OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian

Abstract

The invention relates to the technical field of channel estimation, and discloses an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian, which comprises the following steps: S1, forming a 2D data block in a time delay Doppler domain, and dividing the time delay Doppler domain; s2, acquiring a receiving signal of a time delay Doppler domain; s3, constructing a sparse sensing matrix and performing singular value decomposition; s4, setting a judgment condition for successful channel recovery; s5, calculating posterior distribution of a transmission channel by adopting a generalized approximate message passing strategy based on unitary transformation; s6, obtaining an optimal updating rule of the hyper-parameter in the estimation channel and the hyper-parameter in the noise signal; and S7, judging whether iteration is continued or not according to a set judgment condition. According to the invention, the approximation of the channel posterior distribution information is completed by using the generalized approximation message passing framework based on unitary transformation through the information carried by the pilot frequency position, so that the calculation burden is reduced, and the calculation resource is saved.

Description

Technical Field

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

[0002] With the rapid development of high-speed rail and vehicle networking, the demand for reliable data transmission in high-speed mobile environments is increasing. In these application scenarios, multipath and Doppler effects often have a significant impact on communication performance. To meet these challenges, Orthogonal Time-Frequency-Space (OTFS) modulation technology has emerged. OTFS effectively solves the difficulties faced by traditional modulation technologies in high-speed mobile scenarios by mapping data into the Delay-Doppler (DD) domain. In an OTFS system, the receiver needs to accurately estimate the path delay and Doppler shift experienced by the signal to compensate for the effects caused by the channel, thereby achieving reliable demodulation of the signal and effective recovery of the data. Therefore, accurate estimation of the channel state has become a crucial part of the design of OTFS receivers. This accurate estimation directly affects the system throughput and the reliability of data transmission, which has triggered a lot of research work aimed at improving the accuracy and efficiency of channel estimation to meet the actual needs in high-speed mobile communication environments.

[0003] The main challenges of channel estimation in the DD domain are interference caused by signal overlap, similar delays, and Doppler shift of multipath. Signal overlap increases the impact of delay spread and Doppler spread, complicates time-frequency processing, and reduces the performance of the estimation algorithm. Due to the limited number of effective paths at high speed, the channel impulse response is sparse in the time and frequency domains, so the OTFS channel estimation methods are divided into four categories. The first category is the pilot-based method, which estimates the channel by inserting pilots, which increases the overhead and reduces the spectral efficiency. The second category is overlapping channel estimation, which uses channel sparsity to reduce pilot overhead through superposition technology, but the computational complexity is high. The third category uses frequency domain pilots to estimate the channel in the frequency domain, which is affected by frequency selective fading. The fourth category is based on sparse Bayesian learning (SBL), sparse signal recovery problems and uses Bayesian reasoning to improve performance, but the computational complexity is high and the practical application is limited. Therefore, these algorithms are impractical for practical applications. Summary of the invention

[0004] The purpose of the present invention is to provide an OTFS sparse channel estimation method based on unitary transform and 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 a generalized approximate message passing (GUAMP) strategy based on unitary transform is adopted to effectively reduce the computational complexity of sparse signal recovery and improve system performance.

[0005] The objective of the present invention is achieved through the following technical solutions: an OTFS sparse channel estimation method based on unitary transform and sparse Bayesian, in which 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.

[0006] 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:

[0007] Y=(X P ⊙β)h+W=Φh+W,

[0008] in, is the receiving signal, The pilot signal at the transmitting end, The channel vector to be estimated is represents a Gaussian white noise vector, and β = [conj(β1),...,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 delayed Doppler channel h, a method based on compressed sensing can be used to estimate the channel vector h using the known received signal vector Y and the compensated pilot matrix Φ (the pilot matrix is ​​subjected to singular value matrix decomposition, and the result of the decomposition is first executed using the GAMP algorithm, then the AMP algorithm, and finally the hyperparameter value is updated to complete the estimation of the channel vector), including the following steps:

[0009] Step S1: Select a single pilot with a guard pilot to embed data information, arrange the data in the delay-Doppler domain to form a 2D data block, and divide the delay-Doppler domain into a 2D information grid to input known information;

[0010] 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;

[0011] 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 perform singular value decomposition on the sparse sensing matrix;

[0012] Step S4: selecting a priori Gaussian information that satisfies independent and identical distribution for the channel in the Gaussian scale mixture series, assigning ordinary Gaussian prior information to the noise signal, and performing hyperparameter initialization on the Gaussian distribution of the set original channel and the noise signal, thereby completing the setting of the judgment conditions for successful channel recovery in the entire system;

[0013] Step S5: using a generalized approximate message passing strategy based on unitary transformation to calculate the posterior distribution of the transmission channel; avoiding matrix inversion in the iterative expectation maximization framework, and speeding up the calculation of the posterior distribution of the transmission channel;

[0014] Step S6: Calculate the estimated values ​​of the hyperparameters in the probability model under the iterative expectation maximization framework, and obtain the optimal update rules for the hyperparameters in the estimated channel and the hyperparameters in the noise signal;

[0015] Step S7: 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.

[0016] The beneficial effects of the present invention are:

[0017] (1) The present invention transforms the OTFS channel estimation problem into a sparse signal recovery problem, thereby improving system performance;

[0018] (2) The present invention uses the prior Gaussian information that satisfies independent and identical distribution for delay-Doppler channel allocation, and uses the Bayesian basic criterion and the expectation maximization algorithm to update the posterior distribution parameters and hyperparameter set of the transmitted signal. This method does not need to know the actual number of effective channels in the iterative calculation process, thereby increasing the flexibility of the calculation;

[0019] (3) The present invention utilizes generalized approximate message passing based on unitary transformation to avoid the inverse process of updating the channel covariance, and preprocesses the perception matrix to reduce the irrelevance between the perception matrices, thereby reducing the algorithm complexity and improving the system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian in the present invention;

[0021] Figure 2 is the transmitter symbol in the DD domain.

[0022] Figure 3 is the receiver symbol in the DD domain.

[0023] Figure 4 It is the normalized mean square error analysis diagram of each sparse channel estimation method. DETAILED DESCRIPTION

[0024] 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.

[0025] Traditional channel estimation methods face challenges in highly dynamic, multipath-rich environments, especially when channel states change rapidly, and it is difficult to maintain high-precision estimates. The distribution of OTFS signals in the delay-Doppler domain is sparse, which makes it possible to use sparse signal recovery technology. The present invention transforms the OTFS channel estimation problem into a sparse signal recovery problem, and uses a sparse signal recovery algorithm to perform channel estimation under sparse channel conditions. This can not only obtain more accurate channel information in a dynamic environment, but also significantly reduce computational complexity. In this way, the system can better cope with dynamic channel changes, improve transmission reliability and efficiency, and thus provide more stable communication services in complex and changing wireless communication environments;

[0026] Traditional channel estimation methods often rely on relatively accurate prior knowledge of channel characteristics, especially the need to know the number of effective channels clearly. However, in practical applications, the diversity and dynamics of channels make this difficult to achieve, which greatly limits the application scenarios and effects of these methods. The present invention assumes that the distribution of delay Doppler channels satisfies independent and identically distributed prior Gaussian information, and estimates the posterior distribution parameters and hyperparameter set of the transmitted signal by combining the Bayesian basic criterion with the expectation-maximization algorithm. The significant advantage of this method is that it does not require the number of effective channels to be known in advance, which not only improves the flexibility of the calculation, but also reduces the dependence on prior knowledge, making the method more robust in complex and changing channel environments;

[0027] In the process of channel estimation, 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 and affect the efficiency of real-time communication. The present invention adopts a generalized approximate message passing algorithm based on unitary transformation. GUAMP is an algorithm based on message passing, which can play an important role in problems such as sparse signal recovery and high-dimensional channel estimation. It uses approximate inference to complete channel estimation by using the transmission of messages in the model without directly calculating the complex matrix inversion process, and performs singular matrix decomposition on the sparse perception matrix to reduce the correlation of the perception matrix. The present invention significantly reduces the computational complexity of the system without significantly losing the accuracy of channel estimation, making the channel estimation process in large-scale communication systems more lightweight and efficient.

[0028] 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.

[0029] 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:

[0030] Y=(X P ⊙β)h+W=Φh+W,

[0031] in, is the received signal, The pilot signal at the transmitting end, The channel vector to be estimated is represents a Gaussian white noise vector, and β = [conj(β1),...,conj(β P )] Tis the matrix of compensation phase, where It can be expressed as β i [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;

[0032] See attached Figure 1 , an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian, the specific implementation method is as follows:

[0033] 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.

[0034] 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 is the length of the data symbol in the Doppler domain direction, that is, the number of delay taps; data symbol x d [l,k] and pilot symbol x p The specific distribution of [l,k] 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:

[0035]

[0036] 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.

[0037] 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]}.

[0038] That is, the frequency domain is discretized into an M×N grid.

[0039]

[0040] in It is the matrix form of x[l,k], and x[l,k] only represents the data in the lth row and kth column of this matrix. ISFFT refers to the inverse finite symplectic Fourier transform;

[0041] 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.

[0042] 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):

[0043]

[0044] in represents the Hadamard product, G tX Indicates at time Uniform sampling g tX .

[0045] 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.

[0046] r(t)=∫∫h(τ,υ) s (t-τ)e j2πυ(t-τ) dτdυ+ω(t)

[0047] 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

[0048]

[0049] 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.

[0050] The received time domain signal r(t) is then pulse shaped and Wigner transformed to obtain the received frequency domain signal Y[n,m].

[0051] Y[n,m]=F M G rX R

[0052] Among them G rX Indicates at time For the received pulse g rX Perform uniform sampling. R is a matrix formed by rearranging the discrete sampling of r(t). 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, and R is obtained.

[0053] 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

[0054]

[0055] When both the received and transmitted pulses are rectangular, the received delayed Doppler signal is transformed into

[0056]

[0057] in

[0058]

[0059] 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.

[0060] 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.

[0061] Φ=X p ⊙β

[0062] The pilot signal of the transmitter, and β = [conj(β1),...,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.

[0063] In order to use GUAMP to calculate the channel posterior distribution later, it is necessary to perform singular value decomposition on the sparse perception matrix, so v = Φh is converted to

[0064]

[0065] v=Ub

[0066] in From the singular value decomposition Φ = UΣV T , and rank(Φ) = r, v represents the noise-free received signal; Q = ΣV T ; When GUAMP is used for channel estimation later, the GAMP algorithm is first used to update the mean and variance of v under noise-free conditions, and then the AMP algorithm is used to update the mean and variance of b, thereby estimating the channel h.

[0067] Step 4: The channel impulse response is sparse in the time domain and frequency domain. In the Gaussian scale mixture series, the channel is given a priori Gaussian information that satisfies independent and identical distribution. The initial channel is set to have a mean of 0 and a covariance of Among them, α i is a non-negative variance hyperparameter responsible for controlling the sparsity of the channel, so the Gaussian prior distribution of the DD domain channel h can be expressed as,

[0068]

[0069] The hyperparameter α satisfies the gamma distribution

[0070]

[0071] In this formula represents the gamma function, with parameters a and b being constants controlling the shape and scale respectively.

[0072] The noise is modeled as Gaussian white noise, with an average value of zero over time, and the correlation between different time points or different dimensions is α1 (the inverse of the variance). It also satisfies the gamma distribution p(α1; c, d) = Gamma(α1|c, d). Then the noise matrix satisfies the complex Gaussian distribution p(W|α1) = CN(W|0, α1I). The likelihood distribution of the received signal Y can be expressed as:

[0073]

[0074] Combining the Gaussian prior distribution of the channel and the likelihood distribution of the received signal, we get the joint probability density function

[0075]

[0076] Step 5: In order to simplify the calculation process and enhance the robustness of the joint probability density system, the GUAMP strategy is embedded in the SBL algorithm to avoid the matrix inversion process in the EM algorithm. We set the hyperparameters Θ = {α, α1} to be known and fixed. i The approximate posterior distribution of can be expressed as

[0077]

[0078] in

[0079]

[0080] in for This step is performed in the AMP algorithm.

[0081] Then calculate another approximate posterior distribution v = Ub under noise-free conditions:

[0082]

[0083] in

[0084]

[0085] Where Y = Ub + w, express The specific steps of the GUAMP algorithm are as follows:

[0086] The unitary transform based generalized approximate message passing (GUAMP) process can be divided into two modules, module A and module B. At a high level, module A performs standard approximate message passing (AMP) on the equivalent standard linear measurement matrix with pseudo measurement matrix Q; module B performs generalized approximate message passing (GAMP) on the equivalent generalized linear model with pseudo measurement matrix U. Modules A and B exchange external information with each other in the same way, and the process is performed before convergence.

[0087] Below we describe the implementation details of GUAMP. First, we initialize the initial variance of the variable b in module B Initial means of independent random variables External mean from module A to module B and the external variance from module A to module B And initialize the mean and variance of the intermediate nodes and the posterior mean of the initial channel The number of external iterations between module A and module B is set to T max , while the number of inner iterations of modules A and B during the outer iteration is set to T A and T B Next we introduce the operation details of these two modules respectively.

[0088] and As the external mean and variance passed from module A to module B, it can also be used as the prior mean and variance of b. First run the GAMP algorithm, treat b as the position signal and U as the measurement matrix, first perform the output linear step, and update the mean and variance of the logarithmic domain estimate:

[0089]

[0090] Perform the output linear step to obtain:

[0091]

[0092] Perform the output linear step:

[0093]

[0094] Perform the input nonlinear step to obtain the posterior mean and variance of variable b:

[0095]

[0096] Run T B After iteration, the extrinsic mean and variance from module B to module A are:

[0097]

[0098] The extrinsic mean and variance of module B can be regarded as the pseudo-observation and variance of b in module A, that is,

[0099]

[0100] in Then we can run the above pseudo-linear model with T A Iteration of standard AMP.

[0101] Perform the output nonlinear step:

[0102]

[0103] Next the input linear step is performed:

[0104]

[0105] Perform the input nonlinear step:

[0106]

[0107] Perform the output linear step:

[0108]

[0109] T running AMP on module A A After iteration, the extrinsic mean and variance of module A are

[0110]

[0111] Next, continue to run module B until the number of loops is greater than T max GUAMP is mainly responsible for updating the posterior mean and variance of the channel, and the update steps of the hyperparameters are mainly in the next step.

[0112] Step 6: Given hyperparameters and the current estimate of the observed data Y. In the SBL algorithm, the EM (Expectation-Maximization) algorithm is mainly used to update various parameters. In the GUAMP-SBL algorithm, the E (expectation) step in the EM algorithm is mainly replaced by the GUAMP algorithm to update the posterior distribution of the channel. The M (maximum) step is mainly responsible for the update of the hyperparameters. First, construct (the following steps are mainly to prepare for the update of hyperparameters); calculate the expected value of the complete logarithmic posterior of {α, α1} (relative to the hidden variable h), that is, The operator Represents the posterior distribution The expectation of . This complete logarithmic posterior is also called the Q-function. The hyperparameters Θ = {α, α1} are then estimated by maximizing the Q-function, i.e.:

[0113]

[0114] because

[0115] p(Θ|h,Y)∝p(α)p(h|α)p(α1)p(Y|h,α1)

[0116] The Q-function can be decomposed into the sum of two terms

[0117]

[0118] In the Q-function above, the hyperparameters α and α1 are separated from each other. This decouples the estimation of α and α1 into two independent optimization problems. First, check the update of α. The optimal point is when the first-order derivative of the Q-function with respect to α is equal to 0, that is,

[0119]

[0120] in <·> indicates that an expected calculation is performed.

[0121] Next, based on the Q function, find the zero point of the first-order derivative of α1, that is

[0122]

[0123] in

[0124]

[0125] Step 7: In the present invention, there are two ways to determine whether the delay Doppler channel estimation is successful. One is to check whether the number of runs reaches R. max , and the other is ||μ h (t+1)-μ h (t)|| 2≤ε. If one of the decision conditions is met, the posterior mean of h calculated in the last round of iteration is obtained. In order to improve the accuracy and stability of the estimation, the K elements with the largest amplitude in the set μ are selected, where K is the predetermined number of channel taps, and the estimated channel; if the iteration termination condition is not met, let t = t + 1, and based on the hyperparameter set updated in step S6, return to step S5 for the next round of iteration.

[0126] In the embodiments of the present application, the feasibility of an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian is verified through simulation experiments.

[0127] 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.

[0128] Simulation results: Figure 4 The following is a normalized mean square error analysis of various sparse channel estimation methods. It can be seen that the performance of the sparse Bayesian detection method is better than that of traditional channel estimation methods such as MMSE, MAP and EP. This is because the sparse Bayesian channel estimation method utilizes the prior information of the channel and is suitable for the case of sparse channels. In addition, the GUAMP-SBL algorithm reduces the computational complexity caused by the matrix inversion operation from O(PQ 2 ) is reduced to O(PQ), and the performance of the GUAMP-SBL algorithm is better than that of GAMP-SBL. This is because the algorithm preprocesses the perception matrix, which can effectively reduce the correlation between the perception matrices, thereby improving the performance and stability of the algorithm. And compared with SBL, the performance loss of GUAMP-SBL is negligible.

[0129] 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 OTFS sparse channel estimation method based on unitary transform and sparse Bayesian of the present invention are only used to illustrate and verify the rationality and feasibility of the method, and are not used to limit the method of the present invention. Although the present invention can be effectively illustrated and described through 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 method of the present invention, those skilled in the art may make various corresponding changes or deformations according to the method of the present invention, but these corresponding changes or deformations all belong to the protection scope required by the method of the present invention.

Claims

1. An OTFS sparse channel estimation method based on unitary transform and 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 perform singular value decomposition on the sparse sensing matrix; Step S4: selecting prior Gaussian information that satisfies independent and identical distribution for the channel in the Gaussian scale mixture series, assigning ordinary Gaussian prior information to the noise signal, and performing hyperparameter initialization on the Gaussian distribution of the set original channel and the noise signal; Step S5: using a generalized approximate message passing strategy based on unitary transformation to calculate the posterior distribution of the transmission channel; Step S6: Calculate the estimated values ​​of the hyperparameters in the probability model under the iterative expectation maximization framework, and obtain the optimal update rules for the hyperparameters in the estimated channel and the hyperparameters in the noise signal; Step S7: 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 OTFS sparse channel estimation method based on unitary transform and sparse Bayesian according to claim 1, characterized in that: 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 OTFS sparse channel estimation method based on unitary transform and 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 Among them G rX Indicates at time For the received pulse g rX Perform uniform sampling, R is a matrix formed by rearranging the discrete sampling of r(t), the total number of sampling points is MN, r(t) is expressed as r[k], k=0,1,…,MN-1, and then rearrange these sampling points into a matrix of M*N, that is, R is obtained; 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 the 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 OTFS sparse channel estimation method based on unitary transform and sparse Bayesian according to claim 1, characterized in that: 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 is 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 the sparse sensing matrix in compressed sensing; conj means: find the conjugate of the complex matrix; In order to use GUAMP to calculate the channel posterior distribution later, it is necessary to perform singular value decomposition on the sparse perception matrix, so v = Φh is converted to v=Ub in From the singular value decomposition Φ = UΣV T obtained in , and rank(Φ)=r; v represents the noise-free received signal; Q=ΣV T .

5. The OTFS sparse channel estimation method based on unitary transform and sparse Bayesian according to claim 1, characterized in that: The step S4 comprises: The channel impulse response is sparse in the time domain and frequency domain. In the Gaussian scale mixture series, the channel is selected to satisfy the prior Gaussian information of independent and identical distribution. The initial channel is set to have a mean of 0 and a covariance of Among them, α i is a non-negative variance hyperparameter responsible for controlling the sparsity of the channel, so the Gaussian prior distribution of the DD domain channel h is expressed as, The hyperparameter α satisfies the gamma distribution In this formula represents the gamma function, with parameters a and b being constants that control the shape and scale, respectively; The noise is modeled as Gaussian white noise, with an average value of zero over time, and a correlation of α1 between different time points or different dimensions. It also satisfies the gamma distribution p(α1; c, d) = Gamma(α1|c, d), where parameters c and d are constants that control the shape and scale, respectively. The noise matrix then satisfies the complex Gaussian distribution p(W|α1) = CN(W|0, α1I), and the likelihood distribution of the received signal Y is expressed as: Combining the Gaussian prior distribution of the channel and the likelihood distribution of the received signal, we get the joint probability density function 6. The OTFS sparse channel estimation method based on unitary transform and sparse Bayesian according to claim 1, characterized in that: The step S5 comprises: In order to simplify the calculation process and enhance the robustness of the joint probability density system, the GUAMP strategy is embedded in the SBL algorithm to avoid the matrix inversion process in the EM algorithm; the hyperparameters Θ = {α, α1} are set to be known and fixed. i The approximate posterior distribution of is expressed as in in for The variance of this step is performed in the AMP algorithm; Then calculate another approximate posterior distribution v = Ub under noise-free conditions: in Where Y = Ub + w, express The variance of this step is carried out in GAMP; The generalized approximate message passing based on unitary transformation, namely GUAMP algorithm, is divided into two modules, namely module A and module B. At a high level, module A performs standard approximate message passing, namely AMP algorithm, on the equivalent standard linear measurement matrix with pseudo measurement matrix Q; module B performs generalized approximate message passing, namely GAMP algorithm, on the equivalent generalized linear model with pseudo measurement matrix U. Modules A and B exchange external information with each other in the same way, and this process is performed before convergence. The implementation details of GUAMP include: First, initialize the initial variance of variable b in module B Initial means of independent random variables External mean from module A to module B and the external variance from module A to module B And initialize the mean and variance of the intermediate nodes and the posterior mean of the initial channel The number of external iterations between module A and module B is set to T max , while the number of inner iterations of modules A and B during the outer iteration is set to T A and T B ; Next, the operation details of the two modules are given: and As the external mean and variance passed from module A to module B, and also as the prior mean and variance of b; First, run the GAMP algorithm, treating b as the position signal and U as the measurement matrix, and first perform the output linear step to update the mean and variance of the logarithmic domain estimate: Perform the output linear step to obtain: Perform the output linear step: Perform the input nonlinear step to obtain the posterior mean and variance of variable b: Run T B After iteration, the extrinsic mean and variance from module B to module A are: The external mean and variance of module B are regarded as the pseudo-observation and variance of b in module A, that is, in Then run the above pseudo-linear model with T A Iterated standard AMP; Perform the output nonlinear step: Next the input linear step is performed: Perform the input nonlinear step: Perform the output linear step: T running AMP on module A A After iteration, the extrinsic mean and variance of module A are Next, continue to run module B until the number of loops is greater than T max ; GUAMP is mainly responsible for updating the posterior distribution of the channel, that is, the posterior mean of the channel and the posterior variance 7. The OTFS sparse channel estimation method based on sparse Bayesian learning of generalized approximate message passing according to claim 1, characterized in that: The step S6 comprises: Given hyperparameters The current estimate of the observed data Y is used in the sparse Bayesian learning algorithm, i.e., the SBL algorithm, to update the various parameters using the EM algorithm, and combined with GUAMP to form the GUAMP-SBL algorithm. The E step in the EM algorithm is mainly replaced by the GUAMP algorithm to update the posterior distribution of the channel, and the M step is mainly responsible for the update of the hyperparameters. First, the expected value of the complete logarithmic posterior of {α, α1} is calculated relative to the hidden variable h, i.e. The operator Represents the posterior distribution The expectation of ; this complete logarithmic posterior is also called the Q-function, and then the hyperparameters Θ = {α, α1} are estimated by maximizing the Q-function, that is: Because p(Θ|h,Y)∝p(α)p(h|α)p(α1)p(Y|h,α1) The Q-function is decomposed into the sum of two terms In the above Q-function, the hyperparameters α and α1 are separated from each other, which decouples the estimation of α and α1 into two independent optimization problems; first check the update of α, then the optimal point is when the first-order derivative of the Q-function with respect to α is equal to 0, that is, So the update method of the i-th element in α is: in <·> indicates the expected calculation, where h i for The i-th element in ; Next, based on the Q function, the zero point of the first-order derivative of α1 is found to be the optimal point, that is, So the update method of α1 is: in, 8. The OTFS sparse channel estimation method based on sparse Bayesian learning of generalized approximate message passing according to claim 1, characterized in that: In step S7, when the number of operations reaches the maximum number of cycles t=R max , or the posterior mean obtained in this round of iteration The posterior mean of the previous iteration When the second norm of the difference is less than the set maximum allowable error, the loop operation ends and the posterior mean of h calculated in the last round of iteration is obtained. In order to improve the accuracy and stability of the estimation, the K elements with the largest amplitude in the set μ are selected, where K is the predetermined number of channel taps, and the estimated channel is obtained; If the iteration termination condition is not met, set t=t+1, and return to step S5 for the next round of iteration based on the hyperparameter set updated in step S6.

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