Low-complexity OTFS channel estimation method based on UAMP

Abstract

The invention discloses a low-complexity OTFS channel estimation method based on UAMP, which considers an OTFS system under the condition of fractional Doppler frequency shift and provides a low-complexity iterative channel estimation method, and comprises the following steps: expressing an OTFS channel estimation problem as a linear hybrid model; factorization is carried out on the joint posterior probability density function of the to-be-estimated variable of the OTFS system model, and a corresponding factor graph model is obtained; then obtaining an estimated value of an intermediate variable by using a UAMP algorithm; and taking output after UAMP convergence as prior information, and decoupling estimation of path gain and fractional Doppler frequency shift from an intermediate variable by using a VMP algorithm. The reasonable initialization parameter value can provide a good starting point for iteration of the UAMP algorithm, the algorithm is helped to converge to a solution close to a globally optimal solution more quickly, the accuracy of channel estimation is improved, and compared with an existing algorithm, the algorithm has the same normalized mean square error performance, but the calculation complexity is remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a low-complexity OTFS channel estimation method based on UAMP. Background Art

[0002] Orthogonal Time Frequency Space, abbreviated as OTFS, has the main idea that: OTFS models the time-varying physical channel from the perspectives of time delay and Doppler frequency shift, modulates the data to be transmitted in the delay-Doppler (DD) domain, and then transforms it to the time-frequency (TF) domain through a specific method. After the data symbols in the DD domain are converted to the TF domain, they will occupy the entire TF domain plane, so as to fully utilize the time diversity and frequency diversity of the system and obtain better performance than OFDM under the same conditions. The OTFS technology is considered an important candidate technology for future wireless communication systems, and its main applications include high-speed mobile scenarios and emerging application scenarios, mainly including: vehicle-to-vehicle communication, real-time video streaming, millimeter-wave communication, autonomous vehicle communication, non-terrestrial networks, underwater acoustic communication, etc.

[0003] Since the OTFS technology can effectively cope with the Doppler effect in high-speed mobile scenarios, it has become a waveform technology with development potential in 6G mobile communications. OTFS channel estimation has also been a hot research topic in recent years. K.R. Murali et al. proposed using pseudo-random noise sequences as pilots to accurately estimate the attenuation coefficients of each propagation path. However, the accuracy of the estimation depends to a large extent on the setting of good initial conditions and a sufficiently long PN sequence. P.Raviteja et al. designed pilots and guard symbols in a certain pattern to mitigate inter-carrier interference, and judged whether there was a path and obtained the path gain by comparing the received signal amplitude with a threshold. However, it is very sensitive to the selection of the threshold and performs poorly at low signal-to-noise ratios. W.Shen et al. proposed a three-dimensional structured orthogonal matching pursuit algorithm, which utilizes the normal sparsity, block sparsity, and burst sparsity in the delay domain, Doppler domain, and angle domain. However, when the channel paths are not completely known, its performance will deteriorate. In addition, M.Zhang et al. studied the clustered sparsity characteristics of the time-delay Doppler channel, modeled the prior information of the channel using a Markov random field, and proposed a two-dimensional structured compressive sensing algorithm. Y.Liu et al. utilized the reciprocity between the uplink and downlink to reconstruct the downlink channel parameters. However, they did not consider the existence of fractional Doppler frequency shift. F.Liu et al. proposed an efficient message passing algorithm to recover structured sparse signals based on factor graphs, in which the DD-domain channel matrix with fractional Doppler frequency shift can be reconstructed with high accuracy. However, it involves matrix inversion and has a high complexity. Therefore, it is very important to propose a low-complexity OTFS channel estimation algorithm.

[0004] A bilinear channel estimation method based on UAMP disclosed in a Chinese patent document with the publication number CN1 14584431B. The bilinear channel estimation method based on UAMP includes the following steps: Step A, using the properties of Kronecker product and Khatri-Rao product, perform dimensionality reduction transformation and simplification on the RIS-assisted MIMO communication system model; Step B, factorize the joint posterior probability density function of the system model's quantity to be estimated to obtain the corresponding factor graph model; Step C, set the initial parameter values for the factor graph model in Step B, use the UAMP algorithm framework for bilinear channel estimation, and obtain the estimated values of different channels; Step D, repeat Step C until the algorithm converges. Compared with existing algorithms, this algorithm has greater estimation performance advantages, significantly improved single-iteration complexity and iteration convergence speed, and stronger robustness. However, the bilinear channel estimation method based on UAMP is very sensitive to the selection of the threshold and performs poorly at low signal-to-noise ratios.

[0005] A joint estimation and detection method based on the BP-MF framework and VAMP disclosed in a Chinese patent document with the publication number CN112054975B. The joint estimation and detection method based on the BP-MF framework and VAMP includes the following steps: Step A, factorize the joint posterior probability density function of the quantity to be estimated in the OFDM system model to obtain the corresponding factor graph model; Step B, set the initial parameter values for the factor graph model in Step A, use the BP-MF framework to perform joint convolutional code decoding, soft demodulation, and noise precision estimation, and obtain the estimated value of the frequency-domain channel; Step C, in the factor graph model, according to the obtained estimated value of the frequency-domain channel, use the VAMP algorithm to iteratively execute the denoising step and the LMMSE estimation step, and obtain the estimated values of the time-domain channel and the frequency-domain channel; Step D, repeat Step B to Step C until the algorithm converges; compared with the existing algorithms, this algorithm has the same bit error rate performance, but has a significant improvement in terms of the single-iteration complexity and the iteration convergence speed. However, the joint estimation and detection method based on the BP-MF framework and VAMP involves matrix inversion and has a high complexity.

[0006] To solve the deficiencies existing in the above-mentioned prior art, it is a problem worthy of research to provide a low-complexity OTFS channel estimation method based on UAMP. Summary of the Invention

[0007] The purpose of the present invention is to overcome the drawback that the existing OTFS channel estimation method involves matrix inversion and has a high complexity, and provide a low-complexity OTFS channel estimation method based on UAMP, achieving the technical effect of significantly reducing the computational complexity.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] A low-complexity OTFS channel estimation method based on UAMP includes the following steps:

[0010] Step A, formulate the OTFS channel estimation problem in the delay-Doppler domain as a linear mixing model;

[0011] Step B, factorize the joint posterior probability density function of the quantity to be estimated in the OTFS system model to obtain the corresponding factor graph model;

[0012] Step C, set the initial parameter values for the factor graph model in Step B, and use the UAMP algorithm to iterate until convergence to obtain the estimated values of the intermediate variables;

[0013] Step D, use the output after the UAMP converges as the prior information, and use the VMP algorithm to decouple the estimated values of the path gain and the fractional Doppler shift from the intermediate variables;

[0014] Step E: Repeat Step C to Step D until the algorithm converges.

[0015] Optionally, in Step A, assume that the DD plane is divided into M grids in the time-delay dimension and N grids in the Doppler dimension. The modulation symbols {x[k, l], 0 ≤ k ≤ N - 1, 0 ≤ l ≤ M - 1} are placed in the M×N grids. The input-output relationship of the OTFS system in the time-delay-Doppler domain is as follows:

[0016]

[0017] where and is an integer, k d represents the fractional Doppler shift, h t,d is the signal propagation path gain. The variables t and d represent the time-delay index and the Doppler index respectively, and t ∈ [0, l max , d ∈ [-k max , k max . w[k, l] represents additive white Gaussian noise with a mean of 0 and a variance of γ -1 . In addition, the received symbols {y[k, l]} are reshaped into a vector where the j-th element y j is y[k, l], and j = kM + l. The transmitted symbol vector is constructed from {x[k, l]}, and then the input-output relationship is reformulated as:

[0018] y = H bi x + w

[0019] where represents the effective channel matrix in the DD domain, and is described in detail as:

[0020]

[0021] where I N (-[q - d] N ) is obtained by circularly shifting the rows of the identity matrix by -[q - d] N . The same applies to I M (t);

[0022] To estimate the unknown channel matrix, pilot symbols of M p ×N p are inserted into the DD plane with guard intervals to avoid interference between data and guard symbols. Then, the following model is equivalently obtained:

[0023] y = X bi c + w

[0024] wherein is formed by stacking {y[k, l]} into a vector, obtained by stacking {w[k, l]}. In addition, is constructed based on pilot symbols, and the unknown vector is expressed as:

[0025]

[0026] and

[0027] c j = h j g j

[0028] wherein h j follows a complex Gaussian distribution with a mean of 0 and a variance of l j , that is where the hyperparameter l j follows a gamma distribution, that is p(l j ) = Ga(l j ; e j , h j ). The linear mixing model can flexibly handle the correlations and non-constant variability in the data, which provides a broader modeling ability for OTFS channel estimation.

[0029] Optionally, in step B, according to the OTFS system model, given the observed variables, the joint posterior probability density function distribution of the path gain h, fractional Doppler shift κ, intermediate variable c, auxiliary variable z, noise precision γ, hyperparameter λ, and custom vector g is specifically factorized as:

[0030]

[0031] where p(y k |z k , γ) represents the observation likelihood of the auxiliary variable and the noise precision, p(z k |c) represents the deterministic relationship between the auxiliary variable and the intermediate variable, p(c jb |h j , g jb ) represents the deterministic relationship between the intermediate variable and the path gain and the custom vector, p(h j |l j ) represents the prior distribution of the path gain given the precision l j , p(l j ) represents the prior distribution of the hyperparameter, p(g jb |k j) represents the deterministic relationship between the custom vector and the fractional Doppler shift, p(k j ) represents the prior distribution of the fractional Doppler shift, p(γ) represents the prior distribution of the noise precision, factorize the joint posterior probability density function of the quantities to be estimated in the OTFS system model and obtain the corresponding factor graph model.

[0032] Optionally, in step B, according to the factor graph model construction rules, obtain the corresponding factor graph model of the OTFS system under this problem. The factor graph model can visually display the complex relationships between variables (such as channel coefficients, time delays, Doppler shifts, etc.) and factors (such as the likelihood function of the observed data, prior probability density function, etc.) in the OTFS system in a graphical way. This intuitive representation helps researchers better understand the system model, thereby enabling effective analysis and design.

[0033] Optionally, step C includes the following steps:

[0034] Step C1: Use the message passing UAMP algorithm with unitary transformation to estimate the auxiliary variable z from its noisy observation r = z + w;

[0035] Step C2: Use the message passing UAMP algorithm with unitary transformation to approximately regard the intermediate variable c as q = c + n to recover the intermediate variable c;

[0036] Step C3: Use the message passing UAMP algorithm with unitary transformation to iterate until convergence and output As the prior information of decoupling the path gain h and the fractional Doppler shift k from the intermediate variable c using the mean field MF algorithm in the right subgraph, reasonable initial parameter values can provide a good starting point for the iteration of the UAMP algorithm, helping the algorithm converge to the global optimal solution or a solution close to the global optimal solution more quickly. This helps improve the accuracy of channel estimation. Through the iteration of the UAMP algorithm, the algorithm can gradually approach the true channel parameters, thereby obtaining a more accurate estimate value of the intermediate variable. This iterative convergence process helps reduce errors and improve the accuracy of the estimate.

[0037] Optionally, in step C1, according to the noisy observation r = z + w, the posterior of z is obtained through the following formula:

[0038]

[0039] where the prior information is obtained from the first and second lines of the UAMP algorithm as the prior variance and mean of r = z + w, and then the posterior of z is obtained

[0040]

[0041] where

[0042]

[0043] Optionally, in step C2, UAMP approximately treats c as q = c + n, and its posterior value is obtained by the following formula

[0044]

[0045] where v q and are found in lines 8 and 9 of the UAMP algorithm as the likelihood variance and mean of q = c + n, and p(c) comes from the right subgraph of the factor graph as the prior information of c, that is

[0046]

[0047] Using the conclusion that the product of two Gaussian distributions is still a Gaussian distribution, it is simplified to

[0048]

[0049] where

[0050]

[0051] UAMP iterates until convergence and outputs as the prior information of the right subgraph.

[0052] Optionally, in step D, using the output after UAMP converges as the prior information, the VMP algorithm is used to decouple the estimated values of the path gain and fractional Doppler shift from the intermediate variables. Once the messages transmitted in the right subgraph are completed, it outputs p(c), which plays the role of prior information in the next iteration of UAMP. Then run UAMP again and start the next outer iteration. By using the output after UAMP converges as the prior information of the VMP algorithm, the information accumulated in the previous iterations can be fully utilized, thereby improving the estimation accuracy of the path gain and fractional Doppler shift. The VMP algorithm can perform more refined decoupling and estimation based on this prior information, further reducing the error. Using the prior information can accelerate the convergence speed of the VMP algorithm because the prior information provides a better starting point for the algorithm, reducing the search space. This means that with the same number of iterations, the VMP algorithm using the prior information can approximate the true channel parameters faster. Using the prior information can accelerate the convergence speed of the VMP algorithm because the prior information provides a better starting point for the algorithm, reducing the search space. This means that with the same number of iterations, the VMP algorithm using the prior information can approximate the true channel parameters faster.

[0053] Positive and beneficial effects:

[0054] 1. The low-complexity OTFS channel estimation method based on UAMP considers the OTFS system in the presence of fractional Doppler frequency shift and proposes a low-complexity iterative channel estimation method. By formulating the OTFS channel estimation problem as a linear mixing model, factorizing the joint posterior probability density function of the variables to be estimated in the OTFS system model, and obtaining the corresponding factor graph model, then using the UAMP algorithm to obtain the estimated values of the intermediate variables, and taking the output after the convergence of UAMP as the prior information, using the VMP algorithm to decouple the path gain and the estimation of fractional Doppler frequency shift from the intermediate variables. Compared with the existing algorithms, this algorithm has the same normalized mean square error performance but significantly reduces the computational complexity.

[0055] 2. The low-complexity OTFS channel estimation method based on UAMP can accelerate the convergence speed of the VMP algorithm by using the prior information, because the prior information provides a better starting point for the algorithm and reduces the search space, which means that under the same number of iterations, the VMP algorithm using the prior information can approximate the true channel parameters faster.

[0056] 3. The low-complexity OTFS channel estimation method based on UAMP can use the tools of linear algebra and statistics to solve the problem by formulating the OTFS channel estimation problem as a linear mixing model, which helps to simplify the calculation process, reduce the algorithm complexity, and improve the efficiency of channel estimation. Description of the Drawings

[0057] Figure 1 is the flowchart of the present invention;

[0058] Figure 2 is the factor graph model obtained by factorizing the joint posterior probability distribution of all unknown parameters;

[0059] Figure 3 is the schematic diagram of the simulation result of the comparison of the cumulative running time of the outer iteration;

[0060] Figure 4 is the schematic diagram of the simulation result of the comparison of the cumulative running time of the inner iteration;

[0061] Figure 5 is the schematic diagram of the simulation result of the comparison of the iterative convergence of the algorithm;

[0062] Figure 6 is the schematic diagram of the simulation result of the comparison of the normalized mean square error performance of the reconstructed channel matrix. Detailed Embodiment

[0063] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where like or similar reference numerals denote like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.

[0064] As Figure 1 shown, a low-complexity OTFS channel estimation method based on UAMP includes the following steps:

[0065] Step A: Formulate the OTFS channel estimation problem in the time-delay Doppler domain as a linear mixing model;

[0066] Step B: Factorize the joint posterior probability density function of the quantities to be estimated in the OTFS system model and obtain the corresponding factor graph model;

[0067] Step C: Set the initial parameter values for the factor graph model in Step B, and use the UAMP algorithm to iterate until convergence to obtain the estimated values of the intermediate variables;

[0068] Step D: Use the output after UAMP convergence as prior information, and use the VMP algorithm to decouple the estimated values of the path gain and the fractional Doppler shift from the intermediate variables;

[0069] Step E: Repeat Steps C to D until the algorithm converges.

[0070] In Step A, assume that the DD plane is divided into M grids in the time-delay dimension and N grids in the Doppler dimension. The modulation symbols {x[k, l], 0 ≤ k ≤ N - 1, 0 ≤ l ≤ M - 1} are placed in the M × N grids. The input-output relationship of the OTFS system in the time-delay Doppler domain is as follows:

[0071]

[0072] where and is an integer, k d represents the fractional Doppler shift, h t,d is the signal propagation path gain, the variables t and d represent the time-delay index and the Doppler index respectively, and there are t ∈ [0, l max , d ∈ [-k max , k max , w[k, l] represents additive white Gaussian noise with a mean of 0 and a variance of γ -1 ; in addition, reshape the received symbols {y[k, l]} into a vector where the j-th element y j is y[k, l], and j = kM + l, the transmitted symbol vector Constructed from {x[k, l]}, the input-output relationship is then reformulated as:

[0073] y = H bi x + w

[0074] where represents the effective channel matrix in the DD domain, described in detail as:

[0075]

[0076] where I N (-[q - d] N ) is obtained by circularly shifting the rows of the identity matrix by -[q - d] N and so is I M (t);

[0077] To estimate the unknown channel matrix, pilot symbols of M p ′N p are inserted into the DD plane at the guard interval to avoid interference between data and guard symbols, and then the following equivalent model is obtained:

[0078] y = X bi c + w

[0079] where is formed by stacking {y[k, l]} into a vector, is obtained by stacking {w[k, l]}, and in addition, is constructed based on pilot symbols, and the unknown vector is represented as:

[0080]

[0081] and

[0082] c j = h j g j

[0083] where h j follows a complex Gaussian distribution with mean 0 and variance l j , that is where the hyperparameter l j follows a gamma distribution, that is p(l j ) = Ga(l j ; e j , h j ).

[0084] The aim is to estimate the path gain h j from the intermediate variable c jand the fractional Doppler shift k j , due to h j and k j having some non-zero elements, the sparse characteristic of c is caused. This problem can be solved using sparse Bayesian estimation techniques, which can be implemented through the message passing algorithm on the factor graph.

[0085] The linear mixing model can flexibly handle the correlations and non-constant variabilities in the data, which provides a broader modeling ability for OTFS channel estimation. In an OTFS system, the channel response usually exhibits complex time-varying characteristics, and the linear mixing model can capture these characteristics, thus estimating the channel state more accurately;

[0086] By formulating the OTFS channel estimation problem as a linear mixing model, tools from linear algebra and statistics can be used for solving, which helps simplify the calculation process, reduce the algorithm complexity, and improve the efficiency of channel estimation. Especially in the UAMP algorithm, by locally circularly reconstructing the equivalent channel matrix, the input variables regain the circular characteristics, further simplifying the calculation;

[0087] Furthermore, the linear mixing model is a general framework that can accommodate various extensions and variants. For example, more fixed effects and random effects can be introduced to capture the complex characteristics in the channel, or more complex transformations can be adopted to improve the performance of the model. This makes the OTFS channel estimation method based on the linear mixing model have stronger scalability and flexibility.

[0088] In step B, according to the OTFS system model, given the observed variables, the joint posterior probability density function distribution of the path gain h, fractional Doppler shift κ, intermediate variable c, auxiliary variable z, noise precision γ, hyperparameter λ, and custom vector g is specifically factorized as:

[0089]

[0090] where p(y k |z k ,γ) represents the observation likelihood of the auxiliary variable and noise precision, p(z k |c) represents the deterministic relationship between the auxiliary variable and the intermediate variable, p(c jb |h j ,g jb ) represents the deterministic relationship between the intermediate variable and the path gain as well as the custom vector, p(h j |l j ) represents the prior distribution of the path gain given the precision l j , p(l j ) represents the prior distribution of the hyperparameter, p(g jb |kj ) represents the deterministic relationship between the custom vector and the fractional Doppler shift, p(k j ) represents the prior distribution of the fractional Doppler shift, p(γ) represents the prior distribution of the noise precision. Factorization transforms the complex joint posterior probability density function into the product of multiple local functions, thus simplifying the calculation process. In the UAMP algorithm, the factor graph model can guide the algorithm for iterative updates, avoiding the complexity of directly calculating the high-dimensional joint probability density function. The factor graph model can clearly represent the dependence relationship between variables, thus more accurately capturing the channel characteristics in the OTFS system. Through factorization, the statistical relationship between the quantities to be estimated can be more accurately described, improving the accuracy of channel estimation. Factorizing the joint posterior probability density function of the quantities to be estimated in the OTFS system model and obtaining the corresponding factor graph model has significant advantages in reducing the computational complexity, improving the estimation accuracy, enhancing the algorithm robustness, facilitating parallel processing and distributed computing, and supporting flexible system design and optimization, making the low-complexity OTFS channel estimation method based on UAMP more competitive and practical in practical applications.

[0091] In step B, according to the factor graph model construction rules, the corresponding factor graph model of the OTFS system under this problem is obtained. The factor graph model can visually display the complex relationship between variables (such as channel coefficients, time delays, Doppler shifts, etc.) and factors (such as the likelihood function of the observed data, prior probability density function, etc.) in the OTFS system in a graphical manner. This intuitive representation helps researchers better understand the system model, thus enabling effective analysis and design.

[0092] Step C includes the following steps:

[0093] Step C1: Use the message-passing UAMP algorithm with unitary transformation to estimate the auxiliary variable z from its noisy observation r = z + w;

[0094] Step C2: Use the message-passing UAMP algorithm with unitary transformation to approximately regard the intermediate variable c as q = c + n to recover the intermediate variable c;

[0095] Step C3: Use the message-passing UAMP algorithm with unitary transformation to iterate until convergence and output As prior information for decoupling the path gain h and the fractional Doppler shift κ from the intermediate variable c using the mean field MF algorithm in the right subgraph, reasonable initial parameter values can provide a good starting point for the iteration of the UAMP algorithm, which helps the algorithm converge to the global optimal solution or a solution close to the global optimal solution more quickly. This helps improve the accuracy of channel estimation. Through the iteration of the UAMP algorithm, the algorithm can gradually approach the true channel parameters, thereby obtaining a more accurate estimated value of the intermediate variable. This iterative convergence process helps reduce errors and improve the accuracy of estimation.

[0096] In step C1, according to the noise observation r = z + w, the posterior of z is obtained as follows:

[0097]

[0098] where the prior information is obtained from lines 1 and 2 of the UAMP algorithm as the prior variance and mean of r = z + w, and then the posterior of z is obtained

[0099]

[0100] where

[0101]

[0102] In step C2, UAMP approximately regards c as q = c + n, and its posterior value is obtained as follows

[0103]

[0104] where v q and are found in lines 8 and 9 of the UAMP algorithm as the likelihood variance and mean of q = c + n, and p(c) comes from the right subgraph of the factor graph as the prior information of c, that is

[0105]

[0106] Using the conclusion that the product of two Gaussian distributions is still a Gaussian distribution, it is simplified to

[0107]

[0108] where

[0109]

[0110] UAMP iterates until convergence and outputs as the prior information of the right subgraph.

[0111] In step D, the output after UAMP convergence is used As prior information, the VMP algorithm is used to decouple the estimated values of the path gain and the fractional Doppler shift from the intermediate variables. Once the messages passed in the right subplot are completed, it outputs p(c), which plays the role of prior information in the next iteration of UAMP. Then, run UAMP again and start the next outer iteration. By using the output after UAMP convergence as the prior information of the VMP algorithm, the information accumulated in the previous iterations can be fully utilized, thereby improving the estimation accuracy of the path gain and the fractional Doppler shift. The VMP algorithm can perform more refined decoupling and estimation based on this prior information, further reducing the error. Utilizing prior information can accelerate the convergence speed of the VMP algorithm because prior information provides a better starting point for the algorithm and reduces the search space, meaning that with the same number of iterations, the VMP algorithm using prior information can approximate the true channel parameters faster. Utilizing prior information can accelerate the convergence speed of the VMP algorithm because prior information provides a better starting point for the algorithm and reduces the search space, which means that with the same number of iterations, the VMP algorithm using prior information can approximate the true channel parameters faster.

[0112] Denote the number of inner iterations in UAMP in the left subplot as N inner , and use N outer as the number of iterations between the left and right subplots of the factor graph; First, the proposed algorithm only performs the SVD decomposition once at the beginning, with a complexity of O(TK 2 ). The complexity of the above algorithm mainly focuses on the matrix-vector multiplication operation in the inner iteration of UAMP. For each inner iteration, the complexity is O(TK), so the complexity of each outer iteration is O(TKN inner +T 2 K / N outer ), where N inner <N outer =K<T.

[0113] Figure 2 is the factor graph model obtained by factorizing the joint posterior probability distribution of all unknown parameters;

[0114] The comparison graph of the simulation results is as Figures 3 - 6 shown. The simulation parameters are set as follows: The OTFS system has M = 128 subcarriers and N = 32 time slots, the carrier frequency and the subcarrier spacing are 3 GHz and 2 KHz respectively, the number of paths is set to P = 10, the maximum delay index l max and the maximum Doppler index k max are set to 10 and 4 respectively. The pilot symbols are placed in a row along the Doppler dimension, i.e., M p =1. The delay indices of the paths are uniformly distributed within [0, l max , and the Doppler indices of the paths are within [-kmax , k max ; In addition, the fractional Doppler shift is uniformly distributed in [-0.5, 0.5], and the channel path gain can be independently obtained from the complex Gaussian distribution N(0, 1 / P).

[0115] The simulation results of the experiment are obtained by performing 1000 Monte Carlo simulations. The finally selected comparison algorithm is the OTFS channel estimation algorithm for structured signal recovery based on message passing, denoted by "VMP", while the algorithm proposed in this patent is denoted by "UAMP".

[0116] Set the number of inner iterations in UAMP to 10. VMP has no inner iterations. The number of outer iterations for both is 25. The cumulative running time of the outer iterations of both was tested on a host with a CPU of 2.3 GHz, and the results are as Figure 3 shown;

[0117] It should be noted that for UAMP, the time for SVD decomposition is added to the first outer iteration, and SVD is only required once throughout the iteration process. Obviously, as the number of outer iterations increases, compared with the UAMP algorithm, the running time required by VMP increases significantly. It can be seen that the running time consumed by UAMP is one-third of that of VMP.

[0118] Figure 4 Describes the comparison of the cumulative running time of inner iterations. It should be noted that VMP runs in a non-iterative manner, so the same running time is allocated for each inner iteration. It can be seen that the running time of UAMP gradually increases as the number of inner iterations increases. Although UAMP requires 10 inner iterations, it is significantly superior to VMP in terms of computational efficiency.

[0119] Figure 5 The relationship between the NMSE performance of the path gain and the number of outer iterations was compared. It can be seen that UAMP and VMP showed similar NMSE performance, and the two methods converged at the same rate after 13 outer iterations.

[0120] Figure 6 Evaluated the NMSE performance of the reconstructed channel matrix H bi and added a threshold-based comparison method. It can be seen that UAMP and VMP showed comparable NMSE performance and both significantly exceeded the threshold method by 10 dB.

[0121] The present invention considers an OTFS system in the presence of fractional Doppler shift and proposes a low-complexity iterative channel estimation method. By formulating the OTFS channel estimation problem as a linear mixing model, factorizing the joint posterior probability density function of the variables to be estimated in the OTFS system model, and obtaining the corresponding factor graph model, the UAMP algorithm is then used to obtain the estimated values of the intermediate variables. The output after the UAMP converges is used as prior information, and the VMP algorithm is used to decouple the path gain and the estimation of fractional Doppler shift from the intermediate variables. Compared with the existing algorithms, this algorithm has the same normalized mean square error performance but significantly reduces the computational complexity.

Claims

1. A low-complexity OTFS channel estimation method based on UAMP, characterized in that: The steps include: Step A, formulating the OTFS channel estimation problem in the delay-Doppler domain as a linear mixed model; Step B, factoring the joint posterior probability density function of the estimated quantity of the OTFS system model and obtaining the corresponding factor graph model; Step C: setting initialization parameter values ​​for the factor graph model in step B, and iterating using the UAMP algorithm until convergence to obtain estimated values ​​of intermediate variables; Step D: using the converged output of UAMP as prior information, and using the VMP algorithm to decouple the estimated values ​​of path gain and fractional Doppler shift from the intermediate variables; Step E: Repeat steps C to D until the algorithm converges.

2. The low-complexity OTFS channel estimation method based on UAMP according to claim 1, characterized in that: In step A, it is assumed that the DD plane is divided into M grids in the delay dimension and N grids in the Doppler dimension, and the modulation symbols {x[k,l],0￡k￡N-1,0￡l￡M-1} are placed in M′N grids. The input and output relationship of the OTFS system in the delay-Doppler domain is as follows: in and is an integer, k d represents the fractional Doppler shift, h t,d is the signal propagation path gain, the variables t and d represent the delay index and Doppler index respectively, and t∈[0,l max ],d∈[-k max ,k max ], w[k,l] means the mean is 0 and the variance is γ -1 Additive Gaussian white noise; In addition, the received symbol {y[k,l]} is reshaped into a vector The jth element y j is y[k,l], and j = kM+l, the transmission symbol vector It is constructed by {x[k,l]}, and then the input-output relationship is reformulated as y=H bi x+w in represents the effective channel matrix in the DD domain, which is described in detail as Among them I N (-[qd] N ) is a row cyclic shift of the identity matrix -[qd] N I got M (t) is also true; In order to estimate the unknown channel matrix, M p 'N p The pilot symbols are inserted into the DD plane with a guard interval to avoid interference between data and guard symbols, and then the following model is equivalently obtained: y=X bi c+w in is formed by stacking {y[k,l]} into a vector, Obtained by stacking {w[k,l]}, in addition, It is constructed based on pilot symbols, and the unknown vector is represented as and c j =h j g j in h j It has a mean of 0 and a variance of l j The complex Gaussian distribution of The hyperparameter l j It obeys the gamma distribution, that is, p(l j )=Ga(l j ;e j ,h j ).

3. The low-complexity OTFS channel estimation method based on UAMP according to claim 1, characterized in that: In step B, according to the OTFS system model, when the observed variables are given, the joint posterior probability density function distribution of the path gain h, fractional Doppler shift κ, intermediate variable c and auxiliary variable z, noise accuracy γ, hyperparameter λ and custom vector g is specifically factorized as follows: Among them, p(y k |z k ,γ) represents the observation likelihood of auxiliary variables and noise accuracy, p(z k |c) represents the deterministic relationship between the auxiliary variables and the intermediate variables, p(c jb |h j ,g jb ) represents the deterministic relationship between the intermediate variable, path gain, and custom vector, p(h j |l j ) indicates a given precision l j The prior distribution of the path gain under j ) represents the prior distribution of hyperparameters, p(g jb |k j ) represents the deterministic relationship between the custom vector and the fractional Doppler shift, p(k j ) represents the prior distribution of fractional Doppler shift, and p(γ) represents the prior distribution of noise precision.

4. The low-complexity OTFS channel estimation method based on UAMP according to claim 3, characterized in that: In the step B, the factor graph model construction rules are followed to obtain the corresponding factor graph model of the OTFS system under the problem.

5. The low-complexity OTFS channel estimation method based on UAMP according to claim 1, characterized in that: The step C comprises the following steps: Step C1, using the message passing UAMP algorithm with unitary transformation to estimate the auxiliary variable z from its noisy observation r = z + w; Step C2, using the message passing UAMP algorithm with unitary transformation to approximately regard the intermediate variable c as q=c+n to recover the intermediate variable c; Step C3: Use the message passing UAMP algorithm with unitary transformation to iterate until convergence, and output As in the right subfigure, the mean field MF algorithm is used to decouple the prior information of path gain h and fractional Doppler shift κ from the intermediate variable c.

6. The low-complexity OTFS channel estimation method based on UAMP according to claim 5, characterized in that: In step C1, based on the noise observation r=z+w, the posterior of z is obtained by the following formula The prior information From the first and second lines of the UAMP algorithm, we obtain the prior variance and mean of r = z + w, and then the posterior of z in 7. The low-complexity OTFS channel estimation method based on UAMP according to claim 5, characterized in that: The UAMP in step C2 approximately regards c as q=c+n, and its posterior value is obtained by the following formula where v q and In the 8th and 9th lines of the UAMP algorithm, we find that as the likelihood variance and mean of q = c + n, p(c) comes from the right subgraph of the factor graph as the prior information of c, that is, Using the conclusion that the product of two Gaussian distributions is still a Gaussian distribution, it can be simplified to in UAMP iterates until convergence and outputs As the prior information of the right subgraph.

8. The low-complexity OTFS channel estimation method based on UAMP according to claim 1, characterized in that: In step D, the output after UAMP convergence is used As prior information, the estimated values ​​of path gain and fractional Doppler shift are decoupled from the intermediate variables using the VMP algorithm. Once the message passed in the right subgraph is completed, it outputs p(c), which plays the role of prior information in the next iteration of UAMP. UAMP is run again and the next outer iteration begins.

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