A joint estimation method for multi-target position and velocity in terahertz near-field MIMO-OFDM

Abstract

The present invention provides a terahertz near-field MIMO-OFDM multi-target position and velocity joint estimation method, including a terahertz near-field MIMO-OFDM model establishment step: establishing a near-field MIMO-OFDM signal model, representing the received signal in the near-field MIMO-OFDM signal model as a third-order tensor; a tensor decomposition step: decomposing the received signal tensor, and based on the uniqueness of the tensor decomposition, using the factor matrix after the tensor decomposition to estimate the estimated value of the intermediate parameter; a parameter preliminary estimation step: using the estimated value of the intermediate parameter and the least squares LS algorithm to obtain a preliminary solution to the iterative initial point to establish an optimization equation; a precise positioning and velocity estimation step: performing a Taylor expansion on the nonlinear term of the optimization equation at the initial point to perform a second-order Taylor approximation, converting the optimization equation into a convex optimization equation, and using the cvx toolbox to iteratively solve the convex optimization equation to obtain the estimated value of the target position and velocity. The present invention improves the accuracy of target parameter estimation by jointly processing the inter-antenna phase difference and the inter-subcarrier phase difference through tensor decomposition.

Description

Background Art

[0001] The rapidly growing demand for wireless services is driving wireless technology toward higher frequencies in pursuit of greater bandwidth. Therefore, terahertz (THz) wireless communications, ranging from 0.1THz to 10THz, are considered a crucial technology for future wireless communications. At the same time, the increasing frequency of wireless communications is leading to a gradual overlap between the communication and radar bands. Faced with limited spectrum resources, integrating previously separate communication and radar systems to achieve integrated communication and perception (ISAC) can improve spectrum efficiency and hardware resources. In particular, THz offers spectrum resources in the hundreds or even thousands of GHz, enabling high communication capacity and high-precision perception. Therefore, research on THz communication and perception integration is a highly sought-after topic.

[0002] Due to the high frequency of terahertz, the traditional far-field model is no longer applicable, and a more accurate near-field spherical wave model is needed. In addition, high frequency means high attenuation, so multiple antennas are needed to increase the gain. To ensure that there is no positioning ambiguity, the antenna spacing usually needs to be controlled within half a wavelength. The coupling between antennas caused by too small antenna spacing will affect the perception accuracy. In terms of integrated waveforms, simpler radar waveforms are difficult to embed information bits. If the OFDM waveform commonly used in wireless communications uses a near-field spherical model, the phase difference between antennas is not only related to the azimuth angle but also to the distance between the antenna array and the target, resulting in a significant increase in the complexity of parameter estimation during perception. In summary, there are still the following problems that need to be solved:

[0003] 1. The high frequency of terahertz makes the far-field plane wave model no longer applicable. In the case of dual-array MIMO active sensing, it is necessary to establish an accurate terahertz MIMO-OFDM near-field spherical wave model.

[0004] 2. Terahertz attenuation is large, and multiple antennas are needed to increase gain. It is necessary to study how to reduce the number of antennas and increase the antenna spacing to avoid coupling without causing position ambiguity or reducing the aperture of the antenna array.

[0005] 3. The use of OFDM waveforms in the near-field model will significantly increase the complexity of perception parameter estimation. Further research is needed to improve perception accuracy while reducing algorithm complexity.

[0006] Many perception models are based on the far-field assumption. Researchers have used a second-order Taylor expansion based on a near-field spherical model to approximate the near-field signal model and reduce model complexity. Research on perception based on the near-field spherical wave model and the OFDM waveform commonly used in communications has led to a study estimating target parameters by directly performing maximum likelihood grid search on near-field OFDM multidimensional data. Podkurkov et al. (2018) leveraged the advantages of tensors in processing multidimensional data to jointly estimate target parameters using tensor decomposition and a least-squares algorithm.

[0007] However, applying a second-order Taylor approximation to the near-field spherical wave model introduces systematic errors, affecting parameter estimation accuracy. Directly applying maximum likelihood estimation to multidimensional data results in an algorithm with excessive computational complexity. Podkurkov et al. estimated target position parameters solely using near-field characteristics. However, as the target moves away from the array, the near-field characteristics weaken, resulting in reduced target positioning performance. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method for jointly estimating the position and velocity of multiple targets in terahertz near-field MIMO-OFDM with lower complexity and higher accuracy.

[0009] The technical solution adopted by the present invention to solve the above technical problems is a method for jointly estimating the position and velocity of multiple targets using terahertz near-field MIMO-OFDM, comprising the following steps:

[0010] The steps of establishing the terahertz near-field MIMO-OFDM model are as follows: establishing a near-field MIMO-OFDM signal model and expressing the received signal in the near-field MIMO-OFDM signal model as a third-order tensor;

[0011] The near-field MIMO-OFDM signal model is:

[0012]

[0013] in, Indicates that from The first transmitting antenna to the The received signal of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the root receiving antenna, For u t The group transmits the subarray to the uth r The speed of the lth target in the propagation direction of the group receiving subarray, Indicates the The first transmitting antenna Additive white Gaussian noise of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the receiving antenna; Indicates the Transmitting antenna to The median value of the lth target in the propagation direction of the receiving antenna, β l is the intermediate value of the lth target; Δf is the subcarrier spacing, is the signal propagation delay of the lth target in the propagation direction from the center of the transmitting array to the center of the receiving array, T0 is the duration of a single FO-OFDM signal, f c is the carrier frequency, c is the speed of light;

[0014]

[0015] Among them, α l is the reflection coefficient of the lth target, For the The modulation symbol of the nth subcarrier of the root transmitting antenna at the pth FO-OFDM symbol index, K is a preset value that makes the signals of each transmitting antenna non-intersecting in the frequency domain, For the lth target in the The propagation distance difference between the root transmitting antenna and the center of the transmitting array, For the lth target in the The propagation distance difference between the root receiving antenna and the center of the receiving array, τ l is the signal propagation delay of the lth target;

[0016] Tensor decomposition step: Decompose the received signal tensor, and based on the uniqueness of the tensor decomposition, use the factor matrix after tensor decomposition to estimate the estimated value of the intermediate parameters, which include and

[0017] Parameter preliminary estimation step: Use the estimated value of the intermediate parameter and the least squares LS algorithm to obtain the initial solution of the coordinate value x of the lth target relative to the origin on the x-axis l The initial value of And the signal propagation path distance from the lth target to the center antenna of the receiving array The initial value of according to and The geometric relationship between them is used to solve the azimuth angle θ of the lth target relative to the center antenna of the receiving array. l Estimated value of Using Parameters Represents x l and The initial point of the iteration and And establish the optimization equation;

[0018] Precise positioning and velocity estimation steps: Perform Taylor expansion on the nonlinear term of the optimization equation at the initial point to perform second-order Taylor approximation, transform the optimization equation into a convex optimization equation, and use the cvx toolbox to iteratively solve the convex optimization equation to obtain x l and Estimated value of and Then, according to the geometric relationship of the target position, the coordinate value y of the lth target relative to the origin on the y-axis is obtained. l Estimated value of Finally, the target position parameters and the parameters obtained by tensor decomposition are used Estimate the velocity values ​​of the lth target on the x-axis and y-axis (v x,l ,v y,l ) The joint estimation of the position and velocity of the lth target is completed.

[0019] The beneficial effects of the present invention are as follows: by establishing an accurate terahertz MIMO-OFDM near-field spherical wave model and utilizing the OFDM signal with orthogonal frequency at the transmitting end, the position ambiguity-free condition is transformed from the antenna spacing to the frequency spacing between the transmitting antennas, and multi-dimensional information such as the phase difference between antennas and the phase difference between subcarriers is jointly processed through tensor decomposition to improve the accuracy of target parameter estimation, and the antenna array is grouped to reduce the complexity of the tensor decomposition algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a diagram of the terahertz near-field MIMO uniform linear antenna array model.

[0021] Figure 2 Flowchart of the invented joint estimation of multi-target position and velocity in terahertz near-field MIMO-OFDM based on tensor decomposition.

[0022] Figure 3 Diagram of the terahertz near-field antenna grouping and rough estimation model.

[0023] Figure 4 This is a relationship diagram between the positioning root mean square error and target distance of the algorithm of the present invention and the least squares algorithm.

[0024] Figure 5 This is a relationship diagram between the positioning root mean square error and signal-to-noise ratio of the algorithm of the present invention and the least squares algorithm.

[0025] Figure 6 This is the relationship between the positioning root mean square error and the target distance when the signal-to-noise ratio is 15dB.

[0026] Figure 7 This is the relationship between target distance, velocity root mean square error and target spacing when the signal-to-noise ratio is 15dB.

[0027] Figure 8 is the relationship between signal bandwidth, positioning root mean square error and target distance.

[0028] Figure 9 is the relationship between signal bandwidth, velocity root mean square error and target distance.

[0029] Figure 10 The relationship between antenna grouping, positioning root mean square error and signal-to-noise ratio. DETAILED DESCRIPTION

[0030] For the convenience of description, the symbols that appear are explained: T in the subscript or superscript represents transmission, R represents reception; t Indicates the subarray number variable of the transmit array, u t =1,...,U T ,u r Indicates the subarray number variable of the receiving array, u r =1,...,U R ; The total number of transmitting arrays is U T , the total number of receiving arrays is U R ;M T Indicates the number of transmitting array antennas, Q R represents the number of antennas in the receiving array, M represents the number of antennas in a transmitting array, and Q represents the number of antennas in a receiving array; M T =M*U T , Q R =Q*U R ; Indicates that at the uth t The first in the group transmit subarray Root transmitting antenna, For u r The first receiving subarray of the group receiving antennas; L is the total number of targets, l is the target sequence variable, l = 1, ..., L; n,p is the The nth subcarrier of the root transmit antenna is at the pth FO-OFDM symbol index; p,n represents the The first transmitting antenna The nth subcarrier in the propagation direction of the receiving antenna is under the pth FO-OFDM symbol index; l is the lth target in the Root transmitting antenna to The propagation direction of the receiving antenna; M T / 2,l is the distance from the center of the transmitting array to the lth target, Q R / 2,l receiving array center to the lth target; u t ,u r ,l is the lth target from the uth t The sub-array transmits to the reflection by the uth r The total number of subcarriers of the signal is N, and the subcarrier index variable is n; the total number of FO-OFDM symbol indexes is p, and the FO-OFDM symbol index index variable is P; the number of transmit and receive antenna pairs formed by a group of transmitting subarrays to a group of receiving subarrays is MQ, and the antenna pair number variable is

[0031] ρ is the signal propagation path distance, z is the additive Gaussian white noise, τ is the signal propagation delay, s(t) is the expression of the signal transmitted at time t, represents the modulation symbol, y(t) is the received signal / received signal expression at time t, x represents the coordinate value on the x-axis, y represents the coordinate value on the y-axis, δ is the propagation distance difference, v is the velocity value, α represents the reflection coefficient, and θ represents the azimuth angle.

[0032] like Figure 1 As shown, the number of transmitting array antennas is M T , the number of receiving array antennas is Q R , the transmitting array and the receiving array are divided into U T and U R There are sub-arrays, and the interval between adjacent antennas is d. Assuming that the antenna array is located on the x-axis, the coordinates of the transmitting antenna are The receiving antenna coordinates are in and Respectively represent the uth t The first subarray The root transmitting antenna and the uth r The first subarray The number of moving targets is L, and the coordinates of the lth target relative to the origin are (x l ,y l ), the speed is (v x,l ,v y,l ), x l ,y l are the x-axis and y-axis coordinates of the lth target relative to the origin, v x,l ,v y,l are the speed values ​​of the lth target on the x-axis and y-axis respectively.

[0033] Consider the transmission frequency orthogonal OFDM signal, that is, FO-OFDM signal, Δf is the subcarrier spacing, and the subcarrier index n=1,...,N. T0=T+T cp is the duration of a single FO-OFDM signal, T cp is the duration of the guard interval, T is the effective symbol duration, f c is the carrier frequency, then at time t The root transmitting antenna signal expression is:

[0034]

[0035] Where p=1,...,P is the FO-OFDM symbol index, For the The modulation symbol of the nth subcarrier of the root transmitting antenna under the pth FO-OFDM symbol index, K is a preset value that makes the signals of each transmitting antenna non-intersecting in the frequency domain, and is an integer greater than N.

[0036] The steps of joint estimation of multi-target position and velocity of THz near-field MIMO-OFDM based on tensor decomposition are as follows: Figure 2 As shown:

[0037] S1. Establish a near-field MIMO-OFDM signal model and group it by different antenna subarrays, specifically including:

[0038] Step S110 establishes a near-field MIMO-OFDM signal model.

[0039] Ignoring the Doppler frequency shift caused by the subcarrier, Transmitting antenna to The received signal of the receiving antenna can be expressed as:

[0040]

[0041] Among them, α l is the reflection coefficient of the lth target, is the Doppler frequency shift of the lth target caused by the carrier, c is the speed of light, For the Transmitting antenna to The speed of the lth target in the propagation direction of the receiving antenna, For the lth target, arrive Signal propagation delay in the propagation direction, Indicates from arrive Additive Gaussian white noise in the propagation direction. Signal propagation delay It can be specifically expressed as:

[0042]

[0043] According to the geometric relationship, the signal propagation path distance from the lth target to the center antenna of the transmitting array is and the signal propagation distance from the lth target to the center of the receiving array for:

[0044]

[0045] in, is the coordinate value of the center of the transmitting array relative to the origin on the x-axis, is the coordinate value of the center of the receiving array relative to the origin on the x-axis;

[0046] The first target is in The transmitting antenna and The difference in signal propagation distance between the root receiving antenna and the center antenna of each array for:

[0047]

[0048] The lth target is from arrive Signal propagation delay in the propagation direction Distance difference The relationship can be expressed as:

[0049]

[0050] is the signal propagation delay of the lth target in the propagation direction from the center of the transmitting array to the center of the receiving array.

[0051] Step S120 simplifies the signal model.

[0052] Assuming the antenna aperture is small enough, there is And relative to the symbol duration T0, the propagation delay Very small, yes And the speed of the target relative to the same subarray antenna is roughly the same, so The received signal model is simplified and discrete Fourier transform (DFT) is performed. The final near-field MIMO-OFDM signal model is:

[0053]

[0054] in, Indicates that from Transmitting antenna to The received signal of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the receiving antenna, For u t The group transmits the subarray to the uth r The speed of the lth target in the propagation direction of the group receiving subarray, Indicates the The transmitting antenna to the Additive white Gaussian noise of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the receiving antenna; Indicates the Transmitting antenna to The median value of the lth target in the propagation direction of the receiving antenna, β l is the intermediate quantity of the lth target;

[0055]

[0056] Step S130 Signal tensor representation

[0057] For the u t The signal transmitted by the sub-array is reflected by the target and then r The non-noise term of the group subarray receiving signal can be expressed as a third-order tensor form that satisfies CP decomposition

[0058]

[0059] in, Represents the outer product of tensors.

[0060] Among them, vector The expression is:

[0061]

[0062] in, Indicates that from the u t The group transmits the subarray to the uth r The serial number of the transmit and receive antenna pairs of the group receive subarray.

[0063] In fact, The first transmitting antenna The received signal of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the receiving antenna is Similar to constructing a noise-free third-order tensor The received signal containing noise can be easily constructed as a third-order tensor

[0064] S2. Decompose the grouped received signal tensor and estimate the intermediate parameters using the factor matrix after tensor decomposition. The specific steps include:

[0065] Step S210 CP tensor decomposition

[0066] For u t The signal transmitted by the sub-array is reflected by the target and then r The third-order tensor of the group subarray receiving signal, its rank is equal to the target number L. The third-order tensor of rank L After CP decomposition, it can be expressed as the sum of three-order rank 1 tensors, and the CP decomposition of the tensor is unique if the Kruskal condition is satisfied:

[0067]

[0068] In general, the number of OFDM symbols P, the number of subcarriers N, and the number of antenna pairs MQ will be greater than the target number of symbols L, which can meet the Kruskal condition. l is composed of known or constant quantities, so the tensor After CP decomposition, the vectors that make up the factor matrix are

[0069]

[0070] Step S220: Estimate intermediate parameters

[0071] vector By delay Characterization, hence delay By vector Estimate by averaging:

[0072]

[0073] Where ∠ represents the function of taking the phase angle of a complex number;

[0074] vector By speed Characterization, hence speed By vector Estimate by averaging:

[0075]

[0076] Similarly, vector By distance difference Characterization, therefore the distance difference By vector Estimate by averaging:

[0077]

[0078] in,

[0079] S3. Estimation of parameters θ l , and establish the optimization equation, including:

[0080] Step S310: Preliminary estimation of parameters

[0081] Distance difference The expression contains the parameter x l , Information, so when the tensor is decomposed, the intermediate parameters are estimated Then you can l , Make a preliminary estimate of After the expression is expanded, the parameter x can be estimated using the minimum algorithm. l , The initial value of for:

[0082]

[0083] in, Contains only the known antenna coordinates and the estimated distance difference P and h l All are intermediate amounts.

[0084] Step S320 estimates the parameter θ l

[0085] like Figure 3 As shown, the parameter θ l is the azimuth of the target relative to the center antenna of the receiving array. From the geometric relationship, we can know that:

[0086]

[0087] There are some literatures that show that the estimated value of azimuth is The estimation has high accuracy, and as the distance from the target to the antenna array increases, its estimation accuracy remains almost unchanged.

[0088] Step S330: Establishing the optimization equation

[0089] The position parameter x of the target l , Not only the distance difference Regarding delay Also contains target location information, joint parameters and It can improve positioning accuracy. However and These are all estimated intermediate parameters with estimation errors. If they are substituted into the equation, the equation will not be strictly true. Therefore, the following optimization equation can be constructed:

[0090]

[0091] in, represents the target position parameter, ||·|| F is the F-norm, is the estimated value of P, h l Estimated value, intermediate amount In order to reduce the iterative process, it is necessary to choose a good initial point and make a preliminary estimate of the There will be a large error when the target is far away, and But it still has high accuracy, so according to the geometric relationship, use parameters Indicates the initial point

[0092]

[0093] S4. Convert the equation into a convex optimization problem and solve the optimization equation to further optimize the parameter x. l , Perform estimation, target positioning and speed estimation, including:

[0094] Step S410 converts the equation into a convex optimization problem

[0095] It can be seen that the nonlinear term in the optimization equation makes the optimization non-convex, and it is very difficult to solve it directly. Taylor expansion of the nonlinear term at the initial point:

[0096]

[0097] The nonlinear terms are approximated by first-order linear approximations, so the optimization equation becomes the following convex optimization equation:

[0098]

[0099] Among them, ||·|| is the L2 norm, the intermediate quantity Intermediate amount

[0100] Step S420 solves the convex optimization equation and estimates (x l ,y l ) to locate the target.

[0101] Target position parameter x l , Finally, we can use the cvx toolbox to solve the convex optimization equation and get According to the geometric relationship of the target position, the vertical coordinate y of the target l can be estimated as follows:

[0102]

[0103] Step S430 estimates the speed (v x,l ,v y,l ).

[0104] Depend on Figure 3 As shown, the target speed consists of two parts: in, and + are the radial velocities relative to the transmitting and receiving subarrays, respectively. The radial velocities of the transmitting and receiving arrays are

[0105] The projections on the coordinate axes are superimposed and are v x,l ,v y,l . Using the target position parameters and the parameters obtained by tensor decomposition The target velocity can be estimated:

[0106]

[0107] in

[0108]

[0109] Step S440 estimates the value As the position of the lth target, the estimated value is used as the speed of the lth target Finally, the positions and velocities of L targets are output to complete the joint estimation.

[0110] Complexity Analysis

[0111] The computational complexity of the important steps of the present invention includes CP decomposition, parameter The computational complexity of tensor decomposition for each set of received data is:

[0112]

[0113] Each group The estimated computational complexity is At the same time, the computational complexity of positioning by solving the optimization problem is Where T is the number of iterations. T U R groups, so the total computational complexity is: At the same time, it can be seen that when and It can be ignored when compared. Finally we can get:

[0114]

[0115] It can be seen that the computational complexity varies with the number of groups. T Q R When it is greater than Q, P and N, appropriately increasing the number of groups can reduce the complexity caused by the number of antennas, thereby reducing the overall complexity.

[0116] Simulation test

[0117] Combined with the simulation results, the performance of the implementation plan is further proved. Figures 4 to 10 In the system, the parameters are set as follows: the system carrier frequency is f c=300GHz, subcarrier spacing Δf = 300kHz, OFDM symbol duration T0 = 1.25 / Δf ≈ 4.1667us. The adjacent antenna spacing is d = 1cm, and the total number of transmitting antennas is M T =31, total number of receiving antennas Q R =30. The target area is set as θ∈[-90°,90°], r∈[1m,30m[. Without any special instructions, the transmitting and receiving arrays are divided into U T =1,U R =6, and the signal-to-noise ratio SNR is defined as:

[0118]

[0119] The root mean square error (RMSE) of positioning is defined as:

[0120]

[0121] The root mean square error (RMSE) of velocity is defined as:

[0122]

[0123] Figure 4 and Figure 5 The relationship between the RMSE of the algorithm of the present invention, the distance from the target to the origin and the signal-to-noise ratio is given respectively. At the same time, the algorithm proposed in the present invention is compared with the near-field least squares algorithm proposed by Podkurkov et al. in 2018. Figure 4 It can be seen that the estimation performance of the proposed algorithm is significantly better than that of the least squares algorithm. In general, the accuracy of the algorithm decreases with increasing distance. However, due to the use of a more sophisticated signal model based on the spherical wavefront, the performance of the algorithm proposed in this invention decreases more slowly than that of the near-field least squares algorithm. Figure 5 In the example, the target distance is set to 5m. It can be seen that as the signal-to-noise ratio increases, the estimation performance of both algorithms improves. Furthermore, compared with the existing LS algorithm, the proposed algorithm has better estimation performance and faster calculation speed.

[0124] exist Figure 6Two targets are set in the , and the distance from the first target to the origin (r1) is set to 10m, 20m, 30m and 200m. The x-coordinate represents the distance between the two targets (Δd=r2-r1), and r2 is the distance from the second target to the origin. It can be seen that the estimation accuracy increases as r1 decreases. In addition, when the two targets are too close, it is difficult to distinguish the two targets, so the estimation accuracy decreases as the distance between the two targets decreases. In addition, when Δd is greater than 0.21m, the estimation performance improves slightly with the increase of Δd, and when Δd is greater than 0.068m, the estimation accuracy in the near-field scene can reach the centimeter level. Figure 7 In the example, the speeds of the two targets are set to 0.5m / s and 0.7m / s respectively. Since the estimation accuracy of the speed is affected by the estimation accuracy of the position, it can be seen that the variation trend of the estimation accuracy is similar to that of the Figure 6 Same as in.

[0125] exist Figure 8 and Figure 9 In the example, r1 is set to 10m. The bandwidth increases from 15MHz to 200MHz. It can be seen that the estimation accuracy gradually improves with increasing bandwidth. Furthermore, when the distance between the two targets is greater than 0.030m, 0.044m, and 0.15m at 120MHz, 30MHz, and 15MHz, respectively, the proposed algorithm achieves centimeter-level estimation accuracy. Furthermore, it can be seen that the resolution of the two targets increases with increasing bandwidth.

[0126] Figure 10 The achievable estimation accuracy of the number of sub-array groups in the receive array is shown. The transmit antenna array is considered as a group (U T =1). The number of receiving antennas is Q R =60. Figure 10 As can be seen from the figure, as the number of subarrays increases, the positioning estimation accuracy decreases, but this degradation disappears when the signal-to-noise ratio is greater than -4dB, which is usually the working condition of the system. On the other hand, as analyzed above, dividing the receiving antennas into more groups can reduce the computational complexity of the algorithm. Therefore, a reasonable choice can be made between the complexity of the algorithm and the estimation accuracy. And from Figure 10 As can be seen from the figure, as the signal-to-noise ratio increases, the number of groups has less impact on the estimation performance. Therefore, when the signal-to-noise ratio is high, dividing the antennas into more groups can better reduce the computational complexity.

Claims

1. A method for joint estimation of multi-target position and velocity using terahertz near-field MIMO-OFDM, characterized in that: Including steps: The steps of establishing the terahertz near-field MIMO-OFDM model are as follows: establishing a near-field MIMO-OFDM signal model and expressing the received signal in the near-field MIMO-OFDM signal model as a third-order tensor; The near-field MIMO-OFDM signal model is: in, Indicates that from The first transmitting antenna to the The received signal of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the root receiving antenna, FO-OFDM is frequency orthogonal OFDM, For u t The group transmits the subarray to the uth r The speed of the lth target in the propagation direction of the group receiving subarray, Indicates the The transmitting antenna to the Additive white Gaussian noise of the nth subcarrier at the pth FO-OFDM symbol index in the propagation direction of the receiving antenna; Indicates the Transmitting antenna to The median value of the lth target in the propagation direction of the receiving antenna, β l is the intermediate value of the lth target; Δf is the subcarrier spacing, is the signal propagation delay of the lth target in the propagation direction from the center of the transmitting array to the center of the receiving array, T0 is the duration of a single FO-OFDM signal, f c is the carrier frequency, c is the speed of light; Among them, α l is the reflection coefficient of the lth target, For the The modulation symbol of the nth subcarrier of the root transmitting antenna at the pth FO-OFDM symbol index, T cp is the duration of the guard interval, K is the preset value that makes the signals of each transmitting antenna non-intersecting in the frequency domain, For the lth target in the The propagation distance difference between the root transmitting antenna and the center of the transmitting array, For the lth target in the The propagation distance difference between the root receiving antenna and the center of the receiving array; Tensor decomposition step: Decompose the received signal tensor, and based on the uniqueness of the tensor decomposition, use the factor matrix after tensor decomposition to estimate the estimated value of the intermediate parameters, which include and Parameter preliminary estimation step: Use the estimated value of the intermediate parameter and the least squares LS algorithm to obtain the initial solution of the coordinate value x of the lth target relative to the origin on the x-axis l The initial value of And the signal propagation path distance from the lth target to the center antenna of the receiving array The initial value of according to and The geometric relationship between them is used to solve the azimuth angle θ of the lth target relative to the center antenna of the receiving array. l Estimated value of Using Parameters Represents x l and The initial point of the iteration and And establish the optimization equation; Precise positioning and velocity estimation steps: Perform Taylor expansion on the nonlinear term of the optimization equation at the initial point to perform second-order Taylor approximation, transform the optimization equation into a convex optimization equation, and use the cvx toolbox to iteratively solve the convex optimization equation to obtain x l and Estimated value of and Then, according to the geometric relationship of the target position, the coordinate value y of the lth target relative to the origin on the y-axis is obtained. l Estimated value of Finally, the target position parameters and the parameters obtained by tensor decomposition are used Estimate the velocity values ​​of the lth target on the x-axis and y-axis (v x,l ,v y,l ) The joint estimation of the position and velocity of the lth target is completed.

2. The method according to claim 1, wherein: The received signal in the near-field MIMO-OFDM signal model is expressed as a third-order tensor: in, For u t The signal transmitted by the sub-array is reflected by the target and then r The third-order tensor of the group subarray receiving signal, whose rank is equal to the target number L; Represents the outer product of tensors; tensor After CP decomposition, the vectors of the factor matrix are 3. The method according to claim 2, wherein: Use the vector of the factor matrix after tensor decomposition The average estimate is Estimated value of Using vectors Average Estimated value of Using vectors Average Estimated value of 4. The method according to claim 3, wherein: Solution Specifically: Among them, the intermediate T represents transpose, For Q R / 2 The coordinate value of the receiving antenna on the x-axis relative to the origin; Q R Indicates the total number of receiving array antennas, Q R / 2 receiving antennas are the center of the receiving array; For Q R -1 receiving antenna's coordinate value on the x-axis relative to the origin, For the lth target Qth R -The difference in signal propagation distance between one receiving antenna and the center antenna of the receiving array 5. The method according to claim 4, wherein: according to and The geometric relationship between them is used to solve the azimuth angle θ of the lth target relative to the center antenna of the receiving array. l Estimated value of Specifically:

6. The method according to claim 5, wherein: Using Parameters Represents x l and The initial point of the iteration and Specifically: Among them, the intermediate is the coordinate value of the center of the transmitting array relative to the origin on the y-axis.

7. The method according to claim 6, wherein: The convex optimization equation is specifically: Among them, the intermediate Intermediate amount is the estimated value of P, h l The estimated value of the target location parameter 8. The method according to claim 1, wherein: According to the geometric relationship of the target position, the coordinate value y of the lth target relative to the origin on the y-axis is obtained l Estimated value of Specifically: Receives the coordinate value of the array center relative to the origin on the x-axis.

9. The method according to claim 8, wherein: Finally, the target position parameters and the parameters obtained by tensor decomposition are used Estimate the velocity values ​​of the lth target on the x-axis and y-axis (v x,l ,v y,l ) Specifically: in, T represents transpose, G is the intermediate quantity, and the total number of emission arrays is U T , the total number of receiving arrays is U R , For U T *U R indivual The vector composed of u t =1,...,U T ,u r =1,...,U R ; In the subscript or superscript, T represents transmission, and R represents reception; M represents the number of antennas in a transmitting array, and Q represents the number of antennas in a receiving array.

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