Joint Underdetermined Parameter Estimation Method Based on Higher-Order Statistics and Non-Uniform Arrays

Abstract

The present invention discloses an underdetermined parameter joint estimation method based on high-order statistics and non-uniform arrays, including: obtaining single-sample frequency-domain channel data; calculating the fourth-order cumulant diagonal slice matrix by using the forward-backward smoothing technique, constructing a time-delay estimation spatial spectrum by using the orthogonal propagation operator method, and searching for the spectral peak to obtain the time-delay estimation value; calculating the time-delay domain filtering vector and separating the frequency-domain channel data corresponding to each time-delay estimation value; calculating the high-order cumulant matrix by using the frequency-domain channel data corresponding to each time-delay estimation value, constructing an angle-of-arrival estimation spatial spectrum, and searching for the spectral peak to obtain the angle-of-arrival estimation value; using the already estimated and automatically paired time-delay estimation value and angle-of-arrival estimation value to vectorize the channel data, and estimating the complex gain value of the multipath signal based on the least squares principle. The present invention only requires a single sample, can perform high-precision and high-accuracy multi-parameter joint estimation in an underdetermined scenario, and has a large estimation degree of freedom, high estimation accuracy, small computational complexity, and high robustness to noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of large-scale multi-input multi-output array signal processing, and more specifically, relates to an underdetermined parameter joint estimation method based on high-order statistics and non-uniform arrays. Background Art

[0002] With the advent of the 5G era, research on mobile communications with increasingly higher requirements for data rates and transmission quality has become increasingly popular. As one of the hottest research directions, wireless positioning is also widely used in many aspects of military and civilian use, such as radar, sonar, electronic countermeasures, smart medical care, smart transportation, etc. As a key component of wireless positioning, the accuracy of the joint estimation of wireless signal parameters seriously affects the performance of the wireless positioning system. These positioning parameters mainly include signal arrival delay, signal arrival angle, signal arrival strength, etc. As the spatial environment becomes increasingly complex, the multipath propagation of wireless signals becomes more and more significant. After multipath propagation, the signals have different arrival angles and delays, and the signal strength will also be different. In addition, the number of incoming waves received by the antenna array is often greater than the number of antenna elements, resulting in an underdetermined situation, which in turn causes the performance of some classic positioning methods to drop significantly or even fail. Therefore, how to achieve high-precision joint estimation of wireless positioning parameters in underdetermined scenarios needs to be solved urgently.

[0003] The maximum likelihood method was first proposed for the joint estimation of wireless positioning parameters. It transforms the parameter estimation problem into a multivariable non-linear minimization problem, which not only has high computational complexity but also depends on the initialization of parameters. To avoid the disadvantages of the maximum likelihood method, some more efficient subspace-based methods have been proposed, such as MUSIC and ESPRIT. Among them, the JADE-MUSIC method (M.C. Vanderveen, C.B. Papadias and A. Paulraj, "Joint angle and delay estimation (JADE) for multipath signals arriving at an antenna array", IEEE Commun. Lett., vol. 1, no. 1, pp. 12–14, 1997, doi: 10.1109 / 4234.552142.) realizes the joint estimation of parameters through two-dimensional search by exploring the spatio-temporal structure of the received signal, while the two-dimensional parameter search brings a huge computational burden. The JADE-ESPRIT method (A.-J. van der Veen, M.C. Vanderveen and A.J. Paulraj, "Joint angle and delay estimation using shift-invariance properties", IEEE Signal Process. Lett., vol. 4, no. 5, pp. 142–145, 1997, doi: 10.1109 / 97.575559.) realizes the joint estimation of parameters by constructing the Hankel matrix of the received signal and using the rotational invariance of the subspace.To achieve high-precision joint parameter estimation under single-sample conditions, the SAGE method (B.H. Fleury, M. Tschudin, R. Heddergott, D. Dahlhaus, and K. Ingeman Pedersen, "Channel parameter estimation in mobile radio environments using the SAGE algorithm", IEEE J. Sel. Areas Commun., vol. 17, no. 3, pp. 434–450, March 1999, doi: 10.1109 / 49.753729.) and the MatrixPencil method (A. Bazzi, D.T.M. Slock, and L. Meilhac, "Single snapshot joint estimation of angles and times of arrival: A 2D Matrix Pencil approach", Proceedings of the 2016 IEEE International Conference on Communications (ICC), 2016, pp. 1–6. doi: 10.1109 / ICC.2016.7511158.) are proposed. The SAGE method is based on the EM algorithm, iteratively solving multiple parameters with the expectation maximization as the criterion, and using serial interference cancellation and parallel interference cancellation to combat noise. Although it can work under underdetermined conditions and estimate multiple parameters, similar to the maximum likelihood method, the SAGE method depends on the initialization of parameters on the one hand, and has a high computational complexity on the other hand. Moreover, the more parameters or signal sources there are, the higher the computational complexity. The MatrixPencil method has poor stability in the face of noise or underdetermined scenarios.

[0004] The above-mentioned methods are all for simultaneously estimating multiple parameters, either with high computational complexity, low anti-noise robustness, or poor performance in underdetermined scenarios. Currently, there are many efficient and stable single-parameter estimation algorithms. Another idea for achieving joint estimation is to continue to correctly match multipath parameters after accurately estimating a single parameter. In this regard, the TST method (Y.-Y. Wang and W.-H. Fang, "TST-MUSIC for DOA-delay joint estimation", in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. (Cat. No. 00CH37100), June 2000, Vol. 5, pp. 2565–2568, Vol. 5. doi: 10.1109 / ICASSP.2000.860980.) provides a solution. This method uses a tree structure to implement the parameter matching process, not only achieving high-precision estimation of a single parameter but also being able to distinguish parameter values that are close. However, the TST method can only distinguish the case where one parameter is close, such as similar DOAs but different other parameters. And the TST method is almost ineffective in underdetermined scenarios because when performing spatial beamforming filtering in the TST method, the underdetermined conditions make the filtering matrix not meet the prerequisites required by this method. Summary of the Invention

[0005] In view of the above defects or deficiencies of the prior art, the present invention provides a method for jointly estimating underdetermined parameters based on higher-order statistics and non-uniform arrays, aiming to overcome the technical problems existing in the prior art, such as high computational complexity, low estimation accuracy in low signal-to-noise ratio environments, and inability to effectively estimate multiple parameters in underdetermined scenarios.

[0006] To achieve the above object, in a first aspect, the present invention provides a method for jointly estimating underdetermined parameters based on higher-order statistics and non-uniform arrays, including:

[0007] S1, obtaining the original frequency-domain channel data;

[0008] S2, calculating the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data; dividing the diagonal slice matrix according to the number of multipaths, and calculating the propagation operator based on the divided matrix, and then constructing a time-delay estimation spatial spectrum to search for the spectral peak to obtain the time-delay estimation value;

[0009] S3, calculating the time-delay domain filtering vectors corresponding to each time-delay estimation value, and filtering the current frequency-domain channel data using each time-delay domain filtering vector to separate the frequency-domain channel data corresponding to each time-delay estimation value;

[0010] S4. Calculate the high - order cumulant matrix using the frequency - domain channel data corresponding to each time - delay estimation value, construct an angle - of - arrival estimation spatial spectrum based on the high - order cumulant matrix, and search for the spectrum peak to obtain the angle - of - arrival estimation value corresponding to each time - delay estimation value;

[0011] S5. Construct a time - delay response matrix and an array manifold matrix respectively according to each of the time - delay estimation values and angle - of - arrival estimation values; vectorize the current frequency - domain channel data, and estimate the channel complex gain matrix in combination with the time - delay response matrix and the array manifold matrix.

[0012] Further, the method further includes:

[0013] S6. Determine whether the iteration stop condition is satisfied. If so, end the operation; if not, reconstruct the channel based on the time - delay response matrix, the array manifold matrix, and the channel complex gain matrix, subtract the reconstructed channel from the current frequency - domain channel data, use the remaining frequency - domain channel data as the current frequency - domain channel data, and jump to S2.

[0014] Further, in S2, after calculating the fourth - order cumulant diagonal slice matrix of the current frequency - domain channel data, it further includes: performing forward - backward smoothing processing on the fourth - order cumulant diagonal slice matrix to obtain the forward - backward smoothed fourth - order cumulant diagonal slice matrix.

[0015] Further, in S3, calculating the time - delay domain filtering vector corresponding to each time - delay estimation value includes: using the Lagrange multiplier to calculate the time - delay domain filtering vector corresponding to each time - delay estimation value with the goal of minimizing the average power of the filtered noise.

[0016] Further, in S4, constructing the angle - of - arrival estimation spatial spectrum based on the high - order cumulant matrix includes:

[0017] Performing singular value decomposition or eigenvalue decomposition on the high - order cumulant matrix to obtain a signal subspace and a noise subspace; defining the angle - of - arrival estimation spatial spectrum based on the orthogonality of the signal subspace and the noise subspace.

[0018] Further, in S5, estimating the channel complex gain matrix based on the least - squares principle.

[0019] In a second aspect, the present invention provides an under - determined parameter joint estimation device based on high - order statistics and non - uniform arrays, including:

[0020] An acquisition module, configured to acquire original frequency - domain channel data;

[0021] The time delay estimation module is used to calculate the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data; divide the diagonal slice matrix according to the number of multipaths, calculate the propagation operator based on the divided matrix, and then construct the time delay estimation spatial spectrum to search for the spectral peak to obtain the time delay estimation value;

[0022] The time delay filtering module is used to calculate the time delay domain filtering vectors corresponding to each time delay estimation value, and filter the current frequency-domain channel data by using each time delay domain filtering vector to separate the frequency-domain channel data corresponding to each time delay estimation value;

[0023] The angle of arrival estimation module is used to calculate the high-order cumulant matrix respectively by using the frequency-domain channel data corresponding to each time delay estimation value, construct the angle of arrival estimation spatial spectrum based on the high-order cumulant matrix, and search for the spectral peak to obtain the angle of arrival estimation value corresponding to each time delay estimation value;

[0024] The complex gain estimation module is used to construct a time delay response matrix and an array manifold matrix respectively according to each of the time delay estimation values and the angle of arrival estimation values; vectorize the current frequency-domain channel data, and estimate the channel complex gain matrix in combination with the time delay response matrix and the array manifold matrix.

[0025] In a third aspect, the present invention provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is run by a processor, it controls the device where the storage medium is located to execute the parameter joint estimation method as described in the first aspect.

[0026] Generally speaking, through the above technical solutions conceived by the present invention, the following beneficial effects can be achieved:

[0027] (1) Compared with other parameter joint estimation methods, the design method of the present invention is based on a non-uniform array and high-order statistics, has a large array degree of freedom, and can work in an underdetermined scenario; the high-order cumulant method is used to estimate the angle of arrival corresponding to each time delay estimation value, which can not only increase the accuracy of the angle of arrival estimation and the anti-noise robustness, but also does not increase the computational complexity because the filtered channel data only contains the current path; at the same time, vectorizing the frequency-domain channel is to achieve correct channel complex gain estimation in an underdetermined scenario, because in an underdetermined scenario, the array manifold matrix is row full rank and there is no left inverse, and estimating the channel complex gain based on the least squares principle will fail, while the least squares principle can work properly after vectorizing the frequency-domain channel. Therefore, the design method of the present invention has the advantages of large estimation degree of freedom, high estimation accuracy, small computational complexity, and large robustness to noise.

[0028] (2) The present invention solves the problems of parameter misestimation caused by noise and inestimability of low-energy multipaths through an iterative method.

[0029] (3) By means of forward and backward smoothing techniques, similar parameters of coherent signals can be distinguished. Description of the Drawings

[0030] Figure 1 It is a flowchart of a method for jointly estimating underdetermined parameters based on higher-order statistics and non-uniform arrays provided by the present invention;

[0031] Figure 2 It is a schematic diagram of a six-element non-uniform linear array structure provided by an embodiment of the present invention;

[0032] Figure 3 It is a graph showing the relationship between the correlation of the reconstructed channel and the true channel and the number of iterations provided by an embodiment of the present invention;

[0033] Figure 4 It is a performance curve graph of parameter estimation under different signal-to-noise ratios provided by an embodiment of the present invention, where (a), (b), (c), and (d) are respectively the channel reconstruction similarity curve, the root mean square error graph of delay estimation, the root mean square error graph of arrival angle estimation, and the root mean square error graph of channel complex gain amplitude under different signal-to-noise ratios. Detailed Embodiment

[0034] In order to make the objectives, system components, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0035] In the present invention, terms such as "first" and "second" in the present invention and the drawings (if any) are used to distinguish similar objects and do not necessarily need to describe a specific order or sequence.

[0036] Refer to Figure 1 , the present invention provides a method for jointly estimating underdetermined parameters based on higher-order statistics and non-uniform arrays. The method includes operation S1 to operation S6.

[0037] Operation S1, obtaining original frequency-domain channel data.

[0038] In this embodiment, the non-uniform array at the signal receiving end receives the incoming wave signal and processes it to obtain the frequency-domain channel data H, and H = A(θ)FV T (τ) + W. Where A(θ) = [a(θ1) … a(θ P )] is the array manifold matrix, θ pis the arrival angle of the p-th multipath signal. M is the number of antenna elements, d is the element spacing, and λ is the signal wavelength. F = diag(β1,…,β P ) is the channel complex gain matrix, and β p represents the complex gain of the p-th multipath signal. V(τ) = [v(τ1) … v(τ P )] is the time-delay response matrix, τ p is the time delay of the p-th multipath signal. K is the number of frequency points, and f k represents the frequency.

[0039] Among them, the principle of the non-uniform array design at the signal receiving end is to maximize the non-redundancy of the virtual extended elements obtained from the high-order cumulants. Specifically, the non-uniform antenna array structure is obtained by solving a mixed-integer programming problem, and the mixed-integer programming problem can be described as follows after appropriate relaxation:

[0040]

[0041] subject to 1 - INF·z m ≤q (m) D T ≤ -1 + INF·(1 - z m ) m = 1,…,M - 1,

[0042]

[0043] where represents the coordinates of the antenna elements, and M is the number of antenna elements. The diagonal elements of the (M - 1)×M matrix Q are all -1, and the upper sub-diagonal elements are all 1, that is, Q i,i = -1, Q i,i+1 = 1, i = 1,…,M - 1, and q (m) represents the m-th row of the matrix Q. U = M(M - 1) / 2. J i = [0 M-i,i-1 1 M-i I M-i , i = 1,…,M - 1, 1 U-1 represents the (U - 1)×1 column vector with all elements being 1, j (u) represents the u-th row of the matrix J, J [u] represents the matrix J after deleting the u-th row, J A = [1 U-1 j (1) … 1 U-1 j (U) T and J B = [J [1] … J​[U] T ,[·] T represents the matrix transpose operation. INF is a reasonably large number. This problem can be quickly solved using the CVX toolbox of MATLAB.

[0044] In operation S2, calculate the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data; divide the diagonal slice matrix according to the number of multipaths, and calculate the propagation operator based on the divided matrix, and then construct the time-delay estimation spatial spectrum to search for the spectral peak to obtain the time-delay estimation value.

[0045] It can be understood that when the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data is calculated for the first time, the current frequency-domain channel data is the original frequency-domain channel data.

[0046] S21, calculate the fourth-order cumulant diagonal slice matrix after forward and backward smoothing of the frequency-domain channel data; let y = H H ,press

[0047]

[0048] Calculate the fourth-order cumulant diagonal slice matrix for time-delay estimation. Divide the uniformly distributed frequency points forward into J sub-blocks, and calculate a fourth-order cumulant diagonal slice matrix R T (j), j = 1,..., J. After averaging, the forward-smoothed fourth-order cumulant diagonal slice matrix for time-delay estimation can be obtained

[0049]

[0050] Press

[0051]

[0052] Calculate the corresponding backward-smoothed fourth-order cumulant diagonal slice matrix for time-delay estimation, where Π is a flip matrix with all elements on the anti-diagonal being 1 and other positions being 0. Thus, based on

[0053]

[0054] Obtain the forward and backward smoothed fourth-order cumulant diagonal slice matrix for time-delay estimation

[0055] S22, calculate the equivalent noise subspace using the orthogonal propagation operator method, and divide the matrix into

[0056]

[0057] ​where G1 and G2 are K×P and K×(K - P) dimensional matrices respectively, where P is the number of multipaths. The least - squares estimate of the propagation operator P is

[0058]

[0059] where denotes the generalized inverse of the matrix. Calculate

[0060]

[0061] and orthonormalize it to

[0062] Q0 = Q(Q H Q) -1 / 2

[0063] Construct the time - delay estimation spatial spectrum according to the equivalent noise subspace Q0

[0064]

[0065] Search for the spectral peak to obtain the corresponding time - delay parameter estimation value

[0066] In operation S3, calculate the time - delay domain filtering vectors corresponding to each time - delay estimation value, and use each time - delay domain filtering vector to filter the current frequency - domain channel data to separate the frequency - domain channel data corresponding to each time - delay estimation value.

[0067] S31, use the already estimated time - delay parameter value to construct the time - delay response matrix

[0068] S32, with the goal of minimizing the average power of the filtered noise, the constrained time - delay domain filtering vector calculation scheme is expressed as

[0069]

[0070]

[0071] where is the calculated noise covariance matrix. The time - delay domain filtering vector can be calculated using the Lagrange multiplier

[0072]

[0073] where e i is a q×1 column vector with 1 at the i - th position and 0 at the remaining positions, i = 1, …, q. And filter the frequency - domain channel data

[0074] H i = H·w i

[0075] Separate the frequency-domain channel data corresponding to each time-delay estimation value. Then each H i only contains the corresponding angle of arrival and channel complex gain.

[0076] In operation S4, use the frequency-domain channel data corresponding to each time-delay estimation value to calculate the high-order cumulant matrix respectively, and construct an angle-of-arrival estimation spatial spectrum based on the high-order cumulant matrix, and search for the spectral peak to obtain the angle-of-arrival estimation value corresponding to each time-delay estimation value.

[0077] S41. For the frequency-domain channel data H corresponding to the i-th multipath signal i calculate the fourth-order cumulant matrix

[0078]

[0079] where represents the Kronecker product.

[0080] S42. Perform eigenvalue decomposition to obtain the noise subspace U n

[0081] R 4,i = UΣU H

[0082] U n = U(:,2:end)

[0083] where U(:,2:end) represents the second column to the last column of matrix U. Construct the angle-of-arrival estimation spatial spectrum

[0084]

[0085] where Search for the spectral peak to obtain the corresponding angle-of-arrival parameter estimation value

[0086] In operation S5, construct a time-delay response matrix and an array manifold matrix respectively according to each of the time-delay estimation values and the angle-of-arrival estimation values; vectorize the current frequency-domain channel data, and estimate the channel complex gain matrix in combination with the time-delay response matrix and the array manifold matrix.

[0087] S51. Use the already estimated time-delay parameters angle-of-arrival parameters to construct the time-delay response matrix and the array manifold matrix

[0088] S52. Vectorize the frequency-domain channel, and estimate the corresponding signal complex gain based on the least squares principle

[0089]

[0090] Operation S6: Determine whether the iteration stop condition is satisfied. If so, end the operation; if not, reconstruct the channel based on the time-delay response matrix, the array manifold matrix, and the channel complex gain matrix, subtract the reconstructed channel from the current frequency-domain channel data, use the remaining frequency-domain channel data as the current frequency-domain channel data, and jump to S2.

[0091] Among them, the stop condition can be that the number of iterations reaches, or the channel energy is lower than the threshold value, or the number of estimated multipaths reaches the limit value.

[0092] When the iteration stop condition is not satisfied, reconstruct the channel based on the current time-delay response matrix, the array manifold matrix, and the channel complex gain matrix. The reconstructed channel can be expressed as:

[0093]

[0094] Subtract the current reconstructed channel from the input frequency-domain channel data, that is

[0095]

[0096] Use the remaining frequency-domain channel data as the current frequency-domain channel data and jump to S2.

[0097] Embodiment:

[0098] Figure 2 The following shows a schematic diagram of a six-element non-uniform linear array structure used in an embodiment of the present invention. The method for joint parameter estimation in an underdetermined scenario based on high-order statistics and non-uniform arrays of the present invention is applied to this antenna array and a large-scale multiple-input multiple-output wireless multipath channel to improve the accuracy of joint parameter estimation in an underdetermined scenario. In this embodiment, the center frequency of signal transmission is 3.5 GHz, the bandwidth is 100.8 MHz, and the frequency point interval is 30 kHz. There are 20 multipath incoming waves arriving at the antenna array, and their angles are uniformly distributed between -64° and +64°. The multipath time delays are uniformly distributed from 10 ns to 200 ns, and the multipath complex fading gains follow a standard complex Gaussian distribution. In the time-delay estimation stage, the spatial spectrum peak search granularity is 1 ns, and in the angle-of-arrival estimation stage, the spectrum peak search granularity is 1°. The signal-to-noise ratio is set to 0 dB. The stop criterion is to estimate all the multipath numbers or reach the number of iterations. The specific steps are as follows:

[0099] (1) In the channel data generation stage, the signal transmitting end sends a pilot signal; the signal receiving end receives the incoming wave signal, processes it to obtain channel sampling data, and obtains the frequency-domain channel data through a 3360-point inverse Fourier transform.

[0100] (2) In the time delay estimation stage, calculate the diagonal slice matrix of the fourth-order cumulant after forward and backward smoothing for the frequency-domain channel data, obtain the equivalent noise subspace through the orthogonal propagation operator method, construct the time delay estimation spatial spectrum based on the MUSIC algorithm principle, and search for the spectral peak to obtain the time delay estimation value.

[0101] (3) Calculate the time delay domain filtering vector w. i And filter the frequency-domain channel data H. i = H·w i ;

[0102] (4) For the currently estimated channel data H. i Calculate the fourth-order cumulant matrix R. 4,i , construct the angle of arrival spatial spectrum based on the MUSIC algorithm principle, and search for the spectral peak to obtain the angle of arrival estimation value.

[0103] (5) Construct the array manifold matrix. And the time delay response matrix. Vectorize the frequency-domain channel and estimate the corresponding signal complex gain based on the least squares principle.

[0104] (6) Reconstruct the channel and subtract the current reconstructed channel from the input frequency-domain channel data. If the iteration stop condition is not satisfied, continue to execute steps (2) to (6).

[0105] The present invention realizes high-precision multi-parameter joint estimation in an underdetermined scenario by using high-order cumulants and non-uniform arrays. Different from the method used in the present invention, existing parameter joint estimation methods either cannot achieve underdetermined parameter estimation with a limited number of array elements, or cannot effectively control the computational complexity, or cannot distinguish similar parameter values of coherent signals. At the same time, this method also utilizes the excellent property of high-order cumulants to automatically suppress Gaussian noise theoretically and iterative interference cancellation, achieving strong robustness to noise and being able to still exhibit good estimation performance at low signal-to-noise ratios.

[0106] Figure 3 This is the relationship diagram between the correlation of the reconstructed channel and the true channel and the number of iterations provided by the embodiment of the present invention. From Figure 3 it can be found that the present invention can achieve a channel reconstruction similarity of about 0.98 with only a few iterations.

[0107] Figure 4It is a performance curve graph of parameter estimation provided by the embodiment of the present invention under different signal-to-noise ratios, where (a), (b), (c), and (d) are respectively the channel reconstruction similarity curve, the root mean square error graph of delay estimation, the root mean square error graph of arrival angle estimation, and the root mean square error graph of channel complex gain amplitude under different signal-to-noise ratios. As Figure 4 shown, even at low signal-to-noise ratios, the present invention still has a channel reconstruction similarity above 0.93, and the errors of parameter estimation are all small, which proves that this method can perform high-precision multi-parameter joint estimation in underdetermined scenarios.

[0108] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A joint underdetermined parameter estimation method based on high-order statistics and non-uniform arrays, characterized in that, Including: S1. Obtain the original frequency-domain channel data; S2. Calculate the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data; divide the diagonal slice matrix according to the number of multipaths, calculate the propagation operator based on the divided matrix, then construct the time-delay estimation spatial spectrum, and search for the spectral peak to obtain the time-delay estimation value; S3. Calculate the time-delay domain filtering vectors corresponding to each time-delay estimation value, and use each time-delay domain filtering vector to filter the current frequency-domain channel data to separate the frequency-domain channel data corresponding to each time-delay estimation value; S4. Calculate the high-order cumulant matrix using the frequency-domain channel data corresponding to each time-delay estimation value respectively, and construct the angle-of-arrival estimation spatial spectrum based on the high-order cumulant matrix, and search for the spectral peak to obtain the angle-of-arrival estimation value corresponding to each time-delay estimation value; S5. Construct the time-delay response matrix and the array manifold matrix according to each of the time-delay estimation value and the angle-of-arrival estimation value respectively; vectorize the current frequency-domain channel data, and estimate the channel complex gain matrix in combination with the time-delay response matrix and the array manifold matrix; The specific content of S2 includes: S21. Forwardly divide the evenly distributed frequency points into J sub - blocks, and calculate a fourth - order cumulant diagonal slice matrix R of the time - delay estimation on each sub - block T (j), where j = 1, …, J. After averaging, obtain the forward - smoothed fourth - order cumulant diagonal slice matrix of the time - delay estimation Calculate the fourth-order cumulant diagonal slice matrix of the corresponding backward-smoothed delay estimate Π is a flip matrix with all elements on the anti-diagonal being 1 and other positions being 0, which is the conjugate matrix of R Tf ; Fourth-order cumulant diagonal slice matrix for calculating the time-delay estimation after forward and backward smoothing S22. Calculate the equivalent noise subspace using the orthogonal propagation operator method, and divide the matrix into G1 and G2 are matrices of dimensions K×P and K×(K - P) respectively, where P is the number of multipaths; K is the number of frequency points; The least-squares estimate of the propagation operator P is denotes the generalized inverse of the matrix, and calculates I is the identity matrix of dimension K-P, and Q is orthonormalized to Q0 = Q(Q H Q) -1 / 2 , Q H denotes the conjugate transpose of Q, and constructs the time-delay estimation spatial spectrum according to the equivalent noise subspace Q0 v(τ) is the time-delay response matrix, and v H (τ) is the conjugate transpose of v(τ); search for the spectral peak to obtain the corresponding time-delay parameter estimate value In S3, calculating the time-delay domain filtering vectors corresponding to each time-delay estimation value specifically includes: S31, using the estimated delay parameter values to construct a delay response matrix S32. With the goal of minimizing the average power of the filtered noise, there is a constrained time-delay domain filtering vector calculation scheme, expressed as: R Tn = E{W H W} is the calculated noise covariance matrix; is the time-delay domain filtering vector w i 's conjugate transpose. The time-delay domain filtering vector can be calculated using the Lagrange multiplier: V tH is V t the conjugate transpose of, v * () represents the conjugate matrix of v(), e i is the q×1 column vector with 1 at the i-th position and 0 at the remaining positions, i = 1, …, q; In S4, constructing the angle-of-arrival estimation spatial spectrum based on the high-order cumulant matrix specifically includes: S41. Calculate the fourth-order cumulant matrix for the frequency-domain channel data H corresponding to the i-th multipath signal i ​ wherein represents the Kronecker product; S42, perform eigenvalue decomposition to obtain the noise subspace U n : R 4,i = UΣU H U n = U(:, 2:end) U(:, 2:end) represents the second column to the last column of matrix U, and constructs the angle-of-arrival estimation spatial spectrum; In S5, the channel complex gain matrix is estimated by combining the delay response matrix and the array manifold matrix, which specifically includes: constructing the array manifold matrix and the delay response matrix After vectorizing the frequency-domain channel, the corresponding signal complex gain is estimated based on the least squares principle H is the frequency-domain channel data.

2. The joint parameter estimation method according to claim 1, characterized in that, The method further includes: S6. Determine whether the iteration stop condition is satisfied. If so, end the operation; if not, reconstruct the channel based on the time-delay response matrix, the array manifold matrix, and the channel complex gain matrix, subtract the reconstructed channel from the current frequency-domain channel data, use the remaining frequency-domain channel data as the current frequency-domain channel data, and jump to S2.

3. The joint parameter estimation method according to claim 1 or 2, characterized in that, In S4, constructing the angle-of-arrival estimation spatial spectrum based on the high-order cumulant matrix includes: Perform singular value decomposition or eigenvalue decomposition on the high-order cumulant matrix to obtain the signal subspace and the noise subspace; define the angle-of-arrival estimation spatial spectrum based on the orthogonality of the signal subspace and the noise subspace.

4. A joint underdetermined parameter estimation device based on high-order statistics and non-uniform arrays, comprising: An acquisition module, used to acquire the original frequency-domain channel data; A time-delay estimation module, used to calculate the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data; Divide the diagonal slice matrix according to the number of multipaths, calculate the propagation operator based on the divided matrix, then construct the time-delay estimation spatial spectrum, and search for the spectral peak to obtain the time-delay estimation value; A time-delay filtering module, used to calculate the time-delay domain filtering vectors corresponding to each time-delay estimation value, and use each time-delay domain filtering vector to filter the current frequency-domain channel data to separate the frequency-domain channel data corresponding to each time-delay estimation value; An angle-of-arrival estimation module, used to calculate the high-order cumulant matrix using the frequency-domain channel data corresponding to each time-delay estimation value respectively, and construct the angle-of-arrival estimation spatial spectrum based on the high-order cumulant matrix, and search for the spectral peak to obtain the angle-of-arrival estimation value corresponding to each time-delay estimation value; The complex gain estimation module is configured to construct a time-delay response matrix and an array manifold matrix respectively according to each of the time-delay estimation values and the angle-of-arrival estimation values; vectorize the current frequency-domain channel data, and estimate a channel complex gain matrix in combination with the time-delay response matrix and the array manifold matrix; The time-delay estimation module is specifically configured to execute S21 - S22: S21. Divide the uniformly distributed frequency points forward into J sub-blocks, and calculate a fourth-order cumulant diagonal slice matrix R for time delay estimation on each sub-block T (j), where j = 1,..., J. After averaging, obtain the forward-smoothed fourth-order cumulant diagonal slice matrix for time delay estimation Calculate the fourth-order cumulant diagonal slice matrix of the corresponding backward-smoothed delay estimate Π is a flipping matrix with all elements on the anti-diagonal being 1 and other positions being 0, which is the conjugate matrix of R Tf ; Fourth-order cumulant diagonal slice matrix for calculating the time-delay estimation after forward and backward smoothing S22. Calculate the equivalent noise subspace using the orthogonal propagation operator method, and divide the matrix into where G1 and G2 are matrices of dimensions K×P and K×(K - P) respectively, P is the number of multipaths, and K is the number of frequency points; The least-squares estimate of the propagation operator P is denotes the generalized inverse of the matrix, and calculates I is the identity matrix of dimension K - P, and Q is orthonormalized to Q0 = Q(Q H Q) -1 / 2 , Q H denotes the conjugate transpose of Q, and constructs the time-delay estimation spatial spectrum according to the equivalent noise subspace Q0 v(τ) is the time-delay response matrix, and v H (τ) is the conjugate transpose of v(τ); search for the spectral peak to obtain the corresponding time-delay parameter estimate value The time-delay filtering module calculates a time-delay domain filtering vector corresponding to each time-delay estimation value, specifically including S31 - S32: S31, using the estimated delay parameter values to construct a delay response matrix S32, with the goal of minimizing the average power of the filtered noise, a constrained time-delay domain filtering vector calculation scheme, expressed as: R Tn = E{W H W} is the calculated noise covariance matrix, is the time-delay domain filtering vector w i 's conjugate transpose; The time-delay domain filtering vector can be calculated using the Lagrange multiplier: V tH is V t is the conjugate transpose of, v * () represents the conjugate matrix of v(), e i is the q×1 column vector with 1 at the i-th position and 0 at the remaining positions, i = 1, …, q; In the angle-of-arrival estimation module, an angle-of-arrival estimation spatial spectrum is constructed based on the high-order cumulant matrix, specifically including S41 - S42: S41. Calculate the fourth-order cumulant matrix for the frequency-domain channel data H corresponding to the i-th multipath signal i Calculate the fourth-order cumulant matrix: wherein represents the Kronecker product; S42, perform eigen - decomposition to obtain the noise subspace U n : R 4,i = UΣU H U n = U(:, 2:end) U(:, 2:end) represents the second column to the last column of matrix U, and an angle-of-arrival estimation spatial spectrum is constructed; In the complex gain estimation module, a channel complex gain matrix is estimated by combining the time-delay response matrix and the array manifold matrix, which specifically includes: constructing an array manifold matrix and a time-delay response matrix After vectorizing the frequency-domain channel, the corresponding signal complex gain is estimated based on the least squares principle H is the frequency-domain channel data.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, and when the computer program is run by a processor, it controls the device where the storage medium is located to execute the parameter joint estimation method according to any one of claims 1 to 3.

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