A channel estimation method for AFDM system based on sparse Bayesian learning

Abstract

The present invention belongs to the field of communication technology, and specifically is a channel estimation method for an AFDM system based on sparse Bayesian learning. The present invention uses a sparse Bayesian framework on an AFDM system to propose a two-layer channel estimation method of coarse estimation plus fine estimation. The coarse estimation uses a uniform grid and a larger stopping condition to quickly end the iteration; the fine estimation uses the delay and Doppler output from the previous step to update the perception matrix, turning the perception grid into a non-uniform grid, so that the energy of the channel coefficient is concentrated on the grid, so as to effectively reduce the estimation error and increase the convergence speed. The present invention combines the advantages of the Bayesian learning framework and the compressed sensing algorithm to recover sparse signals, so that the algorithm is suppressive to noise and does not need to know the number of propagation paths; and is supplemented by peak search and zeroing to speed up the convergence speed and prevent overfitting; ultimately, the present invention can achieve high-precision channel estimation under a positive signal-to-noise ratio.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a channel estimation method for 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. AFDM systems combat dual-selective channel fading by using a set of orthogonal chirp bases generated by discrete dummy frequency division transforms (DAFTs). Existing channel estimation methods for AFDM systems using embedded pilots include the embedded pilot-assisted approximate maximum likelihood (EPA-AML) method and the 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 results are significantly affected by noise. It is necessary to increase the pilot power or place multiple pilots to enhance the estimation performance. In addition, this method can only obtain the channel matrix and cannot estimate the various channel parameter information.

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

[0006] To address these issues and shortcomings, and to address the lack of prior information about transmission channels and the inadequate performance of existing channel estimation methods, this paper proposes a channel estimation method for AFDM systems based on sparse Bayesian learning. Taking advantage of 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 into serial and parallel and then make 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 between 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. According to the channel characteristics of different scenarios or the demand 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 shift, and normalized delay are output. ε1 is the stopping condition for the iterative loop of roughly estimating the channel parameters in step 4.

[0015] In this invention, steps 1 and 2 are the demodulation steps at the receiving end of an AFDM system. AFDM is a recently proposed multi-carrier modulation scheme with excellent resistance to time-frequency dual fading. Steps 3 and 4 employ a sparse Bayesian framework to solve the sparse signal recovery problem. Step 5 is an improved step for estimating the AFDM channel using the sparse Bayesian framework, aiming to address the jagged convergence that occurs when approaching the optimal solution.

[0016] In summary, the present invention proposes a two-layer channel estimation method, namely, coarse estimation plus fine estimation, on the AFDM system using a sparse Bayesian framework. Using a uniform grid and a larger stopping condition in the coarse estimation step can quickly end the iteration. In the fine estimation, the delay and Doppler output from 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, effectively reducing the estimation error and increasing the convergence speed. This method inherits the advantages of the Bayesian learning framework and the compressed sensing algorithm to recover sparse signals, models the prior assumptions 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. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0018] Figure 2 The figure 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 with reference to the accompanying drawings and specific embodiments.

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

[0021] Step 1: Convert the input signal into serial and parallel and then make 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 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 is the interception of y[m] [0:α max +k v ] and [N-Q+α max +k v :N-1], the rest of y[m] is the data transmission symbol. According to the input and output relationship of AFDM, we can 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 i-th path, respectively. E is the noise vector; Indicates interception The submatrix composed 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 between 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 obtain 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] a*Nth a*Nth a*Nth α The +b column is calculated as follows:

[0037]

[0038] Perform a first-order linear approximation on equation (5):

[0039]

[0040] Φ(l,α) ′ is Φ E The first-order partial derivative of (l,α) with respect to α is κ, and the off-grid Doppler vector is κ. At this point, the channel estimation model is constructed and the sensing matrix is ​​initialized.

[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 the a priori assumption: Assume that the noise vector has zero mean and variance is The Gaussian distribution of β0 obeys the gamma distribution with parameters c and d; assuming that the channel coefficient vector obeys the 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 Bayes' theorem, 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 expectation maximization 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 line 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, Indicates taking the real part, and ⊙ indicates 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. Then, the new mean and variance are used to update formulas (12), (13) and (14). This cycle is repeated until the stopping condition is reached. The stopping 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 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 perception 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 demand for AFDM diversity gain, by reducing 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 perception matrix, sparse Bayesian learning parameter estimation is performed until the second stopping 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 and 20dB higher than the average power of the data symbols. The data symbols are modulated by 4-QAM. Consider a four-path channel with a Gaussian distribution for the channel coefficients. The Doppler shift is randomly generated using Jake's spectrum, and the delay is an integer delay. In the channel estimation algorithm, the parameters are set as follows: c, d = 1 × 10 -4 , ρ = 0.01, rough estimate ε1 = 5 × 10 -3 , accurate estimate ε2=5×10 -5 .

[0060] The pilot generated based on this parameter is added with random data symbols, modulated by AFDM and passed through the channel. The receiver 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 dB, and 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] From the above embodiments, it can be seen that the present invention aims at the channel estimation problem of 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 and h (step 3), and update the parameters iteratively through the Bayesian prior hypothesis and the EM algorithm (steps 4-5). The present invention proposes a two-layer channel estimation method, namely, coarse estimation plus fine estimation, on the AFDM system using a sparse Bayesian framework. Using a uniform grid and a larger stopping condition in the coarse estimation step can 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 sensing matrix, and the sensing grid is changed into a non-uniform grid, which can concentrate the energy of the channel coefficient on the grid, effectively reducing the first-order linear approximation estimation error and increasing the convergence speed. This method inherits the advantages of the Bayesian learning framework and the compressed sensing algorithm to recover 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 noise suppression 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: Convert the input signal into serial-to-parallel and then perform N-point DAFT transformation, 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 updates the element 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 shift, and normalized delay are output. ε2<ε1 / 10, and ε1 is the stopping condition for the iterative iteration of the rough estimation of 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, c1 is based on the normalized maximum Doppler shift α max Set to α max and k v Are all positive integers, c2 is set to n is the index of the sampling point, and n takes values ​​in the integer group [0, N-1].

3. The AFDM system channel estimation method based on sparse Bayesian learning as claimed in claim 2, 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 is the interception of y[m] [0:α max +k v ] and [N-Q+α max +k v :N-1], the rest of y[m] is the data transmission symbol. According to the input and output relationship of AFDM, we can 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 i-th path, respectively. E is the noise vector; Indicates interception The submatrix composed 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 according to 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 The size of , speeds up convergence.

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