Sparse array virtualization and degree of freedom improvement method based on polynomial interpolation

Abstract

The invention discloses a sparse array virtualization and degree-of-freedom improvement method based on polynomial interpolation. Constructing a virtual array according to a mathematical relationship between the number of physical array elements and a virtual aperture, and further determining a sparse array; receiving the signal by adopting each physical array element in the sparse array and processing to obtain a baseband signal; estimating a covariance matrix of the received signal according to the baseband signal, and constructing a virtual array containing holes; estimating the baseband signal by adopting a polynomial interpolation algorithm to obtain a virtual array element signal at the hole, and further forming a complete virtual array; and obtaining a full-rank covariance matrix for the complete virtual array by adopting a covariance matrix reconstruction method, and performing angle estimation on the full-rank covariance matrix by adopting a DOA (Direction of Arrival) estimation algorithm to obtain incident angle information of the target. According to the method, after the polynomial interpolation is calculated in advance, the calculation complexity is close to that of a traditional uniform linear array, received information can be utilized in a low-complexity mode, and target angle estimation with higher performance is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to an array signal processing method, in particular to a sparse array virtualization and degree of freedom improvement method based on polynomial interpolation. BACKGROUND

[0002] Existing researches mostly use the method of Virtual MIMO to improve the overall performance of multi-target detection, including detection accuracy and target number. However, the existing Virtual MIMO radars all use the method of uniform linear array to design the receiving array. Due to the short wavelength of millimeter wave radar and the sensitivity of parasitic effect, this array arrangement method will cause strong mutual coupling effect between channels, which greatly affects the azimuth estimation accuracy.

[0003] In order to solve this problem, the existing method mostly uses the method of increasing isolation to weaken the mutual coupling between channels, but inevitably increases the hardware complexity of the system. In addition, the high-frequency millimeter wave structure is compact and does not have the space to design isolation. For some already designed commercial millimeter wave radar systems, the antenna array cannot be redesigned. Therefore, the method of increasing the distance between channels through sparse array is the simplest and most effective method to solve the mutual coupling effect. At the same time, the hardware complexity of the radar system can be further reduced.

[0004] There are holes in the sparse array virtual array based on the configuration of coprime array. The existing researches mostly use the interpolation method based on convex optimization or machine learning to fill the holes and realize the expansion of the virtual aperture. However, these methods all have the problems of high computational complexity and high hardware requirements, which are difficult to meet the real-time requirements. SUMMARY

[0005] In order to solve the problems in the background art, the present application proposes a lightweight sparse array virtualization and degree of freedom improvement method based on polynomial interpolation, which is composed of a sparse array design method and a polynomial interpolation algorithm, thereby reducing the mutual coupling effect between antenna arrays, system hardware complexity and computational complexity, while realizing the improvement of degree of freedom, further improving the robustness and practicality of angle estimation, and meeting the real-time processing conditions.

[0006] The technical scheme adopted by the present application is: The present application comprises the following steps: S1, according to the preset physical array element number and the mathematical relationship between the physical array element number and the virtual aperture, the position set of the virtual array is constructed, and then the sparse array is determined; S2, using each physical array element in the sparse array to receive signals, performing signal preprocessing on the received signals to obtain baseband signals, and then performing power balancing processing to obtain balanced baseband signals; S3, estimating a covariance matrix of the received signal according to the equalized baseband signal, and constructing a virtual array with holes according to the covariance matrix and the position set of the virtual array; S4, estimating the virtual array element signal at the holes by using a polynomial interpolation algorithm on the equalized baseband signal, and filling the virtual array with holes to form a complete virtual array; S5, obtaining a full-rank Toeplitz covariance matrix by using a Toeplitz covariance matrix reconstruction method on the complete virtual array, and estimating the angle of arrival information of the detected target by using a DOA estimation algorithm on the full-rank Toeplitz covariance matrix.

[0007] The step 1 is specifically: S1.1, substituting the preset physical array element number into a mathematical relationship between the physical array element number and the virtual aperture to determine a value range of the virtual aperture; S1.2, traversing each value in the value range of the virtual aperture from large to small, constructing a position set of the virtual array according to the preset physical array element number and the current virtual aperture value, and stopping the traversal until the constructed position set of the virtual array satisfies that there is only one hole and the hole is located at the second half axis of the virtual array; S1.3, taking the position set of the virtual array finally generated in step S1.2 and the corresponding value of the virtual aperture as the final virtual array parameters, and taking the physical array element layout corresponding to the position set of the virtual array finally generated in step S1.2 as the sparse array.

[0008] The mathematical relationship between the physical array element number and the virtual aperture is set according to the following formula: Q∈[C 2 X-2 +X+1, C 2 X-1 +X+1] Wherein, Q represents the value of the virtual aperture, X represents the physical array element number, C 2 X-1 represents the number of combinations of taking any 2 different physical array elements from X-1 physical array elements.

[0009] In the step S2, the power equalization processing is specifically using a power equalizer at the receiving end physical array element.

[0010] The step S4 is specifically: S4.1, constructing the virtual array element signal into the form of the power sum of the incoherent target echo signal, and then constructing a polynomial by taking the incoherent target echo signal as the zero point of the polynomial; S4.2, solving the polynomial coefficients according to the equalized baseband signals of each physical array element and the relationship between the equalized baseband signals of each physical array element and the polynomial coefficients; S4.3, substituting the polynomial coefficients into the polynomial to solve the polynomial zero point, and then substituting the polynomial zero point into the virtual array element signal of step S4.1 to obtain the virtual array element signal at the hole; S4.4, and then filling the virtual array element signal at the hole into the virtual array containing the hole to form a complete virtual array.

[0011] The step S4.1 is specifically processed according to the following formula: S q =(-1) q ((y1) q +(y2) q +…+ (y K ) q ) f(t)=(t+ y1)(t+ y2)…(t+ y K )=t K +d1t K-1 + d2t K-2 +…+ d K Wherein, S q represents the virtual array element signal of the qth virtual array element, q∈[-(Q-1),Q-1], Q represents the value of the virtual aperture, f(t) is the polynomial constructed in step S4.1, y1, y2 and y K respectively represent the echo signals of the 1st, 2nd and Kth non-coherent targets, d1, d2 and d K respectively the K-1th, K-2th and constant term coefficients of the polynomial.

[0012] When the number of non-coherent targets existing in the space is less than or equal to the sequence number of the hole in the virtual array minus one, the relationship between the equalized baseband signals of each physical array element and the polynomial coefficients is set according to the following formula: d1=S1 d k =((S1) k -S k ) / C, k∈[2,K] Wherein, d k represents the coefficient of the K-kth term of the polynomial, K represents the number of non-coherent targets existing in the space, K≤Q-1, Q represents the value of the virtual aperture, S k represents the virtual array element signal of the kth virtual array element, and C represents a preset constant term. When the number of non-coherent targets existing in the space is greater than the sequence number of the hole in the virtual array minus one, the relationship between the balanced baseband signal of each physical array element and the polynomial coefficient is set according to the following formula: d1=S1 d k =((S1) k -S k ) / C, k∈[2,H-1]

[0013] Wherein, d k represents the K-kth term coefficient of the polynomial, K represents the number of non-coherent targets existing in the space, K≤Q-1, Q represents the value of the virtual aperture, S k represents the virtual array element signal of the kth virtual array element, d1, d2 and d K K-1th term coefficient, K-2th term coefficient and constant term of the polynomial respectively, and H represents the sequence number of the hole in the virtual array.

[0014] A computer device comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of the polynomial interpolation-based sparse array virtualization and degree of freedom improvement method when executing the computer program.

[0015] A computer readable storage medium, the storage medium stores a computer program, and the computer program is used to execute the steps of the above-mentioned polynomial interpolation-based sparse array virtualization and degree of freedom improvement method.

[0016] The beneficial effects of the present application are: 1. The polynomial interpolation method can fill in the holes in the virtual array through simple mathematical calculation, thereby reducing the calculation complexity of the radar array; 2. After pre-calculating the polynomial interpolation, the calculation complexity of the method tends to be close to that of the traditional uniform linear array, and all received information can be utilized in a low complexity manner.

[0017] 3. The lightweight interpolation method is suitable for most sparse arrays and direction of arrival estimation algorithms. Through the lightweight design method, the degree of freedom performance of the perception radar array can be further improved. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 It is a schematic diagram for MIMO radar system to detect target angle.

[0019] Figure 2 It is a flow chart for MIMO radar system to detect target angle.

[0020] Figure 3This is a schematic diagram of the sparse MIMO radar sensing platform of the present invention.

[0021] Figure 4 This is a diagram illustrating the effect of a 5-element sparse array detecting 8 targets in this embodiment.

[0022] Figure 5 This is a diagram illustrating the effect of a traditional 5-element uniform array detecting four targets. Detailed Implementation

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be 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 do not limit the scope of protection of this invention.

[0025] The embodiments of the present invention are as follows: like Figure 1 As shown, the specific implementation of the method of the present invention includes the mathematical relationship between the number of physical array elements and the virtual aperture of a lightweight sparse array, and the reception of signals by the sparse array. This allows the radar system to detect the direction of arrival of a target.

[0026] This embodiment includes the following steps: S1. Based on the preset number of physical array elements and the mathematical relationship between the number of physical array elements and the virtual aperture, construct the position set of the virtual array, and then determine the sparse array. In this embodiment, the number of physical array elements X is set to 5, and the value of the virtual aperture Q is determined to be 9. The structure is as follows: Figure 1 The lightweight sparse array configuration is shown. The specific value of Q is determined by the actual desired detection performance.

[0027] S2. The received signal S(t) is received by each physical element in the sparse array. The received signal is preprocessed to obtain the baseband signal, and then power equalization is performed to obtain the equalized baseband signal, that is, the power of the received baseband signal is equalized to σ. 2 ; S3. Estimate the covariance matrix R of the received signal based on the equalized baseband signal. x Then, based on the covariance matrix and the location set of the virtual array, a virtual array containing holes H is constructed; S4, the virtual array element signal at the hole is estimated by using a polynomial interpolation algorithm on the equalized baseband signal, and then filled into the virtual array containing the hole to form a complete virtual array; S5, a Toeplitz covariance matrix is obtained by using a Toeplitz covariance matrix reconstruction method on the complete virtual array, and then a DOA estimation algorithm is used on the full-rank Toeplitz covariance matrix to estimate the incident angle information of the detected target, so as to realize the improvement of the degree of freedom of the sparse array and the reduction of the computational complexity.

[0028] The received signal S(t) is collected by the radar system and is subjected to matching filtering, frequency mixing and other steps to obtain the baseband signal, i.e. the signal processing includes matching filtering and frequency mixing steps.

[0029] Based on the mathematical relationship between the number of physical elements and the virtual aperture of the lightweight sparse array given, the lightweight sparse array configuration is designed. Step 1 is specifically: S1.1, the preset physical element number is substituted into the mathematical relationship between the physical element number and the virtual aperture to determine the value range of the virtual aperture; S1.2, traverse each value in the value range of the virtual aperture from large to small, and construct a virtual array position set according to the preset physical element number and the current virtual aperture value, until the constructed virtual array position set meets the condition that there is only one hole and the hole is located in the second half axis of the virtual array, and the traversal stops; S1.3, the position set of the virtual array finally generated in step S1.2 and the corresponding value of the virtual aperture are taken as the final virtual array parameters, and the physical element layout corresponding to the position set of the virtual array finally generated in step S1.2 is taken as the sparse array.

[0030] The mathematical relationship between the number of physical elements and the virtual aperture is set according to the following formula: Q∈[C 2 X-2 +X+1, C 2 X-1 +X+1] Wherein, Q represents the value of the virtual aperture, X represents the number of physical elements, C 2 X-1 represents the number of combinations of taking any 2 different physical elements from X-1 physical elements.

[0031] That is, set the number of physical channels X of the sparse array, and expect to generate a virtual aperture Q. For X and Q at this time, it is judged whether X physical channels can generate a uniform linear array (ULA) with a virtual aperture of Q. The virtual aperture generation method is: fill X physical elements into the empty ULA with length Q by using the traversal method, and generate the corresponding virtual array.

[0032] The method for generating the virtual array V is to perform a difference operation on two physical channels, and the result is a virtual channel. Perform a difference operation on all physical channels two by two, and the corresponding virtual array V will be obtained.

[0033] The decision condition is specifically that the virtual array V generated at this time satisfies: 1) The hole H is located in the rear half axis of the virtual array (H ∈ [Q / 2, …, Q-2]); 2) V has filled all positions in Q except the hole.

[0034] If yes, it indicates that the sparse array design is completed; Otherwise, Q ’ = Q-1, and re-determine.

[0035] The method is suitable for radar system to detect target angle information. The received signal of each physical array element in the sparse array in step S2 is specifically: a radio frequency signal is transmitted by a transmitting end of a radar system for target detection, and the received signal of the physical array element is a baseband signal obtained through down-conversion, matching filtering and other processes of an echo signal collected by a receiving end of the radar system.

[0036] In step S2, the power balance processing is specifically using a power balancer at the receiving end physical array element.

[0037] Then, the received signal covariance matrix is estimated from the received signal, and the sparse array virtual array containing holes is obtained from the received signal covariance matrix. Based on the sparse array virtual array containing holes, a polynomial interpolation algorithm is used to fill the holes to form a complete sparse array virtual array.

[0038] The process of generating a virtual array element from the covariance matrix is specifically: the element r ij in the i-th row and j-th column of the covariance matrix is represented as: r ij = Σ K k=1 σ 2 k ∙exp[-j∙2πsinθ k ∙(i-j) / λ] The physical meaning is that the i-th physical array element and the j-th physical array element generate a virtual array element at the (i-j) position.

[0039] In step S5, the Toeplitz covariance matrix reconstruction method is specifically: the complete virtual array obtained in S4 is denoted as z, which is a second-order statistic, and satisfies the Hermitian positive semi-definite Toeplitz condition, so the Toeplitz covariance matrix reconstruction method can be used to recover the rank of z. The recovered covariance matrix is denoted as R To , and the process is: RTo = toeplitz (z)。

[0040] R To The conventional subspace-based DOA estimation algorithm such as the MUSIC or ESPRIT algorithm can be directly used for angle estimation of the target. Taking the MUSIC algorithm as an example, the spatial spectrum output by the MUSIC algorithm is obtained by the following formula: P MUSIC =1 / ( a H (θ) U N U N H a(θ)) Wherein, U N represents the noise subspace of R to , and a(θ) is the steering vector of the received signal. According to the principle of the MUSIC algorithm, the peak value of the spatial spectrum is the angle information of the target.

[0041] Step S4 is specifically: S4.1, the virtual array element signal is constructed as the power sum of the incoherent target echo signal, and then the incoherent target echo signal is regarded as the zero point of the polynomial to construct the polynomial; S4.2, the polynomial coefficients are solved according to the equalized baseband signals of each physical array element and the relationship between the equalized baseband signals of each physical array element and the polynomial coefficients; S4.3, the polynomial coefficients are substituted into the polynomial to solve the polynomial zero point, and then the polynomial zero point is substituted into the virtual array element signal in the power sum form in step S4.1 to calculate the virtual array element signal at the hole; S4.4, and then the virtual array element signal at the hole is filled into the virtual array containing the hole to form a complete virtual array.

[0042] The step S4.1 is specifically processed according to the following formula: S q =(-1) q ((y1) q +(y2) q +…+ (y K ) q ) f(t)=(t+ y1)(t+ y2)…(t+ y K )=t K +d1t K-1 + d2t K-2 +…+ d K Wherein, S qS q represents a virtual array element signal of the qth virtual array element, q is an index, q ∈ [- (Q-1), Q-1], Q represents a value of a virtual aperture, f (t) is a polynomial constructed in step S4.1, y1, y2 and y K respectively represent echo signals of the 1st, 2nd and Kth non-coherent targets, d1, d2 and d K respectively represent a K-1th order term coefficient, a K-2th order term coefficient and a constant term of the polynomial to be solved.

[0043] An origin of the virtual array is denoted as 0, a virtual aperture is a positive half-axis part of the virtual array origin, S q S q represents a virtual array element signal of the qth virtual array element, q < 0, S q Only contains mathematical meaning, is a negative half-axis part of the virtual array, and is physically meaningless.

[0044] When the number of non-coherent targets existing in the space is less than or equal to the sequence number of the aperture in the virtual array minus one (that is, K ≤ H-1), the subscript value range of S is [2, K], and the relationship between the baseband signals of the balanced physical array elements and the polynomial coefficients is set according to the following formula: d1 = S1 d k = ((S1 k -S k ) / C, k ∈ [2, K] wherein d k represents a K-kth order term coefficient of the polynomial, K represents the number of non-coherent targets existing in the space, K ≤ Q-1, Q represents a value of a virtual aperture, S k represents a virtual array element signal of the kth virtual array element, and C represents a preset constant term. When the number of non-coherent targets existing in the space is greater than the sequence number of the aperture in the virtual array minus one (that is, K > H-1), the subscript value range of S is [- (Q-1), Q-1], and the relationship between the baseband signals of the balanced physical array elements and the polynomial coefficients is set according to the following formula: d1 = S1 d k = ((S1 k -S k ) / C, k ∈ [2, H-1]

[0045] wherein d k represents a K-kth order term coefficient of the polynomial, K represents the number of non-coherent targets existing in the space, the maximum number of targets that can be detected by the array is a virtual aperture value minus one, that is, K ≤ Q-1, Q represents a value of a virtual aperture, S k represents a virtual array element signal of the kth virtual array element, d1, d2 and dK Let H represent the coefficients of the (K-1)th term, the (K-2)th term, and the constant term of the polynomial, respectively. Let H represent the sequence number of the hole in the virtual array, and A represent the coefficients of the (K-1)th term, the (K-2)th term, and the constant term. H H This represents the number of combinations of H physical array elements chosen from H physical array elements.

[0046] The virtual array element S at hole H is calculated using a polynomial interpolation algorithm. H And fill it into the virtual array V containing holes to form a full-rank virtual array Q.

[0047] In this embodiment, the hole appears at position 7, i.e., H=7. The polynomial interpolation algorithm is as follows: S7=(-1) 7 (y1 7 + y2 7 +…+ y K 7 ) Where S7 is the virtual array element at hole 7, K is the number of incoherent targets in space, and y k ∈Y={y1,y2,…,y K} are the zeros of the polynomial f(t).

[0048] like Figure 2 As shown, the experimental setup and simulation results of the interpolation method of the present invention are demonstrated: simulations were performed using MATLAB to verify the feasibility, robustness, practicality, and performance of the interpolation method of the present invention. The experimental setup was implemented in the MATLAB environment, with 8 incoherent random targets in space, and angles randomly generated; the element positions of the sparse array were set to [0, 3, 4, 6, 8]; the system signal-to-noise ratio was 30dB; and the number of snapshots was 500. The received signal S(t) and the received signal covariance matrix R were then generated. x .

[0049] First, interpolation formulas for the eight objectives are calculated using a polynomial interpolation algorithm, and the formulas are set as follows: d1=S1 d2 = (d1) 2 -S2) / 2 d3=(d1 3 -3∙S1∙S2+2∙S3) / 6 d4=(S1 4 -6∙S1 2 •S2+8•S1•S3+3•S2 2 -6∙S4) / 24 d5=(S1 5 -30∙S1∙S4-15∙S2 2- 60*d3*S2 + 60*d2*S3 + 24*S5) / 120; d6 = 6*d5*(S -1 2 - S -2 -1 3 - 7*S -1 -2 - 2*S -3 d7 = 2*d6*S -1 -1 2 - S -2 d8 = d7 / S -1 Then, the hole can be filled by the following formula, which is set as follows: S7 = (-1) 7 (y1 7 + y2 7 +…+ y K 7 ) Finally, the Toeplitz covariance matrix reconstruction method is used to restore the rank of the virtual array, and the commonly used DOA estimation algorithm is used for angle estimation, so as to realize the improvement of the system degree of freedom and the reduction of the calculation complexity. The Toeplitz covariance matrix reconstruction method is represented as: for the second-order statistics z corresponding to the complete sparse array virtual array, it satisfies the Hermitian semi-positive Toeplitz condition, can be restored by using the Toeplitz matrix reconstruction method, and the following formula is used to obtain, which is set as follows: R To = toeplitz (z).

[0050] R To is input into the baseband signal processor, and the traditional DOA estimation algorithm is used, so that the detection effect as shown in Figure 2 can be realized: 8 targets are detected by using 5 receiving array elements. Compared with the traditional method of detecting 4 targets by using 5 receiving array elements, the interpolation method has robustness and practicability.

[0051] The specific embodiments described above have explained the technical solutions and beneficial effects of the present application in detail, and it should be understood that the above description is only the most preferred embodiment of the present application, and is not used to limit the present application. Any modification, supplement and equivalent replacement, etc. made within the principle range of the present application shall be included in the protection scope of the present application.​​​​​

Claims

1. A method for sparse matrix virtualization and degree-of-freedom enhancement based on polynomial interpolation, characterized in that, The method includes the following steps: S1. Based on the preset number of physical array elements and the mathematical relationship between the number of physical array elements and the virtual aperture, construct the position set of the virtual array, and then determine the sparse array. S2. The signals are received by each physical element in the sparse array, the received signals are preprocessed to obtain the baseband signal, and then power equalization is performed to obtain the equalized baseband signal. S3. Estimate the covariance matrix of the received signal based on the equalized baseband signal, and then construct a virtual array containing holes based on the covariance matrix and the location set of the virtual array. S4. The equalized baseband signal is estimated using a polynomial interpolation algorithm to obtain the virtual array element signal at the hole, and then filled into the virtual array containing the hole to form a complete virtual array. S5. The Toeplitz covariance matrix reconstruction method is used to obtain the full-rank Toeplitz covariance matrix of the complete virtual array. Then, the DOA estimation algorithm is used to estimate the angle of the detection target to obtain the incident angle information of the detection target.

2. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 1, characterized in that: Step 1 specifically involves: S1.1 Substitute the preset number of physical array elements into the mathematical relationship between the number of physical array elements and the virtual aperture to determine the range of values ​​for the virtual aperture. S1.

2. Traverse each value from largest to smallest within the range of virtual aperture values. Construct a set of virtual array positions based on the preset number of physical array elements and the current virtual aperture value. The traversal stops when the constructed set of virtual array positions satisfies the condition that there is only one hole and the hole is located on the rear half axis of the virtual array. S1.

3. The position set of the virtual array finally generated in step S1.2 and the corresponding virtual aperture values ​​are used as the final virtual array parameters, and the physical array element layout corresponding to the position set of the virtual array finally generated in step S1.2 is used as a sparse array.

3. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 1, characterized in that: The mathematical relationship between the number of physical array elements and the virtual aperture is set according to the following formula: Q∈[C 2 X-2 +X+1, C 2 X-1 +X+1] Where Q represents the value of the virtual aperture, X represents the number of physical array elements, and C 2 X-1 This represents the number of combinations of randomly selecting two different physical array elements from X-1 physical array elements.

4. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 1, characterized in that: In step S2, the power equalization process specifically involves using a power equalizer on the physical array elements at the receiving end.

5. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 1, characterized in that: Step S4 specifically involves: S4.1 Construct the virtual array element signal into the form of a power sum of incoherent target echo signals, and then use the incoherent target echo signals as polynomial zeros to construct a polynomial. S4.2 Solve for the polynomial coefficients based on the baseband signal after equalization of each physical array element and the relationship between the baseband signal after equalization of each physical array element and the polynomial coefficients. S4.3 Substitute the polynomial coefficients into the polynomial to solve for the polynomial zeros, and then substitute the polynomial zeros into the virtual array element signal in the form of power sum in step S4.1 to calculate the virtual array element signal at the hole. S4.4 Then, the virtual array element signals at the holes are filled into the virtual array containing the holes to form a complete virtual array.

6. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 5, characterized in that: Step S4.1 is specifically processed according to the following formula: S q =(-1) q ((y1) q +(y2) q +…+ (y K ) q ) f(t)=(t+ y1)(t+ y2)…(t+ y K )=t K +d1t K-1 + d2t K-2 +…+ d K Among them, S q Let f(t) represent the virtual element signal of the q-th virtual element, q∈[-(Q-1),Q-1], where Q represents the value of the virtual aperture, f(t) is the polynomial constructed in step S4.1, and y1, y2 and y3 are the virtual array elements. K Let d1, d2, and d3 represent the echo signals of the 1st, 2nd, and Kth incoherent targets, respectively. K Let the coefficients of the (K-1)th term, the (K-2)th term, and the constant term of the polynomial be defined separately.

7. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 6, characterized in that: When the number of incoherent targets in space is less than or equal to the sequence number of the hole in the virtual array minus one, the relationship between the baseband signal after equalization of each physical array element and the polynomial coefficients is set according to the following formula: d1=S1 d k =((S1) k -S k ) / C , k∈[2,K] Where, d k S represents the coefficient of the Kk-th term of the polynomial, where K represents the number of incoherent targets in space, K ≤ Q-1, Q represents the value of the virtual aperture, and S k This represents the virtual element signal of the k-th virtual element, and C represents a preset constant term; When the number of incoherent targets in space is greater than the sequence number of the hole in the virtual array minus one, the relationship between the baseband signal after equalization of each physical array element and the polynomial coefficients is set according to the following formula: d1=S1 d k =((S1) k -S k ) / C , k∈[2,H-1] ； Where, d k Let S represent the coefficient of the Kk-th term of the polynomial, where K represents the number of incoherent targets in space, K ≤ Q-1, and Q represents the value of the virtual aperture. k The virtual element signals d1, d2, and d3 represent the k-th virtual element. K Let H represent the coefficients of the (K-1)th term, the (K-2)th term, and the constant term of the polynomial, respectively, and let H represent the sequence number of the hole in the virtual array.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program for performing the method described in any one of claims 1 to 7.

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