An OTFS Sparse Channel Estimation Method Based on Unitary Transformation and Sparse Bayesian

Abstract

The present invention relates to the technical field of channel estimation, and discloses an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian, including the following steps: Step S1: Form a 2D data block in the time-delay Doppler domain and divide the time-delay Doppler domain; Step S2: Obtain the received signal in the time-delay Doppler domain; Step S3: Construct a sparse sensing matrix and perform singular value decomposition; Step S4: Set the decision condition for successful channel recovery; Step S5: Adopt a generalized approximate message passing strategy based on unitary transformation to calculate the posterior distribution of the transmission channel; Step S6: Obtain the optimal update rules for the hyperparameters in the estimated channel and the hyperparameters in the noise signal; Step S7: Judge whether to continue iteration according to the set decision condition. By using the information carried by the pilot position, the present invention utilizes the generalized approximate message passing framework based on unitary transformation to approximate the posterior distribution information of the channel, reducing the computational burden and saving computational resources.

Description

Technical Field

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

[0002] With the rapid development of high-speed railways and vehicle-to-everything (V2X) networks, the demand for reliable data transmission in high-speed mobile environments is increasing. In these application scenarios, multipath effects and Doppler effects often have a significant impact on communication performance. To address these challenges, orthogonal time-frequency-space (OTFS) modulation technology has emerged. OTFS effectively solves the difficulties faced by traditional modulation techniques in high-speed mobile scenarios by mapping data to the delay-Doppler (DD) domain. In an OTFS system, the receiver needs to accurately estimate the path delay and Doppler frequency shift experienced by the signal to compensate for the effects caused by the channel, thereby achieving reliable signal demodulation and effective data recovery. Therefore, accurate estimation of the channel state is a crucial part of OTFS receiver design. This accurate estimation directly affects the throughput of the system and the reliability of data transmission, leading to a large amount 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 in channel estimation in the DD domain are signal overlap, similar delays, and interference caused by the Doppler frequency shift of multipaths. Signal overlap increases the impact of delay spread and Doppler spread, making time-frequency processing complex and reducing the performance of the estimation algorithm. Since the number of effective paths is limited during high-speed movement, the channel impulse response is sparse in both the time domain and the frequency domain. Therefore, OTFS channel estimation methods are divided into four categories. The first category is pilot-based methods, which estimate the channel by inserting pilots, increasing the overhead and reducing the spectral efficiency. The second category is overlapping channel estimation, which uses channel sparsity to reduce pilot overhead through superposition techniques but has a high computational complexity. 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), which addresses the sparse signal recovery problem and uses Bayesian inference to improve performance but has a high computational complexity and limited practical applications. Therefore, these algorithms are impractical for actual applications. Summary of the Invention

[0004] The object of the present invention is to provide an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian. By utilizing the sparse characteristics of the delay-Doppler channel, the channel estimation problem of the OTFS system is transformed into a sparse signal recovery problem, and a generalized approximate message passing (GUAMP) strategy based on unitary transformation is adopted to effectively reduce the computational complexity of sparse signal recovery and improve system performance.

[0005] The object of the present invention is achieved by the following technical solutions: An OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian. In an OTFS system, a 2D OTFS frame is formed by arranging an M×N quadrature amplitude modulation data sequence in a delay-Doppler (DD) domain to form a 2D data block.

[0006] The DD domain is divided into M×N information grids where N represents the number of Doppler taps, M represents the number of delay taps, and represent the quantization intervals of the delay domain and the Doppler domain respectively. The DD domain signal is converted into a time-frequency domain signal through an inverse spatio-temporal Fourier transform (ISFFT). Subsequently, the signal is converted into a time domain signal using a transmit pulse and a Heisenberg transform. After passing through the channel, the time domain received signal is obtained. Then, pulse shaping and a Wiener transform are performed to obtain the frequency domain signal at the receiving end. Finally, through a two-dimensional finite Fourier transform, the received signal in the DD domain is obtained. When performing channel estimation on the OTFS system, pilots and the received signals corresponding to the pilot modules can be selected for channel estimation. Since the number of effective paths is limited during high-speed movement, the channel impulse response is sparse in both the time domain and the frequency domain. Therefore, assume the number of received signals is P, and the number of pilots in the transmitted signal is Q. Thus, the channel input-output model of the OTFS system can be expressed as a compressed sensing model:

[0007] Y = (X P ⊙β)h + W = Φh + W,

[0008] where, is the received signal, the pilot signal at the transmitting end, the channel vector to be estimated, represents a Gaussian white noise vector, and β = [conj(β1),..., conj(β P )] T is the matrix for compensating the phase, where can be expressed as β[k, l], ⊙ is the Hadamard product, and Φ is equivalent to the sparse sensing matrix in compressed sensing. Utilizing the sparse property of the delay-Doppler channel h, a method based on compressed sensing can be used to estimate the channel vector h through the known received signal vector Y and the compensated pilot matrix Φ (performing singular value matrix decomposition on the pilot matrix, and using the decomposed result to first execute the GAMP algorithm, then execute the AMP algorithm, and finally update the hyperparameter values to complete the estimation of the channel vector), including the following steps:

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

[0010] Step S2: Use the symplectic finite Fourier transform to convert the signal into the time-frequency domain, then convert the signal into a time-domain signal according to the transmitted pulse and the Heisenberg transform. Transmit the time-domain signal through the channel to obtain the time-domain signal at the receiving end, and then perform pulse shaping, Wiener transform, and two-dimensional finite Fourier transform to obtain the received signal in the delay-Doppler domain;

[0011] Step S3: According to the set pilot information, obtain the received signal corresponding to the pilot in the delay-Doppler domain at the receiving end. Then, regard the pilot matrix as the observation matrix in compressive sensing and regard the phase compensation matrix as the sparse matrix, so as to construct a sparse sensing matrix and perform singular value decomposition on the sparse sensing matrix;

[0012] Step S4: Select prior Gaussian information that satisfies independent and identically distributed for the channel in the Gaussian scale mixture series, assign ordinary Gaussian prior information to the noise signal, and initialize the hyperparameters of the set Gaussian distributions of the original channel and the noise signal set in the entire system to complete the setting of the decision condition for successful channel recovery in the entire system;

[0013] Step S5: Adopt the generalized approximate message passing strategy based on unitary transformation to calculate the posterior distribution of the transmission channel; avoid matrix inversion in the iterative expectation maximization framework and accelerate 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: Judge whether to continue the iteration according to the set decision condition. If the decision condition is satisfied, 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 as follows:

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

[0018] (2) The present invention assigns prior Gaussian information that satisfies independent and identically distributed to the delay-Doppler channel and uses the Bayesian fundamental criterion and the expectation maximization algorithm to update the posterior distribution parameters and hyperparameter sets of the transmitted signal. This method does not need to explicitly know the actual number of effective channels during 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 when updating the channel covariance, and preprocesses the sensing matrix to reduce the correlation between sensing matrices, thereby improving the system performance while reducing the algorithm complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flowchart 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 is the normalized mean square error analysis diagram of each sparse channel estimation method. DETAILED DESCRIPTION OF THE INVENTION

[0024] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following description.

[0025] Traditional channel estimation methods face challenges in high-dynamic and multipath-rich environments. Especially in the case of rapidly changing channel states, it is difficult to maintain high-precision estimation. The distribution of OTFS signals in the time-delay Doppler domain is sparse, which provides the possibility of using sparse signal recovery techniques. The present invention transforms the OTFS channel estimation problem into a sparse signal recovery problem and uses a sparse signal recovery algorithm to estimate the channel under sparse channel conditions. This can not only obtain more accurate channel information in a dynamic environment but also significantly reduce the computational complexity. In this way, the system can better cope with dynamic channel changes, improve the reliability and efficiency of transmission, 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 clearly know the number of effective channels. 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 the time-delay Doppler channel satisfies the prior Gaussian information of independent and identically distributed, and estimates the posterior distribution parameters and hyperparameter sets of the transmitted signal by combining the Bayesian fundamental criterion and the expectation maximization algorithm. The significant advantage of this method is that it does not require prior knowledge of the number of effective channels, which not only improves the computational flexibility but also reduces the dependence on prior knowledge, making the method more robust in complex and changing channel environments;

[0027] During the channel estimation process, it is usually necessary to invert the channel covariance matrix, which has extremely high computational complexity. The computational amount of matrix inversion increases exponentially with the increase of the system scale. This not only leads to a large consumption of computing resources, 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 and can play an important role in problems such as sparse signal recovery and high-dimensional channel estimation. It uses the approximation inference method and utilizes the message passing in the model to complete channel estimation without directly calculating the complex matrix inversion process, and performs singular value decomposition on the sparse sensing matrix to reduce the correlation of the sensing matrix. Without significantly sacrificing the channel estimation accuracy, the present invention significantly reduces the computational complexity of the system, 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 formed by arranging an M×N quadrature amplitude modulation data sequence in the delay-Doppler (DD) domain to form a 2D data block.

[0029] The DD domain is divided into an M×N information grid where N represents the number of Doppler taps, M represents the number of delay taps, and represent the quantization intervals in the delay domain and the Doppler domain respectively. The DD domain signal is converted into a time-frequency domain signal through the inverse spatio-temporal Fourier transform (ISFFT), and then the signal is converted into a time domain signal using the transmit pulse and the Heisenberg transform. After passing through the channel, the time domain received signal is obtained. Then, pulse shaping and the Wiener transform are performed to obtain the frequency domain signal at the receiving end. Finally, through the two-dimensional finite Fourier transform, the received signal in the DD domain is obtained. When performing channel estimation on the OTFS system, pilots and the received signals corresponding to the pilot modules can be selected for channel estimation. Since the number of effective paths is limited during high-speed movement, the channel impulse response is sparse in both the time domain and the frequency domain. Therefore, assuming the number of received signals is P and the number of pilots in the transmitted signals is Q. Thus, the channel input-output model of the OTFS system can be expressed as a compressed sensing model:

[0030] Y=(X P ⊙β)h + W = Φh + W,

[0031] where, is the received signal, the pilot signal at the transmitting end, the channel vector to be estimated, represents the Gaussian white noise vector, and β = [conj(β1),..., conj(β P )] Tis the matrix for compensating the phase, where can be expressed as β i [k, l], ⊙ is the Hadamard product, and Φ is equivalent to the sparse sensing matrix in compressive sensing. Utilizing the sparse property of the delay-Doppler channel h, a compressive-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 Appendix Figure 1 , an OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian, and the specific implementation is as follows:

[0033] Step 1: Assume that each frame has M×N symbol numbers. According to the set maximum delay taps and maximum Doppler taps, determine the number of pilot symbols. The number of data symbols is obtained by subtracting the number of pilot symbols from the total number of symbols. Randomly generate data bits to obtain data symbols, and convert them into quadrature 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 coordinate l of the data symbols along the delay direction and the coordinate k of the data symbols along the Doppler domain direction in the DD domain is composed of the data symbol x d [l, k] or the pilot symbol x p [l, k], where l = 0, 1, 2, …, M - 1, k = 0, 1, 2, …, N - 1; where M represents the length of the data symbols in the delay direction, that is, the number of Doppler taps; N is the length of the data symbols in the Doppler domain direction, that is, the number of delay taps; the data symbol x d [l, k] and the pilot symbol x p [l, k] are specifically distributed as Figure 2 shown. The adopted pilot pattern with guard pilots, and the power of the pilot symbols is not equal to the power of the data symbols, which helps to ensure that the pilot signals 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. k v corresponds to the maximum value of the Doppler taps. l τ represents the maximum value of the delay taps, l = 1, 2, …, M, k = 1, 2, …, N.

[0037] Step 2: For the input data Perform the ISFFT operation to convert the signal from the DD domain to the time-frequency domain, obtaining the frequency-domain information {X[n,m], n ∈ [0,N-1], m ∈ [0,M-1]}.

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

[0039]

[0040] where is the matrix form of x[l,k], and x[l,k] only represents the data in the l-th row and k-th 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 time-delay direction in the DD domain, M represents the number of carriers in the time-frequency domain, m = 0,..., M-1. This operation is because the time-delay domain in the DD domain is related to the carriers in the time-frequency domain; where k represents the coordinate of the data symbol along the Doppler domain direction in the DD domain, N represents the number of symbols, n = 0,..., N-1.

[0042] Then convert the time-frequency domain signal to a time-domain signal. Use the transmit pulse g tX (t) and the Heisenberg transform to convert the discrete signal X[n,m] into a continuous time-domain signal s(t):

[0043]

[0044] where represents the Hadamard product, G tX represents the uniform sampling of g at time tX .

[0045] The time-domain signal s(t) is transmitted through the air or other media in the form of radio waves and undergoes a two-dimensional convolution operation with a pulse response of the time-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 delay Doppler channel, which can be expressed as

[0048]

[0049] where K refers to the number of taps of the channel estimation used, i.e., different paths in the channel or different parts of the channel response, h i represents the complex channel gain of the i-th tap, τ i and υ i are the time delay and Doppler shift of the i-th tap.

[0050] Then, the received time-domain signal r(t) is pulse-shaped and subjected to the Wigner transform to obtain the received frequency-domain signal Y[n,m].

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

[0052] where G rX represents uniform sampling of the received pulse g at time rX . Where R is the matrix form rearranged from the discrete samples of r(t), the total number of sampling points is MN, and after sampling, r(t) is expressed as r[k], k = 0, 1, …, MN - 1. Then these sampling points are rearranged into an M*N matrix to obtain R;

[0053] Performing a two-dimensional finite Fourier transform on this 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 delay-Doppler signal is transformed into

[0056]

[0057] where

[0058]

[0059] ω[k,l] is the channel noise, [·] M and [·] N are modulo M and modulo N operations. β i [k,l] serves to compensate for the phase loss during information transmission.

[0060] Step 3: Although the communication environments of high-speed railways and vehicle-to-everything (V2X) are complex and there are many signal propagation paths, due to high-speed movement, the number of effective paths is limited, making the channel impulse response sparse in both the time domain and the frequency domain. Therefore, for the received signal corresponding to the pilot signal such as Figure 3 , assuming the number of received signals is P and the number of pilots in the transmitted signal is Q = (2k ν +1)(l τ+)。 Thus, the channel input-output model of the OTFS system can be expressed as a compressive sensing model. The transmitted pilot is regarded as the observation matrix in the compressive sensing model, and the phase compensation matrix that improves the channel sparsity is regarded as the sparse matrix in compressive sensing. Thus, the sparse sensing matrix in this compressive sensing model can be obtained.

[0061] Φ = X p ⊙β

[0062] The pilot signal at the transmitter, and β = [conj(β1),..., conj(β P )] T is the matrix for compensating the phase, where can be expressed as β[k, l], ⊙ is the Hadamard product, and Φ is equivalent to the sparse sensing matrix in compressive sensing.

[0063] For subsequent calculation of the channel posterior distribution using GUAMP, the sparse sensing matrix needs to be singular value decomposed. Thus, v = Φh is transformed into

[0064]

[0065] v = Ub

[0066] where is obtained from the singular value decomposition Φ = UΣV T , and rank(Φ) = r, v represents the received signal without noise; Q = ΣV T ; When using GUAMP for channel estimation subsequently, first use the GAMP algorithm to update the mean and variance of v under the noise-free condition, and then use the AMP algorithm 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 the frequency domain. Select the prior Gaussian information that satisfies independent and identically distributed for the channel in the Gaussian scale mixture series. The initial channel is set to have a mean of 0 and a covariance of where, α i is a non-negative variance hyperparameter responsible for controlling the sparsity of the channel. Therefore, the Gaussian prior distribution of the DD domain channel h can be expressed as

[0068]

[0069] where the hyperparameter α satisfies the gamma distribution

[0070]

[0071] In this formula represents the gamma function, and the parameters a and b are constants that control the shape and scale respectively.

[0072] The noise is modeled as Gaussian white noise with a mean of zero over time. The correlation between different time points or different dimensions is α1 (the reciprocal of the variance), and 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), and 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, the joint probability density function is obtained

[0075]

[0076] Step 5: 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, and for this channel h i the approximate posterior distribution can be expressed as

[0077]

[0078] where

[0079]

[0080] where is the variance of, and this step is all carried out in the AMP algorithm.

[0081] Next, calculate another approximate posterior distribution v = Ub under the noiseless condition:

[0082]

[0083] where

[0084]

[0085] where Y = Ub + w, represents the variance of, and this step is carried out in GAMP. The specific steps of the GUAMP algorithm are as follows:

[0086] The processing procedure of the Unitary Transform Based Generalized Approximate Message Passing (GUAMP) can be divided into two modules, namely Module A and Module B. At a high level, on the equivalent standard linear measurement matrix with the pseudo measurement matrix Q, Module A performs the Approximate Message Passing (AMP); on the equivalent generalized linear model with the pseudo measurement matrix U, Module B performs the Generalized Approximate Message Passing (GAMP). Module A and Module B exchange external information with each other in the same way, and this process proceeds before convergence.

[0087] Next, we describe the implementation details of GUAMP. First, we initialize the initial variance of the variable b in Module B The initial mean of the independent random variable The 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 outer iterations between Module A and Module B is set to T max , and the number of inner iterations of Module 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 transmitted from Module A to Module B, they can also be used as the prior mean and variance of b. First, run the GAMP algorithm, regard b as the position signal, and regard U as the measurement matrix. First, perform the output linear step to update the mean and variance of the logarithmic domain estimate:

[0089]

[0090] Performing the output linear step gives:

[0091]

[0092] Performing the output linear step:

[0093]

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

[0095]

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

[0097]

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

[0099]

[0100] where Then, the standard AMP with T A iterations can be run on the above pseudo-linear model.

[0101] Execute the output non-linear step:

[0102]

[0103] Next, execute the input linear step:

[0104]

[0105] Execute the input non-linear step:

[0106]

[0107] Execute the output linear step:

[0108]

[0109] Run the T A iterations of AMP on module A, and 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. The update steps for hyperparameters are mainly in the following steps.

[0112] Step 6: Given hyperparameters Given the current estimates of the observed data \(Y\), in the SBL algorithm, the EM (Expectation - Maximization) algorithm is mainly used to update each parameter. 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, and the M (maximization) step is mainly responsible for updating the hyperparameters. First, construct (the following steps are mainly for preparing to update the hyperparameters); calculate the expected value of the complete log - posterior of \(\{\alpha,\alpha_1\}\) (with respect to the hidden variable \(h\)), that is where the operator denotes the expectation with respect to the posterior distribution . This complete log - posterior is also called the Q - function. Then, estimate the hyperparameters \(\Theta=\{\alpha,\alpha_1\}\) by maximizing the Q - function, that is:

[0113]

[0114] Since

[0115] \(p(\Theta|h,Y)\propto p(\alpha)p(h|\alpha)p(\alpha_1)p(Y|h,\alpha_1)\)

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

[0117]

[0118] In the above Q - function, the hyperparameters \(\alpha\) and \(\alpha_1\) are separated from each other. This decouples the estimation of \(\alpha\) and \(\alpha_1\) into two independent optimization problems. First, check the update of \(\alpha\). Then, the optimal point is when the first - order derivative of the Q - function with respect to \(\alpha\) is equal to 0, that is

[0119]

[0120] where \(\langle\cdot\rangle\) represents performing the expectation calculation.

[0121] Next, find the zero of the first - order derivative of \(\alpha_1\) based on the Q - function, that is

[0122]

[0123] where

[0124]

[0125] Step 7: In the present invention, there are two decision methods to check whether the time - delay Doppler channel is estimated successfully. One is that the number of runs reaches \(R\) max , and the other is \(\|\mu\) h (t + 1)-\mu h (t)\| 2≤ ε. If one of the decision conditions is satisfied, the posterior mean of h obtained from the last round of iterative calculation is selected. To improve the accuracy and stability of the estimation, the K elements with the largest magnitudes in the set μ are selected, where K is the predetermined number of channel taps, and the estimated channel is obtained. If the iterative termination condition is not satisfied, let t = t + 1, and based on the set of hyperparameters updated in step S6, return to step S5 for the next round of iteration.

[0126] In an embodiment 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 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, 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 500 Km / h, 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 = 18 dB, the data signal-to-noise ratio SNR d takes values from 15 dB to 40 dB. To evaluate the performance of the system, we conducted numerical verification. In the channel estimation of the OTFS system, 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 the estimated value.

[0128] Simulation results: Figure 4 The normalized mean square error analysis diagrams of various sparse channel estimation methods are shown. 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 channel sparsity. In addition, the GUAMP-SBL algorithm reduces the computational complexity brought by the matrix inversion operation, from O(PQ 2 ) 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 sensing matrix, which can effectively reduce the correlation between the sensing matrices, thereby improving the performance and stability of the algorithm. And compared with SBL, the performance loss of GUAMP-SBL can be ignored.

[0129] The above are the specific implementation manners and simulation validations of the present invention. It should be noted that those of ordinary skill in the art can clearly understand that the above embodiments and simulations of the OTFS sparse channel estimation method based on unitary transformation and sparse Bayesian of the present invention are only used to illustrate and verify the rationality and feasibility of the method, rather than to limit the method of the present invention. Although the present invention can be effectively illustrated and described through the embodiments, there are many variations of 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 can 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 time-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 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, and the channel h 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 Run with T A Iterated standard AMP; performing 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 unitary transform and sparse Bayesian according to claim 1, characterized in that: The step S6 comprises: Given a hyperparameter Θ (t) ={α (t) ,α1 (t) } and the current estimate of the observed data Y. In the sparse Bayesian learning algorithm, namely the SBL algorithm, the EM algorithm is used to update each parameter, and combined with GUAMP to form the GUAMP-SBL algorithm. Among them, the E step in the EM algorithm is mainly replaced by the GUAMP algorithm to update the posterior distribution of the channel. 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, that is, 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 unitary transform and sparse Bayesian 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 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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