A uniform planar array flat-top main beam shaping method for phase response search

Abstract

The application discloses a uniform plane array flat-top main beam shaping method of phase response search, which comprises the following steps: calculating the weight vector of the azimuth direction by using the azimuth beam pointing and azimuth spread width parameters of a radar; calculating the noise output power of the radar to construct the azimuth direction phase search function, and obtaining the minimum phase of the azimuth direction phase search function by means of one-dimensional search; calculating the weight vector of the elevation direction by using the elevation beam pointing and elevation spread width parameters of the radar; calculating the noise output power of the radar to construct the elevation direction phase search function, and obtaining the minimum phase of the elevation direction phase search function by means of one-dimensional search; and calculating the azimuth-elevation joint weight vector by using Kroneckt product according to the azimuth direction phase search function, the elevation direction phase search function, the minimum phase of the azimuth direction phase search function and the minimum phase of the elevation direction phase search function, and completing beam forming. The application improves the output performance of the beam former when the pointing deviation occurs.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of array signal processing. BACKGROUND

[0002] Beamforming technology is widely used in aviation, aerospace, radar and communication systems, which improves the output signal-to-noise ratio by forming gain traps in the target direction. However, there are errors in the arrival angle in the actual working environment, which causes the deviation of the target direction vector constraint. Theoretical research shows that when there is a constraint deviation in the target direction vector, the output performance of the beamforming will deteriorate sharply.

[0003] For the problem of solving the flat-top beamforming weight vector under the target pointing error, the typical solutions are: linearly constrained minimum variance method, double-sided constraint method, optimal response control method, etc., among which:

[0004] Linearly constrained minimum variance method: this method applies amplitude response constraints in the flat-top response area, which can form a flat-top main lobe; but there is a problem of high sidelobe level.

[0005] Double-sided constraint method: this method makes upper and lower constraints on the main lobe response area, which can avoid the lifting of the sidelobe level; but there is a problem of main lobe response fluctuation.

[0006] Optimal response control method: this method is based on adaptive array theory, which controls the main lobe and sidelobe response point by point through iterative method, which can form a nearly flat-top main lobe; but this method needs multiple iterations, and the calculation complexity is very high.

[0007] Therefore, a phase response search uniform planar array flat-top main beamforming method is needed. SUMMARY

[0008] The purpose of the present application is to overcome the shortcomings of the above methods, and to provide a phase response search uniform planar array flat-top main beamforming method.

[0009] To achieve the above purpose, the present application adopts the following technical solutions:

[0010] A phase response search uniform planar array flat-top main beamforming method, comprising the following steps:

[0011] Calculate the weight vector in the azimuth direction using the azimuth beam pointing and azimuth spread parameters of the radar;

[0012] Calculate the noise output power of the radar to construct the azimuth phase search function, and obtain the phase with the minimum azimuth phase search function through one-dimensional search;

[0013] The weight vector in the azimuth direction is calculated by using the azimuth beam pointing and azimuth beamwidth parameters of the radar;

[0014] The noise output power of the radar is calculated to construct an elevation phase search function, and a phase with minimum elevation phase search function is obtained by one-dimensional search;

[0015] According to the azimuth phase search function, the elevation phase search function, the phase with minimum azimuth phase search function and the phase with minimum elevation phase search function, the azimuth-elevation joint weight vector is calculated by using Kroneckt product to complete beam forming.

[0016] Preferably, the calculation of the weight vector in the azimuth direction by using the azimuth beam pointing and azimuth beamwidth parameters of the radar comprises:

[0017] The azimuth constraint steering vector is calculated:

[0018]

[0019]

[0020]

[0021] Where θ0and Δ A represent the azimuth pointing and azimuth beamwidth parameters respectively, d x is the azimuth array element spacing, and λ is the wavelength of the radar. T represents transposition, and j is the imaginary unit.

[0022] Preferably, the calculation of the weight vector in the azimuth direction by using the azimuth beam pointing and azimuth beamwidth parameters of the radar further comprises:

[0023] According to the azimuth constraint steering vector, the weight vector W Azi in the azimuth direction is calculated by using linearly constrained minimum variance criterion.

[0024]

[0025] Where C Azi =[a(θ0-Δ A ),a(θ0),a(θ0+Δ A )], f Azi =[Me -jη ,M,Me jη ] T , and η is the azimuth constraint phase. H represents conjugate transposition.

[0026] Preferably, the calculated noise output power:

[0027]

[0028] Preferably, the azimuthally oriented phase search function is constructed as:

[0029] G Azi = a 1,2 cos(η + b 1,2 ) + a 1,3 cos(2η + b 1,3 ) + a 2,3 cos(3η + b 2,3 )

[0030] where a 1,2 and b 1,2 are the amplitude and phase of the first row, second column value of the matrix a 1,3 and b 1,3 are the amplitude and phase of the first row, third column value of the matrix a 2,3 and b 2,3 are the amplitude and phase of the second row, third column value of the matrix

[0031] Preferably, calculating the weight vector in the elevation direction using the radar's elevation beam pointing and elevation beamwidth parameters further comprises:

[0032] Calculating the elevation direction constraint steering vector:

[0033]

[0034]

[0035]

[0036] where φ0and Δ E represent the elevation pointing and beamwidth parameters, respectively, and d y is the elevation inter-element spacing.

[0037] Preferably, calculating the weight vector in the elevation direction using the radar's elevation beam pointing and elevation beamwidth parameters further comprises:

[0038] Using the linearly constrained minimum variance criterion to calculate the weight vector from the elevation direction constraint steering vector:

[0039]

[0040] where C Ele = [b(φ0- Δ E ), b(φ0), b(φ0+ Δ E )], and f Ele = [Ne -jψ , N, Ne jψ ]​T , ψ is the elevation direction constraint phase.

[0041] Preferably, the noise output power:

[0042]

[0043] Preferably, the constructed elevation direction phase search function:

[0044] G Ele = c 1,2 cos (ψ + d 1,2 ) + c 1,3 cos (2ψ + d 1,3 ) + c 2,3 cos (ψ + d 2,3 )

[0045] Wherein c 1,2 and d 1,2 are the amplitude and phase of the value in the first row and the second column of the matrix , c 1,3 and d 1,3 are the amplitude and phase of the value in the first row and the third column of the matrix , c 2,3 and d 2,3 are the amplitude and phase of the value in the second row and the third column of the matrix .

[0046] Preferably, the azimuth-elevation joint weight vector W Azi-Ele :

[0047]

[0048] Wherein represents the Kroneckt product.

[0049] The beneficial effects of the present application are as follows:

[0050] The present application takes the Kroneckt product of the azimuth direction weight vector and the elevation direction weight vector as the optimal weight vector, which can realize beam forming under angle error and solve the problem of flat main beam shaping in static beam forming technology. The present application improves the output performance of the beam former when there is a pointing deviation, and can be applied to scenarios with high real-time requirements. BRIEF DESCRIPTION OF DRAWINGS

[0051] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0052] Figure 1 The flow chart of the present application is shown.

[0053] Figure 2 ​A schematic diagram of the receiving array of the present invention is shown.

[0054] Figure 3 The diagram shows a one-dimensional radiation pattern of beam response and arrival angle of a conventional beamforming method in the simulation experiment of this invention.

[0055] Figure 4 The diagram shows a one-dimensional radiation pattern of the beam response and arrival angle of the linearly constrained minimum variance method in the simulation experiment of this invention.

[0056] Figure 5 The diagram shows a one-dimensional radiation pattern of the beam response and arrival angle of the method described in this invention during a simulation experiment. Detailed Implementation

[0057] To more clearly illustrate the present invention, the following description is in conjunction with preferred embodiments and accompanying drawings. Figures 1-5 The present invention will be further described below. Similar components in the accompanying drawings are indicated by the same reference numerals. Those skilled in the art should understand that the following detailed description is illustrative rather than restrictive and should not be construed as limiting the scope of protection of the present invention.

[0058] Beamforming technology focuses on distortion-free output to the target while ensuring sufficient noise suppression, which requires accurate estimation of the weight vector. Therefore, this invention provides a method for uniform planar array flat-top main beamforming based on phase response search.

[0059] like Figure 1 As shown, a method for phase response search of a uniform planar array flat-top main beamforming includes the following steps:

[0060] The azimuth weight vector is calculated using the radar's azimuth beam pointing and azimuth broadening parameters.

[0061] The radar noise output power is calculated to construct the azimuth phase search function, and the phase with the minimum azimuth phase search function is obtained by one-dimensional search.

[0062] The elevation weight vector is calculated using the radar's elevation beam pointing and elevation broadening parameters;

[0063] The pitch phase search function is constructed by calculating the noise output power of the radar, and the phase with the minimum pitch phase search function is obtained by one-dimensional search.

[0064] Based on the azimuth phase search function, the elevation phase search function, the phase with the minimum value of the azimuth phase search function, and the phase with the minimum value of the elevation phase search function, the Kroneckt product is used to calculate the azimuth-elevation joint weight vector to complete beamforming.

[0065] Preferably, calculating the azimuth weight vector using the radar's azimuth beam pointing and azimuth broadening parameters includes:

[0066] The azimuth direction-constrained steering vector is calculated as:

[0067]

[0068]

[0069]

[0070] where θ0and Δ A represent the azimuth pointing and azimuth broadening parameters, respectively, d x is the azimuth array element spacing, and λ is the radar wavelength, [·] T denotes the transpose, and j is the imaginary unit.

[0071] Preferably, the calculation of the azimuth direction-constrained steering vector also includes:

[0072] The azimuth direction-constrained steering vector is calculated as: Azi

[0073]

[0074] where C Azi = [a(θ0- Δ A ), a(θ0), a(θ0+ Δ A )], f Azi = [Me -jη , M, Me jη ] T , and η is the azimuth direction-constrained phase, [·] H denotes the conjugate transpose, and the subscript Azi in the formula represents the azimuth.

[0075] Preferably, the calculated noise output power is:

[0076]

[0077] Preferably, the constructed azimuth direction-constrained phase search function is:

[0078] G Azi = a 1,2 cos(η + b 1,2 ) + a 1,3 cos(2η + b 1,3 ) + a 2,3 cos(η + b 2,3 )

[0079] where a 1,2 and b 1,2 are the matrix ​The magnitude and phase of the first row, second column value, a 1,3 and b 1,3 are matrices The magnitude and phase of the first row, third column value, a 2,3 and b 2,3 are matrices The magnitude and phase of the second row, third column value.

[0080] Preferably, the phase that minimizes G Azi is obtained by a one-dimensional search:

[0081] G Azi

[0082] s.t. η ∈ (-π, π).

[0083] Preferably, calculating the weight vector in the elevation direction using the radar's elevation beam pointing and elevation beamwidth parameters comprises:

[0084] Calculating the elevation direction constraint steering vector comprises:

[0085]

[0086]

[0087]

[0088] where φ0and Δ E represent the elevation pointing and beamwidth parameters, respectively, and d y is the elevation inter-element spacing;

[0089] Preferably, calculating the weight vector in the elevation direction using the radar's elevation beam pointing and elevation beamwidth parameters further comprises:

[0090] Calculating the weight vector using a linearly constrained minimum variance criterion based on the elevation direction constraint steering vector comprises:

[0091]

[0092] where C Ele = [b(φ0- Δ E ), b(φ0), b(φ0+ Δ E )], f Ele = [Ne -jψ , N, Ne jψ ] T , and ψ is the elevation direction constraint phase, with the subscript Ele in the formula representing elevation.

[0093] Preferably, the noise output power:

[0094]

[0095] Preferably, the constructed elevation-wise phase search function:

[0096] G Ele = c 1,2 cos(ψ + d 1,2 ) + c 1,3 cos(2ψ + d 1,3 ) + c 2,3 cos(ψ + d 2,3 )

[0097] where c 1,2 and d 1,2 are the amplitude and phase of the first row second column value of the matrix c 1,3 and d 1,3 are the amplitude and phase of the first row third column value of the matrix c 2,3 and d 2,3 are the amplitude and phase of the second row third column value of the matrix

[0098] Preferably, the phase that minimizes G Ele is obtained by one-dimensional search:

[0099] G Ele

[0100] s.t. ψ ∈ (-π, π).

[0101] Preferably, the azimuth-elevation joint weight vector W Azi-Ele :

[0102]

[0103] where denotes the Kroneckt product.

[0104] A specific embodiment, further illustrating the present application, is as follows:

[0105] Step 1. Calculate the azimuth-wise weight vector, which is implemented as follows:

[0106] 1(a) Calculate the azimuth-wise constraint steering vector:

[0107]

[0108]

[0109]

[0110] ​where θ0and Δ A denote the azimuth pointing and azimuth spread parameter, respectively, d x is the azimuth array element spacing, λ is the radar wavelength, [·] T represents the transpose, and j is the imaginary unit.

[0111] 1(b) The weight vector is calculated using the linearly constrained minimum variance criterion:

[0112]

[0113] where C Azi = [a(θ0- Δ A ), a(θ0), a(θ0+ Δ A )], f Azi = [Me -jη , M, Me jη ] T , and η is the azimuth constraint phase, [·] H represents the conjugate transpose.

[0114] Step 2: One-dimensional search of the azimuth response vector phase, which is implemented as follows:

[0115] 2(a) The noise output power is calculated:

[0116]

[0117] 2(b) The phase search function is constructed:

[0118] G Azi = a 1,2 cos(η + b 1,2 ) + a 1,3 cos(2η + b 1,3 ) + a 2,3 cos(η + b 2,3 ) (6)

[0119] where a 1,2 and b 1,2 are the amplitude and phase of the value in the first row and second column of the matrix , a 1,3 and b 1,3 are the amplitude and phase of the value in the first row and third column of the matrix , and a 2,3 and b 2,3 are the amplitude and phase of the value in the second row and third column of the matrix .

[0120] 2(c) The phase that minimizes G Azi is obtained through one-dimensional search:

[0121] G Azi

[0122] s.t.η∈(-π,π) (7)

[0123] Step 3: Compute the elevation steering vector, which is implemented as follows:

[0124] 3(a) Compute the elevation constraint steering vector:

[0125]

[0126]

[0127]

[0128] where φ0and Δ E denote the elevation pointing and elevation lobe parameters, respectively, and d y is the elevation array element spacing;

[0129] 3(b) Compute the weight vector using the linearly constrained minimum variance criterion:

[0130]

[0131] where C Ele = [b(φ0- Δ E ), b(φ0), b(φ0+ Δ E )], f Ele = [Ne -jψ , N, Ne jψ ] T , and ψ is the elevation constraint phase. The subscript Ele in the formulas denotes elevation.

[0132] Step 4: One-dimensional search for the elevation response vector phase, which is implemented as follows:

[0133] 4(a) Compute the noise output power:

[0134]

[0135] 4(b) Construct the phase search function:

[0136] G Ele = c 1,2 cos(ψ+d 1,2 )+c 1,3 cos(2ψ+d 1,3 )+c 2,3 cos(ψ+d 2,3 ) (13)

[0137] where c 1,2 and d 1,2respectively the amplitude and phase of the value in the first row and third column, c 1,3 and d 1,3 respectively the amplitude and phase of the value in the first row and third column, c 2,3 and d 2,3 respectively the amplitude and phase of the value in the second row and third column

[0138] 4(c) the phase that makes G Ele minimum is obtained by one-dimensional search:

[0139] G Ele

[0140] s.t.ψ∈(-π,π) (14)

[0141] Step 5: the azimuth-elevation joint weight vector is calculated, and the specific implementation steps are as follows:

[0142] η and ψ are brought into W Azi and W Ele respectively, and the two-dimensional weight vector W Azi-Ele is calculated by using Kroneckt product as follows:

[0143]

[0144] wherein represents Kroneckt product.

[0145] The application searches the response vector phase of the azimuth / elevation dimension respectively by using the minimum noise power criterion, thereby obtaining the weight vector of the azimuth dimension / elevation dimension, and finally, based on the structural characteristics of the uniform surface array, the Kroneckt product of the weight vector of the azimuth dimension and the weight vector of the elevation dimension is taken as the optimal weight vector, and the beam forming is realized.

[0146] The effect of the application can be further illustrated by the following simulation experiment:

[0147] Experimental conditions: uniform surface array (the number of array elements M=20, N=20), the interval of the azimuth and elevation elements is 0.5λ (λ=0.05), the real azimuth angle and elevation angle of the target are both 10°, the signal-to-noise ratio is 0dB; 200 Monte Carlo simulations are performed each time;

[0148] Simulation parameters: the azimuth constraint parameter and the elevation constraint parameter of the application are both 0.2°, the search interval of η and ψ is both (-π, π), and the angle search interval is π / 180. The prior art for comparison is set as follows: conventional beam forming method; linear constraint minimum variance method with the same constraint angle as the application.

[0149] Experimental results show that, with the elevation and azimuth angles varying from -45° to 45°, the beam response and one-dimensional radiation pattern of the conventional beamforming method relative to the angle of arrival are as follows: Figure 3 As shown, the one-dimensional radiation pattern of beam response and arrival angle using the linearly constrained minimum variance method is as follows. Figure 4 As shown, the one-dimensional radiation pattern of the beam response and arrival angle of the method of the present invention is as follows. Figure 5 As shown;

[0150] observe Figure 3 It was found that conventional beamforming methods can only achieve maximum gain at the beam pointing angle in both the azimuth and elevation dimensions, thus exhibiting generally poor robustness; observation Figure 4 It was found that although the linearly constrained minimum variance method can produce a flat-top response in both azimuth and pitch dimensions within the constrained region, the sidelobe level is very high; observation Figure 5 It was found that the method of the present invention can form a flat-top response in the constrained region in both the azimuth and pitch dimensions, and the sidelobe level meets the requirements, thus achieving the best output performance.

[0151] In summary, this invention discloses a method for flat-top main beamforming of a uniform array using phase response search, solving the problem of flat-top main beamforming in static beamforming technology. The implementation process is as follows: The azimuth weight vector is solved using a given azimuth angle and broadening parameters; the azimuth response vector phase is searched one-dimensionally based on the minimum noise power criterion; the elevation weight vector is solved using a given elevation angle and broadening parameters; the elevation response vector phase is searched one-dimensionally based on the minimum noise power criterion; finally, the Kroneckt product is used to calculate the azimuth-elevation joint weight vector to achieve beamforming. This invention improves the output performance of the beamformer when pointing deviation exists and can be applied to scenarios with high real-time requirements.

[0152] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for phase response search of a uniform planar array flat-top main beam shaping, characterized in that, The method comprises the following steps: calculating the weight vector in the azimuth direction by using the azimuth beam pointing and azimuth beam width of the radar; calculating the noise output power of the radar to construct an azimuth phase search function, and obtaining the phase with the minimum azimuth phase search function by one-dimensional search; calculating the weight vector in the elevation direction by using the elevation beam pointing and elevation beam width of the radar; calculating the noise output power of the radar to construct an elevation phase search function, and obtaining the phase with the minimum elevation phase search function by one-dimensional search; calculating the azimuth-elevation joint weight vector by using Kroneckt product according to the azimuth phase search function, the elevation phase search function, the phase with the minimum azimuth phase search function and the phase with the minimum elevation phase search function, and completing the beam forming.

2. The uniform planar array flat main beamforming method of phase response search according to claim 1, characterized in that, The calculation of the weight vector in the azimuth direction by using the azimuth beam pointing and azimuth beam width of the radar comprises: calculating the azimuth constraint steering vector: where θ0 and Δ A respectively denote the azimuth pointing and azimuth spread parameters, d x is the azimuth inter-element spacing, λ is the radar wavelength, [·] T denotes the transpose, j is the imaginary unit.

3. The uniform planar array flat main beam forming method of phase response search according to claim 2, characterized in that, The calculation of the weight vector in the azimuth direction by using the azimuth beam pointing and azimuth beam width of the radar comprises: According to the azimuth direction constraint steering vector, a linear constraint minimum variance criterion is used to calculate the weight vector W of the azimuth direction Azi : where C Azi = [a(θ0-Δ A ), a(θ0), a(θ0+Δ A )], f Azi = [Me -jη , M, Me jη ] T , and η is the azimuth constraint phase, [·] H denotes the conjugate transpose.

4. The uniform planar array flat main beam forming method of phase response search according to claim 3, characterized in that, the calculated noise output power:

5. The uniform planar array flat main beam forming method of phase response search according to claim 4, characterized in that, the constructed azimuth phase search function: G Azi = a 1,2 cos(η+b 1,2 ) + a 1,3 cos(2η+b 1,3 ) + a 2,3 cos(η+b 2,3 ) where a 1,2 and b 1,2 are matrices the amplitude and phase of the value in the first row and second column, a 1,3 and b 1,3 are matrices the amplitude and phase of the value in the first row and third column, a 2,3 and b 2,3 are matrices the amplitude and phase of the value in the second row and third column.

6. The uniform planar array flat main beam forming method of phase response search according to claim 1, characterized in that, The calculation of the weight vector in the elevation direction by using the elevation beam pointing and elevation beam width of the radar comprises: calculating the elevation constraint steering vector: where φ0and Δ E respectively denote the elevation pointing and elevation spread parameters, d y is the elevation inter-element spacing.

7. The uniform planar array flat main beam forming method of phase response search according to claim 6, characterized in that, The calculation of the weight vector in the elevation direction by using the elevation beam pointing and elevation beam width of the radar comprises: calculating the weight vector by using the linear constraint minimum variance criterion according to the elevation constraint steering vector: where C Ele = [b(φ0-Δ E ), b(φ0), b(φ0+Δ E )], f Ele = [Ne -jψ , N, Ne jψ ] T and ψ is the constrained phase.

8. The uniform planar array flat main beam shaping method of phase response search according to claim 7, characterized in that, the noise output power:

9. The uniform planar array flat main beam forming method of phase response search according to claim 8, characterized in that, the constructed elevation phase search function: G Ele = c 1,2 cos(ψ+d 1,2 ) + c 1,3 cos(2ψ+d 1,3 ) + c 2,3 cos(ψ+d 2,3 ) where c 1,2 and d 1,2 are matrices the amplitude and phase of the value in the first row, second column, c 1,3 and d 1,3 are matrices the amplitude and phase of the value in the first row, third column, c 2,3 and d 2,3 are matrices the amplitude and phase of the value in the second row, third column.

10. The uniform planar array flat main beam shaping method of phase response search according to claim 9, characterized in that, The azimuth-elevation joint weight vector W Azi-Ele : wherein denotes the Kronecker product.

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