AFDM system channel estimation method based on sparse Bayesian learning

Abstract

The invention belongs to the technical field of communication, and particularly relates to an AFDM system channel estimation method based on sparse Bayesian learning. On an AFDM system, a sparse Bayesian framework is utilized, and a two-layer channel estimation method of coarse estimation and fine estimation is provided. The coarse estimation uses a uniform grid and a relatively large stop condition to quickly end iteration; in the fine estimation, a sensing matrix is updated by using the time delay and Doppler output in the previous step, a sensing grid is changed into a non-uniform grid, and the energy of a channel coefficient is concentrated on the grid, so that the estimation error is effectively reduced and the convergence speed is increased. The method has the advantages of a Bayesian learning framework and a compressed sensing algorithm for recovering sparse signals, so that the algorithm has inhibition on noise, and the number of propagation paths does not need to be known; peak value searching and zero setting are assisted, the convergence speed is increased, and overfitting is prevented; finally, high-precision channel estimation can be realized under the positive signal-to-noise ratio.

Description

Technical Field

[0001] The invention belongs to the field of communication technology, and in particular relates to a channel estimation method of an AFDM system based on sparse Bayesian learning. Background Art

[0002] In wireless communication systems, accurate and timely channel estimation is crucial for data detection. In high mobility scenarios with multipath effects, signals are subject to both frequency and time selective channel fading. The AFDM system combats dual selective channel fading by using a set of orthogonal linear frequency modulation bases generated by discrete analog frequency division transform (DAFT). Existing AFDM system channel estimation methods using embedded pilots include: Embedded Pilot Assisted Approximate Maximum Likelihood (EPA-AML) method and Embedded Pilot Assisted Diagonal Reconstruction (EPA-DR) channel estimation method.

[0003] The embedded pilot-assisted approximate maximum likelihood method can achieve a high-precision estimation only when the number of propagation paths is known and a sufficient traversal step size is set.

[0004] The embedded pilot-assisted diagonal reconstruction channel estimation method uses a simple threshold to filter out the channel response. In the case of fractional Doppler, the estimation accuracy is low and the result is greatly affected by noise. It is necessary to enhance the estimation performance by increasing the pilot power or placing multiple pilots. In addition, this method can only obtain the channel matrix and cannot estimate the various parameter information of the channel.

[0005] Therefore, the existing AFDM system lacks a high-precision channel estimation method with a wider range of applications, so as to output more accurate channel state information and improve the performance of the communication system. Summary of the invention

[0006] In view of the above problems or deficiencies, in order to solve the problems of lack of prior information of existing transmission channels and insufficient performance of channel estimation methods, the present invention proposes a channel estimation method for AFDM system based on sparse Bayesian learning. According to the sparsity of DAFT domain channels, the channel estimation problem is transformed into a sparse signal recovery problem, and high-resolution channel estimation is achieved using compressed sensing technology.

[0007] A channel estimation method for an AFDM system based on sparse Bayesian learning, the specific steps are as follows:

[0008] Step 1: Convert the input signal to parallel and then do N (N = 2 t ,t≥1) point DAFT transformation.

[0009] Step 2: According to the embedded pilot frame structure and channel transmission model in the DAFT domain, let the vector related to the channel estimation at the receiving end be y E, the pilot vector is x E ; Separate the channel estimation component and the information component in the DAFT domain received signal.

[0010] Step 3: Set y E With x E The relationship becomes a sparse signal recovery model, and a first-order linear approximation is performed.

[0011] Step 4: Roughly estimate the channel parameters through the sparse Bayesian learning framework and output the estimated vector and path coefficient Normalized delay Normalized Doppler shift

[0012] Step 5: Use step 4 to estimate the output and Update the perception matrix in the first-order linear approximation and accurately estimate the channel parameters through a sparse Bayesian learning framework;

[0013] Output for step 4 The non-zero elements of the peak are searched and the largest ( is less than The maximum integer of , the other elements are set to 0, and the corresponding position of the off-grid component is also set to 0. This number is determined by the principle of compressed sensing. Generally speaking, elements are sufficient to characterize the channel. Depending on the channel characteristics of different scenarios or the requirements for AFDM diversity gain, the The size of N accelerates convergence. l N a is the sensing grid length, the effective length of the channel response in the Q+1 channel transmission model.

[0014] After peak search, according to The index of the non-zero element is used to update the elements of the corresponding column of the perception matrix. After updating the perception matrix, sparse Bayesian learning parameter estimation is performed until the stopping condition ε2 (ε2<ε1 / 10) is reached, and the channel coefficient, normalized Doppler frequency shift, and normalized delay are output. ε1 is the stopping condition for the iterative iteration of the rough estimation of channel parameters in step 4.

[0015] In the present invention, steps 1-2 are demodulation steps at the receiving end in the AFDM system. AFDM is a multi-carrier modulation method newly proposed in recent years, which has good resistance to time-frequency dual fading. Steps 3-4 are sparse Bayesian frameworks for solving sparse signal recovery problems. Step 5 is an improved step for estimating AFDM channels using a sparse Bayesian framework, the purpose of which is to solve the sawtooth convergence that occurs when approaching the optimal solution.

[0016] In summary, the present invention proposes a two-layer channel estimation method, i.e., coarse estimation plus refined estimation, on an AFDM system by using a sparse Bayesian framework. Using a uniform grid and a larger stop condition in the coarse estimation step can quickly end the iteration. In the refined estimation, the delay and Doppler output in the previous step are used to update the perception matrix, and the perception grid is changed into a non-uniform grid, so that the energy of the channel coefficient can be concentrated on the grid, which can effectively reduce the estimation error and increase the convergence speed. This method inherits the advantages of the Bayesian learning framework and the compressed sensing algorithm in recovering sparse signals, models the prior assumptions of the noise, and continuously iterates and calculates the noise variance, so that the algorithm has a certain degree of suppression on the noise, and does not need to know the number of propagation paths. In addition, through peak search and zeroing, areas with greater noise influence can be excluded, the convergence speed can be accelerated, and overfitting can be prevented. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the specific technical solution of the present invention;

[0018] Figure 2 It is a comparison chart of the normalized root mean square error performance of EPA-AML, EPA-DR and the embodiment under different signal-to-noise ratios. DETAILED DESCRIPTION

[0019] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation methods.

[0020] A channel estimation method for AFDM system based on sparse Bayesian learning, such as Figure 1 As shown, the specific steps are as follows:

[0021] Step 1: Convert the input signal to parallel and then do N (N = 2 t ,t≥1) point DAFT transformation;

[0022] Assume that the digital sampling signal at the receiving end is r[n], and after serial-to-parallel conversion and N-point DAFT transformation, we get y[m]:

[0023]

[0024] Where e is a natural constant, j is an imaginary unit, c1 and c2 are the system parameters of AFDM, c1 is based on the normalized maximum Doppler frequency shift α max Set to α max and k v are all positive integers, c2 is set to

[0025] Step 2: According to the embedded pilot frame structure and channel transmission model in the DAFT domain, let the vector related to the channel estimation at the receiving end be y E , the pilot vector is xE ; Separate the channel estimation component and the information component in the DAFT domain received signal.

[0026] Define index sets I and J, I = {0: α max +k v ,N-Q+α max +k v :N-1}, J={0:Qa max +k v ,N-α max -k v ∶N-1},Q=(l max +1)(2α max +2k v +1)-1,l max is the maximum normalized delay. E =y[I], which means to intercept y[m] from [0:α max +k v ] and [N-Q+α max +k v :N-1], the rest of y[m] is the data transmission symbol. From the input-output relationship of AFDM, we know that y E With x E The relationship is as follows:

[0027]

[0028] Where P is the number of transmission paths, h i , l i and α i are the coefficient, normalized delay, and normalized Doppler shift of the ith path, respectively. E is the noise vector; Indicates interception The submatrix consisting of the intersection elements of the I-th row and the J-th column, and The (p,q)th element in the matrix is ​​calculated as follows:

[0029]

[0030] is the phase matrix associated with the time delay, Determines the sparsity of the channel.

[0031] Step 3: Set y E With x E The relationship becomes a sparse signal recovery model, and a first-order linear approximation is performed.

[0032] Assume that the perception grid length is N l Nα , N l and N α are all integers greater than 1, considering integer-order delays, N l = l max +1. In this sensing grid, the delay resolution is 1 and the Doppler resolution is r α =(N α -1) / 2α max . In formula (2), and the known pilot vector x E Perform matrix multiplication and merge to get the perception matrix, and the channel coefficient is used as the vector to be estimated, as shown below:

[0033] y E =Φ E (l,a)h+w E (5)

[0034] Among them, the perception matrix is:

[0035]

[0036] The a*Nth of the perception matrix α The +b column is calculated as follows:

[0037]

[0038] The first-order linear approximation of equation (5) is:

[0039]

[0040] Φ(l,α) ′ Φ E (l,α) is the first-order partial derivative of α, and κ is the off-grid Doppler vector. So far, the channel estimation model has been constructed and the initialization of the sensing matrix has been completed.

[0041] Step 4: Roughly estimate the channel parameters through the sparse Bayesian learning framework and output the estimated vector and path coefficient Normalized delay Normalized Doppler shift

[0042] According to the model of formula (8), we make a priori assumption: Assume that the noise vector has zero mean and variance is The Gaussian distribution of β0 follows the gamma distribution with parameters c and d. Assume that the channel coefficient vector follows a zero-mean Gaussian distribution, specifically: in η follows a gamma distribution with parameter ρ, and the elements in h are independent of each other. k follows a uniform distribution. According to the Bayesian principle, the posterior probability of h is derived as:

[0043]

[0044] And calculate:

[0045]

[0046] After calculating the above equations (10) and (11), the hyperparameters of other hypotheses are updated according to the maximum a posteriori probability rule and the expected maximum algorithm, as follows:

[0047]

[0048] The off-grid Doppler component update rules are as follows:

[0049]

[0050] Among them, {A κ} n Represents the matrix A κ The nth row of κ} n,n Represents the matrix A κ The (n,n)th element of κ} n Represents vector b κ The nth element of κ} n} -n Represents a vector {A κ} n Except for the nth element, represents the real part, and ⊙ represents the matrix dot multiplication.

[0051] After the hyperparameters and off-grid Doppler components are updated, this round of calculation is completed.

[0052] In the next round of calculation, the calculation results of formulas (12), (13) and (14) are used to substitute into formulas (10) and (11) to calculate the mean and variance, and then the new mean and variance are used to update formulas (12), (13) and (14). This cycle is repeated until the stop condition is reached. The stop condition ε1 is:

[0053]

[0054] Output estimate vector in From the current value of μ, It is related to the non-zero position of μ, assuming that a*N α +b is The i-th non-zero value of

[0055] Step 5: Use step 4 to estimate the output and Update the sensing matrix and accurately estimate the channel parameters through a sparse Bayesian learning framework;

[0056] Output for step 4 The non-zero elements of the peak are searched and the largest ( is less than The maximum integer of , the other elements are set to 0, and the corresponding position of the off-grid component is also set to 0. This number is determined by the principle of compressed sensing. Generally speaking, elements are sufficient to characterize the channel. According to the channel characteristics of different scenarios or the requirements for AFDM diversity gain, After the peak search, according to The index of the non-zero element updates the element of the corresponding column of the perception matrix:

[0057]

[0058] After updating the sensing matrix, sparse Bayesian learning parameter estimation is performed until the second stop condition ε2 (ε2<ε1 / 10) is reached, and the channel coefficient, normalized Doppler shift, and normalized delay are output.

[0059] The background of this embodiment is: In the computer MATLAB environment, the AFDM system simulation parameters are set as follows: carrier frequency f c =5GHz, number of carriers N = 256, subcarrier spacing Δf = 15kHz, α max =2, l max =3,k v =8, the pilot power is adaptive, 20dB higher than the average power of the data symbol, and the data symbol is modulated by 4-QAM. Consider a four-path channel, the channel coefficient obeys Gaussian distribution, the Doppler frequency shift is randomly generated by Jake's spectrum, and the delay considers integer delay. In the channel estimation algorithm, the parameters are set as: c, d = 1 × 10 -4 , ρ = 0.01, a rough estimate of ε1 = 5 × 10 -3 , accurate estimate ε2 = 5 × 10 -5 .

[0060] The pilot signal generated according to this parameter plus random data symbols are modulated by AFDM and passed through the channel. The receiving end uses three channel estimation algorithms in the DAFT domain. The performance curves are shown in the figure below. Figure 2 As shown. The normalized root mean square error of the vertical axis is defined as As can be seen from the figure, the method proposed in the present invention has an estimated performance slightly better than the EPA-AML method when the signal-to-noise ratio is 0 to 20 decibels, and is much better than the EPA-DR method. It should be pointed out that the EPA-AML method requires the number of multipaths when used. When the number is unknown, the performance will be significantly reduced.

[0061] It can be seen from the above embodiments that the present invention aims at the channel estimation problem of the AFDM communication system, firstly performs DAFT transformation on the input signal and separates the pilot and information components (steps 1-2), then models the signal transmission model as a sparse signal recovery model, and constructs y E The relationship between h and h (step 3) is calculated, and the parameters are updated iteratively through the Bayesian prior hypothesis and the EM algorithm (steps 4-5). The present invention proposes a two-layer channel estimation method, namely, rough estimation plus fine estimation, on the AFDM system by using a sparse Bayesian framework. In the rough estimation step, a uniform grid and a larger stop condition are used to quickly end the iteration. In the fine estimation, the normalized delay and normalized Doppler shift output in the previous step are used to update the perception matrix, and the perception grid is changed into a non-uniform grid, which can concentrate the energy of the channel coefficient on the grid, and can effectively reduce the first-order linear approximation estimation error and increase the convergence speed. This method inherits the advantages of the Bayesian learning framework and the compressed sensing algorithm to restore sparse signals, models the prior hypothesis of noise and continuously iterates to calculate the noise variance, so that the algorithm has a certain degree of suppression on noise, and does not need to know the number of propagation paths. In addition, through peak search and zeroing, areas with greater noise influence can be excluded, the convergence speed can be accelerated, and overfitting can be prevented. The present invention can achieve high-precision channel estimation under a positive signal-to-noise ratio.

Claims

1. A channel estimation method for an AFDM system based on sparse Bayesian learning, characterized in that: The specific steps are as follows: Step 1: Perform N-point DAFT transformation after serial-to-parallel conversion of the input signal, N = 2 t ,t≥1; Step 2: According to the embedded pilot frame structure and channel transmission model in the DAFT domain, let the vector related to the channel estimation at the receiving end be y E , the pilot vector is x E ; Separate the channel estimation component and the information component in the DAFT domain received signal; Step 3: Set y E With x E The relationship becomes a sparse signal recovery model, and a first-order linear approximation is performed; Step 4: Roughly estimate the channel parameters through the sparse Bayesian learning framework and output the estimated vector: path coefficient Normalized delay Normalized Doppler shift Step 5: Use step 4 to estimate the output and Update the perception matrix in the first-order linear approximation and accurately estimate the channel parameters again through the sparse Bayesian learning framework; Output for step 4 The non-zero elements of the peak are searched and the largest elements, and the other elements are set to 0, and the corresponding positions of the off-grid components are also set to 0; is less than The maximum integer, the perception grid length is N l N α , Q+1 is the effective length of the channel response in the channel transmission model; After peak search, according to The index of the non-zero element is used to update the elements of the corresponding column of the perception matrix. After updating the perception matrix, sparse Bayesian learning parameter estimation is performed until the stopping condition ε2 is reached, and the channel coefficient, normalized Doppler frequency shift, and normalized delay are output. ε2<ε1 / 10, and ε1 is the stopping condition for the iterative loop of roughly estimating the channel parameters in step 4.

2. The AFDM system channel estimation method based on sparse Bayesian learning as claimed in claim 1, characterized in that: The step 1 is specifically as follows: Assume that the digital sampling signal at the receiving end is r[n], and after serial-to-parallel conversion and N-point DAFT transformation, we get y[m]: Where e is a natural constant, j is an imaginary unit, c1 and c2 are the system parameters of AFDM, and c 11 According to the normalized maximum Doppler shift α max Set to α max and k v are all positive integers, c2 is set to 3. The AFDM system channel estimation method based on sparse Bayesian learning as claimed in claim 1, characterized in that: The step 2 is specifically as follows: Define index sets I and J, I = {0: α max +k v ,N-Q+α max +k v :N-1}, J={0:Q-α max +k v ,N-α max -k v ∶N-1},Q=(l max +1)(2α max +2k v +1)-1,l max is the maximum normalized delay; y E =y[I], which means to intercept y[m] from [0:α max +k v ] and [N-Q+α max +k v :N-1], the rest of y[m] is the data transmission symbol. From the input-output relationship of AFDM, we know that y E With x E The relationship is as follows: Where P is the number of transmission paths, h i , l i and α i are the coefficient, normalized delay, and normalized Doppler shift of the ith path, respectively. E is the noise vector; Indicates interception The submatrix consisting of the intersection elements of the I-th row and the J-th column, and The (p,q)th element in the matrix is ​​calculated as follows: is the phase matrix associated with the time delay, Determines the sparsity of the channel.

4. The AFDM system channel estimation method based on sparse Bayesian learning as claimed in claim 3, characterized in that: The step 3 is specifically as follows: Assume that the perception grid length is N l N α , N l and N α are all integers greater than 1, considering integer-order delays, N l = l max +1; in this sensing grid, the delay resolution is 1 and the Doppler resolution is r α =(N α -1) / 2α max , replace the formula (2) and the known pilot vector x E Perform matrix multiplication and merge to get the perception matrix, and the channel coefficient is used as the vector to be estimated, as shown below: y E =Φ E (l,a)h+w E (5) Among them, the perception matrix is: The a*Nth of the perception matrix α The +b column is calculated as follows: The first-order linear approximation of equation (5) is: Φ(l,α) ' Φ E (l,α) is the first-order partial derivative of α, and κ is the off-grid Doppler vector; so far, the channel estimation model is constructed and the initialization of the perception matrix is ​​completed.

5. The AFDM system channel estimation method based on sparse Bayesian learning as claimed in claim 4, characterized in that: The step 4 is specifically as follows: According to the model of formula (8), we make a priori assumption: Assume that the noise vector has zero mean and variance is The Gaussian distribution of β0 follows the gamma distribution with parameters c and d. Assume that the channel coefficient vector follows a zero-mean Gaussian distribution, specifically: in η follows a gamma distribution with parameter ρ, and the elements in h are independent of each other; κ follows a uniform distribution; according to the Bayesian principle, the posterior probability of h is derived as: And calculate: After calculating the above equations (10) and (11), the hyperparameters of other hypotheses are updated according to the maximum a posteriori probability rule and the expected maximum algorithm, as follows: The off-grid Doppler component update rules are as follows: Among them, {A κ } n Represents the matrix A κ The nth row of κ } n,n Represents the matrix A κ The (n,n)th element of κ } n Represents vector b κ The nth element of κ } n } -n Represents a vector {A κ } n Except for the nth element, represents taking the real part, ⊙ represents matrix dot multiplication; After the hyperparameters and off-grid Doppler components are updated, this round of calculation is completed; In the next round of calculation, the calculation results of formulas (12), (13) and (14) are used to substitute into formulas (10) and (11) to calculate the mean and variance, and then the new mean and variance are used to update formulas (12), (13) and (14). This cycle is repeated until the stop condition is reached. The stop condition ε1 is: Output estimate vector in From the current value of μ, It is related to the non-zero position of μ, assuming that a*N α +b is The i-th non-zero value of 6. The AFDM system channel estimation method based on sparse Bayesian learning as claimed in claim 1, characterized in that: In step 5 Adjust according to the channel characteristics of the scene or the demand for AFDM diversity gain, by reducing size to speed up convergence.

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