Method and system for estimating multichannel underwater acoustic channels of MIMO-OTFS system based on 3D-SOMP

Abstract

The invention discloses an MIMO-OTFS system multichannel underwater acoustic channel estimation method based on a 3D-SOMP algorithm, and the method comprises the following steps: intercepting a received signal from an underwater acoustic channel, extracting a pilot signal, and generating a sensing matrix meeting the limited equidistant characteristic according to the pilot signal; calculating a residual error measurement value and obtaining a correlation vector of the residual error measurement value and the sensing matrix, and rearranging the correlation vector into a tensor by using a 3D-SOMP algorithm; expanding the tensor along a time delay dimension, calculating a two-norm of the tensor, and solving a maximum value of an obtained correlation vector along the time delay dimension to obtain a time delay dimension support set of the ith dominant path; and fixing the time delay dimension support set, performing Doppler calculation according to the fixed time delay support set to obtain a Doppler dimension support set and an angle dimension support set, and estimating a channel vector by using the three support sets. According to the method, the calculation complexity in a channel calculation process can be greatly reduced while a relatively accurate underwater acoustic channel estimation result can be achieved with relatively low pilot frequency overhead.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic communication, and in particular relates to a method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm. Background Art

[0002] Underwater acoustic communication is currently the only way to achieve long-distance, high-speed data communication underwater. Underwater acoustic channels have the characteristics of fast time-varying, large delay spread, severe Doppler effect, and limited available bandwidth. If the underwater acoustic channel cannot be accurately estimated, the reliability of communication will be affected. Therefore, accurate estimation of the underwater acoustic channel is particularly important. However, traditional time-varying underwater acoustic channel estimation has problems such as high computational complexity and large pilot overhead, and has certain limitations in practical use. Summary of the invention

[0003] Purpose of the invention: In order to solve the problems of high complexity and huge pilot overhead in the current time-varying underwater acoustic channel estimation, the sparse characteristics of the underwater acoustic channel are utilized to reduce the estimation dimension of the underwater acoustic time-varying channel and reduce the pilot overhead. The present invention proposes a multi-channel underwater acoustic channel estimation method for an underwater MIMO-OTFS system based on a 3D-SOMP algorithm.

[0004] Technical solution: A method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm, comprising the following steps:

[0005] Step 1: intercept the receiving signal from the underwater acoustic channel, extract the pilot signal from the intercepted receiving signal, and generate a perception matrix that satisfies the finite equidistance characteristic RIP according to the pilot signal;

[0006] Step 2: Calculate the residual measurement value and obtain the correlation vector between the residual measurement value and the perception matrix, and rearrange the correlation vector into a tensor using the 3D-SOMP algorithm;

[0007] Step 3: Expand the tensor along the delay dimension and calculate the l2 norm of the tensor, find the maximum value of the related vector along the delay dimension, and obtain the delay dimension support set of the i-th dominant path;

[0008] Step 4: Fix the delay dimension support set, perform Doppler calculation based on the fixed delay support set, obtain the Doppler dimension support set and the angle dimension support set, and use the delay dimension support set, the Doppler dimension support set and the angle dimension support set combined with the channel estimation formula to estimate the channel vector.

[0009] Furthermore, step 1 specifically includes: according to equations (1) to (3), calculating the perception matrix:

[0010]

[0011] y=Φx=ΦΨθ=Aθ (2)

[0012] A=ΦΨ (3)

[0013] Where x represents the signal, the signal length is N, Ψ is the orthogonal basis of the signal ψ=[ψ1,ψ2,…,ψ N ],ψ i is a column vector of N*1 dimensions, θ i is the weighting coefficient, y is the channel after sampling by the observation matrix Φ, with a size of M*1, Φ has a size of M*N, A is the perception matrix, and its size is M*N; if the column vector θ satisfies ||θ||0=K0N, that is, there are a large number of zero values ​​in the column vector θ, and the number of non-zero elements K is much smaller than N, then the signal x is called a strictly K-sparse signal with Ψ as the sparse basis.

[0014] Furthermore, the step 2 comprises:

[0015] According to equations (4) to (6), the relevant vectors are rearranged into a tensor:

[0016] r=yA H h(0) (4)

[0017] e=A H r (5)

[0018]

[0019] Where r is the calculated residual measurement value, assuming that the initial channel estimation value is 0, that is, h(0) = 0, e is the correlation vector between the residual measurement value r and the perception matrix A, ε is the tensor rearranged from the correlation vector e, M g is the number of protection intervals in the delay dimension, N g is the number of Doppler dimension protection intervals, N t is the number of transmitting array elements, E (1) 、E (2) are the matrices of the tensor ε expanded along the first and second dimensions respectively, and H represents the conjugate transpose.

[0020] Furthermore, the step 3 includes: according to equations (7) to (8), the delay dimension support set of the i-th dominant path is calculated:

[0021] e τ (m)=||E (1) (m,:)|| (7)

[0022]

[0023] In the formula, e τ is the correlation vector along the time delay dimension, for E (1) The operation performed is to calculate the l2 norm of the matrix and find its maximum value. is the delay dimension support set of the ith dominant path, m is the row number, and (m,:) means selecting all columns of the matrix in the mth row.

[0024] Furthermore, in step 4, the delay dimension support set is fixed, and Doppler calculation is performed according to the fixed delay support set to obtain the Doppler dimension support set and the angle dimension support set, including:

[0025]

[0026]

[0027] Among them, formula (9) is a function constructed by Doppler calculation based on a fixed delay support set, formula (10) calculates the Doppler dimension support set, formula (11) calculates the angle dimension support set, and formula (12) calculates the three-dimensional support set of the channel through the three-dimensional support sets of delay dimension, Doppler dimension, and angle dimension; where e v (n) is the letter that sets the minimum block function for the delay dimension support set obtained by formula (8), n is the row number, and (n,:) means selecting all columns of the matrix in the nth row. represents the Doppler dimension support set of the ith dominant path of the channel, N g represents the number of discrete points in the Doppler dimension, represents the width of the support range in the Doppler dimension and is calculated from the center point N g / 2 and extend to both sides; represents the angle dimension support set of the i-th dominant path of the channel, p s represents the starting point of the channel angle dimension support set, D represents the width (size) of the angle dimension support set, Ω represents the global support set, ∪ Represents the union operation of sets.

[0028] Furthermore, the estimating the channel vector by combining the channel estimation formula in step 4 includes:

[0029] The channel estimation formula is shown in formula (13):

[0030]

[0031] In the formula, h(i)| Ω is the value of the channel estimate h(i) on the global support set Ω, is the Moore-Penrose generalized inverse, y represents the received signal, Ω cis the complement of the global support set Ω, is the complement Ω of the channel estimate h(i) in the global support set c The value on

[0032] After formula (13), r = y-Ah(i), where h(i) is the channel estimation value of the i-th dominant path; compare i with the maximum number of iterations preset in advance. If it is greater than, the step is terminated, and the output is the estimated channel vector obtained by calculating the residual value r and iteratively updating it multiple times.

[0033] A multi-channel underwater acoustic channel estimation system for a MIMO-OTFS system based on a 3D-SOMP algorithm, comprising a sensing matrix generation module, a 3D-SOMP algorithm module, a multi-dimensional support set module, and a channel vector estimation module;

[0034] The sensing matrix generation module intercepts a receiving signal from the underwater acoustic channel, extracts a pilot signal from the intercepted receiving signal, and generates a sensing matrix satisfying the finite equidistance characteristic RIP according to the pilot signal;

[0035] The 3D-SOMP algorithm module calculates the residual measurement value and obtains the correlation vector between the residual measurement value and the perception matrix, and rearranges the correlation vector into a tensor using the 3D-SOMP algorithm;

[0036] The multi-dimensional support set module expands the tensor along the delay dimension and calculates the l2 norm of the tensor, maximizes the obtained related vector along the delay dimension, and obtains the delay dimension support set of the i-th dominant path; fixes the delay dimension support set, performs Doppler calculation based on the fixed delay support set, and obtains the Doppler dimension support set and the angle dimension support set.

[0037] The channel vector estimation module estimates the channel vector by using the delay dimension support set, the Doppler dimension support set and the angle dimension support set in combination with the channel estimation formula.

[0038] Beneficial effects: The present invention uses known channels in the MIMO-OTFS communication system to estimate the time-varying channel, generates a transmission signal for MIMO-OTFS communication, and incorporates pilot data into the transmission signal. Then, a perception matrix is ​​generated using the pilot data. The 3D-SOMP technology is used to gradually determine the support sets of the three dimensions of delay, Doppler, and angle, and the support set selects data in the perception matrix that is relevant to the time-varying channel to finally estimate the underwater acoustic channel. The present invention estimates the characteristic parameters of the three-dimensional underwater acoustic channel from multiple dimensions in sequence, thereby reconstructing the underwater acoustic channel, and when reconstructing the underwater acoustic channel under the MIMO technology, a relatively accurate underwater acoustic channel estimation result can be achieved with a lower pilot overhead while greatly reducing the computational complexity in the channel calculation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is the system model block diagram of the present invention;

[0040] Figure 2 is the system flow chart of the process experienced when calculating the sensing matrix A;

[0041] Figure 3 is the block diagram of the MIMO-OTFS communication system;

[0042] Figure 4 is the flow chart of the 3D-SOMP algorithm;

[0043] Figure 5 is the structure diagram of an OTFS frame in time-delay Doppler. Detailed implementation manners

[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0045] As Figure 1 shown, the present invention provides a technical solution:

[0046] A multi-channel underwater acoustic channel estimation method for a MIMO-OTFS system based on the 3D-SOMP algorithm mainly includes the following steps:

[0047] Step 1: In the time-delay Doppler (DD) domain, there is a signal x with a length of N. Denote the orthogonal basis Ψ = [ψ1, ψ2,..., ψ N . The signal x can be represented by the orthogonal basis Ψ through a certain linear combination method, that is, formula (1):

[0048]

[0049] where ψ i is an N×1 column vector, θ i is the weighting coefficient, Then, Ψ is called the dictionary matrix. If the number of atoms in Ψ is greater than the dimension of x, then Ψ is called an over-complete dictionary. On the other hand, if θ satisfies ||θ||0 = K << N, that is, there are a large number of zero values in the column vector θ, and the number of non-zero elements K is much smaller than N, then the signal x is called a strictly K-sparse signal with Ψ as the sparse basis.

[0050] In the theory of compressive sensing, the sampling of sparse signals does not need to follow the Nyquist law, but is sampled through the matrix Φ. The matrix Φ is called the observation matrix, and the sampling formula is as follows:

[0051] y = Φx = ΦΨθ = Aθ (2)

[0052] Among them, y is the sampled signal with a size of M×1, x is the sparse signal with a size of N×1, Φ is the observation matrix with a size of M×N. Since most signals in practical applications are non-sparse, it is necessary to convert non-sparse signals. Assume there is a non-sparse signal x. Substituting formula (1) into formula (2) gives

[0053] A = ΦΨ (3)

[0054] Among them, A is called the sensing matrix with a size of M×N. The mathematical model is as Figure 2 shown, Figure 2 where the white color blocks represent zero values, and the other color blocks represent non-zero values.

[0055] In formula (2), the dimension M < N, so the solution of the equation system is not unique. However, the present invention needs to use the compressive sensing algorithm (cs) to select a solution from infinitely many solutions. That is, to reconstruct the sparse signal θ in y with a size of M×1, this requires the sparse signal θ to satisfy the conditions:

[0056] One is that the signal is a strictly K-sparse signal, and the other is that the larger non-zero value K needs to satisfy the condition K << N. At the same time, the sensing matrix A needs to satisfy the restricted isometry property (abbreviation RIP), and the definition of RIP is that for any strictly K-sparse signal θ, there is a constant δ k (0, 1) that satisfies the formula

[0057]

[0058] At this time, the matrix A satisfies the K-order RIP property, and δ k is the K-order RIP constant of the matrix A.

[0059] In practical applications, it is difficult to directly construct the observation matrix to achieve this. Therefore, formulas (1) and (2) will be used, and the determinacy of the sparse basis Ψ will be used to design the observation matrix so that the sensing matrix A satisfies the relevant RIP conditions, such as the commonly used observation matrices today, Gaussian matrices, chaotic matrices, and so on.

[0060] Step 2: Assume in the Figure 3 shown MIMO-OTFS communication system. Without loss of generality, for a certain receiving end, there are N p multipath components from the transmitting end to the receiving end. Each multipath component has N s sub-paths. In the s i th sub-path of the i th multipath component, there is a complex path gain and Doppler frequency shift iThe emission angle (Angle of Departure, AoD) of each subpath is Then in the uniform linear array Relevant spatial angle It can be defined as:

[0061]

[0062] Where d is the array element spacing and λ is the wavelength of the carrier frequency. Assuming that the initial estimated value of the channel is 0, that is, h(0) = 0, then the residual measurement value is recorded as r = yA H h(0), residual measure r The correlation vector between the perception matrix A e Denoted as:

[0063] e=A H r (5)

[0064] In the traditional OMP algorithm, we can find e The maximum value in determines which column in the perception matrix A has a support set for channel h. In the 3D-SOMP algorithm, in order to utilize the three-dimensional structured sparse characteristics of the channel, the relevant vector e , rearranged into a tensor That is, ε=invec{e}where M g is the number of protection intervals in the delay dimension, N g is the number of Doppler dimension protection intervals, N t is the number of transmitting array elements. In the delay-Doppler dimension, an OTFS frame structure is as follows: Figure 5 shown.

[0065] For ease of expression, let E (n) is the matrix of the tensor ε expanded along the nth dimension, such as E (1) 、E (2) The size of

[0066] Step 3: In the 3D-SOMP algorithm, the support sets of different channel dimensions need to be calculated one by one. First, the support set along the delay dimension is calculated, and the tensor ε is expanded along the delay dimension to obtain E (1) , calculate its second norm, and then get the correlation vector e along the delay dimension τ , whose size is M g ×1, the specific formula is:

[0067] e τ (m)=||E (1) (m,:)|| (7)

[0068] Then find its maximum value and get the delay support set of the i-th dominant path:

[0069]

[0070] Step 4: After obtaining the delay support set of the ith dominant path, the Doppler is calculated by fixing the delay support set. The constructor is shown in formula (9):

[0071]

[0072] Since the channel has a block-sparse characteristic in the Doppler dimension and there is only one non-zero block centered at v = 0, but the length of the non-zero region is unknown, when solving the Doppler support set, the minimum block of equation (9) is used for calculation, and the l2 norm of the minimum block is equal to e n The ratio of the l2 norm should be greater than a threshold ∈, that is, the following formula:

[0073]

[0074] The support formula for calculating the Doppler dimension should be as follows:

[0075]

[0076] Then, the support of the fixed delay dimension and the Doppler dimension obtained from the above formula is used to calculate the support of the angle, which needs to satisfy the following formula:

[0077]

[0078] d θ =L H e θ (13)

[0079] Conjugate transpose the energy estimate in the angle dimension related to the time-frequency dimension support set, the Doppler dimension support set and the parameter, e θ Based on the conjugate transpose of matrix L, a projection operation is performed to obtain a new signal d θ , L can be an array response matrix related to the array arrangement or angle.

[0080] Then do g θ (r)=||D θ (r,:)||, extract the angle feature corresponding to the rth path in the matrix and calculate the second norm.

[0081] Then do the formula P s = argmax r g θ (r), that is, find the value of the rth value obtained from the above formula and make it reach the maximum value and assign the maximum index value to P s ,

[0082] Then use the following formula to calculate the support set of the angle dimension Obtain the above three support sets (delay dimension, Doppler dimension, angle dimension) to calculate the three-dimensional support set of the channel

[0083] The final channel estimation formula is as follows:

[0084]

[0085] After the above formula, r=y-Ah(i), h(i) is the channel estimation value of the i-th dominant path; compare i with the maximum number of iterations preset in advance. If it is greater than, the step is terminated, and the output is the estimated channel vector obtained by calculating the residual value r and iteratively updating it multiple times.

Claims

1. A method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm, characterized in that: The following steps are involved: Step 1: intercept the receiving signal from the underwater acoustic channel, extract the pilot signal from the intercepted receiving signal, and generate a perception matrix that satisfies the finite equidistance characteristic RIP according to the pilot signal; Step 2: Calculate the residual measurement value and obtain the correlation vector between the residual measurement value and the perception matrix, and rearrange the correlation vector into a tensor using the 3D-SOMP algorithm; Step 3: Expand the tensor along the delay dimension and calculate the l2 norm of the tensor, find the maximum value of the related vector along the delay dimension, and obtain the delay dimension support set of the i-th dominant path; Step 4: Fix the delay dimension support set, perform Doppler calculation based on the fixed delay support set, obtain the Doppler dimension support set and the angle dimension support set, and use the delay dimension support set, the Doppler dimension support set and the angle dimension support set combined with the channel estimation formula to estimate the channel vector.

2. According to claim 1, a method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm, characterized in that: Step 1 specifically includes: according to equations (1) to (3), calculating the perception matrix: y=Φx=ΦΨθ=Aθ (2) A=ΦΨ (3) Where x represents the signal, the signal length is N, Ψ is the orthogonal basis of the signal ψ=[ψ1,ψ2,…,ψ N ],ψ i is a column vector of N*1 dimension, θ i is the weighting coefficient, y is the channel after sampling by the observation matrix Φ, with a size of M*1, Φ has a size of M*N, A is the perception matrix, and its size is M*N; if the column vector θ satisfies ||θ||0=K0N, that is, there are a large number of zero values ​​in the column vector θ, and the number of non-zero elements K is much smaller than N, then the signal x is called a strictly K-sparse signal with Ψ as the sparse basis.

3. According to claim 2, a method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm, characterized in that: The step 2 comprises: According to equations (4) to (6), the relevant vectors are rearranged into a tensor: r=y-A H h(0) (4) e=A H r (5) Where r is the calculated residual measurement value, assuming that the initial channel estimation value is 0, that is, h(0) = 0, e is the correlation vector between the residual measurement value r and the perception matrix A, ε is the tensor rearranged from the correlation vector e, M g is the number of protection intervals in the delay dimension, N g is the number of Doppler dimension protection intervals, N t is the number of transmitting array elements, E (1) 、E (2) are the matrices of the tensor ε expanded along the first and second dimensions respectively, and H represents the conjugate transpose.

4. According to claim 3, a method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm, characterized in that: The step 3 includes: according to equations (7) to (8), the delay dimension support set of the i-th dominant path is calculated have been τ (m)=||E (1) (m,:)|| (7) In the formula, e τ is the correlation vector along the time delay dimension, for E (1) The operation performed is to calculate the l2 norm of the matrix and find its maximum value. is the delay dimension support set of the ith dominant path, m is the row number, and (m,:) means selecting all columns of the matrix in the mth row.

5. According to claim 4, a method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm is characterized in that: In step 4, the delay dimension support set is fixed, and Doppler calculation is performed according to the fixed delay support set to obtain the Doppler dimension support set and the angle dimension support set, including: Among them, formula (9) is a function constructed by Doppler calculation based on a fixed delay support set, formula (10) calculates the Doppler dimension support set, formula (11) calculates the angle dimension support set, and formula (12) calculates the three-dimensional support set of the channel through the three-dimensional support sets of delay dimension, Doppler dimension, and angle dimension; where e v (n) is the letter that sets the minimum block function for the delay dimension support set obtained by formula (8), n is the row number, and (n,:) means selecting all columns of the matrix in the nth row. represents the Doppler dimension support set of the ith dominant path of the channel, N g represents the number of discrete points in the Doppler dimension, represents the width of the support range in the Doppler dimension and is calculated from the center point N g / 2 and extend to both sides; represents the angle dimension support set of the i-th dominant path of the channel, p s represents the starting point of the channel angle dimension support set, D represents the width of the angle dimension support set, Ω represents the global support set, ∪ Represents the union operation of sets.

6. The method for estimating multi-channel underwater acoustic channels of a MIMO-OTFS system based on a 3D-SOMP algorithm according to claim 5, characterized in that: The step 4 of estimating the channel vector by combining the channel estimation formula includes: The channel estimation formula is shown in formula (13): In the formula, h(i)| Ω is the value of the channel estimate h(i) on the global support set Ω, is the Moore-Penrose generalized inverse, y represents the received signal, Ω c is the complement of the global support set Ω, is the complement Ω of the channel estimate h(i) in the global support set c The value on After formula (13), r = y-Ah(i), where h(i) is the channel estimation value of the i-th dominant path; compare i with the maximum number of iterations preset in advance. If it is greater than, the step is terminated, and the output is the estimated channel vector obtained by calculating the residual value r and iteratively updating it multiple times.

7. A multi-channel underwater acoustic channel estimation system for a MIMO-OTFS system based on a 3D-SOMP algorithm, characterized in that: It includes perception matrix generation module, 3D-SOMP algorithm module, multi-dimensional support set module, and channel vector estimation module; The sensing matrix generation module intercepts a receiving signal from the underwater acoustic channel, extracts a pilot signal from the intercepted receiving signal, and generates a sensing matrix satisfying the finite equidistance characteristic RIP according to the pilot signal; The 3D-SOMP algorithm module calculates the residual measurement value and obtains the correlation vector between the residual measurement value and the perception matrix, and rearranges the correlation vector into a tensor using the 3D-SOMP algorithm; The multi-dimensional support set module expands the tensor along the delay dimension and calculates the l2 norm of the tensor, maximizes the obtained related vector along the delay dimension, and obtains the delay dimension support set of the i-th dominant path; fixes the delay dimension support set, performs Doppler calculation based on the fixed delay support set, and obtains the Doppler dimension support set and the angle dimension support set. The channel vector estimation module estimates the channel vector by using the delay dimension support set, the Doppler dimension support set and the angle dimension support set in combination with the channel estimation formula.

8. The multi-channel underwater acoustic channel estimation system of a MIMO-OTFS system based on a 3D-SOMP algorithm according to claim 7, characterized in that: The perception matrix generation module calculates the perception matrix according to equations (1) to (3): y=Φx=ΦΨθ=Aθ (2) A=ΦΨ (3) Where x represents the signal, the signal length is N, Ψ is the orthogonal basis of the signal ψ=[ψ1,ψ2,…,ψ N ],ψ i is a column vector of N*1 dimension, θ i is the weighting coefficient, y is the channel after sampling by the observation matrix Φ, with a size of M*1, Φ has a size of M*N, A is the perception matrix, and its size is M*N; if the column vector θ satisfies ||θ||0=K0N, that is, there are a large number of zero values ​​in the column vector θ, and the number of non-zero elements K is much smaller than N, then the signal x is called a strictly K-sparse signal with Ψ as the sparse basis.

9. The MIMO-OTFS system multi-channel underwater acoustic channel estimation system based on 3D-SOMP algorithm according to claim 8, characterized in that: The 3D-SOMP algorithm module calculates the tensor by rearranging the relevant vectors according to equations (4) to (6): r=y-A H h(0) (4) e=A H r (5) Where r is the calculated residual measurement value, assuming that the initial channel estimation value is 0, that is, h(0) = 0, e is the correlation vector between the residual measurement value r and the perception matrix A, ε is the tensor rearranged from the correlation vector e, M g is the number of protection intervals in the delay dimension, N g is the number of Doppler dimension protection intervals, N t is the number of transmitting array elements, E (1) 、E (2) are the matrices of the tensor ε expanded along the first and second dimensions respectively, and H represents the conjugate transpose.

10. The multi-channel underwater acoustic channel estimation system of a MIMO-OTFS system based on a 3D-SOMP algorithm according to claim 9, characterized in that: The multi-dimensional support set module calculates the delay dimension support set of the i-th dominant path according to equations (7) to (8): have been τ (m)=||E (1) (m,:)|| (7) In the formula, e τ is the correlation vector along the time delay dimension, for E (1) The operation performed is to calculate the l2 norm of the matrix and find its maximum value. is the delay dimension support set of the ith dominant path, m is the row number, and (m,:) means selecting all columns of the matrix in the mth row; The delay dimension support set is fixed, and Doppler calculation is performed based on the fixed delay support set to obtain the Doppler dimension support set and the angle dimension support set, including: Among them, formula (9) is a function constructed by Doppler calculation based on a fixed delay support set, formula (10) calculates the Doppler dimension support set, formula (11) calculates the angle dimension support set, and formula (12) calculates the three-dimensional support set of the channel through the three-dimensional support sets of delay dimension, Doppler dimension, and angle dimension; where e v (n) is the letter that sets the minimum block function for the delay dimension support set obtained by formula (8), n is the row number, and (n,:) means selecting all columns of the matrix in the nth row. represents the Doppler dimension support set of the ith dominant path of the channel, N g represents the number of discrete points in the Doppler dimension, represents the width of the support range in the Doppler dimension and is calculated from the center point N g / 2 and extend to both sides; represents the angle dimension support set of the i-th dominant path of the channel, p s represents the starting point of the channel angle dimension support set, D represents the width of the angle dimension support set, Ω represents the global support set, and ∪ represents the union operation of the set.

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