Beam broadening phase generation method based on hierarchical optimization

Abstract

The invention discloses a beam broadening phase generation method based on hierarchical optimization, and the method comprises the following steps: 1, the configuration of X-waveband phased array weather radar parameters and primary optimization parameters; 2, the selection of a phase construction function; 3, the rapid calculation of a directional diagram based on matrix operation; 4, the selection of a calculation method of robust beam width; step 6, optimization objective function setting; and step 7, directional diagram secondary optimization based on a random phase. According to the method disclosed by the invention, beam broadening can be realized through the phase weight on the premise of not using variable amplitude weight and reducing the number of used antenna arrays, and the method has important significance in improving wide transmitting and narrow receiving capabilities of an X-band phased array weather radar and improving the time resolution of the radar.

Description

Technical Field

[0001] The present invention belongs to the technical field of X-band phased array weather radar and rain measuring radar, and in particular relates to a beam broadening phase generation method based on hierarchical optimization in this field. Background Art

[0002] X-band phased array weather radar is a new type of meteorological detection equipment that utilizes X-band electromagnetic waves and phased array technology to achieve high-precision and rapid scanning. Compared to traditional mechanical scanning weather radars, it offers significant advantages in detection accuracy, data update rate, and adaptive observation, making it particularly suitable for monitoring and early warning of severe convective weather (such as tornadoes, hail, and short-duration rainstorms). X-band phased array weather radars utilize a wide-beam transmission and narrow-reception operating mode to achieve simultaneous multi-beam detection, thereby improving data update rates. However, in practical engineering applications, beam broadening schemes cannot adjust amplitude weights online, and reducing the number of array elements significantly reduces radar detection capability. Therefore, beam broadening can only be achieved using phase-only weighting. However, in existing phase-only weighted beam broadening schemes, the sidelobe performance of the antenna pattern deteriorates rapidly as the beam width increases. Designing a phase generation method that simultaneously meets the requirements for wide beam and low sidelobe performance is a pressing issue in the development of X-band phased array weather radars. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a beam widening phase generation method based on hierarchical optimization, which can simultaneously meet the wide beam and low sidelobe indicators.

[0004] The present invention adopts the following technical solutions:

[0005] A beam broadening phase generation method based on hierarchical optimization is improved in that it includes the following steps:

[0006] Step 1: X-band phased array weather radar parameter and primary optimization parameter configuration:

[0007] Configure the radar operating frequency, number of antenna elements, antenna element spacing, initial Taylor weight, target beamwidth, and initial target sidelobe level;

[0008] Step 2, phase constructor selection:

[0009] Use adjustable amplitude power rate function as phase constructor;

[0010] Step 3: Quickly calculate the directional pattern based on matrix operations:

[0011] By using matrix operations instead of array number cycles, the calculation result of the directivity pattern can be obtained with only one calculation;

[0012] Step 4: Choose the calculation method for robust beamwidth:

[0013] Calculate beam width by combining multiple methods;

[0014] Step 5, calculation of the maximum sidelobe level:

[0015] Calculate the maximum amplitude of the pattern outside the beam width range and use it as the maximum sidelobe level;

[0016] Step 6: Optimize the objective function settings:

[0017] The objective function is selected as the weighted sum of the absolute value of the difference between the beam width and the target beam width, and the absolute value of the difference between the sidelobe level and the initial target sidelobe level;

[0018] Step 7, Direction based on random phase Figure 2 Level optimization:

[0019] Based on the phase weights given in the previous steps, random phases are introduced, and the in-band flatness index is further added to perform secondary screening on the phase weights to obtain hierarchically optimized phase weights.

[0020] Furthermore, the phase constructor of step 2 is as follows:

[0021]

[0022] In the above formula, is the phase of the nth array, α is the amplitude parameter, N is the number of arrays, m is the power exponent parameter, and q1 and q2 are weight parameters.

[0023] Furthermore, in step 3, the antenna element is a one-dimensional array, and the matrix expression for pattern calculation is:

[0024]

[0025] In the above formula, G is the antenna pattern, w1 and w N is the Taylor weight, N is the number of arrays, M is the number of angles, d is the antenna array spacing, λ is the radar wavelength, θ1 and θ M is the discretized angle.

[0026] Furthermore, in step 4, the beam width is calculated using two methods. The calculation process of method 1 is as follows:

[0027] Calculate the maximum value G of the antenna pattern G peak and the maximum position index I peak :

[0028] [G peak ,I peak ]=max(G) (3)

[0029] Set the search threshold G 3dB for:

[0030] G 3dB =G peak -3 (4)

[0031] Search from the maximum value index position to the left, and the left boundary position of half power is determined if the following conditions are met:

[0032]

[0033] In the above formula, θ i and θ i-1 is the angle between point i and point i-1;

[0034] Search from the maximum value index position to the right, and determine the right boundary position of half power if the following conditions are met:

[0035]

[0036] In the above formula, θ j and θ j+1 is the angle between point j and point j+1;

[0037] The beam width BW1 calculated by method 1 is:

[0038] BW1=|θ j -θ i | (7)

[0039] The calculation process of Method 2 is as follows:

[0040] Using the calculation results of formula (2) and formula (3), calculate the position index I where the power is greater than the threshold up :

[0041] I up =find(G>G 3dB ) (8)

[0042] The beam width BW2 calculated by method 2 is:

[0043]

[0044] In the above formula, is the leftmost angle where the power is greater than the threshold, is the rightmost angle where the power is greater than the threshold. Further, in step 5, the maximum sidelobe level is calculated as follows:

[0045] Calculate the beam width outer angle position index I non-main :

[0046]

[0047] In the above formula, θ is the angle and BW is the beam width;

[0048] Calculate the pattern peak pks and peak position index I locs :

[0049] [pks,I locs ]=findpeaks(G) (11)

[0050] Calculate the intersection of two position index arrays I intersect :

[0051] I intersect =I non-main ∩I locs (12)

[0052] Then the maximum sidelobe level SSL is:

[0053] SSL=max(G(I intersect )) (13).

[0054] Furthermore, in step 6, the phase weights are optimized using a genetic algorithm, and the objective function f is set to obj for:

[0055]

[0056] In the above formula, α is the amplitude parameter to be optimized, m is the power exponent parameter to be optimized, BW obj is the target beam width, is the initial target sidelobe level, k1, k2 and k3 are weight parameters.

[0057] Furthermore, step 7 adds random phase to the primary optimized phase weight

[0058]

[0059] And use the following evaluation function f eval Perform secondary screening:

[0060]

[0061] In the above formula, k4 is the weight coefficient of the in-band flatness, is the average value of the normalized gain within the beam bandwidth.

[0062] The beneficial effects of the present invention are:

[0063] The method disclosed in the present invention can achieve beam broadening through phase weighting without using variable amplitude weighting and reducing the number of antenna elements used. It is of great significance to improve the wide-transmit and narrow-receive capability of X-band phased array weather radar and enhance the radar's time resolution.

[0064] The method disclosed in the present invention can effectively alleviate the deterioration level of antenna side lobes while increasing the beam width, which is of great significance for reducing the side lobe dispersion effect of strong weather targets and improving radar detection performance.

[0065] The method disclosed in the present invention can achieve the same sidelobe level through phase adjustment while reducing power classification, which is of great significance to the cost control of X-band phased array weather radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0067] Figure 2 is the initial Taylor weight graph;

[0068] Figure 3 is the antenna pattern obtained by primary optimization;

[0069] Figure 4 is the phase weight map obtained by primary optimization;

[0070] Figure 5 It is the characteristic diagram of sidelobe degradation caused by power classification;

[0071] Figure 6 is the antenna pattern after multi-level optimization;

[0072] Figure 7 is the phase weight map after multi-level optimization. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present 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 only used to explain the present invention and are not intended to limit the present invention.

[0074] Example 1: This embodiment discloses a beam broadening phase generation method based on hierarchical optimization, such as Figure 1 As shown, the following steps are included:

[0075] Step 1: X-band phased array weather radar parameter and primary optimization parameter configuration:

[0076] Configure radar parameters such as radar operating frequency, number of antenna elements, antenna element spacing, initial Taylor weight, and optimize target parameters such as target beam width and initial target sidelobe level to provide a basis for primary optimization calculations.

[0077] In this embodiment, the configured X-band phased array weather radar parameters are as follows:

[0078] Radar operating frequency: 9400MHz;

[0079] Number of antenna elements: 120;

[0080] Antenna array spacing: 19mm;

[0081] Target beam width: 8°;

[0082] Initial target sidelobe level: -21dB;

[0083] The initial Taylor weights are as follows Figure 2 shown.

[0084] Step 2, phase constructor selection:

[0085] An adjustable amplitude power-rate function is used as a phase constructor, and phase adjustment is achieved by optimizing the amplitude parameter and power exponent, thereby optimizing the antenna pattern.

[0086] To achieve beam broadening, a phase constructor can be used to create an effect similar to wavefront curvature, thereby affecting the focusing or divergence characteristics of the beam. In this embodiment, the phase constructor is as follows:

[0087]

[0088] In the above formula, is the phase of the nth array, α is the amplitude parameter, N is the number of arrays, m is the power exponent parameter, and q1 and q2 are weight parameters.

[0089] Step 3: Quickly calculate the directional pattern based on matrix operations:

[0090] By replacing the array number loop with matrix operations, the calculation result of the directional pattern is obtained through only one calculation, reducing the calculation time of the directional pattern that is frequently repeatedly calculated during the optimization process, thereby improving the optimization efficiency.

[0091] In this embodiment, the antenna element is a one-dimensional array, and the matrix expression for pattern calculation is:

[0092]

[0093] In the above formula, G is the antenna pattern, w1 and w Nis the Taylor weight, N is the number of arrays, M is the number of angles, d is the antenna array spacing, λ is the radar wavelength, θ1 and θ M is the discretized angle, and is the phase of the different arrays given by Equation (1). Through N×M-dimensional matrix operations, we can obtain the amplitude values ​​of different arrays at different angles. Summing the values ​​across the array dimensions yields a 1×M-dimensional directional pattern at different angles. Using matrix operations can improve computational efficiency by approximately 30%.

[0094] Step 4: Choose the calculation method for robust beamwidth:

[0095] In order to prevent overfitting results such as comb-shaped radiation patterns and multi-peak radiation patterns from appearing during the optimization process, the beamwidth is calculated by combining multiple methods, thereby suppressing the optimization process from falling into local extreme values ​​and obtaining more robust optimization results.

[0096] In this embodiment, the beam width is calculated using two methods. The calculation process of method 1 is as follows:

[0097] Calculate the maximum value G of the antenna pattern G peak and the maximum position index I peak :

[0098] [G peak ,I peak ]=max(G) (3)

[0099] Set the search threshold G 3dB for:

[0100] G 3dB =G peak -3 (4)

[0101] Search from the maximum value index position to the left, and the left boundary position of half power is determined if the following conditions are met:

[0102]

[0103] In the above formula, θ i and θ i-1 is the angle between point i and point i-1;

[0104] Search from the maximum value index position to the right, and determine the right boundary position of half power if the following conditions are met:

[0105]

[0106] In the above formula, θ j and θ j+1 is the angle between point j and point j+1;

[0107] The beam width BW1 calculated by method 1 is:

[0108] BW1=|θ j -θ i | (7)

[0109] The calculation process of Method 2 is as follows:

[0110] Using the calculation results of formula (2) and formula (3), calculate the position index I where the power is greater than the threshold up :

[0111] I up =find(G>G 3dB ) (8)

[0112] The beam width BW2 calculated by method 2 is:

[0113]

[0114] In the above formula, is the leftmost angle where the power is greater than the threshold, The rightmost angle where the power is greater than the threshold.

[0115] Using the beamwidths obtained by both methods as constraints can effectively prevent the occurrence of comb-shaped and multi-peak patterns in the optimization results.

[0116] Step 5, calculation of the maximum sidelobe level:

[0117] Calculate the maximum amplitude of the pattern outside the beam width range and use it as the maximum sidelobe level;

[0118] In this embodiment, the maximum sidelobe level is calculated as follows:

[0119] Calculate the beam width outer angle position index I non-main :

[0120]

[0121] In the above formula, θ is the angle and BW is the beam width;

[0122] Calculate the pattern peak pks and peak position index I locs :

[0123] [pks,I locs ]=findpeaks(G) (11)

[0124] Calculate the intersection of two position index arrays I intersect :

[0125] I intersect=I non-main ∩I locs (12)

[0126] Then the maximum sidelobe level SSL is:

[0127] SSL=max(G(I intersect )) (13)

[0128] Step 6: Optimize the objective function settings:

[0129] The weighted sum of the absolute value of the difference between the beamwidth and the target beamwidth, and the absolute value of the difference between the sidelobe level and the initial target sidelobe level is selected as the objective function to provide an optimization direction for the primary optimization calculation.

[0130] In this embodiment, a genetic algorithm is used to optimize the phase weight, and the objective function f is set obj for:

[0131]

[0132] In the above formula, α is the amplitude parameter to be optimized, m is the power exponent parameter to be optimized, BW obj is the target beam width, is the initial target sidelobe level, k1, k2 and k3 are weight parameters.

[0133] When using genetic algorithms for optimization, multiple populations are set up for independent optimization to reduce the problem of premature convergence caused by the emergence of abnormal individuals. The directional patterns and phase weights calculated by the above steps are as follows: Figure 3 and Figure 4 shown.

[0134] Step 7, Direction based on random phase Figure 2 Level optimization:

[0135] Based on the principle that random phase can suppress quantization lobes, random phase is introduced on the basis of the phase weights given in the previous steps. The in-band flatness index is further added to perform secondary screening of the phase weights to obtain hierarchically optimized phase weights.

[0136] In the above calculations, ideal Taylor weights were used for amplitude weighting. However, in practical applications, to maintain system stability, TR components are saturated for amplification. Therefore, due to cost constraints, excessive TR component power levels cannot be used. The constraints of practical conditions (power quantization) lead to the appearance of quantization lobes, which deteriorate the antenna sidelobe indicators, such as Figure 5 As shown in Figure 2, the sidelobe index of the antenna deteriorates from -23dB to -3dB. This embodiment adds a random phase to the primary optimized phase weight.

[0137]

[0138] And use the following evaluation function f eval Perform secondary screening:

[0139]

[0140] In the above formula, k4 is the weight coefficient of the in-band flatness, is the average value of the normalized gain within the beam bandwidth. Using the above formula, we can get the multi-level optimized directivity pattern and phase weight, as shown in the following example: Figure 6 and Figure 7 As shown in the figure, the beamwidth of the directional pattern is 8° and the sidelobe level is -22.29dB. The sidelobe degradation caused by quantization has been effectively alleviated, which can meet the needs of practical applications.

[0141] In summary, the method of the present invention generates phase for X-band phased array weather radar, which meets the wide beam and low sidelobe indicators at the same time. This is of great significance for effectively improving the performance of X-band phased array weather radar and developing new radar products.

Claims

1. A beam broadening phase generation method based on hierarchical optimization, characterized in that: The steps include: Step 1: X-band phased array weather radar parameter and primary optimization parameter configuration: Configure the radar operating frequency, number of antenna elements, antenna element spacing, initial Taylor weight, target beamwidth, and initial target sidelobe level; Step 2, phase constructor selection: Use adjustable amplitude power rate function as phase constructor; Step 3: Quickly calculate the directional pattern based on matrix operations: By using matrix operations instead of array number cycles, the calculation result of the directivity pattern can be obtained with only one calculation; Step 4: Choose the calculation method for robust beamwidth: Calculate beam width by combining multiple methods; Step 5, calculation of the maximum sidelobe level: Calculate the maximum amplitude of the pattern outside the beam width range and use it as the maximum sidelobe level; Step 6: Optimize the objective function settings: The objective function is selected as the weighted sum of the absolute value of the difference between the beam width and the target beam width, and the absolute value of the difference between the sidelobe level and the initial target sidelobe level; Step 7: Secondary optimization of the directional pattern based on random phase: Based on the phase weights given in the previous steps, random phases are introduced, and the in-band flatness index is further added to perform secondary screening on the phase weights to obtain hierarchically optimized phase weights.

2. The beam broadening phase generation method based on hierarchical optimization according to claim 1, characterized in that: The phase constructor in step 2 is as follows: In the above formula, is the phase of the nth array, α is the amplitude parameter, N is the number of arrays, m is the power exponent parameter, and q1 and q2 are weight parameters.

3. The beam broadening phase generation method based on hierarchical optimization according to claim 2, characterized in that: In step 3, the antenna element is a one-dimensional array, and the matrix expression for pattern calculation is: In the above formula, G is the antenna pattern, w1 and w N is the Taylor weight, N is the number of arrays, M is the number of angles, d is the antenna array spacing, λ is the radar wavelength, θ1 and θ M is the discretized angle.

4. The beam broadening phase generation method based on hierarchical optimization according to claim 3, characterized in that: In step 4, the beam width is calculated using two methods. The calculation process of method 1 is as follows: Calculate the maximum value G of the antenna pattern G peak and the maximum position index I peak : [G peak ,I peak ]=max(G) (3) Set the search threshold G 3dB for: G 3dB =G peak -3 (4) Search from the maximum value index position to the left, and the left boundary position of half power is determined if the following conditions are met: In the above formula, θ i and θ i-1 is the angle between point i and point i-1; Search from the maximum value index position to the right, and determine the right boundary position of half power if the following conditions are met: In the above formula, θ j and θ j+1 is the angle between point j and point j+1; The beam width BW1 calculated by method 1 is: BW1=|θ j -θ i | (7) The calculation process of Method 2 is as follows: Using the calculation results of formula (2) and formula (3), calculate the position index I where the power is greater than the threshold up : I up =find(G>G 3dB ) (8) The beam width BW2 calculated by method 2 is: In the above formula, is the leftmost angle where the power is greater than the threshold, The rightmost angle where the power is greater than the threshold.

5. The beam broadening phase generation method based on hierarchical optimization according to claim 4, characterized in that: In step 5, the maximum sidelobe level is calculated as follows: Calculate the beam width outer angle position index I non-main : In the above formula, θ is the angle and BW is the beam width; Calculate the pattern peak pks and peak position index I locs : [pks,I locs ]=findpeaks(G) (11) Calculate the intersection of two position index arrays I intersect : I intersect =I non-main ∩I locs (12) Then the maximum sidelobe level SSL is: SSL=max(G(I intersect )) (13)。 6. The beam broadening phase generation method based on hierarchical optimization according to claim 5, characterized in that: In step 6, the phase weights are optimized using a genetic algorithm, and the objective function f is set obj for: In the above formula, α is the amplitude parameter to be optimized, m is the power exponent parameter to be optimized, BW obj is the target beam width, is the initial target sidelobe level, k1, k2 and k3 are weight parameters.

7. The beam broadening phase generation method based on hierarchical optimization according to claim 6, characterized in that: Step 7: Add random phase to the primary optimized phase weight : And use the following evaluation function f eval Perform secondary screening: In the above formula, k4 is the weight coefficient of the in-band flatness, is the average value of the normalized gain within the beam bandwidth.

Images