Augmented MUSIC-based DOA estimation method assisted by semi-passive intelligent reflection surface

Abstract

The invention discloses a DOA estimation method assisted by a semi-passive intelligent reflection surface based on augmented MUSIC, and belongs to the field of wireless positioning. The method comprises the following steps: firstly, constructing a semi-passive intelligent reflection surface assisted DOA estimation model to obtain a received signal; secondly, calculating a covariance matrix of a received signal, performing characteristic decomposition on the covariance matrix, and estimating noise power; then, calculating a Gram matrix of a received signal, performing characteristic decomposition on the Gram matrix, and estimating noise power; and finally, constructing a cost function, and searching to obtain DOA estimation. According to the DOA estimation method, the target can be effectively sensed under the condition that the base station is shielded, and DOA estimation is carried out.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless positioning, and particularly relates to a DOA estimation method assisted by a semi-passive intelligent reflecting surface based on augmented MUSIC. Background Art

[0002] With the rapid development of modern wireless communication systems, accurate target positioning and direction estimation technologies are of great significance in many fields, such as unmanned driving, radar, wireless communication, and intelligent transportation. Traditional direction estimation methods are mainly based on the Multiple Signal Classification (MUSIC) algorithm, which achieves good direction estimation performance under the array antenna structure. However, this method faces many challenges in complex environments, such as multipath effects, non-line-of-sight propagation, and performance degradation in low signal-to-noise ratio scenarios.

[0003] In recent years, the introduction of semi-passive intelligent reflecting surfaces has provided new possibilities for the fields of wireless communication and positioning. The semi-passive intelligent reflecting surface can significantly enhance the signal propagation path by programmatically regulating the reflected signals, especially in the presence of obstacles or signal fading. However, the traditional MUSIC algorithm fails to fully utilize the angle-related information in the semi-passive intelligent reflecting surface system, especially the potential angle information contained in the Passive Reflecting Elements (PREs), resulting in the DOA (Direction of Arrival) estimation performance not reaching the theoretical optimum.

[0004] To solve the above problems, methods based on Atomic Norm Minimization (ANM) have been proposed in recent years. ANM utilizes the sparse characteristics of signals to reconstruct the target signal through convex optimization techniques. However, the ANM method has a high computational complexity, and in practical applications, fine adjustment of the optimization parameters is required, which poses a high requirement for real-time processing capabilities. Especially in a semi-passive intelligent reflecting surface-assisted system, the ANM algorithm performs excellently in high-precision estimation, but its complexity makes it not practically popularizable in large-scale systems.

[0005] In this context, to make up for the respective deficiencies of the MUSIC and ANM algorithms, there is an urgent need for a new algorithm that can not only fully utilize the angle information in the semi-passive intelligent reflecting surface-assisted system but also improve the DOA estimation accuracy while ensuring a moderate computational complexity. Summary of the Invention

[0006] The present invention provides a DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface, which can combine the low complexity characteristics of the traditional MUSIC algorithm. Meanwhile, by effectively utilizing the information contained in the semi-passive intelligent reflecting surface assisted system, the DOA estimation performance in complex environments is significantly improved. In addition, by introducing an adaptive weighting mechanism, the utilization efficiency of signals is further optimized, and it performs outstandingly in balancing accuracy and complexity.

[0007] An embodiment of the present invention provides a DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface, including the following steps:

[0008] Step 1, construct a DOA estimation model assisted by a semi-passive intelligent reflecting surface, and obtain the received signals of the active sensor array in the DOA estimation model assisted by the semi-passive intelligent reflecting surface;

[0009] Step 2, calculate the covariance matrix of the received signals of the active sensor array, perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues, signal subspace, and noise subspace, and estimate the noise power according to the decomposed eigenvalues;

[0010] Step 3, calculate the Gram matrix of the received signals of the active sensor array, perform eigenvalue decomposition on the Gram matrix to obtain eigenvalues, signal subspace, and noise subspace, and estimate the noise power according to the decomposed eigenvalues;

[0011] Step 4, use the noise subspace, signal subspace, and noise power estimation values obtained in Step 2 and Step 3 to construct a cost function, and perform spectral peak search on the cost function to obtain the DOA estimation result.

[0012] Optionally, in an embodiment of the present invention, in Step 1, both the passive reflection array and the active sensing array equipped in the DOA estimation model assisted by the semi-passive intelligent reflecting surface are uniform linear arrays, and the number of array elements is M R and M S , respectively. The channel between the base station and the passive reflection array is expressed as:

[0013]

[0014] where the superscript H represents conjugate transpose, represents the channel loss, λ is the signal wavelength, d B2R is the distance between the base station and the intelligent reflecting surface, θ B2R and respectively represent the angle of arrival on the passive reflection array and the angle of departure of the base station, a R and a B respectively represent the array response vectors of the passive reflection array and the base station;

[0015] For a uniform linear array with an element spacing of half a wavelength, at a given angle θ, the i-th element of the array response vector is expressed as e j(i-1)πsinθ , where j represents the imaginary unit, and the channel from the passive reflecting array to target k and then to the active sensing array is expressed as:

[0016]

[0017] where, θ k represents the angle of arrival of the k-th target on the active sensing array, a S represents the array response vector of the active sensing array, represents the channel loss from the passive reflecting array to target k and then to the active sensing array, d k represents the distance between the intelligent reflecting surface and target k, γ k is the radar cross section of target k;

[0018] Assume that the targets are all in the far field of the intelligent reflecting surface, and the element spacings of the passive reflecting array, the active sensing array, and the array on the base station are all half a wavelength. The intelligent reflecting surface adjusts its beam every snapshot, with a total of T snapshots. Then, the phase shift vector of the passive reflecting array at the t-th snapshot is:

[0019]

[0020] where the superscript T represents the transpose, represents the phase shift of the i-th element of the passive reflecting array;

[0021] The echo signal received by the active sensing array at the t-th snapshot is expressed as:

[0022]

[0023] where, represents the diagonal matrix composed of , represents the transmit power of the base station, s(t) is the transmit signal with unit power, n(t) is a circularly additive Gaussian white noise vector, and each of its elements follows a complex normal distribution represents the noise power, w is the beamforming vector, and satisfies ||w|| 2 = 1, |||| represents the l 2 norm;

[0024] To maximize the received signal power of the active sensing array, the base station aligns the beam with the intelligent reflecting surface, that is Then there is:

[0025]

[0026] where \(K\) represents the number of far-field targets,

[0027] The received signal obtained by stacking the echo signals of \(T\) snapshots received by the active sensing array is:

[0028]

[0029] where,

[0030]

[0031] Optionally, in an embodiment of the present invention, in step 2, calculate the covariance matrix of the received signal of the active sensor array

[0032]

[0033] Perform eigenvalue decomposition on the covariance matrix to obtain the estimated values of the eigenvalues \(\lambda\) i , the signal subspace \(U\) s , and the noise subspace \(U\) n . The estimated value of the noise power is:

[0034]

[0035] where, represents the estimated value of the eigenvalue \(\lambda\) i .

[0036] Optionally, in an embodiment of the present invention, in step 3, calculate the Gram matrix of the received signal of the active sensor array as:

[0037]

[0038] Perform eigenvalue decomposition on the Gram matrix to obtain the estimated values of the eigenvalues \(\mu\) i , the signal subspace \(V\) s , and the noise subspace \(V\) n . The estimated value of the noise power is:

[0039]

[0040] where, represents the estimated value of the eigenvalue \(\mu\) i .

[0041] Optionally, in an embodiment of the present invention, in step 4, construct the cost function as:

[0042]

[0043]

[0044] wherein, represents the (i, j)-th element of the matrix , and respectively represent the eigenvalue λ obtained by eigenvalue decomposition of the covariance matrix i , the signal subspace U s , and the estimated value of the noise subspace U n . The superscript * represents the conjugate. respectively represent the eigenvalue μ obtained by eigenvalue decomposition of the Gram matrix i , the signal subspace V s , and the estimated value of the noise subspace V n . The superscript * represents the conjugate. and respectively represent the noise powers obtained from the covariance matrix and the Gram matrix;

[0045] When θ = θ k , the cost function reaches an extreme value. Perform a spectral peak search on the cost function, and the coordinates corresponding to the peak are the DOA estimation result.

[0046] The DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface according to the embodiments of the present invention makes full use of the angle information contained in the semi-passive intelligent reflecting surface assisted system, and improves the DOA estimation accuracy compared with the traditional MUSIC algorithm. By designing an adaptive weighting framework, the algorithm proposed in the present invention realizes more efficient information extraction. Compared with the ANM method, the algorithm proposed in the present invention achieves performance close to the CRB while maintaining a low computational complexity. Under various transmission powers and snapshot numbers, the algorithm proposed in the present invention exhibits robust direction estimation capabilities.

[0047] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of the embodiments in conjunction with the drawings, wherein:

[0049] Figure 1 is a flowchart of a DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface according to an embodiment of the present invention;

[0050] Figure 2 is a scene diagram of DOA estimation assisted by a semi-passive intelligent reflecting surface according to an embodiment of the present invention;

[0051] Figure 3 Schematic diagram of the computational complexity of the embodiment of the present invention and the traditional DOA estimation method under different numbers of passive reflecting elements;

[0052] Figure 4 Schematic diagram of the root mean square error performance of the embodiment of the present invention and the traditional DOA estimation method under different transmission powers;

[0053] Figure 5 Schematic diagram of the root mean square error performance of the embodiment of the present invention and the traditional DOA estimation method under different numbers of snapshots. Detailed implementation manners

[0054] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0055] Figure 1 It is a flowchart of a DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface according to an embodiment of the present invention.

[0056] As Figure 1 shown, the DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface includes the following steps:

[0057] Step 1, construct a DOA estimation model assisted by a semi-passive intelligent reflecting surface, and obtain the received signals of the active sensor array in the DOA estimation model assisted by the semi-passive intelligent reflecting surface.

[0058] As Figure 2 shown, consider a sensing scenario assisted by a semi-passive intelligent reflecting surface located in a two-dimensional plane. The system configuration includes K far-field targets and a base station equipped with a uniform linear array with M B antennas. Assume that the line-of-sight path between the base station and the target is blocked. In order to sense the DOA of the target, a semi-passive intelligent reflecting surface is used to construct a non-line-of-sight path. Assume that both the passive reflecting array and the active sensing array equipped in the semi-passive intelligent reflecting surface are uniform linear arrays, and the number of array elements is M R and M S . Then the channel between the base station and the passive reflecting array can be expressed as:

[0059]

[0060] where the superscript H represents conjugate transpose, denotes the channel loss, λ is the signal wavelength, d B2R is the distance between the base station and the intelligent reflecting surface, θ B2R and respectively represent the DOA on the passive reflection array and the departure angle of the base station, a R and a B respectively represent the array response vectors of the passive reflection array and the base station. For a uniform linear array with an element spacing of half a wavelength, at a given angle θ, the i-th element of its array response vector can be expressed as e j(i-1)πsinθ , where j represents the imaginary unit. The channel from the passive reflection array to target k and then to the active sensing array can be expressed as:

[0061]

[0062] where, θ k represents the DOA of the k-th target on the active sensing array, a S represents the array response vector of the active sensing array, represents the channel loss from the passive reflection array to target k and then to the active sensing array, d k represents the distance between the intelligent reflecting surface and target k, γ k is the radar cross section of target k. Assuming that the targets are all in the far field of the intelligent reflecting surface, and the element spacings of the arrays on the passive reflection array, the active sensing array, and the base station are all half a wavelength, the intelligent reflecting surface adjusts the beam once per snapshot, with a total of T snapshots. Then, the phase shift vector of the passive reflection array at the t-th snapshot is:

[0063]

[0064] where the superscript T represents the transpose, represents the phase shift of the i-th element of the passive reflection array. The echo signal received by the active sensing array at the t-th snapshot can be expressed as:

[0065]

[0066] where, represents the diagonal matrix composed of , represents the transmit power of the base station, s(t) is the transmit signal with unit power, n(t) is the circularly additive Gaussian white noise vector, and each of its elements follows a complex normal distribution represents the noise power, w is the beamforming vector, and satisfies ||w|| 2 =1, ||·|| represents l 2Norm. To maximize the received signal power of the active sensing array, the base station should align the beam towards the intelligent reflecting surface, that is We have:

[0067]

[0068] where Stacking the echo signals of the received \(T\) snapshots, we get:

[0069]

[0070] where

[0071]

[0072] Step 2: Calculate the covariance matrix of the received signals of the active sensor array, perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues, signal subspace, and noise subspace, and estimate the noise power based on the decomposed eigenvalues.

[0073] The covariance matrix of the received signals can be expressed as where

[0074] denotes the mathematical expectation, denotes the \(M\) S dimensional identity matrix. Performing eigenvalue decomposition on \(R\) x gives:

[0075]

[0076] where the eigenvalues \(\lambda\) i satisfy The corresponding eigenvectors form the signal subspace \(U\) s and the noise subspace \(U\) n .

[0077] In practical applications, due to the limited number of snapshots, the estimated value of the covariance matrix \(R\) x is obtained through calculation. Performing eigenvalue decomposition on gives the estimated values of the eigenvalues \(\lambda\) i , the signal subspace \(U\) s , and the noise subspace \(U\) n : The estimated value of the noise power is:

[0078]

[0079] Step 3: Calculate the Gram matrix of the received signals of the active sensor array, perform eigenvalue decomposition on the Gram matrix to obtain eigenvalues, signal subspace, and noise subspace, and estimate the noise power according to the decomposed eigenvalues.

[0080] Define the Gram matrix:

[0081]

[0082] When M S tends to infinity, there is:

[0083]

[0084] where G s = Λ H Λ, I T represents the T-dimensional identity matrix. Performing eigenvalue decomposition on G x yields:

[0085]

[0086] where the eigenvalues μ i satisfy The corresponding eigenvectors form the signal subspace V s and the noise subspace V n .

[0087] In practical applications, since M S is finite, the Gram matrix is approximated by . Performing eigenvalue decomposition on yields the estimated values of the eigenvalues μ i , the signal subspace V s , and the noise subspace V n . The estimated value of the noise power is: The estimated value of the noise power is:

[0088]

[0089] Step 4: Use the noise subspace, signal subspace, and the estimated value of the noise power obtained in Step 2 and Step 3 to construct a cost function, and perform a spectral peak search on the cost function to obtain the estimated result of the angle of arrival.

[0090] Using the noise subspace, signal subspace, and the estimated value of the noise power obtained in Step 2 and Step 3, construct the following cost function:

[0091]

[0092] where represents the (i, j)-th element of the matrix ;

[0093]

[0094] When θ = θ k the cost function reaches an extreme value. Then, perform a spectral peak search on the cost function, and the coordinates corresponding to the peak are the estimated result of the DOA.

[0095] Figure 3 Shows the variation of the computational complexity (number of complex multiplications) of the method of the present invention and the traditional DOA estimation method with the number of passive reflecting array elements. The simulation conditions are as follows: 6 targets, the base station, the passive reflecting array, and the active sensor array are all equipped with uniform linear arrays. Among them, the number of array elements of the base station and the passive reflecting array is the same, the active sensor array is equipped with 10 array elements, the number of snapshots is 50, the grid search range is from -90° to 90°, and the search step is 0.1°. From Figure 3 it can be seen that the computational complexity of the method of the present invention is between that of the traditional MUSIC method and the ANM method.

[0096] The performance estimation criterion of the present invention is the root mean square error (RMSE) which is defined as:

[0097]

[0098] where M c is the number of Monte Carlo experiments, represents the DOA estimated value of target k in the i-th experiment, and θ k represents the true value of the DOA of target k.

[0099] Figure 4 Shows the performance curve of the root mean square error of the method of the present invention and the MUSIC method and the ANM method with the change of the transmit power. The simulation conditions are as follows: the signal s(t) = 1, the carrier frequency is 28 GHz, M B = M R = 32, M S = 16, K = 4, d B2R = 40 m, γ k = 10 dBsm, the target DOA is θ 1 = -60°, θ 2 = -10°, θ 3 = 10°, θ 4 = 60°, d 1 = 5 m, d 2 = 6 m, d 3 = 7 m, d 4 = 8 m, and the error tolerance in the ANM algorithm is set to 1000. T = 50, the grid search range is from -90° to 90°, the search step size is 0.01°, and the simulation is performed 500 times. From Figure 4 It can be seen that the DOA estimation accuracy of the present invention is always better than that of the traditional MUSIC method, is close to the ANM method, and can approach the Cramér-Rao bound (CRB).

[0100] Figure 5 The performance curve of the root mean square error of the method of the present invention, the MUSIC method, and the ANM method with respect to the number of snapshots is shown. The simulation conditions are set as follows: the signal s(t) = 1, the carrier frequency is 28 GHz, M B = M R = 32, M S = 16, K = 4, d B2R = 40 m, γ k = 10 dBsm, The target DOA is θ 1 = -60°, θ 2 = -10°, θ 3 = 10°, θ 4 = 60°, d 1 = 5 m, d 2 = 6 m, d 3 = 7 m, d 4 = 8 m, the error tolerance in the ANM algorithm is set to 1000, The grid search range is from -90° to 90°, the search step size is 0.01°, and the simulation is performed 500 times. From Figure 5 It can be seen that the DOA estimation accuracy of the present invention is always better than that of the traditional MUSIC method, is close to the ANM method, and can approach the CRB.

[0101] From the analysis of the simulation effect diagram, it can be known that a DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface proposed by the present invention can effectively estimate the target DOA. In addition, this method can make full use of the characteristics of the semi-passive intelligent reflecting surface, and improves the DOA estimation accuracy compared with the traditional MUSIC algorithm. Compared with the ANM algorithm, the algorithm proposed by the present invention achieves a performance close to the CRB while maintaining a low computational complexity.

[0102] The DOA estimation method based on augmented MUSIC assisted by a semi-passive intelligent reflecting surface according to the embodiments of the present invention. First, construct a DOA estimation model assisted by a semi-passive intelligent reflecting surface to obtain the received signal. Second, calculate the covariance matrix of the received signal, perform eigenvalue decomposition on it, and estimate the noise power. Then, calculate the Gram matrix of the received signal, perform eigenvalue decomposition on it, and estimate the noise power. Finally, construct a cost function and search to obtain the DOA estimation. The DOA estimation method designed by the present invention can effectively sense the target and perform DOA estimation when the base station is blocked. In addition, this method makes full use of the characteristics of the intelligent reflecting surface and introduces an adaptive weighting mechanism, which can robustly estimate the DOA. The simulation results show that the DOA estimation accuracy of the algorithm proposed by the present invention is better than that of the traditional MUSIC method, close to the ANM algorithm and approaching the CRB.

[0103] In the description of this specification, the descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0104] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0105] Any process or method description in the flowchart or described in other ways herein can be understood as representing a module, segment, or part of code including one or N executable instructions for implementing a customized logical function or process, and the scope of the preferred embodiments of the present invention includes additional implementations, where the functions can be executed in a substantially simultaneous manner or in a reverse order according to the involved functions, rather than in the order shown or discussed, which should be understood by those skilled in the art of the embodiments of the present invention.

Claims

1. A DOA estimation method assisted by a semi-passive intelligent reflective surface based on augmented MUSIC, characterized in that: The following steps are involved: Step 1, constructing a semi-passive intelligent reflective surface assisted DOA estimation model, and obtaining a received signal of an active sensor array in the semi-passive intelligent reflective surface assisted DOA estimation model; Step 2, calculating the covariance matrix of the received signal of the active sensor array, performing eigendecomposition on the covariance matrix to obtain eigenvalues, signal subspace, and noise subspace, and estimating noise power according to the decomposed eigenvalues; Step 3, calculating the Gram matrix of the received signal of the active sensor array, performing eigendecomposition on the Gram matrix to obtain eigenvalues, signal subspace, and noise subspace, and estimating noise power according to the decomposed eigenvalues; Step 4: construct a cost function using the noise subspace, signal subspace and noise power estimation value obtained in steps 2 and 3, and perform spectrum peak search on the cost function to obtain an angle of arrival estimation result.

2. The method according to claim 1, characterized in that In step 1, the passive reflection array and active sensor array in the semi-passive intelligent reflection surface assisted DOA estimation model are both uniform linear arrays, and the number of array elements is M and M respectively. R and M S , the channel between the base station and the passive reflective array is expressed as: The superscript H represents the conjugate transpose. represents the channel loss, λ is the signal wavelength, d B2R is the distance between the base station and the smart reflective surface, θ B2R and They represent the arrival angle on the passive reflection array and the departure angle of the base station, respectively. R and a B denote the array response vectors of the passive reflection array and the base station respectively; For a uniform linear array with an element spacing of half a wavelength, at a given angle θ, the i-th element of the array response vector is expressed as e j(i-1)πsinθ , where j represents the imaginary unit, and the channel from the passive reflection array to the target k and then to the active sensing array is expressed as: Among them, θ k represents the arrival angle of the kth target on the active sensor array, a S represents the array response vector of the active sensing array, represents the channel loss from the passive reflection array to the target k and then to the active sensor array, d k represents the distance between the smart reflective surface and the target k, γ k is the radar cross section of target k; Assuming that the targets are all in the far field of the smart reflective surface, the array element spacing of the passive reflective array, active sensor array, and array on the base station is half a wavelength. The intelligent reflective surface adjusts the beam once for each snapshot, with a total of T snapshots. The phase shift vector of the passive reflective array at the tth snapshot is: The superscript T indicates transposition. represents the phase shift of the i-th element of the passive reflective array; The echo signal received by the active sensing array at the tth snapshot time is expressed as: in, Indicated by The diagonal matrix formed by represents the transmission power of the base station, s(t) is the transmission signal of unit power, and n(t) is the circular additive white Gaussian noise vector, each element of which obeys the complex normal distribution represents the noise power, w is the beamforming vector, and satisfies ||w|| 2 =1,|||| represents l2 norm; To maximize the received signal power of the active sensing array, the base station aims the beam at the smart reflective surface, i.e. Then we have: Where K represents the number of far-field targets, The received signal obtained by stacking the T snapshot echo signals received by the active sensor array is: in, 3. The method according to claim 2, characterized in that In step 2, the covariance matrix of the received signal of the active sensor array is calculated Perform eigendecomposition on the covariance matrix to obtain the eigenvalue λ i , signal subspace U s , noise subspace U n The estimated value of the noise power is: in, Denotes the eigenvalue λ i The estimated value of .

4. The method according to claim 2, characterized in that: In step 3, the Gram matrix of the received signal of the active sensor array is calculated as: Perform eigendecomposition on the Gram matrix to obtain the eigenvalue μ i , signal subspace V s , noise subspace V n The estimated value of the noise power is: in, represents the eigenvalue μ i The estimated value of .

5. The method according to claim 2, characterized in that: In step 4, the cost function is constructed as: in, Representation Matrix The (i,j)th element of They represent the eigenvalues ​​λ obtained by eigendecomposition of the covariance matrix. i , signal subspace U s , noise subspace U n The estimated value of They represent the eigenvalues ​​μ obtained by eigendecomposition of the Gram matrix. i , signal subspace V s , noise subspace V n The estimated value of , the superscript * indicates conjugation, and Represent the noise power obtained by the covariance matrix and Gram matrix respectively; When θ=θ k When , the cost function obtains an extreme value, a spectrum peak search is performed on the cost function, and the coordinates corresponding to the peak value are the estimation results of the angle of arrival.

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