula is:

[0051] ;

[0052] wherein matrix H(p,q) is the element in the pth row and the qth column, is the number of subcarriers of the system; is a non-zero positive integer used for approximating the original channel response in the fractional Doppler case, and the parameter is set as , is an arbitrary irrational number; , is the integer part of the normalized Doppler , denotes the modulo operation on N.

[0053] (3) Based on the equivalent channel matrix, a perception matrix is constructed.

[0054] The perception matrix is a matrix; wherein, is the transmission signal of the embedded pilot structure, and is a blank guard interval placed at both ends of the pilot, , are respectively the maximum normalized delay and Doppler shift set by the system.

[0055] S304, based on the sparse recovery model and the perception matrix, a sparse Bayesian learning based on a grouping pre-selection mechanism is used to solve the sparse channel vector in the sparse recovery model.

[0056] Specifically, step S304 includes:

[0057] (1) Grouping the perception matrix according to the delay dimension, and performing two-stage screening based on the received signal to obtain a simplified candidate atom set and a corresponding simplified dictionary matrix .

[0058] Further, step (1) includes:

[0059] (1-1) Delay group level coarse screening.

[0060] Group the perception matrix according to the delay index corresponding to the atom, a total of groups; for each group, calculate the correlation of all atoms in the group with the received signal , and find the maximum correlation value ; if the preset group discard threshold is lower than the preset group discard threshold , discard the entire latency group; the group discard threshold is related to the signal energy.

[0061] the group discard threshold , wherein is a predefined constant scale factor. The maximum correlation value is calculated by the following formula: , wherein is the index set of atoms in the sensing matrix with latency is the corresponding atom in the sensing matrix with latency and Doppler frequency offset . represents taking the absolute value.

[0062] (1-2) Intra-group atom-level fine screening.

[0063] For the latency group passed through the coarse screening, the correlation of each atom in the group with the received signal is calculated, and only the top atoms with the highest correlation in each group are retained to join the reduced candidate atom set ; wherein is a preset positive integer.

[0064] The reduced dictionary matrix is a sub-matrix obtained by taking the reduced candidate atom set in the column from the original sensing matrix , and can be represented as: .

[0065] (2) Sparse Bayesian Learning.

[0066] Based on the reduced dictionary matrix and the received signal , the SBL-EM algorithm is iteratively executed to estimate the sparse channel vector .

[0067] Further, step (2) comprises:

[0068] (2-1) Initialize hyperparameters , noise variance inverse prior value ; is the noise variance.

[0069] (2-2) E step: in the kth iteration, calculate the expectation and variance of the kth iteration estimated channel. ; wherein represents the conjugate transpose of the matrix.​

[0070] (2-3) M-step: In the k-th iteration, update the hyperparameters and noise precision using the posterior statistics: , ; denotes the integer part.

[0071] (2-4) Iteration: Repeat steps (2-2) and (2-3) until the convergence condition is met or the maximum number of iterations is reached.

[0072] (2-5) Output: Take the expectation of the channel obtained in the last iteration as the estimated value of the sparse channel vector .

[0073] S305, according to the sparse channel vector mapping, the delay, Doppler and gain parameters of the channel are obtained.

[0074] This step aims to convert the sparse solution obtained by the compressive sensing algorithm into channel parameters with clear physical meaning, i.e. the number of multipaths of the channel, the delay and Doppler frequency offset of each effective path.

[0075] From the sparse channel vector obtained by solving , identify the index set of all non-zero elements, where the number of non-zero elements represents the sparsity of the channel; for each index, solve the delay of each path according to the formula ; solve the normalized Doppler frequency offset of each path according to the formula .

[0076] The method provided in this embodiment has the comprehensive advantages of not requiring prior information, taking into account the accuracy and complexity in the case of a single observation vector.

[0077] This embodiment compares its performance with representative algorithms and classical compressive sensing algorithms in the prior art. The method provided in this embodiment is referred to as "pre-selected SBL", and is compared with the following five comparison algorithms:

[0078] The comparative algorithm 1 is Diagonal Reconstruction: derived from the paper (H. Yin, X. Wei, Y. Tang and K. Yang, “Diagonally Reconstructed Channel Estimation for MIMO-AFDM With Inter-Doppler Interference in Doubly Selective Channels,” IEEE Trans. on Wireless Commu., vol. 23, no. 10, pp. 14066-14079, Oct. 2024), which represents a channel estimation scheme based on the diagonal reconstructability of the AFDM subchannel matrix.

[0079] The comparative algorithm 2 is Threshold-based: derived from the paper (YIN, H., TANG, Y. Pilot Aided Channel Estimation for AFDM in Doubly Dispersive Channels [C] / / 2022 IEEE / CIC International Conference on Communications in China (ICCC), 2022:308-313.), which represents a channel estimation method based on threshold detection.

[0080] The comparative algorithm 3 is Approximate Maximum Likelihood (AML): derived from the paper (A. Bemani, N. Ksairi, and M. Kountouris, “Affine frequency division multiplexing for next generation wireless communications,” IEEE Trans. Wireless Commun., vol. 22, no. 11, pp. 8214-8229, Nov. 2023.), which represents an embedded pilot-aided channel estimation method based on the Approximate Maximum Likelihood (AML) criterion.

[0081] The comparative algorithm 4 is a standard sparse Bayesian (Standard SBL): the standard sparse Bayesian learning (SBL-EM) algorithm without any optimization is directly used for AFDM channel estimation, referred to as "standard SBL". This comparison aims to quantitatively evaluate the optimization effect of the grouping preselection mechanism proposed in the application on the computational complexity and the influence on the estimation accuracy.

[0082] The comparative algorithm 5 is orthogonal matching pursuit: the classical orthogonal matching pursuit (OMP) algorithm is applied for AFDM channel estimation. OMP is a widely used greedy reconstruction algorithm in the field of compressed sensing, and its performance can be used as an effective benchmark to evaluate the advantages of the Bayesian method proposed in the application.

[0083] The embodiment refers to the performance verification of the above steps S1 to S5. The simulation parameters are as follows: the signal-to-noise ratio ranges from 0 to 25 dB, 1000 independent Monte Carlo simulations are performed, and 100 AFDM symbols are transmitted in each simulation. The estimated channel is used for system equalization and data detection to obtain the bit error rate (BER) and normalized mean square error (NMSE) performance curves.

[0084] The simulation results under the non-ground network TDL-A channel model based on the 3GPP 38.811 standard are as shown in Figure 4 The bit error rate (BER) and Figure 5 The normalized mean square error (NMSE) are shown. The grouping preselection based sparse Bayesian learning (SBL-EM) method (i.e. "preselection SBL") proposed in the application has significantly better BER and NMSE performance than the comparative algorithm 1: diagonal reconstruction, the comparative algorithm 2: threshold detection, the comparative algorithm 3: approximate maximum likelihood (AML), and the comparative algorithm 5: OMP. This result shows that the method of the application can more effectively capture the sparse characteristics under this channel model and achieve more accurate parameter estimation. However, compared with the comparative algorithm 4 (standard SBL), the proposed method still has a certain gap in the NMSE performance. This is mainly due to the active trade-off made in the algorithm design to balance the computational efficiency and performance: by introducing the grouping preselection mechanism, the algorithm complexity is significantly reduced (the size of the candidate set is reduced by 1-2 orders of magnitude), which is more suitable for actual system deployment, but also loses part of the estimation accuracy that can be theoretically achieved. In addition, in Figure 5In the high SNR region, the NMSE performance curve tends to flatten out, showing an "error floor" effect. This is mainly due to the fixed pilot power setting in the embedded pilot scheme, which leads to a lower limit of the estimation error determined by the pilot power itself rather than the Gaussian noise at high SNR.

[0085] The performance based on the NTN TDL-B channel model is shown in Figure 6 and Figure 7 . The TDL-B channel may have multiple paths with different Doppler shifts on the same delay dimension, making the channel conditions more complex. As can be seen from Figure 6 , the BER performance of the "pre-selected SBL" method of the present application is still significantly better than that of the comparative algorithms 1, 2, 3, and 5. It is worth noting that, unlike the performance under the TDL-A channel, in the TDL-B channel, the BER performance of the "pre-selected SBL" method of the present application is even better than that of "standard SBL of comparative algorithm 4" at high SNR (e.g., SNR > 15 dB). This seemingly contradictory phenomenon actually has a reasonable explanation: at high SNR, the pre-screening mechanism actively discards weak path components with energy close to the noise level, although this leads to a slight decrease in the completeness of channel estimation (reflected as a slight increase in NMSE in Figure 7 ), but this "selective discard" effectively reduces the false path estimates introduced by noise, reducing the possibility of error propagation in the subsequent data detection process, thereby improving the final bit error rate performance. This reflects the unique robustness advantage of the method of the present application in complex interference environments.

[0086] Embodiment 2:

[0087] This embodiment extends the method provided in Embodiment 1 to a multi-symbol joint processing scenario (i.e., a multi-observation vector mode).

[0088] The simulation environment and channel model (NTN-TDL-A) of this embodiment are consistent with those of Embodiment 1 to ensure continuity of comparison.

[0089] Step 1: Signal reception: at the receiving end, the received signal of consecutive AFDM symbols is obtained to form a multi-observation vector matrix .

[0090] This embodiment sets .

[0091] Step 2: Problem modeling: based on the short-time stationary characteristic of the channel, the problem is constructed as a multi-observation vector sparse recovery model: , where is a row-sparse channel matrix.

[0092] Step 3: Sensing matrix construction: exactly the same as step S303 of embodiment 1.

[0093] Step 4: Sparse recovery solution: solve the row-sparse channel matrix .

[0094] Further, step 4 includes:

[0095] (1) Multi-observation vector grouping correlation pre-selection.

[0096] (1-1) Delay group level coarse screening:

[0097] Calculate the joint group correlation of each group ; denotes the th vector of matrix ; if is lower than the extended group dropping threshold , the entire group is discarded.

[0098] (1-2) In-group atom level fine screening:

[0099] For the retained group, based on the joint correlation, only the highest joint correlation atoms in the group are selected to form the candidate set .

[0100] (2) Multi-observation vector sparse Bayesian learning:

[0101] (2-1) Initialize hyperparameters and noise precision , which are the same as (2-1) in step S304 of embodiment 1.

[0102] (2-2) Perform E-step: calculate the posterior mean matrix and covariance matrix according to the formula and .

[0103] (2-3) Perform M-step: update the hyperparameters and noise precision shared across symbols, where the update formula for the th element of the hyperparameter is: , and the noise precision , where is the th diagonal element of matrix .

[0104] (2-4) Repeat iterative steps (2-2) and (2-3) until convergence, and output the posterior mean matrix. As an estimate of the channel matrix H.

[0105] Step 5: Parameter mapping: The columns of the estimated row sparse channel matrix H share a common support set; parameter mapping is performed based on this common support set to obtain consistent multipath delay-Doppler parameters, and the gain of each path is extracted from each column of the row sparse channel matrix H.

[0106] The performance verification results of this embodiment are as follows: Figure 8 As shown. Figure 8 The BER performance of single-symbol "pre-selected SBL" and five-symbol joint "pre-selected MSBL" in the NTN-TDL-A channel was compared. It can be seen that the system's bit error rate performance is significantly improved through multi-symbol joint processing. This demonstrates the effectiveness of extending the core scheme to a multi-observation vector framework in this embodiment, which can further improve the estimation accuracy and overall robustness of the system based on single-symbol estimation by utilizing the temporal coherence of the channel.

[0107] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0108] It should be noted that although the method operations of the above embodiments are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the order of execution of the described steps may be changed. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0109] Example 3:

[0110] This embodiment provides a non-terrestrial network channel estimation system based on grouped preselected sparse Bayesian, which is used to implement the non-terrestrial network channel estimation method based on grouped preselected sparse Bayesian provided in Embodiment 1 or Embodiment 2.

[0111] The specific implementation of this embodiment can be found in Embodiment 1 or Embodiment 2 above, and will not be repeated here.

[0112] In summary, for the application of AFDM in NTN high-speed mobile scenarios, in order to accurately capture fractional Doppler effect, a high-resolution virtual grid needs to be constructed, resulting in the problem of dramatic increase in computational complexity of channel estimation algorithm based on sparse Bayesian learning (SBL). Before using SBL-EM iterative solution, the application introduces a grouping correlation pre-selection mechanism: first, the sensing matrix is grouped according to the time delay dimension, the maximum correlation of each group with the received signal is calculated, and the whole group with correlation lower than the threshold is discarded to realize coarse screening; for the retained group, only a few atoms with the highest correlation with the signal in the group are selected to form a simplified candidate set; finally, only the SBL-EM algorithm is used on the candidate set to perform high-precision channel estimation. Further, the application extends the method to the multi-observation vector (MMV) scene, and uses the short-time stationary characteristics of the channel to further improve the estimation accuracy and robustness through multi-symbol joint processing. The application greatly reduces the computational complexity while ensuring the accuracy close to the standard SBL, and solves the key bottleneck of the practicality of SBL in NTN-AFDM systems.

[0113] The above is only a preferred embodiment of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can make equivalent replacement or change according to the technical scheme and the inventive concept of the present application within the scope disclosed by the present application, which is within the protection scope of the present application.

Claims

1. A non-terrestrial network channel estimation method based on grouped preselection sparse Bayes, characterized in that, The method includes: At the receiving end, the received signal of a single AFDM symbol is acquired; Based on the sparse characteristics of satellite channels in the time-delay-Doppler domain and the received signal, the channel estimation problem is constructed as a sparse recovery model; A sensing matrix is ​​constructed based on AFDM modulation parameters and a preset time-delay-Doppler grid. Based on the sparse recovery model and the sensing matrix, a sparse Bayesian learning method with a group pre-selection mechanism is used to solve the sparse channel vector in the sparse recovery model. The method includes: grouping the sensing matrix according to the time delay dimension, performing a two-stage screening at the group level and within the group based on the received signal, and adding the screened atoms to a simplified candidate atom set; obtaining the corresponding simplified dictionary matrix based on the simplified candidate atom set; and iteratively estimating the sparse channel vector using the SBL-EM algorithm based on the simplified dictionary matrix and the received signal. Based on sparse channel vectors, the channel's delay, Doppler, and gain parameters are mapped.

2. The non-terrestrial network channel estimation method according to claim 1, characterized in that, The sparse recovery model is as follows: Where y is the vector corresponding to the received signal. For the perception matrix, Let be the sparse channel vector to be estimated. This is the noise vector.

3. The non-terrestrial network channel estimation method according to any one of claims 1 and 2, characterized in that, The step of iteratively estimating the sparse channel vector using the SBL-EM algorithm based on the simplified dictionary matrix and the received signal includes: Step 1: Initialize k=0, hyperparameters Noise accuracy ;in, For noise variance; Step 2: In the k-th iteration, based on the simplified dictionary matrix, the received signal, hyperparameters, and noise accuracy, calculate the expectation and variance of the channel estimated in the k-th iteration; Step 3: In the k-th iteration, based on the channel expectation and variance estimated in the k-th iteration, update the hyperparameters and noise accuracy using posterior statistics; Step 4: k = k + 1; Repeat steps 2 and 3 until the convergence condition is met or the maximum number of iterations is reached; Step 5: Use the expectation of the channel calculated in the last iteration as the estimate of the sparse channel vector.

4. A non-terrestrial network channel estimation method based on grouped preselection sparse Bayes, characterized in that, The method includes: At the receiving end, the received signal of multiple consecutive AFDM symbols is acquired; Based on the sparse characteristics of satellite channels in the time-delay-Doppler domain and the received signal, the channel estimation problem is constructed as a sparse recovery model; A sensing matrix is ​​constructed based on AFDM modulation parameters and a preset time-delay-Doppler grid. Based on the sparse recovery model and the sensing matrix, a sparse Bayesian learning method with a group pre-selection mechanism is used to solve the sparse channel vector matrix in the sparse recovery model. The method includes: grouping the sensing matrix according to the time delay dimension, performing a two-stage screening at the group level and within the group based on the received signal, and adding the screened atoms to a simplified candidate atom set; obtaining the corresponding simplified dictionary matrix based on the simplified candidate atom set; and iteratively estimating the sparse channel vector matrix using the SBL-EM algorithm based on the simplified dictionary matrix and the received signal. Based on the sparse channel vector matrix, the channel's delay, Doppler, and gain parameters are obtained through mapping.

5. The non-terrestrial network channel estimation method according to claim 4, characterized in that, The sparse recovery model is as follows: ;in, This is the vector matrix corresponding to the received signal. Let H be the sensing matrix, and H be the sparse channel vector matrix to be estimated. This is the noise vector matrix.

6. The non-terrestrial network channel estimation method according to any one of claims 4 and 5, characterized in that, The step of iteratively estimating the sparse channel vector matrix using the SBL-EM algorithm based on the simplified dictionary matrix and the received signal includes: Step 1: Initialize k=0, hyperparameters Noise accuracy ;in, For noise variance; Step 2: In the k-th iteration, based on the simplified dictionary matrix, the received signal, hyperparameters, and noise accuracy, calculate the posterior mean matrix and covariance matrix of the k-th iteration. Step 3: In the k-th iteration, update the hyperparameters and noise accuracy based on the posterior mean matrix and covariance matrix of the k-th iteration; Step 4: k = k + 1; Repeat steps 2 and 3 until the convergence condition is met or the maximum number of iterations is reached; Step 5: Use the posterior mean matrix calculated in the last iteration as an estimate of the sparse channel vector matrix.

7. The non-terrestrial network channel estimation method according to any one of claims 1 and 4, characterized in that, The process of grouping the perception matrix according to the time delay dimension, performing a two-stage screening process based on the received signal at the group level and within the group, and adding the screened atoms to a simplified candidate atom set includes: The sensing matrix is ​​grouped according to the time delay index corresponding to the atom; for each group, the correlation between all atoms in the group and the received signal is calculated, and the maximum correlation value is found; if the maximum correlation value is lower than the preset group discard threshold, the entire time delay group is discarded. For the retained time delay groups, the correlation between each atom in the group and the received signal is calculated, and the atoms with the highest correlation in each group are selected. One atom is added to the simplified candidate atom set; among them... It is a preset positive integer.

8. The non-terrestrial network channel estimation method according to claim 7, characterized in that, The expression for the group discard threshold ,in, A predefined constant scaling factor. The vector or vector matrix corresponding to the received signal. To find the L2 norm.

9. The non-terrestrial network channel estimation method according to any one of claims 1 and 4, characterized in that, The process of constructing the perception matrix includes: Determine the virtual mesh parameters and divide the Doppler delay mesh; Calculate each grid point ( The equivalent channel matrix H is given by the given information; where, Let i be the i-th element of the time delay vector τ. Let be the j-th element of the Doppler vector v; Constructing a sensing matrix based on the equivalent channel matrix. ; where the elements in the perception matrix , For the transmitted signal of the embedded pilot structure, Let be the element in the p-th row and q-th column of matrix H; in, The expression is: ； in, The number of subcarriers in the system; The parameter is a non-zero positive integer used to approximate the original channel response in the fractional Doppler case; , For the determined maximum Doppler spread; parameters Let be any irrational number; , for The integer part, To calculate the modulus of N.

10. A non-terrestrial network channel estimation system based on grouped preselection sparse Bayes, characterized in that, The system is used to implement the non-terrestrial network channel estimation method according to any one of claims 1 to 9.

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