Two-dimensional DOA estimation method and device based on linear antenna array circumferential motion

Abstract

The application discloses a two-dimensional DOA estimation method and device based on linear antenna array circumferential motion, which considers the diversity of array motion direction on one hand, sets the initial array as a general linear array, takes the reference element of the linear array as the center of a circle, controls the linear array to make circumferential motion, carries out signal sampling once every certain central angle of the circle, then carries out phase compensation on the sampling signals at each moment, and comprehensively processes the signals at each moment after processing and the sampling signal at the initial moment, so that the comprehensive receiving signals corresponding to the virtual concentric circle array can be obtained, the leap from the linear array to the virtual concentric circle array is completed, the two-dimensional DOA estimation of the one-dimensional linear array is realized, and the degree of freedom is greatly improved. On the other hand, the complexity and applicability of the traditional MUSIC algorithm are considered, and the application further provides a decoupling reduced-complexity MUSIC algorithm based on polynomial expansion, which can greatly reduce the complexity while ensuring the estimation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a two-dimensional DOA estimation method and device based on circular motion of a linear antenna array. Background Art

[0002] DOA estimation (Direction of Arrival) involves performing a spatial Fourier transform on the received signal, squaring the modulus to obtain the spatial spectrum, and estimating the signal's direction of arrival. Key DOA estimation methods include ARMA spectral analysis, maximum likelihood analysis, entropy spectral analysis, and eigendecomposition. Key eigendecomposition methods include the MUSIC algorithm, ESPRIT algorithm, and WSF algorithm.

[0003] Among existing array motion schemes and corresponding DOA estimation methods, the paper (Ramirez Jr J, Krolik JL. Synthetic aperture processing for passive co-prime linear sensor arrays [J]. Digital Signal Processing, 2017, 61: 62-75.) discloses an enhanced coprime linear array motion method. Considering a coprime linear array, it performs uniform linear motion along its own linear direction. Signal sampling is performed every half wavelength (or after a fixed time delay), and phase correction is performed on the received signal. The signal coherence time (TCP) determines the array motion time. Finally, all received signals obtained during the motion time are comprehensively processed to further improve the degrees of freedom (DOF). In the MUSIC (SS-MUSIC) algorithm based on spatial smoothing technology of coprime arrays, after vectorizing the covariance matrix of the received signal, the idea of ​​array element coordinate difference set can be used to create many virtual array elements. However, it can only use the continuous coordinate part in the difference set, resulting in low utilization rate of virtual array elements. This paper uses the idea of ​​array motion and further fills the breakpoint part in the difference set through the temporal continuity of the signal, making the difference set without breakpoints, thereby making full use of the virtual array elements to improve the degree of freedom.

[0004] However, while the method in this paper significantly increases the degrees of freedom, its array aperture is still limited to one dimension, making it impossible to achieve two-dimensional DOA estimation. Furthermore, the array motion direction in this paper is fixed to the linear direction of the array, failing to account for the diversity of array motion directions, which affects estimation accuracy and the dimensionality of the estimable parameters. This invention, however, fully considers the diversity of array motion directions and proposes a circular motion scheme for the linear array. This scheme can achieve the transition from a linear array to a virtual concentric circular array, completing two-dimensional DOA estimation and further improving estimation accuracy and degrees of freedom. Furthermore, considering that directly using the traditional MUSIC algorithm would result in higher complexity and that existing dimensionality reduction MUSIC algorithms cannot be directly applied to the solution of the present invention, the present invention further proposes a polynomial expansion-based decoupled reduced-complexity MUSIC (PE-DRC MUSIC) algorithm. By using decoupling and dimensionality reduction methods, only two 1-D spectral peak searches are performed, which can expand the array aperture of a general linear array to two dimensions and achieve two-dimensional DOA estimation for a one-dimensional linear array. This method reduces complexity while further improving estimation performance and practicality. Summary of the Invention

[0005] The present invention takes into account the diversity of array motion directions and aims to propose a two-dimensional DOA estimation method and device based on the circular motion of a linear antenna array, breaking through the limitation that a single linear array can only perform one-dimensional DOA estimation. A polynomial expansion-based decoupled reduced complexity MUSIC (PE-DRC MUSIC) algorithm is further proposed to achieve two-dimensional DOA estimation with high degrees of freedom, high estimation accuracy and low complexity.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention provides a two-dimensional DOA estimation method based on the circular motion of a linear antenna array, comprising the following steps:

[0008] S1. Move the linear array in a circular motion with the reference element as the center, and sample the signal every time it moves to the set center angle to obtain the sampled signal at each moment;

[0009] S2. Perform phase compensation on the sampling signal at each moment to obtain a processed phase compensated signal at each moment;

[0010] S3, performing comprehensive processing on the processed phase compensation signals at each moment and the sampling signal at the initial moment to obtain a comprehensive receiving signal corresponding to the virtual concentric circle array;

[0011] S4. Based on the polynomial expansion method, the array flow form of the integrated received signal is converted into the Vandermonde form, and the parameters to be estimated are decoupled at the same time;

[0012] S5. Use the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated and obtain the DOA estimation value.

[0013] Furthermore, in step S1, the sampled signal received by the array at time t is:

[0014]

[0015] Where K is the number of uncorrelated far-field narrowband signals incident on the array in space, s k (t) is the kth received signal, θ k and are the azimuth and elevation angles of the kth signal, n(t) is the noise vector, and the array flow pattern is:

[0016]

[0017] Where Ω is the angular velocity of the circular motion, and φ0 is the phase of the array element relative to the y-axis at the initial position. When the initial position is on the y-axis, φ0 = 0°.

[0018] Furthermore, in step S2, it is assumed that the coherence time of the signal is TCP=N cir τ cir , each circumference of the virtual concentric circle array formed after the movement has N cir +1 array element, then at t+n cir τ cir The array receiving signal at the moment is:

[0019]

[0020] The superimposed phase correction factor is obtained at t+n cir τ cir Phase compensation signal at time:

[0021]

[0022] Where K is the number of uncorrelated far-field narrowband signals incident on the array in space, s k (t) is the kth received signal, θ k and are the azimuth and elevation angles of the kth signal, Ω is the angular velocity of circular motion, n(t+n cir τ cir ) is t+n cir τ cir The noise vector at time , t+n cir τ cir The noise vector after phase compensation at time N cir is the number of elements of a single virtual circular array, τ cir is the sampling interval, n cir Range is 0 to N cir .

[0023] Furthermore, in step S3, the synchronous received signals at each moment are grouped according to the row number and the first row elements are removed to obtain the integrated received signal corresponding to the virtual concentric circle array as follows:

[0024]

[0025] in, express The mth row element of ;

[0026] The virtual array flow pattern after the circular motion of the mth array element is expressed as:

[0027]

[0028] Among them, θ k and are the azimuth and elevation angles of the kth signal, φ0 is the phase of the array element relative to the y-axis at the initial position, Ω is the angular velocity of the circular motion, and d = λ / 2 is half the wavelength.

[0029] Furthermore, step S4 converts the structural form of the array flow pattern into a Vandermonde form based on Jacobi-Anger expansion or Taylor expansion, and simultaneously completes the decoupling of the parameters to be estimated.

[0030] Furthermore, according to the Jacobi-Anger expansion, the virtual array flow pattern after the circular motion of the mth array element is expressed as:

[0031]

[0032] in,

[0033]

[0034]

[0035] Furthermore, based on Taylor expansion, the virtual array flow pattern after the circular motion of the mth array element is expressed as:

[0036]

[0037] in,

[0038] Furthermore, step S5 uses the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated as follows:

[0039] First, construct the DOA estimation problem as:

[0040]

[0041] Based on polynomial decomposition, the above estimation problem can be further written as:

[0042]

[0043] To avoid zero solutions Introduce the following constraints The vector e1 is:

[0044]

[0045] Further construct the optimization problem:

[0046]

[0047]

[0048] According to the Lagrange multiplier method, the following function is defined:

[0049]

[0050] in, ε is a constant.

[0051] Next, the vector Taking partial derivatives we get:

[0052]

[0053] Let the above formula be 0 to get:

[0054]

[0055] in,

[0056] Bringing the above equation back to the original DOA estimation problem, the estimated value of the azimuth angle θ is:

[0057]

[0058] At the same time, the pitch angle is estimated, and the 2K azimuth angle estimates including the fuzzy angle are jointly estimated with the pitch angle, that is:

[0059]

[0060] in, is the estimated value of the azimuth angle θ.

[0061] Furthermore, among the 2K sets of DOA estimates obtained, the spectral function is selected The larger K groups of DOA estimates are taken as the final estimation results.

[0062] On the other hand, the present invention also provides a two-dimensional DOA estimation system based on circular motion of a linear array, comprising the following modules to implement any of the above-mentioned two-dimensional DOA estimation methods based on circular motion of a linear antenna array:

[0063] The signal sampling module is used to move the linear array in a circular motion with the reference array element as the center, and perform signal sampling every time the linear array moves to the set center angle to obtain the sampling signal at each moment;

[0064] A phase compensation module is used to perform phase compensation on the sampling signal at each moment to obtain a processed phase compensated signal at each moment;

[0065] A signal synthesis processing module is used to synthesize the phase compensation signals at each moment after processing and the sampling signal at the initial moment to obtain a synthetic reception signal corresponding to the virtual concentric circle array;

[0066] PE-DRC MUSIC algorithm module, based on the polynomial expansion method, converts the array flow form of the integrated received signal into the Vandermonde form, decouples the parameters to be estimated, and uses the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated to obtain the DOA estimation value.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] The present invention proposes a two-dimensional DOA estimation method and device based on circular motion of a linear antenna array. Taking into account the diversity of array motion directions, the initial array is set as a general linear array. With the reference element of the linear array as the center, the linear array is controlled to perform circular motion. Signal sampling is performed every certain central angle (which can be designed based on the number of virtual elements to be generated). Phase compensation is then performed on the sampled signals at each moment, and the processed signals at each moment are combined with the sampled signals at the initial moment to obtain a composite received signal corresponding to a virtual concentric circular array. This completes the transition from the linear array to the virtual concentric circular array, achieving dimensional expansion of the aperture. This method can expand the array aperture of a general linear array to two dimensions, enabling two-dimensional DOA estimation for a one-dimensional linear array while significantly increasing the degrees of freedom. Furthermore, considering that directly using a traditional MUSIC algorithm would result in high complexity and that existing dimensionality-reduced MUSIC algorithms cannot be directly applied to the present invention's solution, the present invention further proposes a polynomial expansion-based decoupled reduced complexity MUSIC (PE-DRCMUSIC) algorithm, which can improve estimation accuracy while significantly reducing complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments described in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0070] Figure 1 A three-dimensional diagram of the circular motion of a linear array provided by the present invention;

[0071] Figure 2 A top view of the circular motion of the linear array provided by the present invention;

[0072] Figure 3 This is a functional module diagram of the two-dimensional DOA estimation device based on the circular motion of the linear antenna array provided by the present invention.

[0073] Figure 4 This is a structural diagram of the electronic device provided by the present invention.

[0074] Figure 5 This is a flow chart of the two-dimensional DOA estimation method based on the circular motion of a linear antenna array provided by the present invention. DETAILED DESCRIPTION

[0075] In order to better understand the present technical solution, the following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solution in the embodiments of the present invention. Obviously, the examples described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field based on this application fall within the scope of protection of the present invention.

[0076] The present invention proposes a two-dimensional DOA estimation method based on the circular motion of a linear antenna array. Taking into account the diversity of array motion directions, the initial array is set as a general linear array. With the reference element of the linear array as the center, the linear array is controlled to perform circular motion. The time-coherence period (TCP) sets the total duration of the array motion. Signal sampling is performed once every time the linear array moves at a certain central angle (which can be designed based on the number of virtual elements required). Phase compensation is then performed on the sampled signals at each moment, and the processed signals at each moment are combined with the sampled signals at the initial moment to obtain a composite received signal corresponding to the virtual concentric circular array. This completes the transition from the linear array to the virtual concentric circular array, achieving dimensional expansion of the aperture while greatly increasing the degrees of freedom. Finally, a polynomial expansion method and a decoupling complexity reduction algorithm are used to achieve high-precision and low-complexity two-dimensional DOA estimation.

[0077] like Figure 1 As shown in Figure 1, consider a general linear array with M elements. Define d = λ / 2 as half a wavelength. Without loss of generality, assume that the general linear array on the y-axis is in circular motion.

[0078] Assume that there are K uncorrelated far-field narrowband signals incident on the array, and the kth received signal is s k (t), θ k and are the azimuth and elevation angles of the kth signal respectively. Therefore, the received signal of the array at time t is:

[0079]

[0080] Among them, the array flow pattern is:

[0081]

[0082] Ω is the angular velocity of circular motion, φ0 is the phase of the array element relative to the y-axis at the initial position. When the initial position is on the y-axis, φ0 = 0°.

[0083] According to the design rules of the circular array, it is assumed that the coherence time of the signal is TCP = N cir τ cir, each circumference of the virtual concentric circle array formed after the movement has N cir +1 array element. Accordingly, at t+n cir τ cir The array receiving signal at the moment is:

[0084]

[0085] Adding the phase correction factor yields:

[0086]

[0087] By grouping the synchronous received signals at each moment according to the row number and removing the first row elements, the corresponding synthetic array received signal is specifically expressed as follows:

[0088]

[0089] in, express The mth row element of . Array flow type A cir Array flow pattern equivalent to concentric circle array (such as Figure 2 Therefore, the construction of a virtual concentric circle array and the two-dimensional expansion of the aperture can be achieved through circular motion, thereby enhancing the flexible adaptation of the moving route in mobile scenarios.

[0090] According to the array receiving signal model under the above circular motion, the virtual array flow pattern after the circular motion of the mth array element can be expressed as:

[0091]

[0092] Unlike conventional linear or planar arrays, the array flow pattern does not conform to the Vandermonde determinant construction rules. Furthermore, traditional DOA estimation algorithms require a two-dimensional search, which is highly complex. Therefore, the present invention utilizes polynomial expansion methods such as Jacobi-Anger expansion and Taylor expansion to convert the array flow pattern structure into a Vandermonde form, simultaneously decoupling the parameters to be estimated.

[0093] According to Jacobi-Anger expansion J n (z) is the first kind of Bessel function, the nth cir The term can be expanded to:

[0094]

[0095] in, When the order of the Bessel function n J More than several items When , the Bessel function value will approach 0, so nJ The range can be further narrowed to -N J ≤n J ≤N J . The nth array flow pattern cir The term can be further expressed as:

[0096]

[0097] in, Therefore, the array flow pattern can be further written as:

[0098]

[0099] Similarly, based on Taylor expansion The nth array flow pattern cir The term can be expressed as:

[0100]

[0101] because non-negative integer n t The range can be further narrowed to 0≤n t ≤N t ,N t =7, the array flow pattern can be further expressed as:

[0102]

[0103] in, Similarly, the corresponding array flow pattern can be expressed as:

[0104]

[0105] Therefore, the array flow pattern of the virtual concentric circle array can be expressed as:

[0106]

[0107] in, P J (z) and P t (z) is uniformly defined as P(z), and The unified definition is

[0108] According to the above Jacobi-Anger expansion and Taylor expansion, the polynomial expansion can effectively decouple the parameters to be estimated, so that the Lagrange multiplier method can be further used to obtain the equation relationship between the parameters to be estimated, thereby realizing low-complexity, high-precision super-resolution direction finding.

[0109] In particular, the DOA estimation problem is first constructed as:

[0110]

[0111] Based on the above polynomial decomposition analysis, the estimation problem can be further written as:

[0112]

[0113] To avoid zero-value solutions The following constraint condition is introduced where the vector e1 is:

[0114]

[0115] Further, the optimization problem is constructed as:

[0116]

[0117]

[0118] According to the Lagrange multiplier method, the following function is defined:

[0119]

[0120] where, ε is a constant.

[0121] Next, the partial derivative of the vector is taken to obtain:

[0122]

[0123] Setting the above equation to 0 yields:

[0124]

[0125] where,

[0126] Bringing the above equation back to the original DOA estimation problem yields the estimated value of the azimuth angle θ as:

[0127]

[0128] It is worth noting that, here, due to the Bessel function having the following property: J n (-z m ) = (-1) n J n (z m ), and This will cause phase ambiguity in the azimuth angle estimation, and the difference between the true angle and the ambiguous angle is π. To further solve the phase ambiguity problem and estimate the pitch angle at the same time, the present invention jointly estimates the 2K azimuth angle estimates including the ambiguous angle with the pitch angle, namely:

[0129]

[0130] In the final 2K sets of DOA estimates, select the spectral function A larger K groups of DOA estimation values ​​are used as the final estimation result, which can eliminate phase ambiguity and realize automatic pairing of azimuth and elevation angles.

[0131] like Figure 5 As shown, the two-dimensional DOA estimation method based on the circular motion of the linear antenna array proposed in the present invention is summarized as follows:

[0132] S1. Move the linear array in a circular motion with the reference element as the center, and sample the signal every time it moves to the set center angle to obtain the sampled signal at each moment;

[0133] S2. Perform phase compensation on the sampling signal at each moment to obtain a processed phase compensated signal at each moment;

[0134] S3, performing comprehensive processing on the processed phase compensation signals at each moment and the sampling signal at the initial moment to obtain a comprehensive receiving signal corresponding to the virtual concentric circle array;

[0135] S4. Based on the polynomial expansion method, the array flow form of the integrated received signal is converted into the Vandermonde form, and the parameters to be estimated are decoupled at the same time;

[0136] S5. Use the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated and obtain the DOA estimation value.

[0137] Corresponding to the above method, the present invention also provides a two-dimensional DOA estimation device based on the circular motion of a linear antenna array, such as Figure 3 As shown, the following modules are included to implement the above-mentioned two-dimensional DOA estimation method based on the circular motion of the linear antenna array:

[0138] The signal sampling module 301 is used to move the linear array in a circular motion with the reference element as the center, and perform signal sampling once each time the linear array moves to a set central angle to obtain a sampled signal at each moment;

[0139] The phase compensation module 302 is used to perform phase compensation on the sampling signal at each moment to obtain a processed phase compensated signal at each moment;

[0140] The signal synthesis processing module 303 is used to synthesize the processed phase compensation signals at each moment and the sampling signal at the initial moment to obtain a synthetic reception signal corresponding to the virtual concentric circle array;

[0141] The PE-DRC MUSIC algorithm module 305 converts the array flow form of the integrated received signal into the Vandermonde form based on the polynomial expansion method, decouples the parameters to be estimated, and uses the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated to obtain the DOA estimation value.

[0142] Corresponding to the two-dimensional DOA estimation method based on circular motion of a linear antenna array provided in the above-mentioned embodiment of the present invention, an embodiment of the present invention further provides an electronic device, which is a control device in a wireless hierarchical edge network.

[0143] like Figure 4 As shown, the electronic device includes a processor 401, a communication interface 402, a memory 403 and a communication bus 404, wherein the processor 401, the communication interface 402, and the memory 403 communicate with each other via the communication bus 404;

[0144] Memory 403, used for storing computer programs;

[0145] Processor 401 is configured to, when executing the program stored in memory 403, implement the steps of any of the above-described methods for two-dimensional DOA estimation based on circular motion of a linear antenna array provided in the embodiments of the present invention. The foregoing description merely provides a detailed description of the preferred embodiments and principles of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, any modifications, equivalent substitutions, and improvements made based on the concepts provided by the present invention and within the spirit and principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A two-dimensional DOA estimation method based on circular motion of a linear antenna array, characterized in that: The steps include: S1. Move the linear array in a circular motion with the reference element as the center, and sample the signal every time it moves to the set center angle to obtain the sampled signal at each moment; the sampled signal received by the array at time t is: Where K is the number of uncorrelated far-field narrowband signals incident on the array in space, s k (t) is the kth received signal, θ k and are the azimuth and elevation angles of the kth signal, n(t) is the noise vector, and the array flow pattern is: Where Ω is the angular velocity of the circular motion, φ0 is the phase of the array element relative to the y-axis at the initial position. When the initial position is on the y-axis, φ0 = 0°. S2. Perform phase compensation on the sampling signal at each moment to obtain the phase compensated signal at each moment after processing; assuming that the coherence time of the signal is TCP = N cir τ cir , each circumference of the virtual concentric circle array formed after the movement has N cir +1 array element, then at t+n cir τ cir The array receiving signal at the moment is: The superimposed phase correction factor is obtained at t+n cir τ cir Phase compensation signal at time: Where K is the number of uncorrelated far-field narrowband signals incident on the array in space, s k (t) is the kth received signal, θ k and are the azimuth and elevation angles of the kth signal, Ω is the angular velocity of circular motion, n(t+n cir τ cir ) is t+n cir τ cir The noise vector at time , t+n cir τ cir The noise vector after phase compensation at time N cir is the number of elements of a single virtual circular array, τ cir is the sampling interval, n cir Range is 0 to N cir ; S3. The processed phase compensation signals at each moment are integrated with the sampling signals at the initial moment to obtain an integrated received signal corresponding to the virtual concentric circle array; the synchronous received signals at each moment are grouped according to the row number and the first row elements are removed to obtain an integrated received signal corresponding to the virtual concentric circle array as follows: in, express The mth row element of ; The virtual array flow pattern after the circular motion of the mth array element is expressed as: Among them, θ k and are the azimuth and elevation angles of the kth signal, φ0 is the phase of the array element relative to the y-axis at the initial position, Ω is the angular velocity of the circular motion, and d = λ / 2 is half the wavelength; S4, based on the polynomial expansion method of Jacobi-Anger expansion or Taylor expansion, the array flow form of the integrated received signal is converted into the Vandermonde form, and the parameters to be estimated are decoupled at the same time; According to Jacobi-Anger expansion, the virtual array flow pattern after the circular motion of the mth array element is expressed as: in, Based on Taylor expansion, the virtual array flow pattern after the circular motion of the mth array element is expressed as: in, S5. Use the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated and obtain the DOA estimation value.

2. The two-dimensional DOA estimation method based on circular motion of a linear antenna array according to claim 1, characterized in that: Step S5 uses the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated as follows: First, construct the DOA estimation problem as: Based on polynomial decomposition, the above estimation problem can be further written as: To avoid zero solutions Introduce the following constraints The vector e1 is: Further construct the optimization problem: According to the Lagrange multiplier method, the following function is defined: in, ε is a constant; Next, the vector Taking partial derivatives we get: Let the above formula be 0 to get: in, Bringing the above equation back to the original DOA estimation problem, the estimated value of the azimuth angle θ is: At the same time, the pitch angle is estimated, and the 2K azimuth angle estimates including the fuzzy angle are jointly estimated with the pitch angle, that is: in, is the estimated value of the azimuth angle θ.

3. The two-dimensional DOA estimation method based on circular motion of a linear antenna array according to claim 2, characterized in that: Among the 2K groups of DOA estimates obtained, select the spectral function The larger K groups of DOA estimates are taken as the final estimation results.

4. A two-dimensional DOA estimation device based on circular motion of a linear antenna array, characterized in that: The method includes the following modules to implement the two-dimensional DOA estimation method based on circular motion of a linear antenna array according to any one of claims 1 to 3: The signal sampling module is used to move the linear array in a circular motion with the reference array element as the center, and perform signal sampling every time the linear array moves to the set center angle to obtain the sampling signal at each moment; A phase compensation module is used to perform phase compensation on the sampling signal at each moment to obtain a processed phase compensated signal at each moment; A signal synthesis processing module is used to synthesize the processed phase compensation signals at each moment and the sampling signal at the initial moment to obtain a synthetic reception signal corresponding to the virtual concentric circle array; PE-DRC MUSIC algorithm module,The PE-DRC MUSIC algorithm module converts the structural form of the array flow pattern of the integrated received signal into the Vandermonde form based on the polynomial expansion method, and at the same time decouples the parameters to be estimated, and uses the Lagrange multiplier method to obtain the equation relationship between the parameters to be estimated, and obtains the DOA estimation value.

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