A Off-Network Channel Estimation Method for OTFS System Based on Bilinear Vector Approximation Message Passing

Abstract

A method for estimating an off-network channel of an OTFS system based on bilinear vector approximation message passing belongs to the field of wireless communication technology. The present invention solves the problem of low accuracy of equivalent DD domain channel estimation in existing OTFS systems. The on-network matrix and off-network matrix generated by the first-order partial derivative approximation model of the present invention have non-independent and identically distributed and non-orthogonal characteristics. The first-order partial derivative approximation model is converted into a mathematical model of bilinear estimation. The integer delay and integer Doppler are estimated based on the bilinear vector approximation message passing algorithm, and the fractional delay and fractional Doppler are learned. Finally, the off-network estimation result of the DD domain channel is obtained based on the estimation and learning results. The method of the present invention can be applied to off-network channel estimation of an OTFS system.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to an off-network channel estimation method for an OTFS system. Background Art

[0002] Orthogonal time-frequency space (OTFS) modulation has proven to be a promising technology for future high-mobility communication scenarios, such as low-Earth orbit (LEO) satellite communications and high-speed terrestrial communications. OTFS uses the symplectic Fourier transform (SFFT) to transform the time-varying channel in the time-frequency (TF) domain into a quasi-time-invariant channel in the delay-Doppler (DD) domain, ensuring that all transmitted symbols experience the same channel gain. Designing information symbols in the DD domain also allows for full utilization of the Doppler diversity of the time-varying channel. Therefore, accurately estimating the time-varying channel is a key factor influencing the performance of OTFS.

[0003] Several channel estimation methods in the TF domain have been applied to OTFS systems; however, TF domain channel estimation is considered complex because they require conversion back to the DD domain for symbol demodulation. OTFS systems typically design pilots and perform channel estimation in the DD domain. When OTFS channel estimation considers only integer Doppler and delay shifts, the channel response on the DD domain grid does not spread, allowing accurate channel estimation with minimal zero protection. However, considering only integer delay and Doppler shift is unrealistic. Fractional Doppler and delay shifts lead to inter-Doppler interference (IDI) and inter-Delay interference (IDeI), causing the channel response to spread in the DD domain. Therefore, fractional Doppler and delay shift estimation is required, that is, off-grid channel estimation is required to improve the accuracy of the equivalent DD domain channel estimation. Summary of the Invention

[0004] The purpose of the present invention is to improve the accuracy of equivalent DD domain channel estimation in an OTFS system, and to propose an off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: an off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing, the method specifically comprising the following steps:

[0006] On the sending side

[0007] The signal x[k,l] mapped to the DD domain is converted to the time-frequency domain through the inverse symplectic Fourier transform. is a set of complex numbers. The signal converted to the time-frequency domain is then subjected to a Heisenberg transform, and the signal obtained by the Heisenberg transform is sent to the channel, where k represents the Doppler index, l represents the delay index, k∈{0,…,N-1}, l∈{0,…,M-1}, N represents the total number of Dopplers, and M represents the total number of delays;

[0008] On the receiving end

[0009] Step 1: Perform Wiener transform on the time domain signal received from the channel, and then perform sigmoid Fourier transform on the signal obtained by Wiener transform to obtain the received signal in DD domain.

[0010] Step 2: perform first-order partial derivative approximation on the received signal in the DD domain to obtain signal y;

[0011] Step 3: Select a resource block from the DD domain and obtain the received signal y for channel estimation based on the selected resource block. T , and receive the signal y T Rewrite as bilinear recovery signal;

[0012] Step 4: Estimate the off-grid coefficient vector and the channel coefficient vector based on the bilinear recovery signal;

[0013] Step 5: Use the off-grid coefficient vector and the channel coefficient vector estimation results to obtain the equivalent channel estimation result in the DD domain.

[0014] Furthermore, the received signal y[k, l] in the DD domain is:

[0015]

[0016] Among them, n[k,l] represents complex additive noise, and n[k,l] conforms to the complex Gaussian distribution The variances of both the real and imaginary parts are h w [k′,l′] is the equivalent DD domain channel response, k′∈{0,…,N-1}, l′∈{0,…,M-1}.

[0017] Furthermore, the calculation method of the equivalent DD domain channel response is:

[0018] The actual DD domain channel response h(v,τ) is:

[0019]

[0020] Among them, h irepresents the channel coefficient of the i-th path, P is the number of paths, δ(·) represents the Dirac function, v i represents the actual Doppler shift of the i-th path, v i ∈(-v max ,v max ), τ i represents the actual delay of the i-th path, τ i ∈(0,τ max ), v max represents the maximum Doppler shift, τ max is the maximum delay;

[0021] Sample h(v,τ) and use a rectangular window in the time-frequency domain to get h w [k,l]:

[0022]

[0023] in, e is the base of natural logarithms, j is the imaginary unit, is to convert τ i The result of mapping to the delay grid, Is v i The result of mapping to the Doppler grid, It is the DD domain representation of the rectangular window in the time-frequency domain;

[0024]

[0025] in:

[0026]

[0027] The calculated h w [k, l] is the equivalent DD domain channel response h w [k′,l′].

[0028] Furthermore, the signal y is:

[0029]

[0030] Among them, y is the vectorized form of y[k,l], n is the vectorized form of n[k,l], is the virtual Doppler grid set in the DD domain, N v is the number of virtual Doppler grids, It is a virtual delay grid set up in the DD domain. M τ is the number of virtual delay grids, is the channel coefficient vector, is the measurement matrix.

[0031] Furthermore, the measurement matrix The i-th column of is:

[0032]

[0033] in, is the fractional Doppler of column i, is the fractional delay of column i, is the measurement matrix on the grid The i-th column of and is the off-grid measurement matrix, yes right The first-order partial derivative of yes right The first-order partial derivative of is the off-grid measurement matrix The i-th column of is the off-grid measurement matrix Column i of

[0034] The fractional Doppler of the i-th column for:

[0035]

[0036] in, r v is the Doppler resolution of the virtual grid,

[0037] The fractional delay of the i-th column for:

[0038]

[0039] in, r τ is the delay resolution of the virtual grid,

[0040] Furthermore, the measurement matrix The kM+lth element in the i-th column of is:

[0041]

[0042] in, is the measurement matrix The kM+lth element in the i-th column of .

[0043] Furthermore, the specific process of step three is:

[0044] Step 3.1. Record the position of the training sequence as [k p ,l p ], the position range of the selected resource block in the DD domain is recorded as l∈[l p ,l p +l max ] and k∈[-k max +k p ,k p +k max ], the position range of the selected resource block in the DD domain is the determined observation interval;

[0045] Step 3.2: Received signal y for channel estimation within the observation interval T for:

[0046]

[0047] Among them, y T is the signal of y in the observation interval, n T is the noise of n in the observation interval, A0 is In the observation interval, A v yes In the observation interval, A τ yes In the observation interval, and is the off-grid coefficient vector,

[0048] Step 3. Receive signal y T Rewritten as a bilinear restored signal:

[0049]

[0050] Among them, θ A,0 is the identity matrix, A1=A v , A2=A τ ,

[0051] Furthermore, the specific process of step 4 is as follows:

[0052] Step 1: Initialize the signal to be estimated The sparse probability is θ x , the noise power factor is The first reference power coefficient is Off-grid coefficient vector The elements in are all less than Any value of the off-grid coefficient vector The elements in are all less than Any value of

[0053] Step 2: Initialize the number of iterations t=0;

[0054] Step 3: Define x to be independent and identically distributed in Gauss-Bernoulli distribution, that is,

[0055] x l ~p x (x l θ x )

[0056]

[0057] Among them, x l is the lth element in x, θ x,l is θ x The lth element in ;

[0058] but

[0059]

[0060] Step 4: According to the estimated function and p x (x;θ x ) Calculate the intermediate signal

[0061]

[0062] Where I is the identity matrix, It means that the left side of the formula is equal to the right side of the formula;

[0063] Step 5: Calculate the coefficient

[0064]

[0065] Among them, <·> means finding the mean of the elements in the vector, Represents a function Derivative;

[0066] Step 6: Based on the intermediate signal and coefficients Update the first reference power coefficient

[0067]

[0068] Step 7: According to Calculate the second reference power factor

[0069]

[0070] Step 8: According to Calculate intermediate signals

[0071]

[0072] Step 9: According to Calculate intermediate signals

[0073]

[0074] Among them, the superscript H represents the conjugate transpose of the matrix, and the superscript -1 represents the inverse of the matrix.

[0075] Calculated is the estimated x at the tth iteration t ;

[0076] Step 10: Calculate the coefficient

[0077]

[0078] Among them, <·> means finding the mean of the elements in the vector, Represents a function Derivative;

[0079] Then according to the coefficient Update the second reference power coefficient:

[0080]

[0081] in, is the second reference power coefficient;

[0082] Step 11: Based on the intermediate signal estimate and

[0083] Step 12: Calculate the first reference power coefficient and intermediate signal

[0084]

[0085] Step 13: Determine whether the iterative convergence condition is met. The iterative convergence condition is that t=T max Or Δ<σ, T max is the maximum number of iterations set, σ is the minimum update error set, represents the square of the 2-norm;

[0086] If the iterative convergence condition is not met, set t = t + 1 and use and Return to step 4;

[0087] If the iteration convergence condition is reached, the iteration ends and the output is and x t .

[0088] Furthermore, the specific process of step 11 is as follows:

[0089]

[0090] in:

[0091]

[0092] in, represents the real part,

[0093] The following conditions are met:

[0094]

[0095] in,{·} p,q is a matrix The element in the p-th row and q-th column of , |·| means finding the absolute value;

[0096] The final estimated for:

[0097]

[0098] in, is a matrix The nth element on the diagonal, is a matrix The nth element on the diagonal;

[0099] The final estimated for:

[0100]

[0101] in, is a matrix The nth element on the diagonal, is a matrix The nth element on the diagonal;

[0102]

[0103] where tr{·} represents the trace of the matrix.

[0104] Furthermore, the specific process of step five is as follows:

[0105]

[0106] in, is the equivalent channel estimation result in the DD domain.

[0107] The beneficial effects of the present invention are:

[0108] The on-grid matrix and off-grid matrix generated by the first-order partial derivative approximation model of the present invention have non-independent and identically distributed and non-orthogonal characteristics. The first-order partial derivative approximation model is converted into a mathematical model of bilinear estimation, and then the integer delay and integer Doppler are estimated based on the bilinear vector approximation message passing algorithm, and the fractional delay and fractional Doppler are learned. Finally, the off-grid estimation result of the DD domain channel is obtained according to the estimation and learning results. In addition, the use of the first-order partial derivative approximation model can not only improve the accuracy of the equivalent DD domain channel estimation, but also save computational complexity and reduce zero protection to improve spectrum efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 This is a flow chart of a transmitting end of an OTFS system off-network channel estimation method based on bilinear vector approximation message transmission according to the present invention;

[0110] Figure 2 Schematic diagram of the division of DD domain resources among pilot sequence, zero guard sequence, and data sequence;

[0111] Taking the insertion of a single training sequence as an example, the area within the red box is the DD domain resource block used for channel estimation in the received signal;

[0112] Figure 3 The figure is a comparison of the NMSE performance of the present invention and other channel estimation methods at different signal-to-noise ratios (SNRs);

[0113] Figure 4 This is a performance comparison chart between the present invention and other channel estimation methods at different virtual grid densities. DETAILED DESCRIPTION

[0114] Specific implementation method 1: Combination Figure 1 This embodiment describes an off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing, and the method specifically includes the following steps:

[0115] On the sending side

[0116] The signal x[k,l] mapped to the DD domain is converted to the time-frequency domain through the inverse symplectic Fourier transform (ISFFT). is a set of complex numbers. The signal converted to the time-frequency domain is then Heisenberg transformed and the signal obtained by Heisenberg transform is sent to the channel, where k represents the Doppler index and l represents the delay index, k∈{0,...,N-1}, l∈{0,...,M-1}, N represents the total number of Dopplers and M represents the total number of delays.

[0117] The key to the Heisenberg transform is the pulse shaping filter. The present invention adopts an ideal pulse shaping filter with biorthogonal characteristics and uses a rectangular window in the time-frequency domain.

[0118] On the receiving end

[0119] Step 1: Perform Wiener transform on the time domain signal received from the channel, and then perform sigmoid Fourier transform (SFFT) on the signal obtained by Wiener transform to obtain the received signal in DD domain.

[0120] Step 2: perform first-order partial derivative approximation on the received signal in the DD domain to obtain signal y;

[0121] Step 3: Select a resource block from the DD domain and obtain the received signal y for channel estimation based on the selected resource block. T , and receive the signal y T Rewrite as bilinear recovery signal;

[0122] Step 4: Estimate the off-grid coefficient vector and the channel coefficient vector based on the bilinear recovery signal (using a bilinear vector approximation message passing algorithm);

[0123] Step 5: Use the off-grid coefficient vector and the channel coefficient vector estimation results to obtain the equivalent channel estimation result in the DD domain.

[0124] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the received signal y[k, l] in the DD domain is:

[0125]

[0126] Among them, n[k,l] represents complex additive noise, and n[k,l] conforms to the complex Gaussian distribution The variances of both the real and imaginary parts are h w [k′,l′] is the equivalent DD domain channel response, k′∈{0,...,N-1}, l′∈{0,...,M-1}.

[0127] Other steps and parameters are the same as those in the first embodiment.

[0128] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the calculation method of the equivalent DD domain channel response is:

[0129] When the time-varying channel has only a few scattering paths, it can be considered sparse. In this case, the true DD-domain channel response h(v,τ) is:

[0130]

[0131] Among them, h i represents the channel coefficient of the i-th path, P is the maximum number of resolvable paths, δ(·) represents the Dirac function, v i represents the actual Doppler shift of the i-th path, v i ∈(-v max ,v max ), τ i represents the actual delay of the i-th path, τ i ∈(0,τ max ), v max represents the maximum Doppler shift, τ max is the maximum delay, v max and τ max All are experience values;

[0132] Sample h(v,τ) and use a rectangular window in the time-frequency domain to get h w [k,l]:

[0133]

[0134] in, e is the base of natural logarithms, j is the imaginary unit, is to convert τ i The result of mapping to the delay grid, Is v i The result of mapping to the Doppler grid, It is the DD domain representation of the rectangular window in the time-frequency domain;

[0135]

[0136] in:

[0137]

[0138] The calculated h w [k, l] is the equivalent DD domain channel response hw [k′,l′].

[0139] Other steps and parameters are the same as those in the first or second embodiment.

[0140] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the signal y is:

[0141]

[0142] Among them, y is the vectorized form of y[k,l], w is the vectorized form of w[k,l], n is the vectorized form of n[k,l], is the virtual Doppler grid set in the DD domain, N v is the number of virtual Doppler grids, It is a virtual delay grid set up in the DD domain. M τ is the number of virtual delay grids, is the channel coefficient vector, There are only P non-zero values, and P < < M τ N v , In compressed sensing theory it is called the measurement matrix.

[0143] The other steps and parameters are the same as those in the first to third embodiments.

[0144] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the measurement matrix The i-th column of is:

[0145]

[0146] in, is the fractional Doppler of column i, is the fractional delay of column i, is the measurement matrix on the grid The i-th column of and is the off-grid measurement matrix, yes right The first-order partial derivative of yes right The first-order partial derivative of is the off-grid measurement matrix The i-th column of is the off-grid measurement matrix Column i of

[0147] The fractional Doppler of the i-th column for:

[0148]

[0149] in, r v is the Doppler resolution of the virtual grid,

[0150] The fractional delay of the i-th column for:

[0151]

[0152] in, r τ is the delay resolution of the virtual grid,

[0153] The other steps and parameters are the same as those in the first to fourth embodiments.

[0154] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the measurement matrix The kM+lth element in the i-th column of is:

[0155]

[0156] in, is the measurement matrix The kM+lth element in the i-th column of .

[0157] The other steps and parameters are the same as those in the first to fifth embodiments.

[0158] calculate and Only need to Perform partial derivative calculations, where the partial derivatives and Respectively expressed as:

[0159]

[0160] and

[0161]

[0162] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the specific process of step 3 is as follows:

[0163] Step 3.1. Record the position of the training sequence as [k p ,lp ],use Figure 2 The channel estimation is performed on the received sequence in the red box area, and the position range of the selected resource block in the DD domain is recorded as l∈[l p ,l p +l max ] and k∈[-k max +k p ,k p +k max ], the position range of the selected resource block in the DD domain is the determined observation interval;

[0164] Step 3.2: Received signal y for channel estimation within the observation interval T for:

[0165]

[0166] Among them, y T is the signal of y in the observation interval, n T is the noise of n in the observation interval, A0 is In the observation interval, A v yes In the observation interval, A τ yes In the observation interval, and is the off-grid coefficient vector,

[0167] The parameter to be estimated is and And they have the same sparse support, which means that the indices of their non-zero values ​​are the same;

[0168] Step 3. Receive signal y T Rewritten as a bilinear restored signal:

[0169]

[0170] Among them, θ A,0 is the identity matrix, A1=A v , A2=A τ ,

[0171] The other steps and parameters are the same as those in the first to sixth embodiments.

[0172] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the specific process of step four is as follows:

[0173] Step 1: Initialize the signal to be estimated (i.e. bilinear recovery signal), the sparse probability is θ x , the noise power factor is The first reference power coefficient is Off-grid coefficient vector The elements in are all less than Any value of the off-grid coefficient vector The elements in are all less than Any value of

[0174] Step 2: Initialize the number of iterations t=0;

[0175] Step 3: Define x to be independent and identically distributed in Gauss-Bernoulli distribution, that is,

[0176] x l ~p x (x l θ x )

[0177]

[0178] Among them, x l is the lth element in x, θ x,l is θ x The lth element in ;

[0179] but

[0180]

[0181] Step 4: Statistical model Construct a noise reduction estimation function, based on the estimation function and p x (x;θ x ) Calculate the intermediate signal

[0182]

[0183] Where I is the identity matrix, It means that the left side of the formula is equal to the right side of the formula;

[0184] Step 5: Calculate the coefficient

[0185]

[0186] Among them, <·> means finding the mean of the elements in the vector, Represents a function Derivative;

[0187] Step 6: Based on the intermediate signal and coefficients Update the first reference power coefficient

[0188]

[0189] Step 7: According to Calculate the second reference power factor

[0190]

[0191] Step 8: According to Calculate intermediate signals

[0192]

[0193] Step 9: In the posterior probability distribution model Next, through statistical models Construct a linear minimum mean square error estimator; according to Calculate intermediate signals

[0194]

[0195] Among them, the superscript H represents the conjugate transpose of the matrix, and the superscript -1 represents the inverse of the matrix.

[0196] Calculated is the estimated x at the tth iteration t ;

[0197] Step 10: Calculate the coefficient

[0198]

[0199] Among them, <·> means finding the mean of the elements in the vector, Represents a function Derivative;

[0200] Then according to the coefficient Update the second reference power coefficient:

[0201]

[0202] in, is the second reference power coefficient;

[0203] Step 11: Based on the intermediate signal estimate and

[0204] Step 12: Calculate the first reference power coefficient and intermediate signal

[0205]

[0206]

[0207] Step 13: Determine whether the iterative convergence condition is met. The iterative convergence condition is that t=T max Or Δ<σ, T max is the maximum number of iterations set, σ is the minimum update error set, represents the square of the 2-norm;

[0208] If the iterative convergence condition is not met, set t = t + 1 and use and Return to step 4;

[0209] If the iteration convergence condition is reached, the iteration ends and the output is and x t .

[0210] The other steps and parameters are the same as those in the first to seventh embodiments.

[0211] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the specific process of step 11 is as follows:

[0212]

[0213] in:

[0214]

[0215] in, represents the real part,

[0216] The following conditions are met:

[0217]

[0218] in,{·} p,q is a matrix The element in the pth row and qth column of , |·| means to find the absolute value. That is, when When Perform post-processing and use the post-processing results as the final

[0219] The final estimated for:

[0220]

[0221] in, is a matrix The nth element on the diagonal, is a matrix The nth element on the diagonal;

[0222] The final estimated for:

[0223]

[0224] in, is a matrix The nth element on the diagonal, is a matrix The nth element on the diagonal;

[0225]

[0226] where tr{·} represents the trace of the matrix.

[0227] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0228] Specific embodiment 10: This embodiment differs from specific embodiments 1 to 9 in that the specific process of step 5 is as follows:

[0229]

[0230] in, is the equivalent channel estimation result in the DD domain.

[0231] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0232] The present invention proposes to use the Bilinear Vector Approximate Message Passing (Bi-VAMP) algorithm to sparsely estimate integer delay and Doppler shift, and learn fractional delay and fractional Doppler shift respectively. The scalar coefficients of the uncertainty matrix are expanded into vector form, and the first-order approximation model of the effective DD domain channel response is converted into an uncertainty matrix estimation model. Simulation results verify that the Bi-VAMP OTFS off-network channel estimation scheme proposed in this invention shows significant advantages in the normalized mean square error (NMSE) performance indicator compared with other off-network and on-network methods.

[0233] like Figure 3 The figure shows the NMSE performance comparison between the present invention and other channel estimation methods under different signal-to-noise ratios. The resolution of the virtual grid is r v =r τ = 0.5, NMSE is defined as:

[0234]

[0235] like Figure 4 The figure shows the performance comparison of the present invention and other channel estimation methods under different virtual grid densities. The virtual grid density is defined as 1 / r in terms of Doppler and delay. v and 1 / r τ , here r τ The default is 0.5.

[0236] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for estimating off-network channels of an OTFS system based on bilinear vector approximation message passing, characterized in that: The method specifically comprises the following steps: On the sending side The signal x[k, l] mapped to the DD domain is converted to the time-frequency domain by the inverse symplectic Fourier transform. is a set of complex numbers. The signal converted to the time-frequency domain is then Heisenberg transformed and the signal obtained by Heisenberg transform is sent to the channel, where k represents the Doppler index and l represents the delay index, k∈{0,...,N-1}, l∈{0,...,M-1}, N represents the total number of Dopplers and M represents the total number of delays. On the receiving end Step 1: Perform Wiener transform on the time domain signal received from the channel, and then perform sigmoid Fourier transform on the signal obtained by Wiener transform to obtain the received signal in DD domain. Step 2: Approximate the first-order partial derivative of the received signal in the DD domain to obtain the signal y; Step 3: Select a resource block from the DD domain and obtain the received signal y for channel estimation based on the selected resource block. T , and receive the signal y T Rewrite as bilinear recovery signal; Step 4: Estimate the off-grid coefficient vector and the channel coefficient vector based on the bilinear recovery signal; Step 5: Use the off-grid coefficient vector and the channel coefficient vector estimation results to obtain the equivalent channel estimation result in the DD domain.

2. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 1, characterized in that: The received signal y[k, l] in the DD domain is: Among them, n[k, l] represents complex additive noise, and n[k, l] conforms to the complex Gaussian distribution. The variances of both the real and imaginary parts are h w [k′, l′] is the equivalent DD domain channel response, k′∈{0,...,N-1}, l′∈{0,...,M-1}.

3. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 2, characterized in that: The calculation method of the equivalent DD domain channel response is: The actual DD domain channel response h(v, τ) is: Among them, h i represents the channel coefficient of the i-th path, P is the number of paths, δ(·) represents the Dirac function, v i represents the actual Doppler shift of the i-th path, ν i ∈(-v max , v max ), τ i represents the actual delay of the i-th path, τ i ∈(0, τ max ), v max represents the maximum Doppler shift, τ max is the maximum delay; Sample h(v, τ) and use a rectangular window in the time-frequency domain to obtain h w [k, l]: in, e is the base of natural logarithms, j is the imaginary unit, is to convert τ i The result of mapping to the delay grid, Is v i The result of mapping to the Doppler grid, It is the DD domain representation of the rectangular window in the time-frequency domain; in: The calculated h w [k, l] is the equivalent DD domain channel response H w [k′, l′].

4. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 3, characterized in that: The signal y is: Where y is the vectorized form of y[k, l], n is the vectorized form of n[k, l], is the virtual Doppler grid set in the DD domain, N v is the number of virtual Doppler grids, It is a virtual delay grid set up in the DD domain. M τ is the number of virtual delay grids, is the channel coefficient vector, is the measurement matrix.

5. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 4, characterized in that: The measurement matrix The i-th column of is: in, is the fractional Doppler of column i, is the fractional delay of column i, is the measurement matrix on the grid The i-th column of and is the off-grid measurement matrix, yes right The first-order partial derivative of yes right The first-order partial derivative of is the off-grid measurement matrix The i-th column of is the off-grid measurement matrix The i-th column of The fractional Doppler of the i-th column for: in, r v is the Doppler resolution of the virtual grid, The fractional delay of the i-th column for: in, r τ is the delay resolution of the virtual grid, 6. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 5, characterized in that: The measurement matrix The kM+lth element in the i-th column of is: in, is the measurement matrix The kM+lth element in the i-th column of .

7. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 6, characterized in that: The specific process of step three is: Step 3.

1. Record the position of the training sequence as [k p , l p ], the position range of the selected resource block in the DD domain is recorded as l∈[l p , l p +l max ] and k∈[-k max +k p , k p +k max ], the position range of the selected resource block in the DD domain is the determined observation interval; Step 3.2: Received signal y for channel estimation within the observation interval T for: Among them, y T is the signal of y in the observation interval, n T is the noise of n in the observation interval, A0 is In the observation interval, A v yes In the observation interval, Aτ is In the observation interval, and is the off-grid coefficient vector, Step 3. Receive signal y T Rewritten as a bilinear restored signal: Among them, θ A，0 is the identity matrix, A1=A v , A2=A τ , 8. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 7, characterized in that: The specific process of step 4 is as follows: Step 1: Initialize the signal to be estimated The sparse probability is θ x , the noise power factor is The first reference power coefficient is Off-grid coefficient vector The elements in are all less than Any value of the off-grid coefficient vector The elements in are all less than Any value of Step 2: Initialize the number of iterations t=0; Step 3: Define x to be independent and identically distributed in Gauss-Bernoulli distribution, that is, x l ~p x (x l ;θ x ) Among them, x l is the lth element in x, θ x，l is θ x The lth element in ; but Step 4: According to the estimated function and p x (x;θ x ) Calculate the intermediate signal Where I is the identity matrix, It means that the left side of the formula is equal to the right side of the formula; Step 5: Calculate the coefficient Among them, <·> means finding the mean of the elements in the vector, Represents a function Derivative; Step 6: Based on the intermediate signal and coefficients Update the first reference power coefficient Step 7: According to Calculate the second reference power factor Step 8: According to Calculate intermediate signals Step 9: According to Calculate intermediate signals Among them, the superscript H represents the conjugate transpose of the matrix, and the superscript -1 represents the inverse of the matrix. Calculated is the estimated x at the tth iteration t ; Step 10: Calculate the coefficient Among them, <·> means finding the mean of the elements in the vector, Represents a function Derivative; then according to the coefficient Update the second reference power coefficient: in, is the second reference power coefficient; Step 11: Based on the intermediate signal estimate and Step 12: Calculate the first reference power coefficient and intermediate signal Step 13: Determine whether the iterative convergence condition is met. The iterative convergence condition is that t=T max Or Δ<σ, T max is the maximum number of iterations set, σ is the minimum update error set, represents the square of the 2-norm; If the iterative convergence condition is not met, set t = t + 1 and use and Return to step 4; If the iteration convergence condition is reached, the iteration ends and the output is and x t .

9. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 8, characterized in that: The specific process of step 11 is as follows: in: in, represents the real part, The following conditions are met: in,{·} p，q is a matrix The element in the p-th row and q-th column of , |·| means finding the absolute value; The final estimated for: in, is a matrix The nth element on the diagonal, is a matrix The nth element on the diagonal; The final estimated for: in, is a matrix The nth element on the diagonal, is a matrix The nth element on the diagonal; where tr{·} represents the trace of the matrix.

10. The off-network channel estimation method for an OTFS system based on bilinear vector approximation message passing according to claim 9, characterized in that: The specific process of step five is: in, is the equivalent channel estimation result in the DD domain.

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