A low earth orbit satellite orthogonal time frequency space modulation system channel estimation method and device

Abstract

This invention discloses a channel estimation method and apparatus for an orthogonal time-frequency spatial modulation system for low Earth orbit satellites. The method includes: receiving a time-domain signal transmitted from a low Earth orbit satellite, removing the cyclic prefix and applying a window, then sequentially performing Wiener transform, Sin-Fourier transform, truncating a preset portion, and stacking the truncated portion into a vector to obtain the DD-domain received signal; using the DD-domain received signal and a horseshoe-shaped prior variational sparse Bayesian learning channel estimation method, while simultaneously adjusting the shrinkage of global variables based on noise characteristics to improve the accuracy of the channel estimation method, finally obtaining the channel estimate. This invention offers higher accuracy.

Description

Technical Field

[0001] This invention relates to channel estimation technology, and more particularly to a channel estimation method and device for a low Earth orbit satellite orthogonal time-frequency spatial modulation system. Background Technology

[0002] Low-Earth Orbit (LEO) satellite communication systems, due to their wide coverage and low latency, are becoming a key component of future 6G integrated space-ground networks. However, the high-speed motion of LEO satellites poses a significant challenge to traditional modulation techniques. Orthogonal Time-Frequency Space (OTFS) modulation technology, by modulating information symbols in the Delay-Doppler (DD) domain and using Synthymesian Fourier transform to convert them to the time-frequency domain for transmission, has shown great potential in handling highly dynamic channels and is recognized as one of the key physical layer waveforms for LEO satellite communication. Its key advantage lies in transforming the time-varying channel into a quasi-static two-dimensional convolutional channel in the DD domain and fully utilizing Doppler diversity gain. Therefore, accurately estimating the DD domain channel response is a core element in ensuring the performance of the LEO-OTFS system.

[0003] Existing channel estimation methods for LEO-OTFS systems are mostly threshold estimation algorithms or traditional compressed sensing algorithms. When the channel tap delay and Doppler offset fall exactly on a DD domain grid point, the channel response is sparse and energy-concentrated, and threshold estimation or traditional compressed sensing algorithms can effectively estimate the channel response. However, in high-speed LEO satellite scenarios, due to limited bandwidth resources, fractional Doppler characteristics cannot be ignored. Under rectangular pulse shaping, fractional Doppler offsets cause severe Doppler domain spectral diffusion, resulting in the DD domain channel response energy dissipating between adjacent Doppler grid points, significantly disrupting the sparsity of the equivalent DD domain channel. In this case, the performance of traditional channel estimation methods based on integer assumptions deteriorates sharply, while simple off-network model corrections or conventional sparse priors often fail to effectively capture these diffused channel characteristics, resulting in low estimation accuracy and failing to meet the performance requirements of LEO-OTFS systems under high dynamic conditions.

[0004] To suppress spectral spread caused by fractional Doppler, existing studies have explored processing at the receiver. However, research on signal shaping at the transmitter to improve DD-domain channel characteristics without compromising noise Gaussian properties is relatively limited. Furthermore, although sparse Bayesian learning frameworks have been introduced for equivalent DD-domain channel estimation, the prior distributions used in existing methods are difficult to accurately match the significant sparsity characteristics exhibited by the channel after fractional Doppler spread and windowing, resulting in low estimation accuracy. Summary of the Invention

[0005] To address the problems existing in the prior art, the purpose of this invention is to provide a more accurate channel estimation method and device for orthogonal time-frequency spatial modulation systems for low Earth orbit satellites.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0007] A channel estimation method for a low Earth orbit satellite orthogonal time-frequency spatial modulation system includes the following steps:

[0008] (1) Receiving time-domain signals transmitted from low Earth orbit satellites After removing the cyclic prefix and windowing, the time-domain received signal is obtained. ;

[0009] (2) Based on the received signal in the time domain The received signal in the time-delay-Doppler domain is obtained by performing Wiener transform and Synthy Fourier transform sequentially. ;

[0010] (3) From The signal is obtained by extracting portions of the preset time delay index range and the preset Doppler index range. and will Stack the columns into a vector to obtain the signal. ;

[0011] (4) Set the relevant parameters in the sparse Bayesian learning method, specifically including: setting the prior distribution as: and Channel vector below The t-th element h t Follows the pattern with mean 0 and variance of Gaussian distribution, yes The t-th element, For local precision variable vectors, Represents a global precision variable. and This results in a horseshoe-shaped marginal distribution of the channel parameters; the noise follows a mean of 0 and a variance of... The complex Gaussian distribution, It follows a gamma distribution; the likelihood function is set as: channel vector and The following signal Follow the mean The variance is The complex Gaussian distribution, It is a measurement matrix; settings include , , and Hidden variable set ;

[0012] (5) Hide the set of variables variational approximation Decomposed into the product of variational approximations of each latent variable in the latent variable set, and then expressed as variational approximations. With posterior distribution The objective function is to minimize the KL divergence between the variables, and the hidden variable set is obtained by solving this problem. The optimal value of each hidden variable is obtained by approximating the variational value of each hidden variable.

[0013] (6) Obtain the channel vector The mean of the optimal values ​​is used as an estimate of the equivalent delay-Doppler domain channel vector.

[0014] Furthermore, step (1) specifically includes:

[0015] (1.1) Receiving time-domain signals transmitted from low Earth orbit satellites And remove its cyclic prefix to obtain the signal. :

[0016]

[0017]

[0018] in, This represents the matrix with the cyclic prefix removed. This represents a 0 matrix where the number of rows is equal to the value in parentheses. This represents a 1-dimensional matrix with rows equal to the values ​​in parentheses. Indicates the length of the window. Indicates the total number of delay tap indices. Indicates the total number of Doppler tap indices. The length of the cyclic prefix. Indicates the maximum latency tap index;

[0019] (1.2) For the signal By performing aliasing to eliminate the windowing effect of low Earth orbit satellites, the signal can be obtained. :

[0020]

[0021]

[0022] in, This represents an aliasing matrix.

[0023] Furthermore, step (2) specifically includes:

[0024] (2.1) For the signal Restore the matrix by rearranging the columns. ;

[0025] (2.2) For the matrix Perform Wiener transform to obtain the time-frequency domain received signal. :

[0026]

[0027] In the formula, This is the matched filter matrix at the receiving end. express Point discrete Fourier transform matrix, Indicates the total number of delay tap indices;

[0028] (2.3) For the received signal in the time and frequency domain Perform a symmetric Fourier transform to obtain the time-delay-Doppler domain received signal. :

[0029]

[0030] In the formula, express Point discrete Fourier transform matrix, Indicates the total number of Doppler tap indices. This indicates the conjugate transpose operation.

[0031] Furthermore, step (3) specifically includes:

[0032] (3.1) Extracting the received signal in the time-delay-Doppler domain The range of medium-delay index is And the Doppler index range is The part that is obtained ;in, Indicates the delay tap index. Indicates the Doppler tap index. Indicates the delay tap index of the pilot signal. Indicates the Doppler tap index of the pilot frequency. Indicates the maximum latency tap index. Indicates the maximum Doppler tap index. Indicates the number of protection indexes on the Doppler field;

[0033] (3.2) will Stack the columns into a vector to obtain the signal. .

[0034] Furthermore, in step (4):

[0035] Local precision variable vector and global precision variables The hierarchical structure expression is:

[0036]

[0037]

[0038] In the formula, p() represents the probability function, and L represents the signal. Dimensions It is a vector of local precision variables. Auxiliary variable vector, yes The t-th element, It is a global precision variable The auxiliary variable, Gamma(), represents the gamma distribution; and They respectively satisfy the following gamma distributions:

[0039]

[0040]

[0041] in, The inverse scaling parameter of the gamma distribution. To regulate Fine-tuning parameters;

[0042] The set of hidden variables .

[0043] Furthermore, step (5) specifically includes:

[0044] (5.1) Approximating the variation It is decomposed into the product of variational approximations of each latent variable in the latent variable set, and its expression is:

[0045]

[0046] In the formula, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, It is a vector of local precision variables. Auxiliary variable vector, It is a global precision variable Auxiliary variables;

[0047] (5.2) Using variational approximation Approximating the posterior distribution Using KL divergence to describe and The gap between them and The KL divergence expression between them is:

[0048]

[0049] in, express and KL divergence between them;

[0050] (5.3) Set the objective function as:

[0051]

[0052] In the formula, This represents the optimal variational approximation;

[0053] (5.4) Solve the objective function to obtain the optimal variational approximation, and then obtain the optimal value of each hidden variable.

[0054] Furthermore, step (5.4) specifically includes:

[0055] (5.4.1) The objective function is transformed into:

[0056]

[0057] In the formula, Let the joint distribution and the posterior distribution be represented. equal;

[0058] (5.4.2) Set the maximum number of iterations to The error threshold is Initialize the parameters and the number of iterations. ;

[0059] (5.4.3) Calculated according to the following formula. :

[0060]

[0061]

[0062]

[0063] in, Indicates the (i+1)th iteration The value of the first , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. This represents the channel mean vector in the i-th iteration. Indicates the first The channel variance matrix in the next iteration, c and d represent The shape parameters and inverse scaling parameters of the gamma distribution it follows are specifically the values ​​from the previous iteration;

[0064] And thus obtain In the Values ​​in the next iteration:

[0065]

[0066] in, Indicates to Expectations;

[0067] (5.4.4) Calculated according to the following formula. :

[0068]

[0069]

[0070]

[0071]

[0072] in, , They represent the first In the next iteration , , , They represent the first Channel variance matrix and channel mean vector in the next iteration Indicates the first In the next iteration, the diagonal matrix is ​​used as an intermediate variable, and CN() represents a Gaussian distribution. yes The t-th element, The value is taken from the value of the previous iteration;

[0073] (5.4.5) Calculated according to the following formula. :

[0074]

[0075]

[0076]

[0077] ={ }

[0078] in, Indicates the first In the next iteration , , They represent the first In the next iteration Shape parameters and inverse scaling parameters of the gamma distribution it follows; Indicates the first In the next iteration , Indicates the first In the next iteration , , yes The One element, yes The One element, This represents the modulo operation for complex numbers; Indicates the first In the next iteration , Represented as Variational approximation;

[0079] And thus obtain In the Value in the next iteration Its expression is:

[0080] ;

[0081] (5.4.6) Calculated according to the following formula. :

[0082]

[0083]

[0084]

[0085] in, Indicates the first In the next iteration , , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. Indicates the first In the next iteration , Indicates the first In the next iteration ;

[0086] And thus obtain No. Value in the next iteration Its expression is:

[0087]

[0088] (5.4.7) is calculated according to the following formula. :

[0089]

[0090]

[0091]

[0092] ={ }

[0093] in, Indicates the first In the next iteration , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. Indicates the first In the next iteration , Represented as Variational approximation;

[0094] And thus obtain No. Value in the next iteration Its expression is:

[0095]

[0096] (5.4.8) is calculated according to the following formula. :

[0097]

[0098]

[0099]

[0100] in, Indicates the first In the next iteration , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. Indicates the first In the next iteration , To regulate Fine-tuning parameters;

[0101] And thus obtain No. Value in the next iteration Its expression is:

[0102] ;

[0103] (5.4.9) Determine whether the iterative convergence condition is met. The expression for the iterative convergence condition is: or

[0104] (5.4.10) If the iterative convergence condition is not met, set i = i + 1 and return to step (5.4.3); if the iterative convergence condition is met, end the iteration and set the current value accordingly. As an estimate of the equivalent delay-Doppler domain channel vector.

[0105] A channel estimation method for a low Earth orbit satellite orthogonal time-frequency spatial modulation system includes:

[0106] At the LEO satellite end, perform the following steps:

[0107] Step A-1: ​​Insert a single pilot symbol into the time-delay-Doppler grid of the transmitted signal. The guard interval is set as the area around the pilot symbol, with the remaining area being data symbols, thus forming the transmitted signal; the transmitted signals are combined to form a DD domain signal matrix. ;

[0108] Step A-2: Transform the DD domain signal matrix using inverse symplectic Fourier transform. Convert to time-frequency domain signal ;

[0109] Step A-3: For Perform the Heisenberg transform to obtain the time-domain signal. ;

[0110] Step A-4: In the time domain signal Adding the cyclic prefix CP, we get ;

[0111] Step A-5: For the signal Windowing is applied to limit leakage of the Doppler frequency shift, thus obtaining the transmitted signal. ;

[0112] Perform the above method on the ground.

[0113] A computer program product includes a computer program / instructions that, when executed by a processor, implement the above-described method.

[0114] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described above.

[0115] Compared with existing technologies, the advantages of this invention are as follows: This invention provides a channel estimation method for a low Earth orbit satellite orthogonal time-frequency control system. At the ground receiver, this invention utilizes a variational Bayesian framework channel estimation method based on a horseshoe prior, combined with noise characteristics to adjust the contraction of global variables, thereby improving the accuracy of the channel estimation method and obtaining the channel estimate. At the satellite transmitter, a raised cosine window is added using time-domain windowing technology to suppress the spread of the equivalent DD domain channel in the fractional Doppler domain into the Doppler domain. Compared with traditional channel estimation algorithms, this invention solves the problem of large Doppler domain spread and low channel estimation accuracy caused by fractional Doppler, and is efficiently applied to channel estimation in LEO-OTFS systems. Attached Figure Description

[0116] Figure 1 A flowchart of a channel estimation method for an orthogonal time-frequency control system for low Earth orbit satellites provided by this invention;

[0117] Figure 2 This is a schematic diagram of the transmission signal provided by the present invention;

[0118] Figure 3 This is a schematic diagram of the received signal provided by the present invention;

[0119] Figure 4 This is a comparison chart of the NMSE performance of the present invention and other channel estimation methods at different pilot signal-to-noise ratios. Detailed Implementation

[0120] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0121] Example 1

[0122] This invention provides a channel estimation method for a low Earth orbit satellite orthogonal time-frequency spatial modulation system, such as... Figure 1 As shown:

[0123] At the LEO satellite end, the following steps are specifically performed:

[0124] Step A-1: ​​The transmitted signal includes pilot symbols, guard intervals, and data symbols; a single pilot symbol is inserted into the time-delay-Doppler (DD) grid of the transmitted signal in the orthogonal time-frequency spatial modulation (OTFS) system. The guard interval is set as the area around the pilot symbol, with the remaining area being data symbols; the transmitted signal is expressed as:

[0125]

[0126] in, Indicates the delay tap index. Indicates the Doppler tap index. Indicates the delay tap index of the pilot signal. Indicates the Doppler tap index of the pilot frequency. Indicates the maximum latency tap index. Indicates the maximum Doppler tap index. This represents the number of protection indexes on the Doppler field. Representing data symbols; thus obtaining the DD domain signal matrix. ,matrix The Middle The elements are , Indicates the total number of delay tap indices. Indicates the total number of Doppler tap indices; It is a positive integer constant, set to 3; Set to 16, Set it to 32.

[0127] Step A-2: Transform the DD domain signal using inverse symplectic Fourier transform. Convert to time-frequency domain signal Its expression is:

[0128]

[0129] in, express Point discrete Fourier transform matrix, express Point discrete Fourier transform matrix, This represents the conjugate transpose operation;

[0130] Step A-3: For Perform the Heisenberg transform to obtain the time-domain signal. Its expression is:

[0131]

[0132] in, The transmitter pulse shaping matrix, specifically a rectangular pulse, is set to... This leads to the time-domain signal. vector expression ,That

[0133] The expression is:

[0134]

[0135] in, Indicates the Kronecker product. DD domain signal The vector expression, It is a signal from the DD domain. The vector is obtained by stacking columns together, where Indicates the transpose operation;

[0136] Step A-4: In the time domain signal Adding the cyclic prefix CP, we get Its expression is:

[0137]

[0138] in, The expression for the CP matrix is:

[0139]

[0140] in, The length of the CP;

[0141] Step A-5: For the signal Windowing is applied to limit leakage of the Doppler frequency shift, thus obtaining the transmitted signal. Its expression is:

[0142]

[0143] in, For window matrix,

[0144]

[0145] in,

[0146]

[0147] in, Represents the convolution symbol.

[0148] Satellite launches and transmits signals ,like Figure 2 As shown, the ground equipment received ,like Figure 3 As shown, For the equivalent time-domain channel matrix, under integer time delay and fractional Doppler conditions, Set to:

[0149]

[0150] in, For the number of paths, Indicates the first The complex channel gain of each path, Indicates the first The latency tap index of the path, Indicates the first Doppler tap index for each path, It is the first Fractional Doppler tap index of each path;

[0151] It is a permutation matrix based on forward cyclic shift, and is set as follows:

[0152]

[0153] It is a diagonal matrix, set as follows:

[0154]

[0155] in,

[0156] .

[0157] The channel estimation at the ground end specifically includes the following steps:

[0158] (1) Receiving time-domain signals transmitted from low Earth orbit satellites After removing the cyclic prefix and windowing, the time-domain received signal is obtained. .

[0159] Step (1) specifically includes:

[0160] (1.1) Receiving time-domain signals transmitted from low Earth orbit satellites And remove its cyclic prefix to obtain the signal. :

[0161]

[0162]

[0163] in, This represents the matrix with the cyclic prefix removed. , This represents a 0 matrix where the number of rows is equal to the value in parentheses. This represents a 1-dimensional matrix with rows equal to the values ​​in parentheses. Indicates the length of the window. Indicates the total number of delay tap indices. Indicates the total number of Doppler tap indices. The length of the cyclic prefix. Indicates the maximum latency tap index;

[0164] (1.2) For the signal By performing aliasing to eliminate the windowing effect of low Earth orbit satellites, the signal can be obtained. It is a dimension The column vector of is expressed as:

[0165]

[0166]

[0167] in, This represents an aliasing matrix.

[0168] (2) Based on the received signal in the time domain The received signal in the time-delay-Doppler domain is obtained by performing Wiener transform and Synthy Fourier transform sequentially. .

[0169] Step (2) specifically includes:

[0170] (2.1) For the signal Restore the matrix by rearranging the columns. ;

[0171] Specifically:

[0172]

[0173] The expression is:

[0174]

[0175] (2.2) For the matrix Perform Wiener transform to obtain the time-frequency domain received signal. :

[0176]

[0177] In the formula, This is the matched filter matrix at the receiving end. express Point discrete Fourier transform matrix, Indicates the total number of delay tap indices;

[0178] (2.3) For the received signal in the time and frequency domain Perform a symmetric Fourier transform to obtain the time-delay-Doppler domain received signal. :

[0179]

[0180] In the formula, express Point discrete Fourier transform matrix, Indicates the total number of Doppler tap indices. This indicates the conjugate transpose operation.

[0181] vector expression The expression is:

[0182]

[0183] in, Signal received by the DD domain Obtained by stacking columns into a vector;

[0184] Based on this, it is determined and The relational expression is as follows:

[0185]

[0186] in, Represents the equivalent DD-domain channel matrix. Represents the equivalent DD domain noise. It is time-domain Gaussian white noise. express The elements in the dataset have a mean of 0 and a variance of . The complex Gaussian distribution;

[0187] Equivalent DD domain channel matrix The expression is:

[0188] .

[0189] (3) From The signal is obtained by extracting portions of the preset time delay index range and the preset Doppler index range. and will Stack the columns into a vector to obtain the signal. .

[0190] Step (3) specifically includes:

[0191] (3.1) Extracting the received signal in the time-delay-Doppler domain The range of medium-delay index is And the Doppler index range is The part that is obtained ; Indicates the number of protection indexes on the Doppler field;

[0192] (3.2) will Stack the columns into a vector to obtain the signal. , The expression is:

[0193]

[0194] in, It is a dimension column vectors, This represents the corresponding truncated equivalent DD-domain channel vector. This represents the corresponding truncated equivalent DD domain noise. It is a measurement matrix, and its expression is:

[0195]

[0196] in, This indicates a diagonalization operation. and .

[0197] (4) Set the relevant parameters in the sparse Bayesian learning method.

[0198] Specifically, it includes:

[0199] Set the prior distribution as follows:

[0200]

[0201] Follows a Gaussian distribution. express It follows a mean of 0 and a variance of . The complex Gaussian distribution; yes The t-th element, For local precision variable vectors, Represents a global precision variable. and This results in a horseshoe-shaped distribution of the channel parameters at the margins.

[0202] The noise is set to have a mean of 0 and a variance of . The complex Gaussian distribution is expressed as:

[0203]

[0204] in, express The elements in the dataset have a mean of 0 and a variance of . The complex Gaussian distribution, in which, It is a noise vector The reciprocal of the variance, It follows a gamma distribution, and its expression is:

[0205]

[0206] in, Represents the gamma distribution. These are shape parameters. It is the inverse scaling parameter of the gamma distribution; shape parameter Set to 1, inverse scaling parameter Set to 1;

[0207] Based on the characteristics of horseshoe priors, the local precision variable vector and global precision variables The hierarchical structure expression is:

[0208]

[0209]

[0210] in, It is a vector of local precision variables. Auxiliary variable vector, yes The One element, It is a global precision variable Auxiliary variables;

[0211] and The following gamma distribution expressions are respectively satisfied:

[0212]

[0213]

[0214] in, This represents the inverse scaling parameter of the gamma distribution, specifically 0.00001. To regulate With global precision variables The fine-tuning parameters are obtained through the conditional probability function. Global precision variables and Mutual coupling enhances the global precision of variables. Robustness to noise, mitigating excessive shrinkage under high-noise conditions; through local precision variable vectors. and global precision variables The settings ensure The marginal distribution is horseshoe-shaped;

[0215] Set the likelihood function The expression is:

[0216]

[0217] in, express Follow the mean The variance is The complex Gaussian distribution;

[0218] Set the joint probability distribution for the sparse Bayesian learning method, and define... As the set of hidden variables to be estimated, the joint probability distribution function is obtained. The expression is:

[0219] .

[0220] (5) Hide the set of variables variational approximation Decomposed into the product of variational approximations of each latent variable in the latent variable set, and then expressed as variational approximations. With posterior distribution The objective function is to minimize the KL divergence between the variables, and the hidden variable set is obtained by solving this problem. The optimal value of each hidden variable is obtained by approximating the variational value of each hidden variable.

[0221] Step (5) specifically includes:

[0222] (5.1) Approximating the variation It is decomposed into the product of variational approximations of each latent variable in the latent variable set, and its expression is:

[0223]

[0224] In the formula, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, It is a vector of local precision variables. Auxiliary variable vector, It is a global precision variable Auxiliary variables;

[0225] (5.2) Using variational approximation Approximating the posterior distribution Using KL divergence to describe and The gap between them and The KL divergence expression between them is:

[0226]

[0227] in, express and KL divergence between them;

[0228] (5.3) Set the objective function as:

[0229]

[0230] In the formula, This represents the optimal variational approximation;

[0231] (5.4) Solve the objective function to obtain the optimal variational approximation, and then obtain the optimal value of each hidden variable.

[0232] The specific steps to solve this problem are as follows:

[0233] (5.4.1) The objective function is transformed into:

[0234]

[0235] In the formula, Let the joint distribution and the posterior distribution be represented. equal;

[0236] Therefore, variational approximation The optimal variational approximation The following expression must be satisfied:

[0237]

[0238] in, express The One element, express The variational approximation, Indicates to Expectations express Except All of the others The expectation of the product of these two products, where const is a constant, can be solved using the following steps.

[0239] (5.4.2) Set the maximum number of iterations to The value is 500, and the error threshold is... The initial values ​​of each parameter are 0.00001 (initial noise precision). Initialize the channel mean vector The channel variance matrix is ​​initialized as an all-one vector. Initialize the global precision variable for the identity matrix. Auxiliary variables for initializing global precision variables Initialize the local precision variable vector Given a vector of all 1s, initialize the auxiliary variable of the local precision variable vector. (As a vector of all 1s), and initialize the number of iterations. ;

[0240] (5.4.3) Update :

[0241] because:

[0242]

[0243] in, Indicates the first In the next iteration , Indicates proportional to, This represents the 2-norm operation. This represents the trace operation of a matrix. Indicates the first In the next iteration , Indicates the first The channel mean vector in the next iteration. Indicates the first The channel variance matrix in the next iteration;

[0244] so, It follows a gamma distribution, and its expression is:

[0245]

[0246] in, Indicates the first In the next iteration Shape parameters, Indicates the first In the next iteration The inverse scaling parameter of the gamma distribution;

[0247] And thus obtain No. Update value in the next iteration Its expression is:

[0248] ;

[0249] (5.4.4) Update :

[0250] because:

[0251]

[0252] in, Indicates the first In the next iteration , Indicates the first In the next iteration , Indicates the first In the next iteration, the global precision variable is used. and local precision variable vector The diagonal matrix formed;

[0253] so, It follows a Gaussian distribution, and its expression is:

[0254]

[0255] in, This is the update expression for the channel mean vector. This is the update expression for the channel variance matrix;

[0256] (5.4.5) Update ,because:

[0257]

[0258] in, Indicates the first In the next iteration , Indicates the first In the next iteration , Indicates the first In the next iteration , , yes The One element, yes The One element, This represents the modulo operation for complex numbers; Indicates the first In the next iteration , Represented as Variational approximation;

[0259] so, It follows a gamma distribution, and its expression is:

[0260]

[0261] in, Indicates the first In the next iteration Shape parameters, Indicates the first In the next iteration The inverse scaling parameter of the gamma distribution;

[0262] And thus obtain No. Update value in the next iteration Its expression is:

[0263] ;

[0264] (5.4.6) Update ,because:

[0265]

[0266] in, Indicates the first In the next iteration , Indicates the first In the next iteration , Indicates the first In the next iteration ;

[0267] so, It follows a gamma distribution, and its expression is:

[0268]

[0269] in, Indicates the first In the next iteration Shape parameters,

[0270]

[0271] Indicates the first In the next iteration The inverse scaling parameter of the gamma distribution;

[0272] And thus obtain No. Update value in the next iteration Its expression is:

[0273]

[0274] Further obtain No. Update value in the next iteration Its expression is:

[0275] ;

[0276] (5.4.7) Update The specific process is as follows:

[0277]

[0278] in, Indicates the first In the next iteration , Indicates the first In the next iteration , Represented as The variational approximation is therefore, It follows a gamma distribution, and its expression is:

[0279]

[0280] in, Indicates the first In the next iteration Shape parameters, Indicates the first In the next iteration The inverse scaling parameter of the gamma distribution;

[0281] And thus obtain No. Update value in the next iteration Its expression is:

[0282] ;

[0283] (5.4.8) Update ,because:

[0284]

[0285] in, Indicates the first In the next iteration , Indicates the first In the next iteration ;so, It follows a gamma distribution, and its expression is:

[0286]

[0287] in, Indicates the first In the next iteration Shape parameters, Indicates the first In the next iteration The inverse scaling parameter of the gamma distribution;

[0288] And thus obtain No. Update value in the next iteration Its expression is:

[0289] ;

[0290] (5.4.9) Determine whether the iterative convergence condition is met. The expression for the iterative convergence condition is:

[0291]

[0292] or

[0293]

[0294] (5.4.10) If the iterative convergence condition is not met, then set i = i + 1 and utilize... , , , , and Return to step (5.4.3); if the iterative convergence condition is met, end the iteration. As an estimate of the equivalent delay-Doppler domain channel vector.

[0295] (6) Obtain the channel vector The mean of the optimal values ​​is used as an estimate of the equivalent delay-Doppler domain channel vector.

[0296] Example 2

[0297] This invention provides a computer device that provides services for implementing the method described in Embodiment 1. The device may include: a memory storing a computer-executable program; a processor coupled to the memory; and the processor calling the computer-executable program stored in the memory to execute the steps of the method described in Embodiment 1.

[0298] The memory may include computer system readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The device may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the memory may be used to read and write non-removable, non-volatile magnetic media (commonly referred to as a "hard disk drive"). A program / utility having a set (at least one) of program modules may be stored in, for example, memory. Such program modules include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. The computer-executable program of the program modules typically performs the functions and / or methods described in the embodiments of the present invention.

[0299] The processor executes various functional applications and data processing by running programs stored in memory, such as the method provided in Embodiment 1 of the present invention.

[0300] The code of a computer executable program can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages.

[0301] Example 3

[0302] This invention provides a storage medium containing a computer-executable program, which, when executed by a computer processor, is used to perform the method of Embodiment 1.

[0303] The storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0304] Of course, the computer-executable program provided in the embodiments of the present invention is not limited to the above-described method operations, but can also perform related operations in the methods provided in any embodiment of the present invention.

[0305] It should be understood that the embodiments and descriptions above are only the principles, main features and advantages of the present invention. Various changes and modifications can be made to the present invention without departing from the spirit and scope of the invention, and all such changes and modifications fall within the protection scope of the present invention.

Claims

1. A method for channel estimation of a low earth orbit satellite orthogonal time frequency space modulation system, characterized in that, Includes the following steps: (1) Receiving time-domain signals transmitted from low Earth orbit satellites After removing the cyclic prefix and windowing, the time-domain received signal is obtained. ; (2) According to the time domain received signal The Wiener transform and the symplectic Fourier transform are sequentially performed to obtain a time delay-Doppler domain received signal ; (3) from the part of the preset time delay index range and the preset Doppler index range, obtain a signal , and stack by column into a vector to obtain a signal ; (4) Set the relevant parameters in the sparse Bayesian learning method, specifically including: setting the prior distribution as: and Channel vectors below The t-th element h t Follows the pattern with mean 0 and variance of Gaussian distribution, yes The t-th element, For local precision variable vectors, Represents a global precision variable. and This results in a horseshoe-shaped marginal distribution of the channel parameters; the noise follows a mean of 0 and a variance of... The complex Gaussian distribution, It follows a gamma distribution; the likelihood function is set as: channel vector and The following signal Follow the mean The variance is The complex Gaussian distribution, It is a measurement matrix; settings include , , and Hidden variable set ; (5) Hide the set of variables variational approximation Decomposed into the product of variational approximations of each latent variable in the latent variable set, and then expressed as variational approximations. With posterior distribution The objective function is to minimize the KL divergence between the variables, and the hidden variable set is obtained by solving this problem. The optimal value of each hidden variable is obtained by approximating the variational value of each hidden variable. (6) Acquiring channel vector The mean of the optimum values as an estimate of the estimated equivalent time-delay-Doppler domain channel vector.

2. The method of claim 1, wherein the channel estimation method is applied to a low earth orbit satellite quadrature time and frequency spatial modulation system. Step (1) specifically includes: (1.1) receiving a time domain signal transmitted from a low earth orbit satellite and removing its cyclic prefix to obtain a signal : ， ， in, This represents the matrix with the cyclic prefix removed. This represents a 0 matrix where the number of rows is equal to the value in parentheses. This represents a 1-dimensional matrix with rows equal to the values ​​in parentheses. Indicates the length of the window. Indicates the total number of delay tap indices. Indicates the total number of Doppler tap indices. The length of the cyclic prefix. Indicates the maximum latency tap index; (1.2) aliasing the signal to remove the low earth orbit satellite windowing effect to obtain a signal : ， ， wherein denotes the aliasing matrix.

3. The channel estimation method for a low Earth orbit satellite orthogonal time-frequency spatial modulation system according to claim 1, characterized in that, Step (2) specifically includes: (2.1) For the signal Restore the matrix by rearranging the columns. ; (2.2) on the matrix performing a Wiener transform to obtain a time-frequency domain received signal : ， wherein is a matched filter matrix at the receiving end, denotes is a point discrete Fourier transform matrix, denotes the total number of delay tap indices; (2.3) Time-frequency domain received signal performing a Sine Fourier transform to obtain a time-delay-Doppler domain received signal : ， wherein denotes point discrete Fourier transform matrix, denotes the total number of Doppler taps, denotes the conjugate transpose operation.

4. The method of claim 1, wherein the channel estimation method is used for a low earth orbit satellite orthogonal time frequency space modulation system. Step (3) specifically includes: (3.1) Extracting the received signal in the time-delay-Doppler domain The range of medium-delay index is And the Doppler index range is The part that is obtained ;in, Indicates the delay tap index. Indicates the Doppler tap index. Indicates the delay tap index of the pilot signal. Indicates the Doppler tap index of the pilot frequency. Indicates the maximum latency tap index. Indicates the maximum Doppler tap index. Indicates the number of protection indexes on the Doppler field; (3.2) will Stack the columns into a vector to obtain the signal. .

5. The method of claim 1, wherein, In step (4): local precision variable vector and global precision variable The hierarchical structure expression is: ， ， In the formula, p() represents the probability function, and L represents the signal. Dimensions It is a vector of local precision variables. Auxiliary variable vector, yes The t-th element, It is a global precision variable The auxiliary variable, Gamma(), represents the gamma distribution; and They respectively satisfy the following gamma distributions: ， ， in, The inverse scaling parameter of the gamma distribution. To regulate Fine-tuning parameters; the set of hidden variables .

6. The method of claim 1, wherein, Step (5) specifically includes: (5.1) Approximating the variation It is decomposed into the product of variational approximations of each latent variable in the latent variable set, and its expression is: ， In the formula, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, Represented as The variational approximation, It is a vector of local precision variables. Auxiliary variable vector, It is a global precision variable Auxiliary variables; (5.2) Using variational approximation Approximating the posterior distribution Using KL divergence to describe and The gap between them and The KL divergence expression between them is: ， wherein, represents between KL divergence; (5.3) Set the objective function as: ， In the formula, denotes the optimal variational approximation; (5.4) Solve the objective function to obtain the optimal variational approximation, and then obtain the optimal value of each hidden variable.

7. The method of claim 6, wherein the channel estimation method is used for a low earth orbit satellite orthogonal time frequency space modulation system. Step (5.4) specifically includes: (5.4.1) The objective function is transformed into: ， In the formula, Denotes the joint distribution and the posterior distribution. equal; (5.4.2) set the maximum iteration number as , the error threshold as , the initial values of the parameters, and initialize the iteration number ; (5.4.3) was calculated according to the following formula : ， ， ， in, Indicates the (i+1)th iteration The value of the first , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. This represents the channel mean vector in the i-th iteration. Indicates the first The channel variance matrix in the next iteration, c and d represent Shape parameters and inverse scaling parameters of the gamma distribution it follows; Further, we obtain In the first Value in the second iteration: ， wherein represents a desire for . (5.4.4) was calculated according to the following formula : ， ， ， ， in, , They represent the first In the next iteration , , , They represent the first Channel variance matrix and channel mean vector in the next iteration Indicates the first In the next iteration, the diagonal matrix is ​​used as an intermediate variable, and CN() represents a Gaussian distribution. yes The t-th element, The value is taken from the value of the previous iteration; (5.4.5) was calculated according to the following formula : ， ， ， ={ }， in, Indicates the first In the next iteration , , They represent the first In the next iteration Shape parameters and inverse scaling parameters of the gamma distribution it follows; Indicates the first In the next iteration , Indicates the first In the next iteration , , yes The One element, yes The One element, This represents the modulo operation for complex numbers; Indicates the first In the next iteration , Represented as Variational approximation; Further, we obtain In the first iteration, the value whose expression is ； (5.4.6) was calculated according to the formula : ， ， ， in, Indicates the first In the next iteration , , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. Indicates the first In the next iteration , Indicates the first In the next iteration ; And thus obtain No. Value in the next iteration Its expression is: ， (5.4.7) was calculated according to the formula : ， ， ， ={ }， in, Indicates the first In the next iteration , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. Indicates the first In the next iteration , Represented as Variational approximation; Further, we obtain The first The value in the second iteration The expression is: ， (5.4.8) was calculated according to the formula : ， ， ， in, Indicates the first In the next iteration , They represent the first In the next iteration The shape parameters and inverse scaling parameters of the gamma distribution it follows. Indicates the first In the next iteration , To regulate Fine-tuning parameters; And thus obtain No. Value in the next iteration Its expression is: ； (5.4.9) determining whether an iteration convergence condition is satisfied, the iteration convergence condition expressed as: or ; (5.4.10) If the iterative convergence condition is not met, set i = i + 1 and return to step (5.4.3); if the iterative convergence condition is met, end the iteration and set the current value accordingly. As an estimate of the equivalent delay-Doppler domain channel vector.

8. A method for channel estimation of a low earth orbit satellite orthogonal time frequency space modulation system, characterized in that, include: At the LEO satellite end, perform the following steps: Step A-1: Inserting a single pilot symbol in a time-delay-Doppler grid of a transmission signal and setting a guard interval to a region around the pilot symbol and the rest to data symbols, thereby forming a transmission signal; combining the transmission signals to form a DD-domain signal matrix ; Step A-2: Transform the DD domain signal matrix XDDto the time- frequency domain signal matrix XTFby inverse cosine Fourier transform transforming the signal to the time-frequency domain ; Step A-3: The Heisenberg transformation is performed on to obtain the time-domain signal ; Step A-4: In time domain signal with an added cyclic prefix CP, resulting in ; Step A-5: Windowing the signal Windowing to limit leakage of Doppler shift, resulting in a transmitted signal ; Perform the method described in any one of claims 1-7 at the ground end.

9. A computer program product, comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by the processor, they implement the method of any one of claims 1-7.

10. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: The processor executes the computer program to implement the method as described in any one of claims 1-7.

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