OTFS relay channel estimation method based on variational Bayesian inference

Abstract

The invention discloses an OTFS relay channel estimation method based on variational Bayesian inference, and relates to the technical field of wireless communication and smart cities. Comprising the following steps of: 1, converting an input signal into a time domain signal through a base station S, sending the time domain signal to a relay R, amplifying the received time domain signal through the relay, forwarding the time domain signal to a mobile terminal D, cascading channels of an S-R link and an R-D link to obtain a time domain signal representation received by the mobile terminal, converting the time domain signal received by the mobile terminal to a time delay Doppler domain, and transmitting the time domain signal to the relay R; and 2, establishing a model by using variational Bayes, performing relay channel estimation by using the model, regarding yp as a variable by using the model, and iteratively updating posterior probability distribution of a hidden variable to obtain channel estimation.

Description

Technical Field

[0001] The present invention discloses an OTFS relay channel estimation method based on variational Bayesian inference, which relates to the technical fields of wireless communication and smart city. Background Art

[0002] In the construction of smart cities, as an emerging wireless communication technology, OTFS technology has significant application potential. By modulating signals on a two-dimensional grid in the time-frequency domain, OTFS can effectively combat the Doppler effect and multipath interference, and is particularly suitable for communication requirements in high-speed mobile and complex urban environments. In the context of smart cities, OTFS technology can significantly improve the communication capabilities of urban infrastructure. For example, in intelligent transportation systems, OTFS can provide stable and low-latency communication connections for high-speed vehicles, thereby supporting vehicle-to-everything (V2X) applications and improving traffic management efficiency and safety. In these scenarios, relay communication is a key technology to achieve wide coverage and high reliability, and accurate estimation of the relay channel is the core link to ensure communication performance. However, in the complex and changing wireless environment of smart cities, especially in the multi-hop communication scenarios of relay nodes, channel estimation faces technical problems such as high-dimensional parameter estimation, robustness under non-ideal channel conditions, and error accumulation introduced by relay nodes. Summary of the Invention

[0003] Aiming at the problems of the prior art, the present invention provides an OTFS relay channel estimation method based on variational Bayesian inference, which can effectively improve the communication performance in high-mobility scenarios in smart cities, support key applications such as intelligent transportation, remote monitoring, and smart grid, and provide technical support for the deployment of 5G and future wireless communication networks in smart cities.

[0004] The specific solution proposed by the present invention is as follows:

[0005] The present invention also provides an OTFS relay channel estimation method based on variational Bayesian inference, including:

[0006] Step 1: The base station S converts the input signal into a time-domain signal and sends it to the relay R. The relay amplifies the received time-domain signal and forwards it to the mobile terminal D. The S-R link and the R-D link channels are cascaded to obtain the expression of the time-domain signal received by the mobile terminal, and the time-domain signal received by the mobile terminal is converted into the delay-Doppler domain to obtain the expression y of the time-domain signal received by the mobile terminal in the delay-Doppler domain D ,

[0007] Step 2: Use variational Bayesian to establish a model, and use the model for relay channel estimation. The relationship between the pilot symbol and the channel response obtained by using the model is as follows:

[0008] is the observation matrix, Ξ p = LΞ, is the matrix for extracting pilot data, and β is the coefficient for relaying and amplifying the time-domain signal,

[0009] Using the model, regard y p as a variable, iteratively update the posterior probability distribution of the latent variable, and obtain the channel estimation:

[0010] Set the received pilot signal y p , the observation matrix Ξ p ;

[0011] Initialization: the maximum number of iterations N max , the iteration stop error ζ;

[0012] Calculate the initial values of each latent variable, q (i+1) (α), q (i+1) (h), q (i+1) (γ), i = 1,

[0013] Update q (i+1) (α), q (i+1) (h), q (i+1) (γ), and calculate the error,

[0014] If the number of iterations i > N max or the error ≤ ζ, then output the channel estimation result

[0015] Furthermore, in step 1 of the above-mentioned OTFS relay channel estimation method based on variational Bayesian inference, the input signal is converted into a time-domain signal by the base station S and sent to the relay R, including:

[0016] The base station S performs serial-to-parallel conversion on the random input bit stream in the delay-Doppler domain, then performs inverse finite symplectic Fourier transform on the signal, transforms the delay-Doppler domain signal to the time-frequency domain for processing, performs Heisenberg transform on the time-frequency domain transmitted signal, converts it into a time-domain signal, and obtains the time-domain signal through the base station S and sends it to the relay.

[0017] Furthermore, in step 1 of the above-mentioned OTFS relay channel estimation method based on variational Bayesian inference, the delay-Doppler domain channel response expression from the base station to the relay is:

[0018]

[0019] where, g i represents the channel gain of the i-th path from the base station to the relay, τ g,i and ν g,i respectively represent the delay spread and Doppler frequency shift of the i-th path from the base station to the relay, L gLet \(L\) be the number of channel taps from the base station to the relay. Then the time-domain signal received by the relay is:

[0020]

[0021] where \(v(t)\) represents additive white Gaussian noise with a mean of 0 and a variance of on the S-R link.

[0022] Furthermore, in step 1 of the OTFS relay channel estimation method based on variational Bayesian inference, after the relay amplifies the received time-domain signal \(r in (t)\) and forwards it, with an amplification factor of \(\beta\), the expression for the signal \(r out (t)\) transmitted by the relay R is:

[0023]

[0024] where E r is the transmit power of the relay, and \(E s is the transmit power of the base station. represents the channel power, and represents the average power of the noise;

[0025] After the relay amplifies the signal and sends it to the mobile terminal, the time-delay Doppler domain channel response from the relay to the mobile terminal is:

[0026]

[0027] where \(f j represents the channel gain of the \(j\)-th path from the relay to the user, \(\tau f,j and \(\nu f,j represent the delay spread and Doppler shift of the \(j\)-th path from the relay to the mobile terminal respectively, and \(L f is the number of channel taps from the relay to the mobile terminal.

[0028] Furthermore, in step 1 of the OTFS relay channel estimation method based on variational Bayesian inference, the S-R link and the R-D link channels are cascaded to obtain the time-delay Doppler domain channel response of the S-D link:

[0029]

[0030] Then the time-domain signal received by the mobile terminal is expressed as:

[0031]

[0032] The complete input-output relationship from the base station to the mobile terminal is:

[0033]

[0034] The Doppler shift of each cascaded base station S to mobile channel is ν q =(ν f,j +ν g,i ), the delay spread is τ q =(τ f,j +τ g,i ), the channel gain in the delay-Doppler domain is h q =f f,j g g,i , L = L f +L g -1 is the number of cascaded channel paths;

[0035] Discrete sampling of the time-domain signal gives the time-domain received signal as:

[0036]

[0037] where n = 0, 1,..., NM-1;

[0038] The time-domain signal is first subjected to the Wigner transform and then the SFFT transform to be converted to the delay-Doppler domain, obtaining the expression of the time-domain signal in the delay-Doppler domain

[0039] After arrangement:

[0040] The above formula is arranged as:

[0041] The present invention also provides an OTFS relay channel estimation device based on variational Bayesian inference, including a transmission management module and a channel estimation module,

[0042] The transmission management module converts the input signal into a time-domain signal through the base station S and sends it to the relay R, amplifies the received time-domain signal through the relay and forwards it to the mobile terminal D, cascades the S-R link and the R-D link channels, obtains the expression of the time-domain signal received by the mobile terminal, and converts the time-domain signal received by the mobile terminal to the delay-Doppler domain, obtaining the representation y of the time-domain signal received by the mobile terminal in the delay-Doppler domain D ,

[0043] The channel estimation module uses variational Bayesian to establish a model and uses the model for relay channel estimation. Among them, the relationship between the pilot symbol and the channel response obtained by using the model is as follows:

[0044] is the observation matrix, Ξ p =LΞ, is the matrix for extracting pilot data, β is the coefficient for amplifying the time-domain signal by the relay,

[0045] Regarding y as a variable using the model, iteratively update the posterior probability distribution of the latent variable, and obtain the channel estimation: p

[0046] Set the received pilot signal y p , and the observation matrix Ξ p ;

[0047] Initialization: the maximum number of iterations N max , and the iteration stop error ζ;

[0048] Calculate the initial values of each latent variable, q (i+1) (α), q (i+1) (h), q (i+1) (γ), i = 1,

[0049] Update q (i+1) (α), q (i+1) (h), q (i+1) (γ), and calculate the error,

[0050] If the number of iterations i > N max or the error ≤ ζ, then output the channel estimation result

[0051] Furthermore, the transmission management module of the OTFS relay channel estimation device based on variational Bayesian inference converts the input signal into a time-domain signal through the base station S and sends it to the relay R, including:

[0052] Perform serial-to-parallel conversion on the random input bit stream in the time-delay Doppler domain through the base station S, then perform inverse finite symplectic Fourier transform on the signal, transform the time-delay Doppler domain signal to the time-frequency domain for processing, perform Heisenberg transform on the time-frequency domain transmitted signal, convert it to the time-domain signal, and obtain the time-domain signal through the base station S and send it to the relay.

[0053] Furthermore, the time-delay Doppler domain channel response expression from the base station to the relay of the OTFS relay channel estimation device based on variational Bayesian inference is:

[0054]

[0055] where g i represents the channel gain of the i-th path from the base station to the relay, τ g,i and ν g,i represent the delay spread and Doppler frequency shift of the i-th path from the base station to the relay respectively, L g is the number of channel taps from the base station to the relay, then the time-domain signal received by the relay is:

[0056]

[0057] Among them, v(t) represents the additive white Gaussian noise with a mean of 0 and a variance of in the S-R link,

[0058] Furthermore, the transmission management module of the OTFS relay channel estimation device based on variational Bayesian inference amplifies and forwards the received time-domain signal r in (t) from the relay. If the amplification factor is β, then the signal r out (t) sent by the relay R is expressed as:

[0059]

[0060] Among them, E r is the transmission power of the relay, and E s is the transmission power of the base station. represents the channel power, and represents the average power of the noise;

[0061] After being amplified by the relay, the signal is sent to the mobile terminal. The time-delay Doppler domain channel response between the relay and the mobile terminal is:

[0062]

[0063] Among them, f j represents the channel gain of the j-th path from the relay to the user, τ f,j and ν f,j respectively represent the delay spread and Doppler shift of the j-th path from the relay to the mobile terminal, and L f is the number of channel taps from the relay to the mobile terminal.

[0064] Furthermore, the transmission management module of the OTFS relay channel estimation device based on variational Bayesian inference cascades the S-R link and the R-D link channels to obtain the time-delay Doppler domain channel response of the S-D link:

[0065]

[0066] Then the time-domain signal received by the mobile terminal is expressed as:

[0067]

[0068] The complete input-output relationship from the base station to the mobile terminal is:

[0069]

[0070] The Doppler shift of each cascaded base station S to mobile terminal channel is ν q =(ν f,j+ν g,i ) and the delay spread is τ q =(τ f,j +τ g,i ), and the channel gain in the delay - Doppler domain is h q =f f,j g g,i , L = L f +L g -1 is the number of cascaded channel paths;

[0071] Discretely sampling the time - domain signal, the received time - domain signal is:

[0072]

[0073] where n = 0, 1,..., NM - 1;

[0074] Performing the Wigner transform and the SFFT transform on the time - domain signal successively to convert it to the delay - Doppler domain, the expression of the time - domain signal in the delay - Doppler domain is obtained

[0075] After arrangement, it is:

[0076] The above formula is arranged as:

[0077] The advantages of the present invention are:

[0078] Through the variational Bayesian inference framework, the computational complexity of high - dimensional channel estimation is significantly reduced, and the algorithm efficiency is improved; it can still maintain high - precision estimation under low signal - to - noise ratio and non - ideal channel conditions, enhancing the robustness of the system; at the same time, it effectively suppresses the error accumulation in multi - hop relay communication, improves the reliability of the communication link, and provides an efficient and stable channel estimation solution for high - speed mobile communication scenarios in smart cities. Brief Description of the Drawings

[0079] Figure 1 is a schematic diagram of the OTFS amplify - and - forward relay communication architecture.

[0080] Figure 2 is a schematic diagram comparing OTFS transmitted symbols and received symbols.

[0081] Figure 3 is a schematic diagram of the probabilistic graphical model.

[0082] Figure 4 is a schematic diagram of the variational Bayesian iteration process. Detailed Implementation Manner

[0083] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited do not limit the present invention.

[0084] Embodiment 1

[0085] The present invention also provides an OTFS relay channel estimation method based on variational Bayesian inference, including:

[0086] Step 1: The base station S converts the input signal into a time-domain signal and sends it to the relay R. The relay amplifies the received time-domain signal and forwards it to the mobile terminal D. The S-R link and the R-D link channels are cascaded to obtain the expression of the time-domain signal received by the mobile terminal, and the time-domain signal received by the mobile terminal is converted to the delay-Doppler domain to obtain the representation y of the time-domain signal received by the mobile terminal in the delay-Doppler domain. D 。

[0087] Among them, in Step 1, converting the input signal into a time-domain signal by the base station S and sending it to the relay R includes:

[0088] The base station S performs serial-parallel conversion on the random input bit stream in the delay-Doppler domain, then performs inverse finite symplectic Fourier transform on the signal, transforms the delay-Doppler domain signal to the time-frequency domain for processing, performs Heisenberg transform on the time-frequency domain transmitted signal, converts it to the time-domain signal, and obtains the time-domain signal through the base station S and sends it to the relay.

[0089] When passing through the channel of the S-R link, considering the delay spread and Doppler frequency shift on the path, the corresponding delay-Doppler domain channel response h(τ g , ν g ) is used to represent the path parameters. Specifically, the expression of the delay-Doppler domain channel response from the base station to the relay is:

[0090]

[0091] g i represents the channel gain of the i-th path from the base station to the relay, τ g,i and ν g,i represent the delay spread and Doppler frequency shift of the i-th path from the base station to the relay respectively, and L g is the number of channel taps from the base station to the relay. Then the time-domain signal received by the relay is:

[0092]

[0093] Among them, v(t) represents the additive white Gaussian noise with a mean of 0 and a variance of on the S-R link,

[0094] The relay amplifies the received time-domain signal r in (t) and then forwards it. If the amplification factor is β, the signal r out (t) transmitted by the relay R is expressed as:

[0095]

[0096] where, E r is the transmission power of the relay, and E s is the transmission power of the base station. represents the channel power, and represents the average power of the noise;

[0097] After the signal is amplified by the relay, it is sent to the mobile terminal. The time-delay Doppler domain channel response between the relay and the mobile terminal is:

[0098]

[0099] where f j represents the channel gain of the j-th path from the relay to the user, τ f,j and ν f,j represent the delay spread and Doppler shift of the j-th path from the relay to the mobile terminal respectively, and L f is the number of channel taps from the relay to the mobile terminal.

[0100] By cascading the channels of the S-R link and the R-D link, the time-delay Doppler domain channel response of the S-D link is obtained:

[0101]

[0102] Then the time-domain signal received by the mobile terminal is expressed as:

[0103]

[0104] The complete input-output relationship from the base station to the mobile terminal is:

[0105]

[0106] The Doppler shift of each cascaded channel from the base station S to the mobile terminal is ν q =(ν f,j +ν g,i ), the delay spread is τ q =(τ f,j +τ g,i ), the channel gain in the time-delay Doppler domain is h q =f f,j g g,i , and L = L f +L g -1 is the number of paths of the cascaded channel;

[0107] The time-domain signal is discretely sampled to obtain the time-domain received signal as follows:

[0108]

[0109] where n = 0, 1,..., NM - 1;

[0110] The time-domain signal is first subjected to the Wigner transform and then the SFFT transform, and is converted to the delay-Doppler domain to obtain the expression of the time-domain signal in the delay-Doppler domain

[0111] Sorted out as:

[0112] The above formula is sorted out as:

[0113] Step 2: Use variational Bayes to establish a model, and use the model for relay channel estimation. The relationship between the pilot symbol and the channel response obtained by using the model is as follows:

[0114]

[0115] is the observation matrix, Ξ p = LΞ, is the matrix used to extract the pilot data, and β is the coefficient of the relay amplified time-domain signal.

[0116] Combined with Figure 2 , the base station sets the pilot symbol, the guard symbol, and the data symbol. The power of the pilot symbol is the same as that of the data symbol. Based on the arrangement of the pilot symbol, the guard symbol, and the data symbol in the figure, only the known pilot symbol information is included in the red frame of the mobile receiving end and will not be affected by the unknown data symbol. Therefore, it can be used for channel estimation. The relationship between the received pilot symbol and the channel impulse response is formula (11).

[0117] Figure 3 Shows the probabilistic graphical model. Squares represent model parameters, circles represent latent variables, and double circles represent observed variables. The subsequent discussion will introduce the prior distribution of each random variable to apply the variational Bayes inference algorithm for solution.

[0118] In the variational Bayes framework, the sparse channel vector is usually regarded as a random variable and is assumed to follow a specific prior distribution. On this basis, the variational Bayes inference is used to calculate the posterior probability distribution of the channel, so as to realize the estimation of the channel.

[0119] The channel gain h of the sparse channel h l Is modeled as an independent complex Gaussian distribution:

[0120]

[0121] where \(l = 0,\cdots,L - 1\), and \(L=(l τ + 1)(2k v + 1)\), \(\gamma=[\gamma_0,\gamma_1,\cdots,\gamma L-1 T , and \(\gamma l \) is the precision of the channel gain \(h l . \(\mathcal{CN}(\mu,\Sigma)\) represents a complex Gaussian distribution with mean \(\mu\) and variance \(\Sigma\).

[0122] The hyperparameter \(\gamma=[\gamma_0,\gamma_1,\cdots,\gamma L-1 T is modeled as a Gamma distribution, and the prior probability is:

[0123]

[0124] where \(\Gamma(\cdot)\) is the Gamma function, and \(a\) and \(b\) represent the shape parameter and the scale parameter respectively. Generally, very small values are assigned to these two parameters, such as \(a = b = 10 -6 .

[0125] Suppose follows a complex Gaussian distribution with mean zero and precision \(\alpha\), then its prior probability is described as:

[0126]

[0127] When performing channel estimation according to , the likelihood function of \(y p can be expressed as:

[0128] p(y p |h,\alpha)=\mathcal{CN}(y p |\beta\Xi p h,\alpha -1 I)

[0129] =( \pi) -Z \alpha Z \exp(-\alpha||y p -\beta\Xi p h|| 2 )(15)

[0130] According to the mean - field theory, \(h\), \(\gamma\), and \(\alpha\) are independent variables. Let \(\mathcal{T}=\{\alpha,h,\gamma\}\) denote the latent variables to be estimated. Therefore, \(q(\mathcal{T})\) can be decomposed into the product of probabilities of multiple latent variables:

[0131] q(\mathcal{T}) = q(\alpha)q(h)q(\gamma)(16)

[0132] ​​The optimal solution is calculated by the alternative update probability function, i.e.:

[0133]

[0134] Figure 4 For the iterative process of variational Bayes, the formulas for the entire iterative update process will be derived below:

[0135] (1) Update q(α)

[0136]

[0137] According to the Gamma expression, we can obtain:

[0138]

[0139]

[0140] Then the approximate posterior distribution of α follows a Gamma distribution Therefore, the average value of α after the (i + 1)-th iteration can be expressed as:

[0141]

[0142] (2) Update q(h)

[0143]

[0144] The approximate posterior probability distribution of h can be obtained from the above formula to follow a complex Gaussian distribution:

[0145]

[0146] where and The specific expressions are:

[0147]

[0148] 3) q(γ)

[0149]

[0150] where denotes the (l, l)-th element of denotes the l-th element of. The approximate posterior probability distribution of γ follows a Gamma distribution:

[0151]

[0152] where Therefore, the mean value of γ after the (i + 1)-th iteration can be expressed as:

[0153]

[0154] It can be obtained that:

[0155]

[0156] Through iteration, approximate distributions q(α), q(h), and q(γ) of each posterior probability distribution can be obtained. And only the means and variances of these posterior probability distributions need to be obtained, and only the means and variances of each variable need to be updated during the iteration process. Until convergence or the number of iterations is reached, finally, the mean value of q(h) is the channel estimation result

[0157] The complexity of the iteration mainly depends on μ h and Σ h The calculation complexity is O(N 3 M 3 K). Among them, K represents the number of iterations. The steps to execute the algorithm are as follows:

[0158] 1: Set the input received pilot signal y p , the observation matrix Ξ p ;

[0159] 2: Initialization: The maximum number of iterations N of the algorithm max , the iteration stop error ζ;

[0160] 3: Calculate the initial values of each vector, that is, set a = b = c = d = 10 -6 , the mean matrix of the channel vector The covariance matrix of the channel vector and the channel vector precision γ (1) = diag(γ0, γ1,..., γ L-1 ) = I;

[0161] 4: Let i = 1;

[0162] 5: Based on formula (19), use q (i) (h) to update q (i+1) (α), and then update formula (20);

[0163] 6: Based on formula (23), use q (i+1) (α) and q (i) (γ) to update q (i+1) (h);

[0164] 7: Based on equation Use q (i+1) (h) to update q(i+1) (γ), and then update Equation (27);

[0165] 8: If or the number of iterations i > N max , then jump to line 9; otherwise, set i = i + 1 and jump back to line 5;

[0166] 9: Output the channel vector

[0167] 10: Use the least mean square error algorithm for data detection and output the transmitted symbol

[0168] The method of the present invention uses the variational Bayesian inference framework to transform the channel estimation problem into a probability inference problem. By iteratively updating the variational distribution to approximate the true channel posterior distribution, more accurate channel estimation results can be obtained. The core of the present invention is to transform the high-dimensional integral problem into an optimization problem by introducing the variational distribution, significantly reducing the computational complexity and making it more suitable for resource-constrained Internet of Things devices. At the same time, by using the noise and interference suppression ability of variational Bayesian inference, high estimation accuracy can still be maintained under low signal-to-noise ratio and non-ideal channel conditions, adapting to the complex and changing wireless environment of smart cities. In addition, by making full use of the dependence relationship between prior information and observation data, the error accumulation introduced by relay nodes is effectively suppressed, improving the reliability and stability of multi-hop communication.

[0169] Embodiment 2

[0170] The present invention also provides an OTFS relay channel estimation device based on variational Bayesian inference, including a transmission management module and a channel estimation module.

[0171] The transmission management module converts the input signal into a time-domain signal through the base station S and sends it to the relay R. After amplifying the received time-domain signal through the relay, it is forwarded to the mobile terminal D. The S-R link and the R-D link channels are cascaded to obtain the time-domain signal representation received by the mobile terminal, and the time-domain signal received by the mobile terminal is converted to the delay-Doppler domain to obtain the representation y of the time-domain signal received by the mobile terminal in the delay-Doppler domain. D ,

[0172] The channel estimation module uses variational Bayesian to establish a model and uses the model for relay channel estimation. The relationship between the pilot symbol and the channel response obtained by using the model is as follows:

[0173] is the observation matrix, Ξ p = LΞ, is the matrix for extracting pilot data, β is the coefficient for amplifying the time-domain signal by the relay,

[0174] Regarding y as a variable using the model, iteratively update the posterior probability distribution of the latent variable to obtain channel estimation: p

[0175] Set the received pilot signal y p , and the observation matrix Ξ p ;

[0176] Initialization: The maximum number of iterations N max , and the iteration stop error ζ;

[0177] Calculate the initial values of each latent variable, q (i+1) (α), q (i+1) (h), q (i+1) (γ), i = 1,

[0178] Update q (i+1) (α), q (i+1) (h), q (i+1) (γ), and calculate the error,

[0179] If the number of iterations i > N max or the error ≤ ζ, then output the channel estimation result

[0180] Regarding the information interaction and execution process among the modules in the above device, since they are based on the same concept as the method embodiment of the present invention, the specific content can be referred to the description in the method embodiment of the present invention, and will not be elaborated here.

[0181] Similarly, the device of the present invention significantly reduces the computational complexity of high-dimensional channel estimation through the variational Bayesian inference framework, improves the algorithm efficiency; can still maintain high-precision estimation under low signal-to-noise ratio and non-ideal channel conditions, enhancing the robustness of the system; at the same time, effectively suppresses the error accumulation in multi-hop relay communication, improves the reliability of the communication link, and provides an efficient and stable channel estimation solution for high-speed mobile communication scenarios in smart cities.

[0182] It should be noted that not all steps and modules in the above processes and device structures are necessary, and some steps or modules can be ignored according to actual needs. The execution order of each step is not fixed and can be adjusted according to needs. The system structure described in the above embodiments can be a physical structure or a logical structure, that is, some modules may be implemented by the same physical entity, or some modules may be implemented by multiple physical entities respectively, or some components in multiple independent devices can be jointly implemented.

[0183] ​The above-described embodiments are merely preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. An OTFS relay channel estimation method based on variational Bayesian inference, characterized in that including: Step 1: Convert the input signal into a time-domain signal through base station S and send it to relay R. After amplifying the received time-domain signal through the relay, forward it to mobile terminal D. Cascade the S-R link and the R-D link channels to obtain the representation of the time-domain signal received by the mobile terminal, and convert the time-domain signal received by the mobile terminal into the delay-Doppler domain to obtain the representation y of the time-domain signal received by the mobile terminal in the delay-Doppler domain D , Step 2: Establish a model using variational Bayes, and use the model for relay channel estimation. The relationship between the pilot symbol and the channel response obtained using the model is as follows: is the observation matrix, Ξ p = LΞ, is the matrix for extracting pilot data, and β is the coefficient for relaying and amplifying the time-domain signal Using the model, regarding y p as a variable, iteratively updating the posterior probability distribution of the latent variable, and obtaining the channel estimation: Set the received pilot signal y p , the observation matrix Ξ p ; Initialization: maximum number of iterations N max , iteration stop error ζ; Calculate the initial values of each latent variable, q (i+1) (α), q (i+1) (h), q (i+1) (γ), i = 1, update q (i+1) (α), q (i+1) (h), q (i+1) (γ), and calculate the error If the number of iterations \(i > N\) max or the error \(\leq\zeta\), then output the channel estimation result 2. The OTFS relay channel estimation method based on variational Bayesian inference according to claim 1, characterized in that In step 1, the base station S converts the input signal into a time-domain signal and sends it to the relay R, including: The base station S performs serial-to-parallel conversion on the random input bit stream in the time-delay Doppler domain, then performs an inverse finite symplectic Fourier transform on the signal, transforms the time-delay Doppler domain signal to the time-frequency domain for processing, performs a Heisenberg transform on the time-frequency domain transmitted signal to convert it into a time-domain signal, and obtains the time-domain signal through the base station S and sends it to the relay.

3. The OTFS relay channel estimation method based on variational Bayesian inference according to claim 1, characterized in that In step 1, the time-delay Doppler domain channel response expression from the base station to the relay is: Among them, g i represents the channel gain of the i-th path from the base station to the relay, τ g,i and ν g,i represent the delay spread and Doppler frequency shift of the i-th path from the base station to the relay respectively, and L g is the number of channel taps from the base station to the relay. Then, the time-domain signal received by the relay is: where \(v(t)\) represents the additive white Gaussian noise with a mean of 0 and a variance of in the S-R link, 4. The OTFS relay channel estimation method based on variational Bayesian inference according to claim 3, characterized in that In step 1, the time-domain signal r in (t) received from the relay is amplified and then forwarded. If the amplification factor is β, the signal r out (t) transmitted by relay R is expressed as: Among them, E r is the transmission power of the relay, and E s is the transmission power of the base station, represents the channel power, represents the average power of the noise; After the relay amplifies the signal and sends it to the mobile terminal, the time-delay Doppler domain channel response between the relay and the mobile terminal is: where, f j represents the channel gain of the j-th path relayed to the user, τ f,j and ν f,j represent the delay spread and Doppler shift of the j-th path from the relay to the mobile terminal respectively, and L f is the number of channel taps from the relay to the mobile terminal.

5. The OTFS relay channel estimation method based on variational Bayesian inference according to claim 4, characterized in that In step 1, the S-R link and the R-D link channels are cascaded to obtain the S-D link time-delay Doppler domain channel response: Then the time-domain signal received by the mobile terminal is expressed as: The complete input-output relationship from the base station to the mobile terminal is: The Doppler shift of each cascaded base station S to mobile terminal channel is ν q =(ν f,j +ν g,i ), the delay spread is τ q =(τ f,j +τ g,i ), the channel gain in the delay-Doppler domain is h q =f f,j g g,i , L = L f +L g -1 is the number of cascaded channel paths; The time-domain received signal obtained by discretely sampling the time-domain signal is: where n = 0, 1,..., NM - 1; Perform the Wigner transform and the SFFT transform on the time-domain signal successively, convert it to the delay-Doppler domain, and obtain the expression of the time-domain signal in the delay-Doppler domain Rearranged as: The above formula is arranged as follows:

6. An OTFS relay channel estimation device based on variational Bayesian inference, characterized in that including a transmission management module and a channel estimation module, The transmission management module converts the input signal into a time-domain signal through base station S and sends it to relay R. After amplifying the received time-domain signal through the relay, it forwards it to mobile terminal D, cascades the S-R link and the R-D link channels, obtains the representation of the time-domain signal received by the mobile terminal, and converts the time-domain signal received by the mobile terminal into the delay-Doppler domain to obtain the representation y of the time-domain signal received by the mobile terminal in the delay-Doppler domain D , The channel estimation module uses variational Bayesian to establish a model and uses the model for relay channel estimation. The relationship between the pilot symbol and the channel response obtained by using the model is as follows: is the observation matrix, Ξ p = LΞ, is the matrix for extracting pilot data, and β is the coefficient for relaying and amplifying the time-domain signal Using the model, regard y p as a variable, iteratively update the posterior probability distribution of the latent variable, and obtain the channel estimation: Set the received pilot signal y p , the observation matrix Ξ p ; Initialization: maximum number of iterations N max , iteration stop error ζ; Calculate the initial values of each latent variable, q (i+1) (α), q (i+1) (h), q (i+1) (γ), i = 1, Update q (i+1) (α), q (i+1) (h), q (i+1) (γ), and calculate the error If the number of iterations \(i > N\) max or the error \(\leq\zeta\), then output the channel estimation result 7. The OTFS relay channel estimation device based on variational Bayesian inference according to claim 6, characterized in that The transmission management module converts the input signal into a time-domain signal through the base station S and sends it to the relay R, including: The base station S performs serial-to-parallel conversion on the random input bit stream in the time-delay Doppler domain, then performs an inverse finite symplectic Fourier transform on the signal, transforms the time-delay Doppler domain signal to the time-frequency domain for processing, performs a Heisenberg transform on the time-frequency domain transmitted signal to convert it into a time-domain signal, and obtains the time-domain signal through the base station S and sends it to the relay.

8. The OTFS relay channel estimation device based on variational Bayesian inference according to claim 6, characterized in that The time-delay Doppler domain channel response expression from the base station to the relay of the transmission management module is: Among them, g i represents the channel gain of the i-th path from the base station to the relay, τ g,i and ν g,i represent the delay spread and Doppler frequency shift of the i-th path from the base station to the relay respectively, and L g is the number of channel taps from the base station to the relay. Then, the time-domain signal received by the relay is: Among them, v(t) represents the additive white Gaussian noise with a mean of 0 and a variance of on the S-R link, 9. The OTFS relay channel estimation device based on variational Bayesian inference according to claim 8, characterized in that The transmission management module amplifies the received time-domain signal r in (t) from the relay and then forwards it. If the amplification factor is β, the signal r out (t) sent by the relay R is expressed as: Among them, E r is the transmission power of the relay, and E s is the transmission power of the base station. represents the channel power, and represents the average power of the noise; After the relay amplifies the signal and sends it to the mobile terminal, the time-delay Doppler domain channel response between the relay and the mobile terminal is: Among them, f j represents the channel gain of the j-th path relayed to the user, τ f,j and ν f,j represent the delay spread and Doppler shift of the j-th path from the relay to the mobile terminal respectively, and L f is the number of channel taps from the relay to the mobile terminal.

10. The OTFS relay channel estimation device based on variational Bayesian inference according to claim 9, characterized in that The transmission management module cascades the S-R link and the R-D link channels to obtain the S-D link time-delay Doppler domain channel response: Then the time-domain signal received by the mobile terminal is expressed as: The complete input-output relationship from the base station to the mobile terminal is: The Doppler shift of each cascaded base station S to mobile channel is ν q =(ν f,j +ν g,i ), the delay spread is τ q =(τ f,j +τ g,i ), the channel gain in the delay-Doppler domain is h q =f f,j g g,i , L = L f +L g -1 is the number of cascaded channel paths; The time-domain received signal obtained by discretely sampling the time-domain signal is: where n = 0, 1,..., NM - 1; Perform the Wigner transform and the SFFT transform on the time-domain signal successively, convert it to the time-delay Doppler domain, and obtain the expression of the time-domain signal in the time-delay Doppler domain Sorted as: The above equation is rearranged as follows:

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