A waveform optimization method and system for improving radar angle estimation accuracy

Abstract

The present invention discloses a waveform optimization method and system for improving the accuracy of radar angle estimation, and relates to the technical field of radar transmission waveform optimization. The method comprises: step S1, using a MIMO radar to transmit a first transmission waveform to space, the first transmission waveform is used to roughly detect the angle and amplitude information of an aerial target; step S2, using the angle and amplitude information of the aerial target to generate an optimized second transmission waveform, using the MIMO radar to transmit the second transmission waveform to the space, the second transmission waveform is used to determine the precise position of the aerial target. The method can automatically obtain the rough position and amplitude of the target, and use the information to design a transmission waveform to improve the angle estimation accuracy; through the low peak-to-average ratio constraint, the transmission waveform can be power amplified by a nonlinear amplifier, improve the transmission efficiency, reduce the distortion of the transmission waveform, and reduce the difficulty and cost of engineering implementation; the proposed algorithm can ensure convergence, and the complexity of the algorithm is low; in addition, the designed waveform can improve the angle resolution capability of the MUSIC algorithm, and has a certain robustness, and can better adapt to complex electromagnetic environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar transmission waveform optimization, and in particular relates to a waveform optimization method and system for improving radar angle estimation accuracy. Background Art

[0002] Angle-Of-Arrival (AOA) estimation is one of the key research areas in array signal processing and is widely used in radar, communication, sonar, precision guidance and other fields. Traditional array AOA estimation methods include: Multiple Signal Classification (MUSIC) algorithm, Capon algorithm, Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT), Maximum Likelihood Estimation algorithm, etc. Among them, the MUSIC algorithm lays the foundation for the theory of spatial spectrum estimation and direction finding. The MUSIC algorithm is a typical subspace-based angle estimation algorithm with low computational complexity and high angular resolution. Whether it is analyzing its performance or exploring more advanced robust MUSIC algorithms, there are a lot of studies, such as proving the performance lower bound of the MUSIC algorithm.

[0003] In recent years, Multiple-Input-Multiple-Output (MIMO) arrays have flourished as a new technology. Each channel can transmit an independent waveform, and the waveform diversity capability it brings can significantly improve the performance of traditional systems. It has been applied in radar, communications and other fields. AOA estimation based on MIMO arrays has also received extensive attention from scholars. In the existing technology, algorithms such as MUSIC, Capon, and ESPRIT have been successfully applied to the AOA estimation of MIMO arrays, and certain results have been achieved. On this basis, it is further proposed to use matching a given directional pattern as a criterion to design a waveform to improve the accuracy of AOA estimation. For example, Figure 1 As shown in the figure, the lower bound of the AOA estimation of the MUSIC algorithm of the MIMO communication system under the energy constraint is derived, and then the precoder is designed based on the derived lower bound to obtain the optimal transmission waveform. The waveform designed by this algorithm only meets the energy constraint, and in practical applications, expensive linear amplifiers are required, which makes engineering implementation difficult.

[0004] It can be seen that the waveform envelope designed by the existing technology has large fluctuations and needs to be amplified by an expensive linear amplifier, which makes engineering implementation difficult. In addition, the synthesized transmission waveform has a small power, which affects the system performance. Moreover, the existing method cannot guarantee convergence and requires parameter selection. It has poor resolution for targets at close angular distances. When the amplitude error is large, the performance of the existing method drops sharply. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a waveform optimization method for improving the accuracy of radar angle estimation. The present invention optimizes the asymptotic Cramer-Rao lower bound of the MUSIC algorithm as the transmit waveform design criterion to improve the AOA estimation performance of the MUSIC algorithm.

[0006] The differences between the present invention and the prior art (reference 2: Wenjun Wu; Bo Tang. Waveform Design for Higher-Resolution Localization with MIMO Radar [J]. Signal Processing, 2023,: 108999) are: (1) The prior art adopts the ADMM method to solve the non-convex optimization problem, which may have convergence problems, while the present invention adopts a loop iteration method to ensure the convergence of the algorithm; (2) In the prior art, it is necessary to debug the penalty coefficient, which has a high computational cost, while the method proposed in the present invention does not require parameter setting and is simpler and more direct; (3) The prior art has poor ability to distinguish targets with similar angular distances, while the method proposed in the present invention can significantly improve the angular resolution capability; (4) If there is an error in the amplitude information of the first transmitted waveform estimation, the performance of the prior art method is significantly reduced, while the method proposed in the present invention has better robustness; (5) Compared with the prior art method, the method proposed in the present invention has lower computational complexity, less running time, and is more efficient.

[0007] The first aspect of the present invention discloses a waveform optimization method for improving the accuracy of radar angle estimation. The method comprises: step S1, using a MIMO radar to transmit a first transmission waveform into space, the first transmission waveform is used to detect the angle information of an aerial target; step S2, using the angle information of the aerial target to generate an optimized second transmission waveform, using the MIMO radar to transmit the second transmission waveform into space, the second transmission waveform is used to determine the specific position of the aerial target; wherein the number of transmitting antennas of the MIMO radar is N T , the number of receiving antennas is N R , in the space θ1,θ2,…,θ P There are P targets in the direction.

[0008] According to the method of the first aspect, in step S1, in step S1, the first transmitted waveform S, its autocorrelation matrix R ss for:

[0009]

[0010] in, s l represents the transmitted signal at the lth sampling time, l = 1, 2, ..., L, L is the transmitted waveform code length;

[0011] In the absence of prior information about the aerial target, the first transmission waveform emitted to the space is an orthogonal waveform, and its radiation power at any position is the same.

[0012] According to the method of the first aspect, in step S1, under far field and narrow band setting conditions, a first echo of the aerial target is received. The calculation formula is:

[0013]

[0014] in:

[0015]

[0016] Among them, α p is the target amplitude of the space target, a R (θ p ) and a T (θ p ) are θ p The receive and transmit steering vectors in angle; in the case of a uniform linear array, a R (θ p ) and a T (θ p ) is:

[0017]

[0018] Among them, ω p,R =2πd R sin(θ p ) / λ,ω p,T =2πd T sin(θ p ) / λ,d T and d R are the transmitting and receiving array spacings respectively, λ is the wavelength of the first transmitting waveform, p=1,2,…,P, is the receiver noise, which has a mean of 0 and a variance of σ 2 Gaussian white noise.

[0019] According to the method of the first aspect, in step S1, the angle information of the aerial target is determined by the following calculation process:

[0020] Calculate the received signal covariance matrix R of the first echo yy , the calculation formula is:

[0021]

[0022] Calculate the covariance matrix R yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​are used to form the noise matrix E n ;

[0023] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions to determine the spectrum peak. The angle corresponding to the spectrum peak is the rough position of the aerial target. The spectrum peak search calculation formula is:

[0024]

[0025] The rough angle information can be obtained by using the peak search method based on the spectrum

[0026] The APES (amplitude and phase estimation) technique is used to traverse the angles in all directions to determine the spectrum peak. The height of the spectrum peak is the amplitude of the target. The spectrum peak search calculation formula is:

[0027]

[0028] in,

[0029]

[0030] The target amplitude information can be roughly estimated using the APES method.

[0031] The rough angle and amplitude information obtained are used to calculate the target’s prior information. The calculation formula is:

[0032]

[0033] According to the method of the first aspect, in the step S2, the optimized second transmission waveform is generated using the angle information of the aerial target, wherein the optimization process refers to optimizing the following problems:

[0034]

[0035]

[0036] Wherein, tr(·) represents the trace of the matrix, 1≤ρ≤L, and the constraint condition of the optimization process is the peak-to-average power ratio PAPR constraint:

[0037]

[0038] Among them, s n (l) is the transmitted signal s of the nth antenna n The lth (l=1,2,…,L) element of .

[0039] According to the method of the first aspect, the optimization process specifically includes:

[0040] S2-1. Considering only the energy constraint, the optimization problem is:

[0041]

[0042] sttr(SS H )=e T / L

[0043] This problem is equivalent to

[0044]

[0045] sttr(R ss )=e T / L,R ss ≥0

[0046] This is a semi-positive programming problem, and its optimal solution can be obtained by the following steps

[0047] S2-1-1. Matrix A α,T Perform singular value decomposition and convert the singular value ν a,p Arrange from small to large

[0048] ν a,1 ≥ν a,2 ≥…≥v a,P

[0049] S2-1-2. Calculate V A , which is a semi-unitary matrix V A The pth column of the matrix A is α,T The right singular vector corresponding to the pth (arranged from large to small, p = 1, 2, ..., P) singular value.

[0050] S2-1-3. Calculate intermediate variables

[0051]

[0052] S2-1-4. Calculate the optimal solution

[0053]

[0054] in, is a diagonal matrix (diag means to convert the vector into a diagonal matrix).

[0055] S2-2, impose the peak-to-average power ratio PAPR constraint and construct the covariance matrix matching problem as follows

[0056]

[0057]

[0058] This is a quartic optimization problem about the transmission waveform S. It is difficult to solve it directly. Consider its approximate equivalent problem

[0059]

[0060]

[0061]

[0062] Among them, T is a semi-unitary matrix. When

[0063]

[0064] To solve the approximate optimization problem, a loop optimization method can be used. That is, in the k+1th iteration, S is fixed. k , optimize T k+1 ; Then fix T k+1 , update S k+1 .

[0065] S2-3, Fixed S k , optimize T k+1

[0066] Ignoring irrelevant constant terms, the corresponding optimization problem (a) is

[0067]

[0068]

[0069] in,

[0070] Perform singular value decomposition on Among them U H and VH H k The (semi) unitary matrix composed of the left singular vector and the right singular value vector, Λ H H k The diagonal matrix composed of the singular values ​​of (arranged from large to small).

[0071] Can get optimized T k+1 The closed-form solution is

[0072]

[0073] S2-4, Fixed T k+1 , update S k+1

[0074] Ignoring irrelevant constant terms, the corresponding optimization problem (b) is:

[0075]

[0076]

[0077] in, From the properties of matrix trace we can get:

[0078]

[0079] in, For the matrix Therefore, the problem (b) can be transformed into N T There are unrelated sub-problems, where the nth sub-problem (c) is expressed as

[0080]

[0081]

[0082] The equivalent problem of this problem is

[0083]

[0084]

[0085] This problem can be solved by using the optimal solution of Algorithm 2 in Reference 1. When ρ = 1,

[0086]

[0087] When ρ=L,

[0088]

[0089] According to the updated results of all sub-problems, the optimized emission waveform for the k+1th time can be obtained as

[0090]

[0091] When the following conditions are met, the iteration is stopped and the optimized second transmission waveform is obtained:

[0092]

[0093] in, is the matching error value of the kth iteration, η is the threshold for controlling the algorithm to stop, and the emission waveform obtained when the algorithm stops is recorded as S′.

[0094] According to the method of the first aspect, in step S2:

[0095] The second transmission waveform S′ is transmitted to the space by using the MIMO radar, and the second echo Y′ of the aerial target is received:

[0096] Y′=A R Aα ,T S′

[0097] Calculate the received signal covariance matrix R′ of the second echo Y′ yy , the calculation formula is:

[0098]

[0099] Calculate the covariance matrix R′ yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​constitute the noise matrix E′ n ;

[0100] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions and find the spectrum peak again. The spectrum peak found again is the precise position of the space target, and its calculation formula is:

[0101]

[0102] The second aspect of the present invention discloses a waveform optimization system for improving the accuracy of radar angle estimation; the system comprises: a first processing unit, configured to: use a MIMO radar to transmit a first transmission waveform into space, the first transmission waveform is used to detect the angle information of an aerial target; a second processing unit, configured to: use the angle information of the aerial target to generate an optimized second transmission waveform, use the MIMO radar to transmit the second transmission waveform into space, the second transmission waveform is used to determine the specific position of the aerial target; wherein the number of transmitting antennas of the MIMO radar is NT , the number of receiving antennas is N R , in the space θ1,θ2,…,θ P There are P targets in the direction.

[0103] According to the system of the second aspect, the first transmission waveform S, its autocorrelation matrix R ss for:

[0104]

[0105] in:

[0106]

[0107] in, s l represents the transmitted signal at the lth sampling time, l = 1, 2, ..., L, L is the transmitted waveform code length;

[0108] Wherein, in the absence of prior information of the aerial target, the first transmission waveform emitted to the space is an orthogonal waveform, and its radiation power at any position is the same.

[0109] According to the system of the second aspect, under the far field and narrow band setting conditions, a first echo of the aerial target is received. The calculation formula is:

[0110]

[0111] in:

[0112]

[0113] Among them, α p is the target amplitude of the space target, a R (θ p ) and a T (θ p ) are θ p The receive and transmit steering vectors in angle; in the case of a uniform linear array, a R (θ p ) and a T (θ p ) is:

[0114]

[0115] Among them, ω p,R =2πd R sin(θ p ) / λ,ω p,T =2πd T sin(θp ) / λ,d T and d R are the transmitting and receiving array spacings respectively, λ is the wavelength of the first transmitting waveform, p=1,2,…,P, is the receiver noise, which has a mean of 0 and a variance of σ 2 Gaussian white noise.

[0116] According to the system of the second aspect, the angle information of the aerial target is determined by the following calculation process:

[0117] Calculate the received signal covariance matrix R of the first echo yy , the calculation formula is:

[0118]

[0119] Calculate the covariance matrix R yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​are used to form the noise matrix E n ;

[0120] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions to determine the spectrum peak. The angle corresponding to the spectrum peak is the rough position of the aerial target. The spectrum peak search calculation formula is:

[0121]

[0122] The rough angle information can be obtained by using the peak search method based on the spectrum

[0123] The APES (amplitude and phase estimation) technique is used to traverse the angles in all directions to determine the spectrum peak. The height of the spectrum peak is the amplitude of the target. The spectrum peak search calculation formula is:

[0124]

[0125] in,

[0126]

[0127] The target amplitude information can be roughly estimated using the APES method.

[0128] The rough angle and amplitude information obtained are used to calculate the target’s prior information. The calculation formula is:

[0129]

[0130] According to the system of the second aspect, the optimized second transmission waveform is generated by using the angle information of the aerial target, wherein the optimization process refers to optimizing the following problems:

[0131]

[0132]

[0133] Wherein, tr(·) represents the trace of the matrix, 1≤ρ≤L, and the constraint condition of the optimization process is the peak-to-average power ratio PAPR constraint:

[0134]

[0135] Among them, s n (l) is the transmitted signal s of the nth antenna n The lth (l=1,2,…,L) element of .

[0136] According to the system of the second aspect, the optimization process specifically includes:

[0137] S2-1. Considering only the energy constraint, the optimization problem is:

[0138]

[0139] sttr(SS H )=e T / L

[0140] This problem is equivalent to

[0141]

[0142] sttr(R ss )=e T / L,R ss ≥0

[0143] This is a semi-positive programming problem, and its optimal solution can be obtained by the following steps

[0144] S2-1-1. Matrix A α,T Perform singular value decomposition and convert the singular value v a,p Arrange from small to large

[0145] v a,1 ≥v a,2 ≥…≥v a,P

[0146] S2-1-2. Calculate V A , which is a semi-unitary matrix V AThe pth column of the matrix A is α,T The right singular vector corresponding to the pth (arranged from large to small, p = 1, 2, ..., P) singular value.

[0147] S2-1-3. Calculate intermediate variables

[0148]

[0149] S2-1-4. Calculate the optimal solution

[0150]

[0151] in, is a diagonal matrix (diag means to convert the vector into a diagonal matrix).

[0152] S2-2, impose the peak-to-average power ratio PAPR constraint and construct the covariance matrix matching problem as follows

[0153]

[0154]

[0155] This is a quartic optimization problem about the transmission waveform S. It is difficult to solve it directly. Consider its approximate equivalent problem

[0156]

[0157]

[0158]

[0159] Among them, T is a semi-unitary matrix. When

[0160]

[0161] To solve the approximate optimization problem, a loop optimization method can be used. That is, in the k+1th iteration, S is fixed. k , optimize T k+1 ; Then fix T k+1 , update S k+1 .

[0162] S2-3, Fixed S k , optimize T k+1

[0163] Ignoring irrelevant constant terms, the corresponding optimization problem (a) is

[0164]

[0165]

[0166] in,

[0167] Perform singular value decomposition on Among them U H and V H H k The (semi) unitary matrix composed of the left singular vector and the right singular value vector, Λ H H k The diagonal matrix composed of the singular values ​​of (arranged from large to small).

[0168] Can get optimized T k+1 The closed-form solution is

[0169]

[0170] S2-4, Fixed T k+1 , update S k+1

[0171] Ignoring irrelevant constant terms, the corresponding optimization problem (b) is:

[0172]

[0173]

[0174] in, From the properties of matrix trace we can get:

[0175]

[0176] in, For the matrix Therefore, the problem (b) can be transformed into N T There are unrelated sub-problems, where the nth sub-problem (c) is expressed as

[0177]

[0178]

[0179] The equivalent problem of this problem is

[0180]

[0181]

[0182] This problem can be solved by using the optimal solution of Algorithm 2 in Reference 1. When ρ = 1,

[0183]

[0184] When ρ=L,

[0185]

[0186] According to the updated results of all sub-problems, the optimized emission waveform for the k+1th time can be obtained as

[0187]

[0188] When the following conditions are met, the iteration is stopped and the optimized second transmission waveform is obtained:

[0189]

[0190] in, is the matching error value of the kth iteration, η is the threshold for controlling the algorithm to stop, and the emission waveform obtained when the algorithm stops is recorded as S′.

[0191] According to the system of the second aspect, the MIMO radar is used to transmit the second transmission waveform S′ to the space, and a second echo Y′ of the aerial target is received:

[0192] Y′=A R Aα ,T S′

[0193] Calculate the received signal covariance matrix R′ of the second echo Y′ yy , the calculation formula is:

[0194]

[0195] Calculate the covariance matrix R′ yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​constitute the noise matrix E′ n ;

[0196] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions and find the spectrum peak again. The spectrum peak found again is the precise position of the space target, and its calculation formula is:

[0197]

[0198] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps in the waveform optimization method for improving the accuracy of radar angle estimation described in any one of the first aspects of the present disclosure are implemented.

[0199] The fourth aspect of the present invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in any one of the waveform optimization methods for improving radar angle estimation accuracy described in the first aspect of the present disclosure are implemented.

[0200] In summary, the technical solution proposed in the present invention can automatically obtain the angle of the target, and use the information to design a transmission waveform to improve the angle estimation accuracy; by designing a waveform with a low peak-to-average ratio, the transmission waveform can be power amplified by a nonlinear amplifier, thereby improving the transmission efficiency, reducing the distortion of the transmission waveform, and reducing the difficulty and cost of engineering implementation; the proposed algorithm can ensure convergence, and the complexity of the algorithm is low; the designed waveform can improve the angular resolution capability of the MUSIC algorithm, and has a certain robustness, and can better adapt to complex electromagnetic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0201] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0202] Figure 1 It is a schematic diagram of an implementation scheme in the prior art;

[0203] Figure 2 A schematic diagram of a flow chart of a waveform optimization method for improving radar angle estimation accuracy according to an embodiment of the present invention;

[0204] Figure 3 A schematic diagram of MIMO radar detection according to an embodiment of the present invention;

[0205] Figure 4 Schematic diagram of RMSE of a designed waveform when the target angle is relatively close according to an embodiment of the present invention;

[0206] Figure 5 A schematic diagram of target resolution probability of a waveform designed when the target angle is relatively close according to an embodiment of the present invention;

[0207] Figure 6 It is a schematic diagram of RMSE of a designed waveform when there is an error in the amplitude information according to an embodiment of the present invention;

[0208] Figure 7 FIG. 4 is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0209] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments 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 without making creative work are within the scope of protection of the present invention.

[0210] The first aspect of the present invention discloses a waveform optimization method for improving the accuracy of radar angle estimation. Figure 2 As shown, the method includes: step S1, using MIMO radar to transmit a first transmission waveform to space, the first transmission waveform is used to detect the angle information of the aerial target; step S2, using the angle information of the aerial target to generate an optimized second transmission waveform, using the MIMO radar to transmit the second transmission waveform to the space, the second transmission waveform is used to determine the specific position of the aerial target. Figure 3 As shown, where the number of transmitting antennas of the MIMO radar system is assumed to be N T , the number of receiving antennas is N R (If the transmitting and receiving antennas are shared N T =N R ), assuming that in θ1,θ2,…,θ P There are P targets in the direction.

[0211] Estimation of target position

[0212] (1) Using MIMO radar to transmit detection waveform S into space, its autocorrelation matrix R ss for:

[0213]

[0214] in, in, s l It represents the transmitted signal at the lth sampling (l=1,2,…,L), where L is the code length of the transmitted waveform. That is, in the absence of prior information about the target position, an orthogonal waveform (such as a Hadamard coded signal) is transmitted into space, and the radiation power of the signal at any position is the same.

[0215] (2) Under the far-field and narrow-band assumptions, receiving the target echo The calculation formula is:

[0216]

[0217] in:

[0218]

[0219] Among them, α p is the target amplitude of the space target, a R (θ p ) and a T (θ p ) are θ p The receive and transmit steering vectors in angle; in the case of a uniform linear array, a R (θ p ) and a T (θ p ) is:

[0220]

[0221] Among them, ω p,R =2πd R sin(θ p ) / λ,ω p,T =2πd T sin(θ p ) / λ,d T and d R are the transmitting and receiving array spacings, respectively, λ is the wavelength of the first transmitting waveform, p=1,2,…,P, is the receiver noise, which has a mean of 0 and a variance of σ 2 Gaussian white noise.

[0222] (3) Calculate the received signal covariance matrix R yy , the calculation formula is:

[0223]

[0224] (4) Calculate the covariance matrix R yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​are used to form the noise matrix E n .

[0225] (5) The multi-signal classification algorithm MUSIC technology is used to traverse the angles in each direction to determine the spectrum peak. The angle corresponding to the spectrum peak is the rough position of the aerial target. The spectrum peak search calculation formula is:

[0226]

[0227] The rough angle information can be obtained by using the peak search method based on the spectrum

[0228] (6) APES (amplitude and phase estimation) is used to traverse the angles in all directions to determine the spectrum peak. The height of the spectrum peak is the amplitude of the target. The spectrum peak search calculation formula is:

[0229]

[0230] in,

[0231]

[0232] The target amplitude information can be roughly estimated using the APES method.

[0233] (7) The obtained rough angle and amplitude information are used to calculate the target’s prior information, and the calculation formula is:

[0234]

[0235] Step 2: Use the calculated A α,T , design the transmission waveform S

[0236] That is, we need to solve the following optimization problem:

[0237]

[0238]

[0239] Where tr(·) represents the trace of the matrix, and the constraint condition is the peak-to-average-power-ratio (PAPR, also referred to as peak-to-average-power-ratio) constraint. Where 1≤ρ≤L.

[0240]

[0241] Among them, s n (l) is the signal s transmitted by the nth antenna n The lth (l=1,2,…,L) element of .

[0242] (1) Considering only the energy constraint, the optimization problem is:

[0243]

[0244] sttr(SS H )=e T / L

[0245] This problem is equivalent to

[0246]

[0247] sttr(R ss )=e T / L,R ss ≥0

[0248] This is a semi-positive programming problem, and its optimal solution can be obtained by the following steps

[0249] (1-1) For matrix A α,T Perform singular value decomposition and convert the singular value v a,p Arrange from small to large

[0250] v a,1 ≥v a,2 ≥…≥ν a,P

[0251] (1-2) Calculate V A , which is a semi-unitary matrix V A The pth column of the matrix A is α,T The right singular vector corresponding to the pth (arranged from large to small, p = 1, 2, ..., P) singular value.

[0252] (1-3) Calculate intermediate variables

[0253]

[0254] (1-4) Calculate the optimal solution

[0255]

[0256] in, is a diagonal matrix (diag means to convert the vector into a diagonal matrix).

[0257] (2) Applying the peak-to-average power ratio (PAPR) constraint, the covariance matrix matching problem is constructed as follows:

[0258]

[0259]

[0260] This is a quartic optimization problem about the transmission waveform S. It is difficult to solve it directly. Consider its approximate equivalent problem

[0261]

[0262]

[0263]

[0264] Among them, T is a semi-unitary matrix. When

[0265]

[0266] To solve the approximate optimization problem, a loop optimization method can be used. That is, in the k+1th iteration, S is fixed. k , optimize T k+1 ; Then fix T k+1 , update S k+1 .

[0267] (3) Fixed S k , optimize T k+1

[0268] Ignoring irrelevant constant terms, the corresponding optimization problem (a) is

[0269]

[0270]

[0271] in,

[0272] Perform singular value decomposition on Among them U H and V H H k The (semi) unitary matrix composed of the left singular vector and the right singular value vector, Λ H H k The diagonal matrix composed of the singular values ​​of (arranged from large to small).

[0273] Can get optimized T k+1 The closed-form solution is

[0274]

[0275] (4) Fixed T k+1 , update S k+1

[0276] Ignoring irrelevant constant terms, the corresponding optimization problem (b) is:

[0277]

[0278]

[0279] in, From the properties of matrix trace we can get:

[0280]

[0281] in, For the matrix Therefore, the problem (b) can be transformed into N T There are unrelated sub-problems, where the nth sub-problem (c) is expressed as

[0282]

[0283]

[0284] The equivalent problem of this problem is

[0285]

[0286]

[0287] This problem can be solved by using the optimal solution of Algorithm 2 in Reference 1. When ρ = 1,

[0288]

[0289] When ρ=L,

[0290]

[0291] According to the updated results of all sub-problems, the optimized emission waveform for the k+1th time can be obtained as

[0292]

[0293] (5) When the following conditions are met, the iteration is stopped to obtain the optimized second transmission waveform:

[0294]

[0295] in, is the matching error value of the kth iteration, η is the threshold for controlling the algorithm to stop, and the emission waveform obtained when the algorithm stops is recorded as S′.

[0296] In summary, based on the rough position information obtained by initial detection, the transmission waveform that can be used for precise positioning is calculated.

[0297] Accurate estimation of target position

[0298] The second transmission waveform S′ is transmitted to the space by using the MIMO radar, and the second echo Y′ of the aerial target is received:

[0299] Y′=A R Aα ,T S′

[0300] Calculate the received signal covariance matrix R′ of the second echo Y′ yy , the calculation formula is:

[0301]

[0302] Calculate the covariance matrix R′ yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​constitute the noise matrix E′ n ;

[0303] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions and find the spectrum peak again. The spectrum peak found again is the precise position of the space target, and its calculation formula is:

[0304]

[0305] Finally, the precise position of the target is obtained and the estimation of the target is completed. Specific embodiment 1

[0307] Assume that the number of transmitting antennas used in the MIMO radar system is N T is 6, the number of receiving antennas is N R is 6, the array elements are evenly spaced, and the spacing is half a wavelength. The signal code length L is 100, and the total transmission energy e T is 50, and the peak-to-average ratio is 1. Assume there are two targets (P = 2), the target amplitudes α are 0.8 and 0.6 respectively, and the variance of the noise σ 2 is 1. The threshold η for the algorithm to stop iterating is 10 -3 .

[0308] Under the same experimental environment, the waveform designed by the present invention is compared with the waveform designed by the ADMM method proposed in reference 2 using the MUISC algorithm. The target angle distances are set to 0.08θ spa , 0.10θ spa , 0.12θ spa , 0.14θ spa , 0.16θ spa , 0.18θ spa , 0.20θ spa 、(θ spa =0.891λ / (N R d T ) in radians), and examine the performance of the MUSIC algorithm for low angular spacing (replacing ω p,R The RMSE of the sum of variances and the target resolution probability are used as evaluation indicators, ω p,R =2πd R sin(θ p ) / λ, repeat the experiment 5000 times), such as Figure 4and Figure 5 As shown in the figure, it can be seen that the performance of the waveform designed by the present invention is significantly better than that of the quasi-orthogonal waveform and the algorithm proposed in reference 2, and can greatly improve the angular resolution ability of the waveform. Even if the two target angles are close to each other, the algorithm proposed by the present invention can successfully resolve them. In order to test the robustness of the waveform designed by the algorithm, it is assumed that there is an error in the estimated angle amplitude using the first waveform, and the RMSE curve is plotted as the amplitude error changes. Figure 5 As shown, it can be seen that when the amplitude error is greater than 28%, the waveform performance of the algorithm designed by Reference 2 decreases significantly, while the method proposed by the present invention is basically not affected, which shows that the algorithm designed by the present invention has good robustness.

[0309] The second aspect of the present invention discloses a waveform optimization system for improving the accuracy of radar angle estimation; the system comprises: a first processing unit, configured to: use a MIMO radar to transmit a first transmission waveform into space, the first transmission waveform is used to detect the angle information of an aerial target; a second processing unit, configured to: use the angle information of the aerial target to generate an optimized second transmission waveform, use the MIMO radar to transmit the second transmission waveform into space, the second transmission waveform is used to determine the specific position of the aerial target; wherein the number of transmitting antennas of the MIMO radar is N T , the number of receiving antennas is N R , in the space θ1,θ2,…,θ P There are P targets in the direction.

[0310] In some embodiments, the first transmit waveform S has an autocorrelation matrix R ss for:

[0311]

[0312] in:

[0313]

[0314] in, s l represents the transmitted signal at the lth sampling time, l = 1, 2, ..., L, L is the transmitted waveform code length;

[0315] Wherein, in the absence of prior information of the aerial target, the first transmission waveform emitted to the space is an orthogonal waveform, and its radiation power at any position is the same.

[0316] In some embodiments, receiving the first echo of the aerial target under far field and narrow band settings The calculation formula is:

[0317]

[0318] in:

[0319]

[0320] Among them, α p is the target amplitude of the space target, a R (θ p ) and a T (θ p ) are θ p The receive and transmit steering vectors in angle; in the case of a uniform linear array, a R (θ p ) and a T (θ p ) is:

[0321]

[0322] Among them, ω p,R =2πd R sin(θ p ) / λ,ω p,T =2πd T sin(θ p ) / λ,d T and d R are the transmitting and receiving array spacings, respectively, λ is the wavelength of the first transmitting waveform, p=1,2,…,P, is the receiver noise, which has a mean of 0 and a variance of σ 2 Gaussian white noise.

[0323] In some embodiments, the angle information of the aerial target is determined by the following calculation process:

[0324] Calculate the received signal covariance matrix R of the first echo yy , the calculation formula is:

[0325]

[0326] Calculate the covariance matrix R yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​are used to form the noise matrix E n ;

[0327] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions to determine the spectrum peak. The angle corresponding to the spectrum peak is the rough position of the aerial target. The spectrum peak search calculation formula is:

[0328]

[0329] The rough angle information can be obtained by using the peak search method based on the spectrum

[0330] The APES (amplitude and phase estimation) technique is used to traverse the angles in all directions to determine the spectrum peak. The height of the spectrum peak is the amplitude of the target. The spectrum peak search calculation formula is:

[0331]

[0332] in,

[0333]

[0334] The target amplitude information can be roughly estimated using the APES method.

[0335] The rough angle and amplitude information obtained are used to calculate the target’s prior information. The calculation formula is:

[0336]

[0337] In some embodiments, the optimized second transmission waveform is generated using the angle information of the aerial target, wherein the optimization process refers to optimizing the following problems:

[0338]

[0339]

[0340] Wherein, tr(·) represents the trace of the matrix, 1≤ρ≤L, and the constraint condition of the optimization process is the peak-to-average power ratio PAPR constraint:

[0341]

[0342] Among them, s n (l) is the transmitted signal s of the nth antenna n The lth (l=1,2,…,L) element of .

[0343] In some embodiments, the optimization process specifically includes:

[0344] S2-1. Considering only the energy constraint, the optimization problem is:

[0345]

[0346] sttr(SSH )=e T / L

[0347] This problem is equivalent to

[0348]

[0349] sttr(R ss )=e T / L,R ss ≥0

[0350] This is a semi-positive programming problem, and its optimal solution can be obtained by the following steps

[0351] S2-1-1. Matrix A α,T Perform singular value decomposition and convert the singular value v a,p Arrange from small to large

[0352] v a,1 ≥v a,2 ≥…≥v a,P

[0353] S2-1-2. Calculate V A , which is a semi-unitary matrix V A The pth column of the matrix A is α,T The right singular vector corresponding to the pth (arranged from large to small, p = 1, 2, ..., P) singular value.

[0354] S2-1-3. Calculate intermediate variables:

[0355] S2-1-4. Calculate the optimal solution: in, is a diagonal matrix (diag means to convert the vector into a diagonal matrix).

[0356] S2-2, impose the peak-to-average power ratio PAPR constraint and construct the covariance matrix matching problem as follows

[0357]

[0358]

[0359] This is a quartic optimization problem about the transmission waveform S. It is difficult to solve it directly. Consider its approximate equivalent problem

[0360]

[0361]

[0362]

[0363] Among them, T is a semi-unitary matrix. When

[0364]

[0365] To solve the approximate optimization problem, a loop optimization method can be used. That is, in the k+1th iteration, S is fixed. k , optimize T k+1 ; Then fix T k+1 , update S k+1 .

[0366] S2-3, Fixed S k , optimize T k+1

[0367] Ignoring irrelevant constant terms, the corresponding optimization problem (a) is

[0368]

[0369]

[0370] in,

[0371] Perform singular value decomposition on Among them U H and V H H k The (semi) unitary matrix composed of the left singular vector and the right singular value vector, Λ H H k The diagonal matrix composed of the singular values ​​of (arranged from large to small).

[0372] Can get optimized T k+1 The closed-form solution is:

[0373] S2-4, Fixed T k+1 , update S k+1

[0374] Ignoring irrelevant constant terms, the corresponding optimization problem (b) is:

[0375]

[0376]

[0377] in, From the properties of matrix trace we can get:

[0378]

[0379] in, For the matrix Therefore, the problem (b) can be transformed into N T There are unrelated sub-problems, where the nth sub-problem (c) is expressed as

[0380]

[0381]

[0382] The equivalent problem of this problem is

[0383]

[0384]

[0385] This problem can be solved by using the optimal solution of Algorithm 2 in Reference 1. When ρ = 1,

[0386]

[0387] When ρ=L,

[0388]

[0389] According to the updated results of all sub-problems, the optimized emission waveform for the k+1th time can be obtained as

[0390]

[0391] When the following conditions are met, the iteration is stopped and the optimized second transmission waveform is obtained:

[0392]

[0393] in, is the matching error value of the kth iteration, η is the threshold for controlling the algorithm to stop, and the emission waveform obtained when the algorithm stops is recorded as S′.

[0394] In some embodiments, the MIMO radar is used to transmit the second transmission waveform S′ to the space, and a second echo Y′ of the aerial target is received:

[0395] Y′=A R A α,T S′

[0396] Calculate the received signal covariance matrix R′ of the second echo Y′ yy , the calculation formula is:

[0397]

[0398] Calculate the covariance matrix R′ yyThe eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​constitute the noise matrix E′ n ;

[0399] The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions and find the spectrum peak again. The spectrum peak found again is the precise position of the space target, and its calculation formula is:

[0400]

[0401] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps in the waveform optimization method for improving the accuracy of radar angle estimation described in any one of the first aspects of the present disclosure are implemented.

[0402] Figure 7 is a structural diagram of an electronic device according to an embodiment of the present invention, such as Figure 6 As shown, the electronic device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. Among them, the processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the electronic device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, near field communication (NFC) or other technologies. The display screen of the electronic device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the electronic device can be a touch layer covered on the display screen, or a button, a trackball or a touch pad set on the housing of the electronic device, or an external keyboard, touch pad or mouse, etc.

[0403] Those skilled in the art will understand that Figure 7 The structure shown in the figure is only a structural diagram of the part related to the technical solution of the present disclosure, and does not constitute a limitation on the electronic device to which the technical solution of the present application is applied. The specific electronic device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0404] The fourth aspect of the present invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in any one of the waveform optimization methods for improving radar angle estimation accuracy described in the first aspect of the present disclosure are implemented.

[0405] In summary, the technical solution proposed in the present invention can automatically obtain the angle of the target, and use the information to design a transmission waveform to improve the angle estimation accuracy; by designing a waveform with a low peak-to-average ratio, the transmission waveform can be power amplified by a nonlinear amplifier, thereby improving the transmission efficiency, reducing the distortion of the transmission waveform, and reducing the difficulty and cost of engineering implementation; the proposed algorithm can ensure convergence, and the complexity of the algorithm is low; the designed waveform can improve the angular resolution capability of the MUSIC algorithm, and has a certain robustness, and can better adapt to complex electromagnetic environments.

[0406] The technical solution proposed in the present invention can also: (1) improve the accuracy of MIMO radar angle parameter estimation, and has broad application prospects in the fields of early warning detection, target imaging, and autonomous driving; (2) recognize the external environment by transmitting a conventional detection waveform, and then use the cognitive information to optimize the transmission waveform, ultimately achieving the purpose of improving the angle estimation accuracy; therefore, the present invention can intelligently adapt to the external electromagnetic environment; (3) the transmission waveform designed by the present invention meets the peak-to-average ratio constraint, which can avoid the use of expensive linear amplifiers, save costs, and facilitate engineering implementation; (4) when the waveform designed by the present invention is used for spatial spectrum estimation, the spectrum peak formed is sharper, the angle estimation accuracy and resolution are higher, and it is very close to the theoretical error lower bound.

[0407] Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. The above-mentioned embodiments only express several implementation methods of the present application, and their descriptions are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, without departing from the concept of the present application, several variations and improvements can be made, which all belong to the scope of protection of the present application. Therefore, the scope of protection of the patent in this application shall be based on the attached claims.

Claims

1. A waveform optimization method for improving radar angle estimation accuracy, characterized in that: The method comprises: Step S1, using a MIMO radar to transmit a first transmission waveform into space, wherein the first transmission waveform is used to detect angle information of an aerial target; Step S2, using the angle information of the aerial target to generate an optimized second transmission waveform, using the MIMO radar to transmit the second transmission waveform to the space, wherein the second transmission waveform is used to determine the specific position of the aerial target; Among them, the number of transmitting antennas of the MIMO radar is N T , the number of receiving antennas is N R , in the space θ1,θ2,…,θ P There are P targets in the direction; Among them, in the step S1, the first transmission waveform S, its autocorrelation matrix R ss for: in: in, s l represents the transmitted signal at the lth sampling time, l = 1, 2, ..., L, L is the transmitted waveform code length; Wherein, in the absence of prior information of the aerial target, the first transmission waveform transmitted to the space is an orthogonal waveform, and its radiation power at any position is the same; Wherein, in the step S1, under the far field and narrow band setting conditions, the first echo of the aerial target is received The calculation formula is: in: Among them, α p is the target amplitude of the space target, a R (θ p ) and a T (θ p ) are θ p The receive and transmit steering vectors in angle; in the case of a uniform linear array, a R (θ p ) and a T (θ p ) is: Among them, ω p,R =2πd R sin(θ p ) / λ,ω p,T =2πd T sin(θ p ) / λ,d T and d R are the transmitting and receiving array spacings, respectively, λ is the wavelength of the first transmitting waveform, p=1,2,…,P, is the receiver noise, which has a mean of 0 and a variance of σ 2 Gaussian white noise; Wherein, in the step S1, the angle information of the aerial target is determined by the following calculation process: Calculate the received signal covariance matrix R of the first echo yy , the calculation formula is: Calculate the covariance matrix R yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​are used to form the noise matrix E n ; The multi-signal classification algorithm MUSIC technology is used to traverse the angles in each direction to determine the spectrum peak. The angle corresponding to the spectrum peak is the rough position of the aerial target. The spectrum peak search calculation formula is: Calculate the rough angle information based on the peak search formula APES technology is used to traverse the angles in all directions to determine the spectrum peak. The spectrum peak height is the target amplitude information. The spectrum peak search calculation formula is: in, Estimation of target amplitude information based on the APES technique According to the rough angle information and the target amplitude information, the target prior information is calculated, and the calculation formula is: Wherein, in the step S2, the optimized second transmission waveform is generated using the angle information of the aerial target, wherein the optimization process refers to optimizing the following problems: Wherein, tr(·) represents the trace of the matrix, 1≤ρ≤L, and the constraint condition of the optimization process is the peak-to-average power ratio PAPR constraint: Among them, s n (l) is the transmitted signal s of the nth antenna n The lth element of , l = 1, 2, ..., L; The optimization process specifically includes: S2-1. Considering only the energy constraint, the optimization problem is: s.t.tr(SS H )=e T / L is equivalent to: s.t.tr(R ss )=e T / L,R ss ≥0 The optimal solution is obtained through the following steps: S2-1-1. Matrix A α,T Perform singular value decomposition and convert the singular value v a,p Arrange from smallest to largest: in a,1 ≥v a,2 ≥…≥v a,P S2-1-2. Calculate V A , which is a semi-unitary matrix, V A The pth column is the matrix A arranged from largest to smallest α,T The right singular vector corresponding to the pth singular value, p = 1, 2, ..., P; S2-1-3. Calculate intermediate variables: S2-1-4. Calculate the optimal solution: in, is a diagonal matrix, diag means to convert the vector into a diagonal matrix; S2-2. Apply peak-to-average power ratio (PAPR) constraints and construct the covariance matrix matching problem: The equivalent problem is: Among them, T is a semi-unitary matrix. When , we get: For the approximate optimization problem, the loop optimization method is used to solve it, and S is fixed in the k+1th iteration. k , optimize T k+1 ; Then fix T k+1 , update S k+1； S2-3, Fixed S k , optimize T k+1 ; Ignoring irrelevant constant terms, the corresponding optimization problem (a) is: in, Perform singular value decomposition and get Among them U H and V H H k The semi-unitary matrix composed of the left singular vector and the right singular value vector, Λ H H k The diagonal matrix formed by arranging the singular values ​​of from large to small; Get optimized T k+1 The closed-form solution is: S2-4, Fixed T k+1 , update S k+1 ; Ignoring irrelevant constant terms, the corresponding optimization problem (b) is: in, From the properties of matrix trace we get: in, For the matrix The nth row vector of T There are unrelated sub-problems, among which the nth sub-problem (c) is expressed as: The equivalent problem is: When ρ=1, When ρ=L, According to the updated results of all sub-problems, the optimized emission waveform for the k+1th time is obtained as follows: When the following conditions are met, the iteration is stopped and the optimized second transmission waveform is obtained: in, is the matching error value of the kth iteration, η is the threshold for controlling the algorithm to stop, and the emission waveform obtained when the algorithm stops is recorded as S′.

2. A waveform optimization method for improving radar angle estimation accuracy according to claim 1, characterized in that: In step S2: The second transmission waveform S′ is transmitted to the space by using the MIMO radar, and the second echo Y′ of the aerial target is received: And now R TO α,T S′ Calculate the received signal covariance matrix R′ of the second echo Y′ yy , the calculation formula is: Calculate the covariance matrix R′ yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​constitute the noise matrix E′ n ; The multi-signal classification algorithm MUSIC technology is used to traverse the angles in all directions and find the spectrum peak again. The spectrum peak found again is the precise position of the space target, and its calculation formula is:

3. A waveform optimization system for improving radar angle estimation accuracy, characterized in that: The system comprises: The first processing unit is configured to: use the MIMO radar to transmit a first transmission waveform into space, wherein the first transmission waveform is used to detect angle information of an aerial target; Among them, the first transmission waveform S, its autocorrelation matrix R ss for: in: in, s l represents the transmitted signal at the lth sampling time, l = 1, 2, ..., L, L is the transmitted waveform code length; Wherein, in the absence of prior information of the aerial target, the first transmission waveform transmitted to the space is an orthogonal waveform, and its radiation power at any position is the same; Wherein, under the far field and narrow band setting conditions, the first echo of the aerial target is received The calculation formula is: in: Among them, α p is the target amplitude of the space target, a R (θ p ) and a T (θ p ) are θ p The receive and transmit steering vectors in angle; in the case of a uniform linear array, a R (θ p ) and a T (θ p ) is: Among them, ω p,R =2πd R sin(θ p ) / λ,ω p,T =2πd T sin(θ p ) / λ,d T and d R are the transmitting and receiving array spacings, respectively, λ is the wavelength of the first transmitting waveform, p=1,2,…,P, is the receiver noise, which has a mean of 0 and a variance of σ 2 Gaussian white noise; The angle information of the aerial target is determined by the following calculation process: Calculate the received signal covariance matrix R of the first echo yy , the calculation formula is: Calculate the covariance matrix R yy The eigenvalue of And the feature vector Select the smallest N R -The eigenvectors corresponding to the P eigenvalues ​​are used to form the noise matrix E n ; The multi-signal classification algorithm MUSIC technology is used to traverse the angles in each direction to determine the spectrum peak. The angle corresponding to the spectrum peak is the rough position of the aerial target. The spectrum peak search calculation formula is: Calculate the rough angle information based on the peak search formula APES technology is used to traverse the angles in all directions to determine the spectrum peak. The spectrum peak height is the target amplitude information. The spectrum peak search calculation formula is: in, Estimation of target amplitude information based on the APES technique According to the rough angle information and the target amplitude information, the target prior information is calculated, and the calculation formula is: The second processing unit is configured to: generate an optimized second transmission waveform using the angle information of the aerial target, and transmit the second transmission waveform to the space using the MIMO radar, wherein the second transmission waveform is used to determine the specific position of the aerial target; Among them, the number of transmitting antennas of the MIMO radar is N T , the number of receiving antennas is N R , in the space θ1,θ2,…,θ P There are P targets in the direction; The optimized second transmission waveform is generated by using the angle information of the aerial target, wherein the optimization process refers to optimizing the following problems: Wherein, tr(·) represents the trace of the matrix, 1≤ρ≤L, and the constraint condition of the optimization process is the peak-to-average power ratio PAPR constraint: Among them, s n (l) is the transmitted signal s of the nth antenna n The lth element of , l = 1, 2, ..., L; The optimization process specifically includes: Considering only the energy constraint, the optimization problem is: s.t.tr(SS H )=e T / L is equivalent to: s.t.tr(R ss )=e T / L,R ss ≥0 The optimal solution is obtained through the following steps: For the matrix A α,T Perform singular value decomposition and convert the singular value v a,p Arrange from smallest to largest: in a,1 ≥v a,2 ≥…≥v a,P Calculate V A , which is a semi-unitary matrix, V A The pth column is the matrix A arranged from largest to smallest α,T The right singular vector corresponding to the pth singular value, p = 1, 2, ..., P; Calculate intermediate variables: Calculate the optimal solution: in, is a diagonal matrix, diag means to convert the vector into a diagonal matrix; Apply the peak-to-average power ratio (PAPR) constraint and construct the covariance matrix matching problem: The equivalent problem is: Among them, T is a semi-unitary matrix. When , we get: For the approximate optimization problem, the loop optimization method is used to solve it, and S is fixed in the k+1th iteration. k , optimize T k+1 ; Then fix T k+1 , update S k+1； Fixed S k , optimize T k+1 ; Ignoring irrelevant constant terms, the corresponding optimization problem (a) is: in, Perform singular value decomposition and get Among them U H and V H H k The semi-unitary matrix composed of the left singular vector and the right singular value vector, Λ H H k The diagonal matrix formed by arranging the singular values ​​of from large to small; Get optimized T k+1 The closed-form solution is: Fixed T k+1 , update S k+1 ; Ignoring irrelevant constant terms, the corresponding optimization problem (b) is: in, From the properties of matrix trace we get: in, For the matrix The nth row vector of T There are unrelated sub-problems, among which the nth sub-problem (c) is expressed as: The equivalent problem is: When ρ=1, When ρ=L, According to the updated results of all sub-problems, the optimized emission waveform for the k+1th time is obtained as follows: When the following conditions are met, the iteration is stopped and the optimized second transmission waveform is obtained: in, is the matching error value of the kth iteration, η is the threshold for controlling the algorithm to stop, and the emission waveform obtained when the algorithm stops is recorded as S′.

4. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps in the waveform optimization method for improving the accuracy of radar angle estimation as described in any one of claims 1-2 are implemented.

5. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in the waveform optimization method for improving the accuracy of radar angle estimation described in any one of claims 1-2 are implemented.

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