A method for sparse matrix virtualization and degree of freedom promotion based on polynomial interpolation

Abstract

The application discloses a kind of sparse matrix virtualization and degree of freedom promotion method based on polynomial interpolation.The virtual array is constructed according to the mathematical relationship between the number of physical array elements and virtual aperture, and then the sparse array is determined.The baseband signal is obtained by receiving signal and processing using each physical array element in the sparse array.The covariance matrix of the received signal is estimated according to the baseband signal, and the virtual array containing holes is constructed.The virtual array element signal at the hole is estimated by using polynomial interpolation algorithm to estimate the baseband signal, and then the complete virtual array is formed.The full rank covariance matrix is obtained by using covariance matrix reconstruction method on the complete virtual array, and then the DOA estimation algorithm is used on the full rank covariance matrix to estimate the angle and obtain the incident angle information of the target.In the application, the complexity of the calculation is close to that of the traditional uniform linear array after the polynomial interpolation is calculated in advance, and the received information can be used in a low complexity way to achieve higher performance target angle estimation.

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, the parasitic effect is sensitive, and 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, by using the method of sparse array, the distance between channels is increased, which 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 arrays, and the existing researches mostly use interpolation methods 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, the system hardware complexity and the computational complexity, while realizing the improvement of the 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:

[0007] The present application comprises the following steps:

[0008] 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;

[0009] S2, receiving signals by each physical array element in the sparse array, performing signal preprocessing on the received signals to obtain baseband signals, and then performing power equalization processing to obtain the equalized baseband signals;

[0010] S3, estimating the covariance matrix of the received signals according to the equalized baseband signals, and then constructing a virtual array with holes according to the covariance matrix and the position set of the virtual array;

[0011] S4, estimating the virtual array element signals at the holes by using a polynomial interpolation algorithm on the equalized baseband signals, and then filling the virtual array with holes to form a complete virtual array;

[0012] S5, obtaining a full-rank Toeplitz covariance matrix by using a Toeplitz covariance matrix reconstruction method on the complete virtual array, and then estimating the angle by using a DOA estimation algorithm on the full-rank Toeplitz covariance matrix to obtain the incident angle information of the detected target.

[0013] The step 1 is specifically:

[0014] S1.1, substituting 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 value range of the virtual aperture;

[0015] 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 number of physical array elements 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 on the second half axis of the virtual array;

[0016] 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.

[0017] The mathematical relationship between the number of physical array elements and the virtual aperture is set according to the following formula:

[0018] Q∈[C 2 X-2 +X+1, C 2 X-1 +X+1]

[0019] Wherein, Q represents the value of the virtual aperture, X represents the number of physical array elements, C 2 X-1 represents the number of combinations of taking any 2 different physical array elements from X-1 physical array elements.

[0020] The power equalization processing in the step S2 is specifically using a power equalizer at the receiving end physical array element.

[0021] The step S4 is specifically:

[0022] S4.1, constructing the virtual array element signal into a form of power sum of the non-coherent target echo signals, and further constructing the non-coherent target echo signals as the zero points of the polynomial;

[0023] 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;

[0024] S4.3, substituting the polynomial coefficients into the polynomial to solve the polynomial zero points, and further substituting the polynomial zero points into the virtual array element signal in the power sum form in the step S4.1 to calculate the virtual array element signal at the hole;

[0025] S4.4, and further filling the virtual array element signal at the hole into the virtual array containing the hole to form a complete virtual array.

[0026] The step S4.1 is specifically processed according to the following formula:

[0027] S q =(-1) q ((y1) q +(y2) q +…+ (y K ) q )

[0028] f(t)=(t+ y1)(t+ y2)…(t+ y K )=t K +d1t K-1 + d2t K-2 +…+ d K

[0029] 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 the step S4.1, y1, y2 and y K represent the echo signals of the 1st, 2nd and Kth non-coherent targets respectively, d1, d2 and d K represent the K-1th, K-2th and constant term coefficients of the polynomial respectively.

[0030] 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:

[0031] d1=S1

[0032] d k =((S1) k -S k ) / C, k∈[2,K]

[0033] 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.

[0034] 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, the relationship between the balanced baseband signal of each physical array element and the polynomial coefficient is set according to the following formula:

[0035] d1=S1

[0036] d k =((S1) k -S k ) / C, k∈[2,H-1]

[0037]

[0038] 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, d1, d2 and d K represent the coefficient of the K-1th term, the coefficient of the K-2th term and the constant term of the polynomial respectively, and H represents the sequence number of the aperture in the virtual array.

[0039] 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 promotion method when executing the computer program.

[0040] A computer readable 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 promotion method.

[0041] The beneficial effects of the present application are:

[0042] 1. The polynomial interpolation method can fill the aperture in the virtual array through simple mathematical calculation, thereby reducing the calculation complexity of the radar array.

[0043] 2. After pre-compiling the polynomial interpolation, the computational complexity of the method approaches that of a traditional uniform linear array, enabling the use of all received information in a low-complexity manner.

[0044] 3. Lightweight interpolation methods are applicable to most sparse arrays and direction-of-arrival estimation algorithms. Lightweight design methods can further enhance the degree-of-freedom performance of sensing radar arrays. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the angle at which a MIMO radar system detects a target.

[0046] Figure 2 A flowchart for the target angle detection of a MIMO radar system.

[0047] Figure 3 This is a schematic diagram of the sparse MIMO radar sensing platform of the present invention.

[0048] Figure 4 This is a diagram illustrating the effect of a 5-element sparse array detecting 8 targets in this embodiment.

[0049] Figure 5 This is a diagram illustrating the effect of a traditional 5-element uniform array detecting four targets. Detailed Implementation

[0050] 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.

[0051] 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.

[0052] The embodiments of the present invention are as follows:

[0053] 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.

[0054] This embodiment includes the following steps:

[0055] 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.

[0056] The number of physical array elements X in this embodiment is set to 5, and the value of the virtual aperture Q is determined to be 9, and the lightweight sparse array configuration as shown in Figure 1 The specific number of Q is determined by the actual expected detection effect.

[0057] S2, receive signals S(t) using each physical array element in the sparse array, perform signal preprocessing on the received signals to obtain baseband signals, and then perform power equalization processing to obtain equalized baseband signals, i.e. equalized received signal baseband signal power, so that it is unified as σ 2 ;

[0058] S3, estimate the covariance matrix R x of the received signal based on the equalized baseband signal, and then construct a virtual array containing holes H based on the covariance matrix and the position set of the virtual array;

[0059] S4, estimate the virtual array element signal at the hole using the polynomial interpolation algorithm on the equalized baseband signal, and then fill in the virtual array containing holes to form a complete virtual array;

[0060] S5, use the Toeplitz covariance matrix reconstruction method on the complete virtual array to obtain a full-rank Toeplitz covariance matrix, and then use the DOA estimation algorithm on the full-rank Toeplitz covariance matrix to estimate the angle to obtain the incident angle information of the detection target, thereby realizing the improvement of the degrees of freedom of the sparse array and the reduction of the computational complexity.

[0061] The received signal S(t) is collected by the radar system and is processed through steps such as matched filtering and frequency mixing to obtain the baseband signal, i.e. the signal processing includes steps such as matched filtering and frequency mixing.

[0062] Based on the mathematical relationship between the number of physical array elements and the virtual aperture of the lightweight sparse array, the lightweight sparse array configuration is designed. Step 1 is specifically:

[0063] 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 value range of the virtual aperture;

[0064] S1.2, traverse each value in the value range of the virtual aperture from large to small, construct a position set of the virtual array according to the preset number of physical array elements and the current value of the virtual aperture, and stop traversing until the constructed position set of the virtual array satisfies that there is only one hole and the hole is located in the second half axis of the virtual array;

[0065] S1.3, taking the position set of the final virtual array generated in step S1.2 and the value of the corresponding virtual aperture as the final virtual array parameter, and taking the position set of the final virtual array generated in step S1.2 corresponding to the physical element layout as the sparse array.

[0066] The mathematical relationship between the number of physical elements and the virtual aperture is set according to the following formula:

[0067] Q∈[C 2 X-2 +X+1, C 2 X-1 +X+1]

[0068] 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.

[0069] That is, the number of physical channels X of the sparse array is set, and the virtual aperture Q is expected to be generated. At this time, X and Q are judged to verify whether the X physical channels can generate a uniform linear array (ULA) with a virtual aperture of Q. The virtual aperture generation method is to fill the X physical elements into the empty ULA with a length of Q in a traversal method, and to generate the corresponding virtual array.

[0070] The generation method of the virtual array V is to perform difference operation on two physical channels, and the result obtained is a virtual channel. All physical channels are pairwise difference operated to obtain the corresponding virtual array V.

[0071] The judgment condition is specifically that the virtual array V generated at this time satisfies:

[0072] 1) The hole H is located in the rear half axis of the virtual array (H∈[Q / 2,…,Q-2]);

[0073] 2) V has been filled with all positions in Q except the hole.

[0074] If yes, it indicates that the sparse array design is completed;

[0075] Otherwise, Q ’ =Q-1, and the judgment is re-performed.

[0076] The method is suitable for radar system to detect target angle information. The physical elements in the sparse array in step S2 receive signals specifically as follows: the radar system transmits radio frequency signals from the transmitting end for target detection, the physical elements receive signals are the echo signals collected by the receiving end of the radar system, and the baseband signals obtained after down-conversion, matching filtering and other processes.

[0077] In step S2, the power balancing process is specifically using a power balancer at the receiving end physical array element.

[0078] Then, the received signal covariance matrix is estimated from the received signal, and a sparse matrix virtual array with holes is obtained from the received signal covariance matrix. Based on the sparse matrix virtual array with holes, the holes are filled using a polynomial interpolation algorithm to form a complete sparse matrix virtual array.

[0079] The process of generating a virtual array element from the covariance matrix is specifically: the element r ij is expressed as:

[0080] r ij =Σ K k=1 σ 2 k ∙exp[-j∙2πsinθ k ∙(i-j) / λ]

[0081] The physical meaning is that the difference between the i-th physical array element and the j-th physical array element generates a virtual array element at the (i-j) position.

[0082] 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 satisfying 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: R To = toeplitz (z).

[0083] R To The traditional subspace-based DOA estimation algorithm such as 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 algorithm is obtained by the following formula:

[0084] P MUSIC =1 / ( a H (θ) U N U N H a(θ))

[0085] Where 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.

[0086] Step S4 is specifically:

[0087] S4.1, construct the virtual array element signal into the form of power sum of the non-coherent target echo signal, and then construct the polynomial with the non-coherent target echo signal as the zero point of the polynomial;

[0088] S4.2, solve 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;

[0089] S4.3, substitute the polynomial coefficients into the polynomial to solve the zero point of the polynomial, and then substitute the zero point of the polynomial 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;

[0090] S4.4, and then fill the virtual array element signal at the hole into the virtual array containing the hole to form a complete virtual array.

[0091] The step S4.1 is specifically processed according to the following formula:

[0092] S q =(-1) q ((y1) q +(y2) q +…+ (y K ) q )

[0093] f(t)=(t+ y1)(t+ y2)…(t+ y K )=t K +d1t K-1 + d2t K-2 +…+ d K

[0094] Wherein, S q represents the virtual array element signal of the qth virtual array element, q is an index, 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 represent the echo signals of the 1st, 2nd and Kth non-coherent targets respectively, d1, d2 and d K represent the K-1th term coefficient, K-2th term coefficient and constant term of the polynomial to be solved respectively.

[0095] The origin of the virtual array is 0, the virtual aperture is the origin and the positive half axis part of the virtual array, S q represents the virtual array element signal of the qth virtual array element, when q<0, S q only contains mathematical meaning, and is the negative half axis part of the virtual array, which has no physical meaning.

[0096] 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 (that is, K≤H-1), the subscript value of S is in the range of [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:

[0097] d1=S1

[0098] d k =((S1) k -S k ) / C, k∈[2,K]

[0099] 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.

[0100] 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 (that is, K>H-1), the subscript value of S is in the range of [- (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:

[0101] d1=S1

[0102] d k =((S1) k -S k ) / C, k∈[2,H-1]

[0103]

[0104] 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, the maximum number of targets that can be detected by the array is the virtual aperture value minus one, that is, 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 are respectively the coefficient of the K-1th term, the coefficient of the K-2th term and the constant term of the polynomial, H represents the sequence number of the hole in the virtual array, and A H H represents the number of combinations of taking any H physical array elements from the H physical array elements.

[0105] The virtual array element S H at the hole H is calculated by using the polynomial interpolation algorithm, and is filled into the virtual array V containing the hole to form a full-rank virtual array Q.

[0106] In this embodiment, the hole appears at position 7, that is, H=7. The polynomial interpolation algorithm is specifically:

[0107] S7=(-1) 7 (y1 7 + y2 7 +…+ y K 7 )

[0108] Wherein, S7 is a virtual element at hole 7, K is the number of non-coherent targets existing in space, y k ∈Y={y1,y2,…,y K} is a zero point of the polynomial f(t).

[0109] As Figure 2 shown, the experimental setup and simulation results of the interpolation method of the application are demonstrated: MATLAB is used for simulation, and the feasibility, robustness, practicality and performance of the interpolation method of the application are verified. The experimental device is realized in the MATLAB environment, 8 non-coherent random targets existing in the space are set, and the angles are randomly generated; the element positions of the sparse array are set as [0, 3, 4, 6, 8]; the signal-to-noise ratio of the system is 30dB; the number of shots is 500. And the received signal S(t) is generated, and the received signal covariance matrix R x .

[0110] First, the interpolation formula under 8 targets is calculated based on the polynomial interpolation algorithm, and the formula is set as follows:

[0111] d1=S1

[0112] d2=(d1 2 -S2) / 2

[0113] d3=(d1 3 -3∙S1∙S2+2∙S3) / 6

[0114] d4=(S1 4 -6∙S1 2 ∙S2+8∙S1∙S3+3∙S2 2 -6∙S4) / 24

[0115] d5=(S1 5 -30∙S1∙S4-15∙S2 2 -60∙d3∙S2+60∙d2∙S3+24∙S5) / 120;

[0116] d6=6∙d5∙(S -1 2 -S -2 ) / (S -13 -7∙S -1 ∙S -2 -2∙S -3 )

[0117] d7 = 2∙d6∙S -1 / (S -1 2 -S -2 )

[0118] d8=d7 / S -1

[0119] The hole can then be filled using the following formula, which is set as follows:

[0120] S7=(-1) 7 (y1 7 + y2 7 +…+ y K 7 )

[0121] Finally, the Toeplitz covariance matrix reconstruction method is used to recover the rank of the virtual array, and the commonly used DOA estimation algorithm is used for angle estimation, thereby increasing the system's degrees of freedom and reducing computational complexity. The Toeplitz covariance matrix reconstruction method is expressed as follows: For the second-order statistic z corresponding to the complete sparse matrix virtual array, it satisfies the Hermitian positive semi-definite Toeplitz condition, and can be recovered using the Toeplitz matrix reconstruction method, obtained using the following formula, which is set as follows:

[0122] R To = toeplitz (z).

[0123] R To The input is fed into the baseband signal processor, and using a traditional DOA estimation algorithm, it can achieve the following: Figure 2 The detection results shown demonstrate that 8 targets are detected using 5 receiver elements. Compared to the traditional method of detecting 4 targets using 5 receiver elements, the interpolation method of this invention is robust and practical.

[0124] The specific embodiments described above illustrate the technical solution and beneficial effects of the present invention in detail. It should be understood that the above description is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

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. 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; 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.

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: In step S2, the power equalization process specifically involves using a power equalizer on the physical array elements at the receiving end.

4. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 1, 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.

5. The sparse matrix virtualization and degree-of-freedom enhancement method based on polynomial interpolation according to claim 4, 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.

6. 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 5.

7. 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 5.

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