CN114884841A - Underdetermined parameter joint estimation method based on high-order statistics and non-uniform array - Google Patents
Underdetermined parameter joint estimation method based on high-order statistics and non-uniform array Download PDFInfo
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Abstract
The invention discloses an underdetermined parameter joint estimation method based on high-order statistics and a non-uniform array, which comprises the following steps: acquiring single-sample frequency domain channel data; calculating a fourth-order cumulant diagonal slice matrix by adopting a forward and backward smoothing technology, constructing a time delay estimation space spectrum by utilizing an orthogonal propagation operator method, and searching a spectrum peak to obtain a time delay estimation value; calculating a time delay domain filtering vector, and separating frequency domain channel data corresponding to each time delay estimation value; calculating a high-order cumulant matrix by using frequency domain channel data corresponding to each time delay estimation value, constructing an arrival angle estimation space spectrum, and searching a spectrum peak to obtain an arrival angle estimation value; and vectorizing channel data by using the estimated and automatically-paired time delay estimation value and arrival angle estimation value, and estimating a multipath signal complex gain value based on a least square principle. The method only needs a single sample, can carry out high-precision and high-accuracy multi-parameter joint estimation in an underdetermined scene, and has the advantages of large estimation freedom, high estimation precision, small calculation complexity and high noise robustness.
Description
Technical Field
The invention belongs to the technical field of large-scale multi-input multi-output array signal processing, and particularly relates to an underdetermined parameter joint estimation method based on high-order statistics and a non-uniform array.
Background
With the advent of the 5G era, research into mobile communication with higher and higher data rate and transmission quality requirements has been increasingly hot. The wireless positioning problem, one of the most popular research directions, is also widely applied to military and civil aspects, such as radar, sonar, electronic countermeasure, smart medicine, intelligent transportation, and so on. As a key component of wireless positioning, the performance of a wireless positioning system is seriously affected by the accuracy of wireless signal parameter joint estimation. These positioning parameters mainly include signal arrival time delay, signal arrival angle, signal arrival strength, and the like. The space environment is increasingly complex, and the multipath propagation of wireless signals is more remarkable. The signals after multipath propagation have different arrival angles and time delays, and the signal strengths are also different. And the number of incoming waves received by the antenna array is often more than the number of antenna array elements, which causes an underdetermined condition, and further causes the performance of some classical positioning methods to be greatly reduced and even to be invalid. Therefore, how to realize high-precision wireless positioning parameter joint estimation under an underdetermined scene needs to be solved.
The maximum likelihood method is firstly proposed to perform joint estimation of wireless positioning parameters, and converts the parameter estimation problem into a multivariate nonlinear minimization problem, which not only has higher computational complexity, but also relies on the initialization of parameters. To avoid the disadvantages of the maximum likelihood approach, more efficient subspace-based approaches have been proposed, such as MUSIC, ESPRIT. Among them, the JADE-MUSIC method (m.c. vanderveen, c.b. papadas and a.paulraj, Joint and delay estimation (JADE) for multipath signaling at an anti-array, IEEE com.lett., volume 1, phase 1, pages 12-14,1997, doi:10.1109/4234.552142.) realizes Joint estimation of parameters by two-dimensional search by exploring the space-time structure of the received signal, and the two-dimensional parameter search brings huge calculation 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, p.142-145, 1997, doi:10.1109/97.575559.) achieves Joint estimation of parameters using rotational invariance of subspaces by constructing a Hankel matrix of received signals. In order to achieve high precision joint estimation of parameters under a Single sample, SAGE methods (B.H. flow, M.Tschudin, R.Heddergott, D.Dahlhaus and K.Ingeman Pedersen, < Channel parameter estimation in mobile radio environment using the SAGE algorithm, IEEE J.Sel.Area Commun, volume 17, phase 3, page 434. 450,3 month 1999, doi:10.1109/49.753729.) and Matrix Xencil methods (A.Bazzi, D.T.M.Slock and L.Meilhac, < Single snapshot joint estimation of angles and times of arrival: A2D Matrix Peachsoil, 2016. 500. C., contact 2016. 2016, 500. Coder), were proposed. The SAGE method is based on an EM algorithm, a plurality of parameters are solved in an iterative mode according to a desired maximization criterion, and meanwhile serial interference elimination and parallel interference elimination are utilized to resist noise. Although it can work under underdetermined conditions and can estimate multiple parameters, similar to the maximum likelihood method, the SAGE method relies on the initialization of parameters on one hand and has high computational complexity on the other hand, and the higher the number of parameters or sources, the higher the computational complexity. The MatrixPencil method has poor stability when facing noise or an underdetermined scene.
The methods are all used for estimating various parameters simultaneously, or have higher calculation complexity, or have low noise robustness, or have poor performance under an underdetermined scene. At present, many efficient and stable single-parameter estimation algorithms exist. Another idea for implementing joint estimation is to continue to complete the correct matching of multipath parameters after implementing accurate estimation of single parameters. For this purpose, the TST method (Y. -Y.Wang and W. -H.Fang, ` TST-MUSIC for DOA-delay joint evaluation `, income 2000IEEE International Conference on Acoustics, Speech, and Signal processing. proceedings (Cat. No.00CH37100),6 month 2000, volume 5, page 2565-. The method realizes the matching process of the parameters by utilizing a tree structure, not only reaches the high-precision estimation of single parameters, but also can distinguish the parameter values with short distance. However, the TST method can only distinguish cases where one parameter is close, such as DOA close but other parameters far away. And the TST method is nearly invalid in an underdetermined scenario because the filtering matrix does not have the premise required by the method due to the underdetermined condition when the TST method performs spatial beamforming filtering.
Disclosure of Invention
Aiming at the defects or shortcomings in the prior art, the invention provides an underdetermined parameter joint estimation method based on high-order statistics and a non-uniform array, and aims to solve the technical problems that in the prior art, the calculation complexity is high, the estimation precision is low in the environment with low signal-to-noise ratio, the effective estimation of multiple parameters in an underdetermined scene cannot be carried out, and the like.
In order to achieve the above object, in a first aspect, the present invention provides an underdetermined parameter joint estimation method based on high-order statistics and a non-uniform array, including:
s1, acquiring original frequency domain channel data;
s2, calculating a fourth-order cumulant diagonal slice matrix of the current frequency domain channel data; dividing the diagonal slice matrix according to the number of multipath, calculating a propagation operator based on the divided matrix, further constructing a time delay estimation space spectrum, and searching a spectrum peak to obtain a time delay estimation value;
s3, calculating time delay domain filtering vectors corresponding to the time delay estimated values, and filtering the current frequency domain channel data by using the time delay domain filtering vectors to separate the frequency domain channel data corresponding to the time delay estimated values;
s4, calculating high-order cumulant matrixes by using frequency domain channel data corresponding to each time delay estimation value, constructing an arrival angle estimation space spectrum based on the high-order cumulant matrixes, and searching a spectrum peak to obtain the arrival angle estimation value corresponding to each time delay estimation value;
s5, constructing a delay response matrix and an array manifold matrix according to each delay estimated value and arrival angle estimated value; vectorizing the current frequency domain channel data, and estimating by combining the time delay response matrix and the array manifold matrix to obtain a channel complex gain matrix.
Further, the method further comprises:
s6, judging whether the iteration stop condition is met, if yes, ending the operation; if not, reconstructing the channel based on the delay response matrix, the array manifold matrix and the channel complex gain matrix, subtracting the reconstructed channel from the current frequency domain channel data, taking the residual frequency domain channel data as the current frequency domain channel data, and jumping to S2.
Further, in S2, after calculating the fourth-order cumulative quantity diagonal slice matrix of the current frequency-domain channel data, the method further includes: and performing forward and backward smoothing treatment on the fourth-order cumulant diagonal slice matrix to obtain a fourth-order cumulant diagonal slice matrix after forward and backward smoothing.
Further, in S3, the calculating a delay domain filter vector corresponding to each delay estimation value includes: and calculating a time delay domain filtering vector corresponding to each time delay estimation value by using a Lagrange multiplier with the aim of minimizing the noise average power after filtering.
Further, in S4, constructing an angle-of-arrival estimation spatial spectrum based on the high-order cumulant matrix, including:
performing singular value decomposition or characteristic decomposition on the high-order cumulant matrix to obtain a signal subspace and a noise subspace; an angle-of-arrival estimation spatial spectrum is defined based on orthogonality of the signal subspace and the noise subspace.
Further, in S5, the channel complex gain matrix is estimated based on the least square principle.
In a second aspect, the present invention provides an underdetermined parameter joint estimation apparatus based on high-order statistics and non-uniform arrays, including:
the acquisition module is used for acquiring the data of the original frequency domain channel;
the time delay estimation module is used for calculating a fourth-order cumulant diagonal slice matrix of the data of the current frequency domain channel; dividing the diagonal slice matrix according to the number of multipath, calculating a propagation operator based on the divided matrix, further constructing a time delay estimation space spectrum, and searching a spectrum peak to obtain a time delay estimation value;
the time delay filtering module is used for calculating time delay domain filtering vectors corresponding to the time delay estimation values and filtering the current frequency domain channel data by utilizing the time delay domain filtering vectors so as to separate the frequency domain channel data corresponding to the time delay estimation values;
the arrival angle estimation module is used for calculating a high-order cumulant matrix by using frequency domain channel data corresponding to each time delay estimation value, constructing an arrival angle estimation space spectrum based on the high-order cumulant matrix, and searching a spectrum peak to obtain the arrival angle estimation value corresponding to each time delay estimation value;
a complex gain estimation module used for constructing a delay response matrix and an array manifold matrix according to each delay estimation value and arrival angle estimation value; vectorizing the current frequency domain channel data, and estimating by combining the time delay response matrix and the array manifold matrix to obtain a channel complex gain matrix.
In a third aspect, the present invention provides a computer-readable storage medium comprising a stored computer program, wherein when the computer program is executed by a processor, the computer program controls a device in which the storage medium is located to perform the parameter joint estimation method according to the first aspect.
Generally, by the above technical solution conceived by the present invention, the following beneficial effects can be obtained:
(1) compared with other parameter joint estimation methods, the design method is based on the non-uniform array and high-order statistics, has larger array freedom degree, and can work in an underdetermined scene; the arrival angle estimation corresponding to each time delay estimation value is carried out by using a high-order accumulation method, so that the accuracy of the arrival angle estimation and the noise robustness can be improved, and the calculation complexity cannot be increased because the filtered channel data only contains one current path; meanwhile, the vectorization frequency domain channel is used for realizing correct channel complex gain estimation in an underdetermined scene, because in the underdetermined scene, the full rank of the array manifold matrix row does not have left inversion, the channel complex gain estimation based on the least square principle is invalid, and the least square principle can work normally after the vectorization frequency domain channel. Therefore, the design method has the advantages of large estimation freedom degree, high estimation precision, small calculation complexity and high noise robustness.
(2) The invention solves the problems of parameter misestimation and low-energy multipath incapability of estimation caused by noise in an iteration mode.
(3) Through a forward and backward smoothing technique, the similar parameters of the coherent signal can be distinguished.
Drawings
FIG. 1 is a flow chart of an underdetermined parameter joint estimation method based on high-order statistics and non-uniform arrays according to the present invention;
FIG. 2 is a schematic diagram of a six-element non-uniform linear array structure according to an embodiment of the present invention;
fig. 3 is a diagram of a relationship between a correlation between a reconstructed channel and a real channel and an iteration number according to an embodiment of the present invention;
fig. 4 is a performance curve diagram of parameter estimation under different signal-to-noise ratios according to the embodiment of the present invention, where (a), (b), (c), and (d) are a channel reconstruction similarity curve, a time delay estimation root-mean-square error graph, an arrival angle estimation root-mean-square error graph, and a channel complex gain amplitude root-mean-square error graph under different signal-to-noise ratios, respectively.
Detailed Description
In order to make the objects, system components, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In the present application, the terms "first," "second," and the like (if any) in the description and the drawings are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order.
Referring to fig. 1, the present invention provides a joint estimation method of underdetermined parameters based on high order statistics and non-uniform arrays. The method includes operations S1 through S6.
In operation S1, original frequency-domain channel data is acquired.
In this embodiment, the non-uniform array of the signal receiving end receives the incoming wave signal, and the frequency domain channel data H is obtained by processing the incoming wave signal, where H is a (θ) FV T (τ) + W. Wherein a (θ) ═ a (θ) 1 ) … a(θ P )]In the form of an array manifold matrix,
θ p is the angle of arrival of the p-th multipath signal. M is the number of antenna elements, d is the gap between the elements, and lambda is the wavelength of the signal. F ═ diag (beta) 1 ,…,β P ) For a channel complex gain matrix, beta p Representing the complex gain of the p-th multipath signal. V (τ) ═ V (τ) 1 ) … v(τ P )]In order to be a time-delay response matrix,
τ p the time delay of the p-th multipath signal. K is the number of frequency points, f k Representing the frequency.
The principle of the non-uniform array design of the signal receiving end is to maximize the non-repeatability of the virtual extended array element obtained by high-order cumulant. Specifically, the non-uniform antenna array structure is obtained by solving a mixed integer programming problem, which, when properly relaxed, can be described as follows:
subject to 1-INF·z m ≤q (m) D T ≤-1+INF·(1-z m )m＝1,…,M-1,
wherein
And M is the number of the antenna elements. The diagonal elements of the (M-1) xM matrix Q are all-1, the upper minor diagonal elements are all 1, i.e. Q i,i ＝-1、Q i,i+1 ＝1,i＝1,…,M-1，q (m) Representing the mth row of the matrix Q. And U is M (M-1)/2.
J i ＝[0 M-i,i-1 1 M-i I M-i ]，i＝1,…,M-1，1 U-1 (U-1). times.1 column vector, j, representing elements all 1 (u) Represents the u-th row of the matrix J, J [u] Represents the matrix J after the deletion of 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 Representing a matrix transpose operation. INF is a reasonably large number. This problem can be solved quickly using the CVX toolkit of MATLAB.
Operation S2, calculating a fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data; and dividing the diagonal slice matrix according to the number of the multipath, calculating a propagation operator based on the divided matrix, further constructing a time delay estimation space spectrum, and searching a spectrum peak to obtain a time delay estimation value.
It can be understood that when the fourth-order cumulative amount diagonal-slice matrix of the current frequency-domain channel data is first calculated, the current frequency-domain channel data is the original frequency-domain channel data.
S21, calculating a fourth-order cumulant diagonal slice matrix after forward and backward smoothing of the frequency domain channel data; let y be H H Push and press
And calculating a fourth-order cumulant diagonal slice matrix of the time delay estimation. Forward dividing the uniformly distributed frequency points into J sub-blocks, and calculating a fourth-order cumulant diagonal slice matrix R of time delay estimation on each sub-block T (j) J is 1. Fourth-order cumulant diagonal slice matrix of forward smooth delay estimation can be obtained after averaging
Push button
And calculating a fourth-order cumulant diagonal slice matrix of the corresponding backward smooth time delay estimation, wherein pi is a turnover matrix with all elements on the anti-diagonal being 1 and other positions being 0. Thereby according to
Obtaining a fourth-order cumulant diagonal slice matrix of time delay estimation after forward and backward smoothing
S22, calculating equivalent noise subspace by using an orthogonal propagation operator method, and converting the matrix into a matrix
Is divided into
Wherein G is 1 And G 2 Are K × P and K × (K-P) dimensional matrices, respectively, where P is the number of multipaths. Least squares estimation of the propagation operator P of
Wherein
Representing the generalized inverse of the matrix. Computing
And orthonormalizing it to
Q 0 ＝Q(Q H Q) -1/2
From the equivalent noise subspace Q 0 Constructing a time-delayed estimated spatial spectrum
Searching spectral peaks to obtain corresponding time delay parameter estimation values
Operation S3 is to calculate a delay domain filter vector corresponding to each delay estimation value, and filter the current frequency domain channel data using each delay domain filter vector to separate the frequency domain channel data corresponding to each delay estimation value.
S31, using the estimated time delay parameter value
Constructing a time delay response matrix
S32, the constrained time delay domain filtering vector calculation scheme is expressed as
Wherein
The resulting noise covariance matrix is calculated. Using Lagrange multipliers, delay domain filter vectors can be computed
Wherein
e i The i-th position is 1, and the remaining positions are 0, and the q × 1 column vector is represented by i ═ 1, …, and q. And filtering the frequency domain channel data
H i ＝H·w i
And separating the frequency domain channel data corresponding to each time delay estimation value. Then each H i All comprise only
The corresponding angle of arrival and the channel complex gain.
Operation S4, calculating a high-order cumulant matrix by using the frequency domain channel data corresponding to each time delay estimation value, constructing an arrival angle estimation spatial spectrum based on the high-order cumulant matrix, and searching a spectrum peak to obtain an arrival angle estimation value corresponding to each time delay estimation value.
S41, for the frequency domain channel data H corresponding to the ith multipath signal i Calculating the fourth-order cumulant matrix
Wherein
Representing the Kronecker product.
S42, decomposing the characteristics to obtain a noise subspace U n
R 4,i ＝UΣU H
U n ＝U(:,2:end)
Where U (: 2: end) represents the second to last columns of the matrix U. Constructing angle-of-arrival estimated spatial spectra
Wherein
Searching spectral peaks to obtain corresponding arrival angle parameter estimation values
Operation S5, constructing a delay response matrix and an array manifold matrix according to each of the delay estimation values and the arrival angle estimation values, respectively; vectorizing the current frequency domain channel data, and estimating by combining the time delay response matrix and the array manifold matrix to obtain a channel complex gain matrix.
S51, using the estimated time delay parameter
Angle of arrival parameter
Constructing a time delay response matrix
And array manifold matrix
S52, vectorizing the frequency domain channel, and estimating the corresponding signal complex gain based on the least square principle
Operation S6, determining whether an iteration stop condition is satisfied, and if so, ending the operation; if not, reconstructing the channel based on the delay response matrix, the array manifold matrix and the channel complex gain matrix, subtracting the reconstructed channel from the current frequency domain channel data, taking the residual frequency domain channel data as the current frequency domain channel data, and jumping to S2.
Wherein the stop condition may be that the number of iterations reaches, or the channel energy is lower than a threshold value, or the number of estimated multipaths reaches a limit value.
Under the condition that the iteration stop condition is not met, reconstructing a channel based on the current time delay response matrix, the array manifold matrix and the channel complex gain matrix, and reconstructing the channel
Can be expressed as:
subtracting the currently reconstructed channel from the input frequency domain channel data, i.e.
The remaining frequency-domain channel data is taken as the current frequency-domain channel data and the process proceeds to S2.
Example (b):
fig. 2 is a schematic diagram of a six-array-element non-uniform linear array structure used in the embodiment of the present invention, and the parameter joint estimation method in the underdetermined scene based on the high-order statistics and the non-uniform array of the present invention is applied to the antenna array and the large-scale multiple-input multiple-output wireless multipath channel to improve the accuracy of the parameter joint estimation in the underdetermined scene. In this embodiment, the center frequency of signal transmission is 3.5GHz, the bandwidth is 100.8MHz, and the frequency point interval is 30 kHz. The multi-path time delay is uniformly distributed from 10ns to 200ns, and the multi-path complex fading gain follows standard complex Gaussian distribution. The search granularity of the space spectrum peak in the time delay estimation stage is 1ns, and the search granularity of the spectrum peak in the arrival angle estimation stage is 1 degree. The signal-to-noise ratio is set to 0 dB. And taking the number of all the multipath obtained by estimation or the number of arrival iterations as a stopping criterion. The method specifically comprises the following steps:
(1) in the channel data generation stage, a signal sending end sends a pilot signal; the signal receiving end receives the incoming signalProcessing the signals to obtain channel sampling data, and obtaining frequency domain channel data through 3360-point inverse Fourier transform
(2) In the time delay estimation stage, a fourth-order cumulant diagonal slice matrix after forward and backward smoothing is calculated for frequency domain channel data, an equivalent noise subspace is obtained through an orthogonal propagation operator method, a time delay estimation space spectrum is constructed based on the MUSIC algorithm principle, and a spectrum peak is searched to obtain a time delay estimation value
(3) Computing a delay domain filter vector w i And filtering the frequency domain channel data H i ＝H·w i ；
(4) For the current estimated channel data H i Calculating a fourth-order cumulant matrix R 4,i Constructing an arrival angle space spectrum based on the MUSIC algorithm principle, searching a spectrum peak to obtain an arrival angle estimated value
(5) Constructing an array manifold matrix
And a delay response matrix
Estimating corresponding signal complex gain based on least square principle after vectorizing frequency domain channel
(6) Reconstruct the channel and subtract the current reconstructed channel from the input frequency domain channel data. And (5) in the case that the iteration stop condition is not met, continuing to execute the steps (2) to (6).
The high-precision multi-parameter joint estimation method realizes high-precision multi-parameter joint estimation under an underdetermined scene by utilizing the high-order cumulant and the non-uniform array. Different from the method used by the invention, the existing parameter joint estimation method can not realize underdetermined parameter estimation under the limited array element quantity, can not effectively control on the computational complexity, or can not distinguish the similar parameter values of the coherent signals. Meanwhile, the method also utilizes the excellent characteristic of automatically inhibiting Gaussian noise in a high-order cumulant theory and iterative interference elimination, realizes stronger robustness on the noise, and can still show good estimation performance under the condition of low signal-to-noise ratio.
Fig. 3 is a diagram of a relationship between a correlation between a reconstructed channel and a true channel and an iteration number according to an embodiment of the present invention. As can be seen from fig. 3, the channel reconstruction similarity of about 0.98 can be achieved with only a few iterations.
Fig. 4 is a performance curve diagram of parameter estimation under different signal-to-noise ratios according to the embodiment of the present invention, where (a), (b), (c), and (d) are a channel reconstruction similarity curve, a time delay estimation root-mean-square error graph, an arrival angle estimation root-mean-square error graph, and a channel complex gain amplitude root-mean-square error graph under different signal-to-noise ratios, respectively. As shown in fig. 4, even under low signal-to-noise ratio, the method still has channel reconstruction similarity of more than 0.93, and errors of parameter estimation are small, which proves that the method can perform high-precision multi-parameter joint estimation under an underdetermined scene.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. An underdetermined parameter joint estimation method based on high-order statistics and a non-uniform array is characterized by comprising the following steps:
s1, acquiring original frequency domain channel data;
s2, calculating a fourth-order cumulant diagonal slice matrix of the current frequency domain channel data; dividing the diagonal slice matrix according to the number of multipath, calculating a propagation operator based on the divided matrix, further constructing a time delay estimation space spectrum, and searching a spectrum peak to obtain a time delay estimation value;
s3, calculating time delay domain filtering vectors corresponding to the time delay estimated values, and filtering the current frequency domain channel data by using the time delay domain filtering vectors to separate the frequency domain channel data corresponding to the time delay estimated values;
s4, calculating high-order cumulant matrixes by using frequency domain channel data corresponding to each time delay estimation value, constructing an arrival angle estimation space spectrum based on the high-order cumulant matrixes, and searching a spectrum peak to obtain the arrival angle estimation value corresponding to each time delay estimation value;
s5, constructing a delay response matrix and an array manifold matrix according to each delay estimated value and arrival angle estimated value; vectorizing the current frequency domain channel data, and estimating by combining the time delay response matrix and the array manifold matrix to obtain a channel complex gain matrix.
2. The method for joint estimation of parameters according to claim 1, characterized in that said method further comprises:
s6, judging whether the iteration stop condition is met, if yes, ending the operation; if not, reconstructing the channel based on the delay response matrix, the array manifold matrix and the channel complex gain matrix, subtracting the reconstructed channel from the current frequency domain channel data, taking the residual frequency domain channel data as the current frequency domain channel data, and jumping to S2.
3. The parameter joint estimation method according to claim 1 or 2, wherein in S2, after calculating the fourth-order cumulant diagonal slice matrix of the current frequency-domain channel data, further comprising: and performing forward and backward smoothing treatment on the fourth-order cumulant diagonal slice matrix to obtain a fourth-order cumulant diagonal slice matrix after forward and backward smoothing.
4. The parameter joint estimation method according to claim 1 or 2, wherein in S3, calculating the delay domain filter vector corresponding to each delay estimation value includes: and calculating a time delay domain filtering vector corresponding to each time delay estimation value by using a Lagrange multiplier with the aim of minimizing the noise average power after filtering.
5. The parameter joint estimation method according to claim 1 or 2, wherein in S4, constructing the angle of arrival estimation spatial spectrum based on the high-order cumulant matrix includes:
performing singular value decomposition or characteristic decomposition on the high-order cumulant matrix to obtain a signal subspace and a noise subspace; an angle-of-arrival estimation spatial spectrum is defined based on orthogonality of the signal subspace and the noise subspace.
6. The method of joint estimation of parameters according to claim 1 or 2, wherein in S5, the channel complex gain matrix is estimated based on the least square principle.
7. An underdetermined parameter joint estimation device based on high-order statistics and a non-uniform array comprises the following components:
the acquisition module is used for acquiring the data of the original frequency domain channel;
the time delay estimation module is used for calculating a fourth-order cumulant diagonal slice matrix of the data of the current frequency domain channel; dividing the diagonal slice matrix according to the number of multipath, calculating a propagation operator based on the divided matrix, further constructing a time delay estimation space spectrum, and searching a spectrum peak to obtain a time delay estimation value;
the time delay filtering module is used for calculating time delay domain filtering vectors corresponding to the time delay estimation values and filtering the current frequency domain channel data by utilizing the time delay domain filtering vectors so as to separate the frequency domain channel data corresponding to the time delay estimation values;
the arrival angle estimation module is used for calculating a high-order cumulant matrix by using frequency domain channel data corresponding to each time delay estimation value, constructing an arrival angle estimation space spectrum based on the high-order cumulant matrix, and searching a spectrum peak to obtain the arrival angle estimation value corresponding to each time delay estimation value;
a complex gain estimation module, configured to construct a delay response matrix and an array manifold matrix according to each of the delay estimation values and the arrival angle estimation values; vectorizing the current frequency domain channel data, and estimating by combining the time delay response matrix and the array manifold matrix to obtain a channel complex gain matrix.
8. A computer-readable storage medium, comprising a stored computer program, wherein the computer program, when executed by a processor, controls an apparatus in which the storage medium is located to perform the method of jointly estimating parameters according to any one of claims 1 to 6.
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