An efficient OTFS sparse channel estimation method based on fast sparse Bayes

Abstract

The present invention relates to the technical field of channel estimation, and discloses an efficient OTFS sparse channel estimation method based on fast sparse Bayes, comprising the following steps: step S1: forming a 2D data block in the delay Doppler domain, and dividing the delay Doppler domain; step S2: acquiring the received signal in the delay Doppler domain; step S3: constructing a sparse perception matrix, and then using an adaptive particle swarm optimization algorithm to optimize the perception matrix; step S4: setting the judgment condition for successful channel recovery; step S5: using a fast sparse Bayes based on Laplace prior to update the channel posterior distribution and hyperparameters; step S6: judging whether to continue iteration according to the set judgment condition. The present invention improves system performance by optimizing the perception matrix using an adaptive particle swarm optimization algorithm, and then uses a fast sparse Bayes method to update the posterior distribution and hyperparameters of the channel, thereby reducing computational complexity and saving computational resources.

Description

Technical Field

[0001] The invention relates to a channel estimation method for an orthogonal time-frequency-space system, and in particular to an efficient OTFS sparse channel estimation method based on fast sparse Bayes. Background Art

[0002] Orthogonal frequency division multiplexing (OFDM) is a key technology deployed in 4G long-term evolution (LTE) mobile systems. However, with the increase of high-speed mobile environments such as high-speed rail mobile communications, the time-varying channels generated by high Doppler spread have become increasingly irresistible, and the multipath effect and Doppler effect seriously affect the performance of OFDM technology. To address this problem, new modulation schemes that are robust to channel time variations have been explored, resulting in orthogonal time-frequency-space (OTFS) modulation. OTFS effectively handles the Doppler effect by mapping data into the delay-Doppler (DD) domain and has the advantage of sparse channels. However, OTFS also faces challenges such as the peak-to-average power ratio (PAPR) problem, detection complexity caused by symbol overlap in the DD domain, and channel estimation accuracy. Summary of the invention

[0003] The purpose of the present invention is to provide an efficient OTFS sparse channel estimation method based on fast sparse Bayesian. The sparse characteristics of the delay Doppler channel are utilized to convert the channel estimation problem of the OTFS system into a sparse signal recovery problem, and an adaptive particle swarm optimization (APSO) algorithm is used to optimize the perception matrix to improve the system performance. Then, a fast Bayesian method is used to reformulate the joint cost function and apply the block coordinate descent method to minimize it to solve the challenge of non-convex optimization, eliminate the need for complex matrix inversion, and effectively reduce the computational complexity of sparse signal recovery.

[0004] The objective of the present invention is achieved through the following technical solution: an efficient OTFS sparse channel estimation method based on fast sparse Bayes, characterized in that: in an OTFS system, a 2D OTFS frame is a 2D data block formed by arranging M×N orthogonal amplitude modulation data sequences in a delay Doppler (DD) domain.

[0005] The DD domain is divided into M×N information grids Where N is the number of Doppler taps, M is the number of delay taps, and Represent the quantization intervals in the delay domain and Doppler domain respectively. The DD domain signal is converted into a time-frequency domain signal by the inverse finite sigmoid Fourier transform (ISFFT), and then the signal is converted into a time domain signal using the transmitted pulse and the Heisenberg transform. The time domain received signal is obtained through the channel, and then pulse shaping and Wiener transform are performed to obtain the frequency domain signal at the receiving end. Finally, the received signal in the DD domain is obtained by the two-dimensional finite Fourier transform. When performing channel estimation on the OTFS system, the pilot and the received signal corresponding to the pilot module can be used for channel estimation. Due to the limited number of effective paths at high speed, the channel impulse response is sparse in the time domain and frequency domain. Therefore, it is assumed that the number of received signals is P and the number of pilots in the transmitted signal is Q. In this way, the channel input and output model of the OTFS system can be expressed as a compressed sensing model:

[0006] Y=(X P ⊙β)h+W=Φh+W,

[0007] in, is the received signal, The pilot signal at the transmitting end, The channel vector to be estimated is represents the Gaussian white noise vector, and β = [conj(β 1 ),...,conj(β P )] T is the matrix of compensation phase, where It can be expressed as β[k,l], ⊙ is the Hadamard product, and Φ is equivalent to the sparse sensing matrix in compressed sensing. Using the sparse nature of the delay Doppler channel h, a compressed sensing-based method can be used to estimate the channel vector h through the known received signal vector Y and the compensated pilot matrix Φ, including the following steps:

[0008] Step S1: Select single pilot information with guard pilots to embed data information, arrange these data in the delay-Doppler domain to form 2D data blocks, and divide the delay-Doppler domain into input known information of the 2D information grid;

[0009] Step S2: using symplectic finite Fourier transform to convert the signal into time-frequency domain, then converting the signal into time domain signal according to the transmitted pulse and Heisenberg transform, transmitting the time domain signal through the channel to obtain the time domain signal of the receiving end, then performing pulse shaping and Wiener transform and two-dimensional finite Fourier transform to obtain the received signal in delay Doppler domain;

[0010] Step S3: According to the set pilot information, the received signal corresponding to the pilot in the delay-Doppler domain at the receiving end is obtained, and then the pilot matrix is ​​regarded as the observation matrix in compressed sensing, and the phase compensation matrix is ​​regarded as a sparse matrix, so as to construct a sparse sensing matrix, and then the adaptive particle swarm optimization algorithm is used to optimize the sensing matrix;

[0011] Step S4: selecting Laplace priors that satisfy independent and identical distribution for the channels in the Gaussian scale mixture series, assigning ordinary Gaussian prior information to the noise signal, and performing hyperparameter initialization on the set prior distributions of the original channel and the noise signal;

[0012] Step S5: using a fast sparse Bayesian algorithm to update the posterior distribution of the channel, and to update the optimal update rules of the hyperparameters in the estimated channel and the hyperparameters in the noise signal;

[0013] Step S6: Determine whether to continue iteration according to the set decision conditions. If the decision conditions are met, output the estimated channel, channel hyperparameters and noise signal hyperparameters. If not, return to step S5 for a new round of iteration.

[0014] The beneficial effects of the present invention are:

[0015] (1) The present invention transforms the OTFS channel estimation problem into a sparse signal recovery problem, thereby improving system performance;

[0016] (2) The present invention uses an adaptive particle swarm optimization algorithm to optimize the sensing matrix and reduce the correlation between pairs within the sensing matrix, thereby improving the performance of the system in recovering channels;

[0017] (3) The present invention constructs a channel that satisfies the Laplace prior distribution, uses a fast sparse Bayesian method to update the channel posterior distribution and hyperparameters, solves the challenge of non-convex optimization by reformulating the joint cost function and applying the block coordinate descent method to minimize it, eliminates the need for complex matrix inversion, and reduces the computational complexity of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of an efficient OTFS sparse channel estimation method based on fast sparse Bayesian in the present invention;

[0019] Figure 2 is the transmitter symbol in the DD domain.

[0020] Figure 3 is the receiver symbol in the DD domain.

[0021] Figure 4 It is the normalized mean square error analysis diagram of each sparse channel estimation method. DETAILED DESCRIPTION

[0022] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0023] In order to solve the challenges of channel estimation in OTFS systems, more and more scholars have carried out relevant research. Wen proposed a channel estimation algorithm based on mean field orthogonal approximate message passing (MF-OAMP), which improved the system performance, but was limited in practical applications due to its complexity and convergence problems. Li proposed a solution that combines unitary approximate message passing (UAMP) with hidden Markov model (HMM), which effectively reduces the complexity, but still faces challenges related to model dependence and parameter optimization. Choubey uses the OTFS generative channel estimation (GCEO) method based on conditional generative adversarial network (CGAN) to perform channel estimation in OTFS systems. This method provides powerful nonlinear fitting capabilities, but its high computational complexity and data requirements affect real-time performance. Tang uses a three-layer prior sparse Bayesian learning (T-SBL) method combined with particle swarm optimization (PSO) for channel estimation, which enhances the performance under low signal-to-noise ratio (SNR) conditions. However, its high computational cost and sensitivity to parameters make the implementation of large-scale systems challenging. The present invention proposes a fast sparse Bayesian learning (FSBL) algorithm using the Laplace prior model, which reduces the algorithm complexity and improves the computational efficiency of channel estimation. In addition, an adaptive particle swarm optimization (APSO) algorithm is introduced to optimize the sensor matrix and improve the pilot accuracy and overall channel estimation efficiency;

[0024] In the channel estimation process, it is usually necessary to invert the channel covariance matrix. The computational complexity of this process is extremely high, and the amount of calculation for matrix inversion will increase exponentially with the increase of system scale. This not only leads to a large amount of computing resource consumption, but also may prolong the response time of the system, affecting the efficiency of real-time communication. The commonly used GAMP algorithm avoids the matrix inversion process. However, this algorithm introduces an iterative method to replace the E step of SBL based on EM, which still cannot reduce the computational burden of large-scale data sets. The present invention adopts a fast sparse Bayesian algorithm. The introduction of a proxy function approximates the Gaussian likelihood function, resulting in a loose posterior density of the model parameters to avoid matrix inversion, and then the matrix maximization method is used to optimize the hyperparameters. And before performing parameter optimization, the APSO algorithm is used to optimize the perception matrix, reduce the internal correlation, and make the system have better performance.

[0025] Specifically, in an OTFS system, a 2D OTFS frame is a 2D data block formed by arranging M×N orthogonal amplitude modulation data sequences in a delay-Doppler (DD) domain.

[0026] The DD domain is divided into M×N information grids Where N is the number of Doppler taps, M is the number of delay taps, and Represent the quantization intervals in the delay domain and Doppler domain respectively. The DD domain signal is converted into a time-frequency domain signal by the inverse finite sigmoid Fourier transform (ISFFT), and then the signal is converted into a time domain signal using the transmitted pulse and the Heisenberg transform. The time domain received signal is obtained through the channel, and then pulse shaping and Wiener transform are performed to obtain the frequency domain signal at the receiving end. Finally, the received signal in the DD domain is obtained by the two-dimensional finite Fourier transform. When performing channel estimation on the OTFS system, the pilot and the received signal corresponding to the pilot module can be used for channel estimation. Due to the limited number of effective paths at high speed, the channel impulse response is sparse in the time domain and frequency domain. Therefore, it is assumed that the number of received signals is P and the number of pilots in the transmitted signal is Q. In this way, the channel input and output model of the OTFS system can be expressed as a compressed sensing model:

[0027] Y=(X P ⊙β)h+W=Φh+W,

[0028] in, is the received signal, The pilot signal at the transmitting end, The channel vector to be estimated is represents the Gaussian white noise vector, and β = [conj(β 1 ),...,conj(β P )] T is the matrix of compensation phase, where It can be expressed as β[k,l], ⊙ is the Hadamard product, and Φ is equivalent to the sparse sensing matrix in compressed sensing. Using the sparse nature of the delay Doppler channel h, a compressed sensing-based method can be used to estimate the channel vector h through the known received signal vector Y and the compensated pilot matrix Φ;

[0029] See attached Figure 1 , an efficient OTFS sparse channel estimation method based on fast sparse Bayes, the specific implementation method is as follows:

[0030] Step 1: Assume that each frame has M×N symbols. According to the set delay tap maximum value and Doppler tap maximum value, determine the number of pilot symbols. Divide the number of pilot symbols by the total number of symbols to obtain the number of data symbols. Randomly generate data bits to obtain data symbols, and convert them into orthogonal phase shift keying data sequences.

[0031] The pilot symbols and data symbols are arranged in the DD domain using OTFS modulation to form a 2D data block. The data information at the data symbol coordinate l along the delay direction in the DD domain and the data symbol coordinate k along the Doppler domain direction is represented by the data symbol x d[l,k] or pilot symbol x p [l,k], l = 0, 1, 2, ..., M-1, k = 0, 1, 2, ..., N-1; where M represents the length of the data symbol in the delay direction, that is, the number of Doppler taps; N is the length of the data symbol in the Doppler domain direction, that is, the number of delay taps, and the specific distribution is as follows: Figure 2 As shown. The pilot mode with guard pilots and the pilot symbol power not equal to the data symbol power help ensure that the pilot signal can be more easily distinguished and accurately detected at the receiver, thus facilitating more accurate channel estimation. The signal transmitted by the transmitter in the delay-Doppler domain can be expressed as:

[0032]

[0033] where k p and l p Represent the midpoints of N and M respectively. v Corresponds to the maximum value of the Doppler tap. τ Represents the maximum value of the delay tap, l = 1, 2, ..., M, k = 1, 2, ..., N, DD domain refers to the delay Doppler domain.

[0034] Step 2: Input data Perform ISFFT operation to convert the signal from DD domain to time-frequency domain and obtain frequency domain information {X[n,m],n∈[0,N-1],m∈[0,M-1]}.

[0035] That is, the frequency domain is discretized into an M×N grid.

[0036]

[0037] Apply the normalized discrete Fourier transform to the rows and columns of X. The normalized discrete Fourier transform is expressed as Where l represents the coordinate of the data symbol along the delay direction in the DD domain, M represents the number of carriers in the time-frequency domain, m=0,...,M-1. This operation is done because the delay domain in the DD domain is related to the carrier in the time-frequency domain; Wherein k represents the data symbol coordinates in the DD domain along the Doppler domain direction, N represents the number of symbols, and n=0,...,N-1.

[0038] Then, the time-frequency domain signal is converted into a time domain signal. tX (t) and Heisenberg transform to convert the discrete signal X[n,m] into a continuous time domain signal s(t):

[0039]

[0040] in represents the Hadamard product, G tX Indicates at time Uniform sampling g tX .

[0041] The time domain signal s(t) is transmitted through the air or other medium in the form of radio waves and undergoes a two-dimensional convolution operation whose impulse response is a delay-Doppler channel, thereby generating a time domain signal r(t) at the receiver.

[0042] r(t)=∫∫h(τ,υ)s(t-τ)e j2πυ(t-τ) dτdυ+ω(t)

[0043] Where ω(t) is the interference introduced during signal transmission, and h(τ,υ) is the response of the delayed Doppler channel, which can be expressed as

[0044]

[0045] where K refers to the number of taps used for channel estimation, i.e., different paths in the channel or different parts of the channel response, and h i represents the complex channel gain of the ith tap, τ i and i is the time delay and Doppler shift of the ith tap.

[0046] The received time domain signal r(t) is then pulse shaped and Wigner transformed to obtain the received frequency domain signal Y[n,m].

[0047] Y[n,m]=F M G rX R

[0048] Where R is a matrix formed by rearranging r(t) discrete sampling, with a total number of sampling points of MN. r(t) is represented by r[k] after sampling, k=0,1,…,MN-1, and then these sampling points are rearranged into a matrix of M*N, that is, R is obtained;

[0049] Among them G rX Indicates at time For the received pulse g rX Perform uniform sampling.

[0050] By performing a two-dimensional finite Fourier transform on the signal, we obtain the received signal y[k,l] in the delay Doppler domain, which is expressed as

[0051]

[0052] When both the received and transmitted pulses are rectangular, the received delayed Doppler signal is transformed into

[0053]

[0054] in

[0055]

[0056] ω[k,l] is the channel noise, [·] M and[] N It is a modulo M and modulo N operation. i The role of [k,l] is to compensate for the phase loss during information transmission.

[0057] Step 3: Although the communication environment of high-speed rail and IoV is complex and there are many signal propagation paths, the number of effective paths is limited due to high-speed movement, making the channel impulse response sparse in the time domain and frequency domain. Therefore, the received signal corresponding to the pilot signal is as follows Figure 3 , assuming that the number of received signals is P, and the number of pilots in the transmitted signal is Q = (2k ν +1)(l τ +1). In this way, the channel input and output model of the OTFS system can be expressed as a compressed sensing model, the transmitted pilot is regarded as the observation matrix in the compressed sensing model, and the phase compensation matrix that improves the channel sparsity is regarded as the sparse matrix in the compressed sensing model. Thus, the sparse sensing matrix in the compressed sensing model can be obtained.

[0058] Φ=X p ⊙β

[0059] The pilot signal at the transmitting end, and β = [conj(β 1 ),...,conj(β P )] T is the matrix of compensation phase, where It can be expressed as β i [k,l], ⊙ is the Hadamard product, Φ is equivalent to the sparse sensing matrix in compressed sensing, and conj means: finding the conjugate of the complex matrix.

[0060] From the compressed sensing expression, we can see that when the received signal Y and the channel noise W are known, the size of the sensing matrix Φ directly affects the channel h to be estimated, so we will use the estimated channel and the actual channel h of the current perception matrix as the metric for optimizing the perception matrix. The optimization problem of the perception matrix can be regarded as

[0061]

[0062] Among them, E represents expectation, that is, finding the mean of the elements in the matrix;

[0063] APSO is used to solve the above optimization problem. Expand the real and imaginary parts of the initial perception matrix and set the total number of particles to Initialize the population

[0064] The fitness of each particle can be expressed as where h i represents the channel estimated by the i-th particle; finally, the particle swarm updates each particle Φ by the fitness value i The individual optimal solution p best and the global optimal solution g best During the iteration, the position and velocity Φ of each particle i Update according to the following equation:

[0065]

[0066] in and Represents particle Φ i The velocity and position at the t-1 iteration, c 1 and c 2 represents the acceleration coefficient, which is 2.0 and 0.2 respectively, r 1 and r 2 Two uniformly distributed random numbers are independently generated in [0,1], and w decreases linearly with iteration, that is,

[0067]

[0068] where w max and w min are the maximum and minimum values ​​of the inertia weight, which are set to 1.0 and 0.4 respectively, j represents the iteration index of the current evolution iteration number, and J represents the predefined maximum number of iterations. APSO optimizes the perception matrix Φ using the channel error as a metric, and the entire process can be completed outside the OTFS system.

[0069] Step S4: The channel impulse response is sparse in the time domain and frequency domain. In the Gaussian scaled mixture series, the Laplace prior distribution information that satisfies independent and identical distribution is selected for the channel. Therefore, the prior distribution of the DD domain channel h can be expressed as,

[0070]

[0071] Assume that the hyperparameter γ i Exponential distribution

[0072]

[0073] Given the parameter ε>0, by i Integration, channel response h iThe prior of follows the Laplace distribution. In order to simplify the calculation of the subsequent cost function, γ i The distribution of is log-transformed by -2ln():

[0074]

[0075] The noise is modeled as Gaussian white noise with a mean of zero over time and a correlation of α between different time points or dimensions. 1 , which also satisfies the gamma distribution p(α 1 ; a 0 ,b 0 )=Gamma(α 1 |a 0 ,b 0 ),

[0076] Then the noise matrix satisfies the complex Gaussian distribution p(W|α 1 )=CN(W|0,α 1 I), the likelihood distribution of the received signal Y is expressed as:

[0077]

[0078] In order to reduce the complexity of the FSBL (Fast Sparse Bayesian) algorithm and speed up the system channel estimation, Lemma 1: Let is a continuously differentiable function with a Lipschitz continuous gradient and a Lipschitz constant L. Then, for any

[0079]

[0080] We relax the lower bound of the similarity function according to Lemma 1. The term in the likelihood function f(h): = ||Y-Φh|| 2 It has a smooth gradient property, that is, its gradient is Lipschitz continuous, and its smoothness is limited by a specific constant L ≥ 2eig (Φ T Φ), where eig(.) is the maximum eigenvalue of the square matrix,

[0081] f(h)≤R(h,θ):=||Y-Φθ|| 2 +2(h-θ) H Φ H (Φθ-Y)+s||h-θ|| 2

[0082] Where R(·,·) is the correlation between two matrices. and s = eig(Φ T Φ)+τ, where τ=10 -3is a constant. If and only if h=θ, f(h)=R(h,θ). The likelihood function of the received signal can be rewritten as:

[0083]

[0084] Step S5: Through Bayesian reasoning, the posterior conditional probability distribution function of the channel response model h can be obtained

[0085]

[0086] Σ h =(D -1 +sα 1 I) -1

[0087] μ h =α 1 Σ h (sθ-Φ H Φθ+Φ H Y)

[0088] Where D represents the diagonal matrix of γ, combined with the prior distribution of the channel, noise and the likelihood function of the received signal, the cost function of the model is obtained:

[0089]

[0090] Where n 1 =Q+2-P-2a 0 ,if So that the term n in the cost function 1 lnα 1 Convert to -n 1 lnσ 2 , then in σ 2 Convex, where Then the cost function L in the above formula can be decomposed into concave terms and convex terms The sum of

[0091]

[0092] where f 1 (γ)=0, The concave function is an optimization of the main function. Therefore, the cost function L can be further improved into a convex proxy function We then iteratively minimize this convex surrogate function using a max-min framework

[0093]

[0094] according to The decomposable characteristics of , the block coordinate descent method, namely the BCD method, is used to iteratively update the hyperparameters:

[0095]

[0096] The above four objective functions reach their minimum values ​​at the zero gradient point. Therefore, the gradient is adjusted to zero, and the update formula is obtained:

[0097]

[0098] θ (t+1) =h (t+1) ,

[0099]

[0100] Step S6: When the number of operations reaches the maximum number of cycles t = R max , or the posterior mean h obtained in this round of iteration (t +1) and the posterior mean h of the previous iteration (t) When the second norm of the difference is less than the set maximum allowable error, the loop operation ends and the h of the last round of iterative calculation is obtained; in order to improve the accuracy and stability of the estimation, the K elements with the largest amplitude in the set h are selected, where K is the predetermined number of channel taps, and the estimated channel;

[0101] If the iteration termination condition is not met, set t=t+1, and return to step S4 for the next round of iteration based on the hyperparameter set updated in step S5.

[0102] In the embodiments of the present application, the feasibility of an OTFS sparse channel estimation method based on generalized approximate message passing is verified through simulation experiments.

[0103] Simulation parameters: The modulation scheme of the present invention is quaternary quadrature amplitude modulation (4QAM), the total number of symbols is N = 64, the number of carriers is M = 128, the carrier frequency is set to 4 GHz, the subcarrier spacing is set to 15 KHz, the number of effective channel taps is K = 5, and the maximum value of the delay tap is l τ = 5 and the maximum value of the Doppler tap is k υ =5, and the maximum user speed is 500Km / h, and the maximum number of iterations is R max =500, the maximum allowable error is ε=10 -6 , the pilot signal-to-noise ratio is SNR p =18dB, data signal-to-noise ratio SNR d The value is 15dB to 40dB. In order to evaluate the performance of the system, we conducted numerical verification. In the OTFS system channel estimation, the normalized mean square error (NMSE) is used to evaluate the performance of the system, where the NMSE algorithm is defined as where h is the true value, is an estimate.

[0104] Simulation results: Figure 4 The figure shows the normalized mean square error analysis of various sparse channel estimation methods. It can be seen that the performance of the sparse Bayesian estimation method is better than that of traditional channel estimation methods such as MMSE, MAP and IR. This is because the sparse Bayesian channel estimation method utilizes the prior information of the channel and is suitable for the case where the channel is sparse. In addition, the FSBL algorithm introduces a surrogate function to approximate the Gaussian likelihood function, which results in a loose posterior density of the model parameters to avoid matrix inversion. The matrix maximization method is then used to optimize the hyperparameters, so the complexity is reduced from O(PQ 2 ) is reduced to O(Q 2 ). Before parameter optimization, the APSO algorithm is used to optimize the perception matrix, reducing the internal correlation and making the system have better performance.

[0105] The above are specific implementation methods and simulation verifications of the present invention. It should be pointed out that those skilled in the art can clearly understand that the above embodiments and simulations of the present invention's efficient OTFS sparse channel estimation method based on fast sparse Bayes are only used to illustrate and verify the rationality and feasibility of the method, and are not used to limit the present invention. Although the present invention can be effectively illustrated and described by the embodiments, there are many changes in the present invention without departing from the spirit of the present invention. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes or deformations according to the present invention, but these corresponding changes or deformations all belong to the protection scope required by the present invention.

Claims

1. An efficient OTFS sparse channel estimation method based on fast sparse Bayes, characterized by: The following steps are involved: Step S1: Select single pilot information with guard pilots to embed data information, arrange these data in the delay-Doppler domain to form 2D data blocks, and divide the delay-Doppler domain into input known information of the 2D information grid; Step S2: using symplectic finite Fourier transform to convert the signal into time-frequency domain, then converting the signal into time domain signal according to the transmitted pulse and Heisenberg transform, transmitting the time domain signal through the channel to obtain the time domain signal of the receiving end, then performing pulse shaping and Wiener transform and two-dimensional finite Fourier transform to obtain the received signal in delay Doppler domain; Step S3: According to the set pilot information, the received signal corresponding to the pilot in the delay-Doppler domain at the receiving end is obtained, and then the pilot matrix is ​​regarded as the observation matrix in compressed sensing, and the phase compensation matrix is ​​regarded as a sparse matrix, so as to construct a sparse sensing matrix, and then the adaptive particle swarm optimization algorithm is used to optimize the sensing matrix; Step S4: selecting Laplace priors that satisfy independent and identical distribution for the channels in the Gaussian scale mixture series, assigning ordinary Gaussian prior information to the noise signal, and performing hyperparameter initialization on the set prior distributions of the original channel and the noise signal; Step S5: using a fast sparse Bayesian algorithm to update the posterior distribution of the channel, and to update the optimal update rules of the hyperparameters in the estimated channel and the hyperparameters in the noise signal; Step S6: Determine whether to continue iteration according to the set decision conditions. If the decision conditions are met, output the estimated channel, channel hyperparameters and noise signal hyperparameters. If not, return to step S5 for a new round of iteration.

2. The method according to claim 1, wherein: The step S1 comprises: S101. Assume that each frame has M×N symbols, determine the number of pilot symbols according to the set delay tap maximum value and Doppler tap maximum value, obtain the number of data symbols by dividing the number of pilot symbols by the total number of symbols, randomly generate data bits to obtain data symbols, and convert them into orthogonal amplitude modulation data sequences; S102. Use OTFS modulation to arrange the pilot symbols and data symbols in the DD domain to form a 2D data block. The data information at the data symbol coordinate l along the delay direction in the DD domain and the data symbol coordinate k along the Doppler domain direction is represented by the data symbol x d [l,k] or pilot symbol x p [l,k], l = 0, 1, 2, ..., M-1, k = 0, 1, 2, ..., N-1; where M represents the length of the data symbol in the delay direction, that is, the number of Doppler taps; N represents the length of the data symbol in the Doppler domain direction, that is, the number of delay taps; The pilot mode with guard pilot is adopted, and the pilot symbol power is not equal to the data symbol power. The signal transmitted by the transmitter in the delay Doppler domain is expressed as: x[l,k] is the input known information of the 2D information grid, where k p and l p Represent the midpoints of N and M, k v Corresponding to the maximum value of the Doppler tap, l τ Represents the maximum value of the delay tap, l = 1, 2, ..., M, k = 1, 2, ..., N, DD domain refers to the delay Doppler domain.

3. The method of efficient OTFS sparse channel estimation based on fast sparse Bayesian according to claim 1, characterized in that: The step S2 comprises: S201. Input data Perform ISFFT operation to convert the signal from DD domain to time-frequency domain and obtain frequency domain information {X[n,m],n∈[0,N-1],m∈[0,M-1]}. That is, the frequency domain is discretized into an M×N grid. in It is the matrix form of x[l,k], and x[l,k] represents the data in the lth row and kth column of this matrix. ISFFT refers to the inverse finite symplectic Fourier transform; Apply the normalized discrete Fourier transform to the rows and columns of X. The normalized discrete Fourier transform is expressed as Where l represents the coordinate of the data symbol along the delay direction in the DD domain, M represents the number of carriers in the time-frequency domain, m=0,...,M-1. This operation is done because the delay domain in the DD domain is related to the carrier in the time-frequency domain; Where k represents the data symbol coordinates in the DD domain along the Doppler domain direction, N represents the number of symbols, n = 0, ..., N-1; S202. Then, the time-frequency domain signal is converted into a time domain signal, and the transmission pulse g is used tX (t) and Heisenberg transform to convert the discrete signal X[n,m] into a continuous time domain signal s(t): in represents the Hadamard product, G tX Indicates at time Uniform sampling g tX ; S203. The time domain signal s(t) is transmitted through the air or other medium in the form of radio waves, and a two-dimensional convolution operation is performed with the impulse response being a delay Doppler channel, thereby generating a time domain signal r(t) at the receiver; r(t)=∫∫h(τ,υ)s(t-τ)e j2πυ(t-τ) dτdυ+ω(t) Where ω(t) is the interference introduced during signal transmission, e j2πυ(t-τ) is the Doppler frequency shift caused by the mobile state. If it is a stationary communication υ=0, this item does not exist; h(τ,υ) is the response of the delayed Doppler channel, expressed as where K refers to the number of taps used for channel estimation, i.e., different paths in the channel or different parts of the channel response, and h i represents the complex channel gain of the ith tap, τ i and i is the time delay and Doppler shift of the ith tap; S204. Perform pulse shaping and Wigner transform on the received time domain signal r(t) to obtain a received frequency domain signal Y[n,m]; Y[n,m]=F M G rX R Where R is a matrix formed by rearranging r(t) discrete sampling. The total number of sampling points is MN. After r(t) sampling, it is represented as r[k], k=0,1,…,MN-1. Then these sampling points are rearranged into a matrix of M*N, that is, R is obtained. Where G rX Indicates at time For the received pulse g rX Perform uniform sampling; S205. Perform a two-dimensional finite Fourier transform to obtain the received signal y[k,l] in the delayed Doppler domain, which is expressed as When both the received and transmitted pulses are rectangular, the received delayed Doppler signal is transformed into in ω[k,l] is the channel noise, [·] M and[·] N is modulo M and modulo N operation, β i The role of [k,l] is to compensate for the phase loss during information transmission.

4. The method of claim 1, wherein: The step S3 comprises: Assume that the number of received signals is P, and the number of pilots in the transmitted signal is Q = (2k ν +1)(l τ +1), the channel input and output model of the OTFS system can be expressed as a compressed sensing model. The transmitted pilot is regarded as the observation matrix in the compressed sensing model, and the phase compensation matrix that improves the channel sparsity is regarded as the sparse matrix in the compressed sensing model. Thus, the sparse sensing matrix in the compressed sensing model is obtained: Φ=X p ⊙β The pilot signal of the transmitter, and β = [conj(β1),...,conj(β P )] T is the matrix of compensation phase, where Denoted as β i [k,l], ⊙ is the Hadamard product, Φ is equivalent to the sparse sensing matrix in compressed sensing, and conj means: find the conjugate of the complex matrix; From the compressed sensing expression, when the received signal Y and the channel noise W are known, the size of the sensing matrix Φ directly affects the channel h to be estimated. and the actual channel h of the current perception matrix as the metric for optimizing the perception matrix. The optimization problem of the perception matrix is ​​regarded as Among them, E represents expectation, that is, finding the mean of the elements in the matrix; APSO is used to solve the above optimization problem; the real and imaginary parts of the initial perception matrix are expanded, and the total number of particles is set to Initialize the population The fitness of each particle is expressed as where h i represents the channel estimated by the i-th particle; finally, the particle swarm updates each particle Φ by the fitness value i The individual optimal solution p best and the global optimal solution g best ; During the iteration process, the position and velocity of each particle Φ i Update according to the following equation: in and Φ i t-1 Represents particle Φ i The velocity and position at the t-1 iteration, c1 and c2 represent the acceleration coefficients, r1 and r2 are two uniformly distributed random numbers independently generated in [0,1], and w gradually decreases linearly with the iteration, that is, where w max and w min are the preset maximum and minimum values ​​of the inertia weight, j represents the iteration index of the current evolution iteration number, J represents the predefined maximum number of iterations, and APSO optimizes the perception matrix Φ based on the channel error. The whole process is completed outside the OTFS system, where APSO refers to the adaptive particle swarm algorithm.

5. The method of claim 1, wherein: The step S4 comprises: The channel impulse response is sparse in the time domain and frequency domain. In the Gaussian scaled mixture series, the channel is given an independent and identically distributed Laplace prior distribution information, so the prior distribution of the DD domain channel h is expressed as, Assume that the hyperparameter γ i Exponential distribution Given the parameter ε>0, by i Integration, channel response h i The priori follows the Laplace distribution. In order to simplify the calculation of the subsequent cost function, γ i The distribution of is log-transformed by -2ln(): The noise is modeled as Gaussian white noise with an average value of zero over time, a correlation of α1 between different time points or different dimensions, and a gamma distribution p(α1; a0, b0) = Gamma(α1|a0, b0). Then the noise matrix satisfies the complex Gaussian distribution p(W|α1)=CN(W|0,α1I), and the likelihood distribution of the received signal Y is expressed as: In order to reduce the complexity of the fast sparse Bayesian algorithm FSBL and speed up the system channel estimation, Lemma 1: Assume is a continuously differentiable function with a Lipschitz continuous gradient and a Lipschitz constant L; then, for any According to Lemma 1, we relax the lower bound of the similarity function, and the term f(h) in the likelihood function is: = ||Y-Φh|| 2 It has a smooth gradient property, that is, its gradient is Lipschitz continuous, and its smoothness is limited by a specific constant L ≥ 2eig (Φ T Φ), where eig(.) is the maximum eigenvalue of the square matrix, f(h)≤R(h,θ):=||Y-Φθ|| 2 +2(h-θ) H F H (Φθ-Y)+s||h-θ|| 2 Where R(·,·) is the correlation between two matrices. and s = eig(Φ T Φ)+τ, where τ=10 -3 is a constant; if and only if h=θ,f(h)=R(h,θ); the likelihood function of the received signal is rewritten as:

6. The method of claim 1, wherein: The step S5 comprises: Through Bayesian inference, we get the posterior conditional probability distribution function of the channel response model h: S h =(D -1 +sα1I) -1 m h =α1Σ h (sθ-Φ H Fth+F H Y) Where D represents the diagonal matrix of γ, combined with the prior distribution of the channel, noise and the likelihood function of the received signal, the cost function of the model is obtained: Where n1 = Q + 2 - P - 2a0; if So that the term n1lnα1 in the cost function is converted to -n1lnσ 2 , then in σ 2 Convex, where The cost function L decomposes into concave terms and convex terms The sum of Where f1(γ)=0, The concave function is an optimization of the main function; therefore, the cost function L can be further improved into a convex proxy function We then iteratively minimize this convex surrogate function using a max-min framework according to The decomposable characteristics of , the block coordinate descent method, namely the BCD method, is used to iteratively update the hyperparameters: The above four objective functions reach their minimum values ​​at the zero gradient point, so the gradient is adjusted to zero and the update formula is obtained:

7. The method of claim 1, wherein: In step S6, when the number of operations reaches the maximum number of cycles t=R max , or the posterior mean h obtained in this round of iteration (t+1) and the posterior mean h of the previous iteration (t) When the second norm of the difference is less than the set maximum allowable error, the loop operation ends and the h of the last round of iterative calculation is obtained; in order to improve the accuracy and stability of the estimation, the K elements with the largest amplitude in the set h are selected, where K is the predetermined number of channel taps, and the estimated channel; If the iteration termination condition is not met, set t=t+1, and return to step S4 for the next round of iteration based on the hyperparameter set updated in step S5.

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