A method for suppressing the spatial variation of the synthesized characteristics of randomly distributed array beams

Abstract

This invention belongs to the field of antenna design technology, and specifically relates to a method for suppressing the spatial variability of beam synthesis characteristics in randomly distributed arrays. Step 1: Determine the task's spatial beam scanning range; Step 2: Establish the mapping relationship between the coordinate systems of each subarray and the random array polar coordinate system. Based on the task's spatial beam scanning range and the mapping relationship, select subarrays that satisfy the beam spatial coverage range; Step 3: For each beam arranged within the beam scanning range, perform beam synthesis based on the selected subarrays; Step 4: Determine whether the synthesized beam meets the constraints. If yes, proceed to Step 6; otherwise, proceed to Step 5; Step 5: Adjust the number and distribution of subarrays, perform beam synthesis again, and return to Step 4; Step 6: Output the beam synthesis result corresponding to the current beam; Step 7: Determine whether other beams exist within the beam scanning range. If yes, proceed to Step 3; otherwise, proceed to Step 8; Step 8: Statistically analyze the subarray resource allocation results corresponding to different beams in the task.

Description

Technical Field

[0001] This invention belongs to the field of antenna design technology, and specifically relates to a method for suppressing the spatial variation of the synthesized characteristics of randomly distributed array beams. Background Technology

[0002] Current phased array antenna arrays are mostly uniform linear arrays and planar arrays. Linear arrays can only cover an azimuth angle of about 120°, and their gain and radiation pattern characteristics change with different scanning angles, which greatly limits their application range. Planar arrays also have problems such as narrow beam scanning range, beamwidth increasing with the scanning angle, and mutual coupling effects between array elements being a function of the scanning angle.

[0003] Synthesis of randomly distributed array patterns in three-dimensional space has the potential to solve the above problems. There are three main structural forms of array antennas that meet full spatial coverage: multi-faceted arrays, curved or conformal arrays, and lens array antennas. Conformal array antennas often need to achieve low or ultra-low sidelobe patterns, but using conventional amplitude-weighted conformal array antennas results in a very high excitation amplitude dynamic ratio, which places stringent requirements on feed accuracy. To obtain a wider multi-beam coverage space to improve radar interception probability, a concept of combining multiple rectangular planar array antennas into a multi-faceted array antenna can be adopted. This combines the beam coverage areas formed by multiple arrays to expand the beam coverage area of ​​the planar array. Based on this concept, the spatial arrangement of multiple arrays is specifically designed using solid geometry, and then a wide-coverage multi-faceted array multi-beamforming method is formed according to multi-beamforming algorithms. The multi-faceted splicing structure reduces the number of planar subarrays, further reducing the implementation difficulty while maintaining wide-area coverage performance.

[0004] Although randomly distributed multi-faceted arrays have advantages such as wide spatial coverage, their spatial distribution has greater uncertainty compared to traditional planar arrays, resulting in greater "spatial variability" in their beamforming performance. Summary of the Invention

[0005] The purpose of this invention is to propose a method to suppress the spatial variability of beam synthesis characteristics of randomly distributed arrays, and to solve the problem that the shape and beam gain of the formed beam change with the scanning angle in the beam synthesis of complex distributed arrays such as conformal opportunistic arrays, randomly distributed conformal arrays, and randomly distributed multifaceted arrays in radar system platforms.

[0006] The technical solution of the present invention:

[0007] A method for suppressing the spatial variation of synthesized characteristics of randomly distributed array beams, comprising the following steps:

[0008] Step 1: Determine the mission airspace beam scanning range;

[0009] Step 2: Establish the mapping relationship between the coordinate system of each subarray and the random array polar coordinate system. Based on the mission spatial beam scanning range and the mapping relationship, select the subarray that meets the beam spatial coverage range.

[0010] Step 3: For each beam arranged within the beam scanning range, perform beam synthesis based on the selected subarray.

[0011] Step 4: Determine whether the synthesized beams meet the constraints. If yes, proceed to Step 6; otherwise, proceed to Step 5.

[0012] Step 5: Adjust the number and distribution of subarrays, re-perform beam synthesis, and return to Step 4;

[0013] Step 6: Output the beam synthesis result corresponding to the current beam;

[0014] Step 7: Determine if there are other beams in the beam scanning range. If yes, proceed to Step 3; otherwise, proceed to Step 8.

[0015] Step 8: Statistically analyze the subarray resource allocation results for different beams in the task.

[0016] Furthermore, in step one, the azimuth range of the mission's spatial beam scanning range is [ f min , f max The pitch angle range is [ i min , i max ].

[0017] Furthermore, in step two, the process is as follows:

[0018] The array distribution of a typical aircraft is modeled, which includes eight sub-arrays, and the beam space coverage range corresponding to different arrays is fixed.

[0019] Select subarrays or combinations of subarrays that overlap with the mission's airspace beam coverage requirements.

[0020] The complete coverage of the beam space where the mission is located is provided by I The beams are scanned at different times to achieve this, and the first beam is scanned at different times to achieve this. i (1≤ i ≤ I The beam synthesis results of each beam are optimized.

[0021] The mapping relationship is established as follows:

[0022] First, let the random array in polar coordinates be... iAzimuth-Pitch Angle of Each Beam Mapped to a random array Cartesian coordinate system x i , y i , z i Then transform to the Cartesian coordinate system of the subarray. Finally, it is transformed to the polar coordinate system of the subarray. ;

[0023] and Let be the azimuth-elevation angles of the beam in the polar coordinate system of the random array, and satisfy . f imin ≤ f i ≤ f imax , i imin ≤ i i ≤ i imax ; x i , y i , z i These are the coordinate values ​​in the Cartesian coordinate system of the random array; The respective u The coordinate values ​​of each sub-array in the Cartesian coordinate system; The respective u Azimuth-elevation angles of individual array surfaces in polar coordinates;

[0024] set up and These represent the azimuth and elevation dimensions of the array element patterns in the subarray, respectively, and the 3dB beamwidth. If the... u Each sub-array must satisfy the following conditions:

[0025] (1)

[0026] Then it is determined that the subarray can participate in beamforming;

[0027] make Through statistics Within different variation ranges, the number of sub-arrays satisfying condition (1) on a certain array surface is determined to be greater than the minimum number of sub-arrays required for beamforming when the number of sub-arrays satisfying the condition is greater than the minimum number of sub-arrays required for beamforming. In this case, it is determined that the beam formed by the corresponding array surface can cover the spatial angle. .

[0028] Furthermore, in step three, the beamforming process is as follows:

[0029] Suppose that a randomly distributed array has U planar subarrays with normals pointing in different directions. The position of each subarray is randomly variable, and the direction of the normals of the subarray surfaces changes with the curvature of the aircraft surface. Each of the U subarray surfaces is a regular surface array composed of N*M array elements.

[0030] For a uniformly fed area array, assuming the radar transmits a narrowband signal, the array antenna elements are arranged according to... d = l 0 / 2 interval layout, l 0= c / f 0;

[0031] If we consider the first u The normal direction of each sub-array is ( f ( u ), i ( u )),when U A random array composed of subarrays needs to be positioned in the beam pointing direction ( f i , i i To form a beam, let the amplitude weighting coefficient of each subarray / element of the random array be... W ( f i , i i , u , m , n );

[0032] The antenna beam gain of a randomly distributed array can then be expressed as:

[0033] (2)

[0034] In the formula, ( f i , i i ) represents the pointing angle of the formed beam, which is an angle in spherical coordinates; U The number of sub-arrays; M and N These represent the number of rows and columns of array elements within each subarray; W ( f i , i i , u , m , n ) is in the direction of beamforming ( f i , ii ), sub-array u Element number in sub-array m and n The relevant weighting coefficients; α i ( u )and β i ( u ) are respectively with the first u The normal direction of each sub-array is ( f ( u ), i ( u )), beam pointing direction ( f i , i i The two associated angular parameters represent the direction in which the random array forms the beam ( ). f i , i i Transform to the first u Azimuth and elevation angles in each sub-array;

[0035] For array antenna pattern design implemented using beam synthesis methods, the influence of sidelobes on beam gain cannot be ignored; if the normalized amplitude of the main lobe of the beam is assumed to be... a 0, P The normalized amplitude of the larger sidelobe level is a p ( p =1,2,…, P Then the main lobe receiving and radiation efficiency of the array antenna can be expressed as: or p :

[0036] (3)

[0037] In the same sub-array cos[ α i ( u )] and cos[ β i ( u )] will not follow n and m If the equation changes, then equation (2) can be expressed as:

[0038] (4)

[0039] Furthermore, in step four, the constraints include:

[0040] 1) The beam gain of the random array beam synthesis is not less thanG 0;

[0041] 2) The maximum main lobe-to-side lobe ratio of random array beamforming is not less than a p0 .

[0042] Furthermore, in step five, the process of adjusting the number of sub-arrays is as follows:

[0043] When determining the number of subarrays participating in the synthesis, the constraint condition of the allowable range of beam gain variation is used as the verification and discrimination condition. The search interval of variables such as the number of subarrays participating in the beam synthesis is reduced by combining the bisection method to reduce the computational load of the algorithm.

[0044] Assume the beam gain is a fixed value. ,as follows:

[0045] (5)

[0046] in, It depends on the beam pointing angle. The number of participating beam synthesizer subarrays changes;

[0047] Solve equation (4) using the bisection method to make it possible in the direction The beam synthesis result on the beam has a beam gain of The process can be described as follows:

[0048] (1) Step 1 Half-interval verification calculation

[0049] Let the initial number of subarrays participating in beam synthesis be... To further narrow the range of values ​​for U, Divide into halves and calculate the midpoint of the number of subarrays. And order Perform beam synthesis or consult a table of beam synthesis results for the relevant array. Then, calculate the beam gain value based on the main lobe gain value obtained from the beam synthesis or table lookup results. ;

[0050] (2) Step 2: Half-interval verification calculation

[0051] like Then take ,make ;

[0052] like Then take ,make ;

[0053] Again Beam synthesis is performed, and then the main lobe gain value of the beam is obtained from the beam synthesis. Numerical values; iterating sequentially;

[0054] ( k ) No. k Step-by-step half-interval verification calculation

[0055] like Then take ,make ;

[0056] like Then take ,make ;

[0057] Again Beam synthesis is performed, and then the main lobe gain value of the beam is obtained from the beam synthesis. Until the condition is met: or number of iterations K The iterative calculation ends when the set value is exceeded.

[0058] Through the above iterative process based on the bisection method, the range of the maximum possible variation of the number of subarrays that satisfy the main lobe beam gain under different scanning angle conditions can be obtained, and the subarray search range can be effectively reduced without reducing the reliability of the subarray number distribution.

[0059] Because the subarray positions and normal directions of a randomly distributed array cause the subarray's operating state to be random, the beam synthesis results sometimes cannot fully meet the optimization objectives. Therefore, the beam synthesis results are optimized when the confidence level of the constraint conditions is not less than a pre-given confidence level. The problem of the beam with a specified gain changing with the beam pointing angle in this step is treated as a dynamic optimization allocation problem of subarray resources of a randomly distributed array and solved accordingly.

[0060] use This indicates the deviation between the beam gain after beam synthesis and the expected value:

[0061] (6)

[0062] An uncertainty constraint for beam synthesis optimization can be expressed as follows:

[0063] (7)

[0064] In the formula, The number of subarrays participating in beam synthesis;

[0065] Fuzzy variables are used to describe the number of units participating in pattern synthesis;

[0066] For a pre-given confidence level The credibility of the number of subarrays / elements participating in pattern synthesis satisfying the constraints is not less than [a certain value]. The probability is not less than β ;

[0067] Therefore, the fuzzy chance-constrained programming model for multi-faceted pattern synthesis is obtained as follows:

[0068] (8)

[0069] In the formula, It is a predetermined chance measure, representing the confidence and probability of satisfying the constraints; ch {} represents the chance measure;

[0070] To effectively utilize equation (7) to address the uncertainty in beam synthesis of randomly distributed array antennas, the number of sub-arrays or array elements participating in beam synthesis is... x As an interval random variable, its range of variation The beam pointing angle varies, determined based on prior simulation calculations; the interval The larger the value, the higher the reliability of satisfying the constraints;

[0071] exist Within the interval, x For a random variable that satisfies a certain probability distribution; thus, by determining the number of sub-arrays... x The range of values ​​and probability statistics of ξ describe the uncertainty of ξ, thereby reducing the computational complexity brought about by complex hybrid intelligent algorithms.

[0072] Furthermore, in step six, the output results include the following parameters:

[0073] 1) Number of subarrays participating in beamforming ;

[0074] 2) Beam main lobe gain ;

[0075] 3) Reliability of beam synthesis results α Sum of probabilities β .

[0076] Furthermore, in step seven, the constraints include: beam number. i Equal to the total number of beams covering the mission's airspace. I , i=I .

[0077] Furthermore, in step eight, the output results are as follows:

[0078] 1) Beam pointing of different beams within the mission airspace coverage area;

[0079] 2) Beam gain for each beam direction;

[0080] 3) The number and distribution of subarrays required for each beam;

[0081] 4) The credibility and probability of each beam.

[0082] The beneficial effects of this invention are:

[0083] This invention provides a method for suppressing the spatial variability of beamforming performance based on the "bisection method" and optimization of the number and spatial layout of randomly distributed array sub-arrays. This solves the problem of maintaining the beam shape and beam gain of randomly distributed arrays over a wide angular range. The conclusions of this invention have significant guiding significance for improving the beamforming performance of randomly distributed arrays and realizing multi-functional and multi-tasking capabilities. Attached Figure Description

[0084] Figure 1 is a flowchart of a method for suppressing the spatial variation of the overall performance of randomly distributed array beams.

[0085] Figure 2 is a schematic diagram of the spatial random distribution of array elements / subarrays on a typical aircraft body.

[0086] Figure 3 is a schematic diagram showing the change in beam gain of the array on the left side of the aircraft's nose as the beam direction changes.

[0087] Figure 4 is a schematic diagram showing the change in beam gain of the array on the left side of the aircraft fuselage as the beam direction changes.

[0088] Figure 5 is a simulation diagram of the beam synthesis results of the randomly distributed array. Detailed Implementation

[0089] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0090] A method for suppressing the spatial variation of the overall performance of randomly distributed array beams, such as Figure 1 As shown, the specific steps are as follows:

[0091] (1) Method for determining the spatial coverage of randomly distributed array beams

[0092] Typical aircraft and other platforms have complex geometries, with subarrays located on the left and right sides of the nose, cockpit, fuselage, and wings. Because the positions and normal directions of the randomly distributed subarrays are somewhat random, the resulting beam gain and beamwidth parameters have complex mapping relationships with the number and distribution of subarrays participating in beam synthesis. A typical example of a randomly distributed array on an aircraft's surface is shown below. Figure 2 As shown.

[0093] For each of the eight distributed arrays on the aircraft, simulation results (forming a data table) are first obtained using a beam synthesis algorithm under different numbers of subarrays and different beam pointing angles. Then, by looking up the table and interpolating, the subarray allocation results that satisfy the constraint conditions of main lobe beam gain (beamwidth) and sidelobe level under different scanning angles (beam pointing) are obtained. It is not necessary to completely satisfy the constraint conditions for every beam position within the beam scanning angle range; it is only necessary to ensure that the probability and reliability of satisfying the constraint conditions within the scanning angle range (a number of discrete beam positions) meet the requirements. The result of this approach is a significant reduction in the number of subarrays participating in beam synthesis.

[0094] The beam coverage area is different for each array face. The azimuth angle of the beam to be formed in the coordinate system of the randomly distributed array is transformed using coordinate transformation. Find this point Mapped to the subarray coordinate system of each antenna element in the subarray Coordinate rotation transformations can be divided into... The transformation is performed in three steps: first, from the random array polar coordinate system to the random array rectangular coordinate system; then, from the random array rectangular coordinate system to the subarray rectangular coordinate system; and finally, from the subarray rectangular coordinate system to the subarray polar coordinate system.

[0095] Let the half-power beamwidth of each element in each subarray be... If the first u Each sub-array must satisfy the following conditions:

[0096]

[0097] Then it is determined that the subarray can participate in beamforming.

[0098] make Statistical analysis through calculation algorithms Within different ranges of variation, the number of sub-arrays satisfying the conditions on a certain array surface is considered. When the number of sub-arrays satisfying the conditions exceeds the minimum number of sub-arrays required for beamforming (threshold value), it is determined that the beam formed by the corresponding array surface can cover that spatial angle. .

[0099] (2) The "dichotomy method" for determining the number and distribution of sub-arrays participating in beam synthesis.

[0100] To address the issue of beamwidth and beam gain of array antennas varying with beam direction obtained based on beam synthesis methods, the gain of the formed beam is kept constant by changing the number of array elements involved in beam synthesis, thereby achieving the goal of suppressing the "space variability" of array beamwidth and beam gain.

[0101] To ensure the performance of the array antenna, beam synthesis must first guarantee that the beam shape and beam gain remain essentially unchanged within the array beam scanning area, and that performance degradation is not significant. When determining the number of subarrays to participate in the synthesis, the constraint of the allowable range of beam gain variation can be used as a verification criterion. Combining this with the bisection method reduces the search interval for variables such as the number of subarrays participating in beam synthesis, thereby reducing the computational load of the algorithm.

[0102] By solving the following equations, while ensuring that the beam gain remains essentially constant, the solution can be obtained. U numerical value

[0103]

[0104] in, M and N On each subarray face x Xianghe y Number of array elements.

[0105] In the same sub-array , Neither follows n and m Therefore, the above equation can be transformed into:

[0106]

[0107] Assume the beam gain is a fixed value. ,make

[0108]

[0109] in, It depends on the beam pointing angle. The number of participating beam synthesizer subarrays changes.

[0110] The bisection method for linear optimization is based on finding the roots of the objective function: First, determine the range of values ​​for the objective function roots and then divide the range into two equal parts. By judging the value of the objective function, gradually narrow the range where the function roots are distributed until the range where the function roots are distributed is small enough to find an approximate root that meets the accuracy requirements.

[0111] Solving using the bisection method allows us to find the direction... The beam synthesis result on the beam has a beam gain of The process can be described as follows.

[0112] (1) Step 1 Half-interval verification calculation

[0113] Let the initial number of subarrays participating in beam synthesis be... To further narrow the range (range of variation) of U, Divide into halves and calculate the midpoint of the number of subarrays. And order Perform beam synthesis (or consult a table of beam synthesis results for the relevant array), and then calculate the beam gain value based on the main lobe gain value obtained from the beam synthesis (table lookup result). .

[0114] (2) Step 2: Half-interval verification calculation

[0115] like Then take ,make This step is actually a process of increasing the number of subarrays (making the value of the number of subarrays move towards the upper limit of the interval).

[0116] like Then take ,make This step is actually a process of reducing the number of subarrays (making the value of the number of subarrays move towards the lower limit of the interval);

[0117] Again Beam synthesis is performed, and then the main lobe gain value of the beam is obtained from the beam synthesis. Numerical values. Iterate through the values ​​sequentially.

[0118] (k) the k Step-by-step half-interval verification calculation

[0119] like Then take ,make ;

[0120] like Then take ,make ;

[0121] Again Beam synthesis is performed, and then the main lobe gain value of the beam is obtained from the beam synthesis. Until the condition is met: ,here e To allow for deviation, the iterative calculation can be terminated at this point. Alternatively, the number of iterations can be determined using the method described above. KWhen there are enough iterations, the iteration can be terminated.

[0122] Through the above iterative process based on the bisection method, the range of the maximum possible variation of the number of subarrays that satisfy the main lobe beam gain (beamwidth) under different scanning angles (beam pointing) can be obtained, and the subarray search range can be effectively reduced without reducing the reliability of the subarray number distribution.

[0123] The relationship between the number of subarrays required for beamforming and the beam pointing angle for the aircraft's left nose and fuselage left side arrays, implemented using the above-mentioned dichotomy method, is detailed below. Figure 3 and Figure 4 As shown.

[0124] (3) Methods to reduce the gain and spatial variability of beam shape in randomly distributed arrays

[0125] This module proposes a subarray resource allocation method to optimize beamforming performance. The problem of the number of array elements / subarrays required for the formed beam varying with the beam pointing angle is treated as a dynamic optimization allocation problem of array element / subarray resources for a randomly distributed array. Since the subarray positions, array surface normal directions, and occlusions of the distributed random array cause randomness in the subarray's operating state, the beamforming results sometimes cannot fully achieve the optimization objective. Therefore, optimization is performed only when the confidence level of the constraints is not less than a pre-defined confidence level.

[0126] Let the spatial positions of the randomly distributed array elements be... One constraint of pattern synthesis is that the expected value of the main lobe gain is... Using functions Indicates the direction of beam pointing The main lobe beam gain of the combined radiation pattern.

[0127] use This indicates the deviation between the beam gain after beam synthesis and the expected value:

[0128]

[0129] An uncertainty constraint for beam synthesis optimization can be expressed as follows:

[0130]

[0131] In the formula, The number of subarrays participating in beamforming is given. Due to the randomness of the number and location of elements selected for pattern combining in each iteration, it is impossible to obtain a random distribution function through extensive experimentation. Therefore, fuzzy variables are used to describe the number of elements participating in pattern combining. Due to the influence of fuzziness, it is assumed that the total number of participating elements satisfies certain constraints during beam combining. That's fine. Then, for the pre-defined confidence level... The credibility of the number of elements participating in the pattern synthesis satisfying the constraints is not less than [a certain value]. The probability is not less than β .

[0132] Therefore, the fuzzy chance-constrained programming model for multi-faceted array pattern synthesis can be obtained as follows:

[0133]

[0134] In the formula, ( α , β ) is a predetermined measure of chance. This indicates the confidence level and probability of satisfying the constraints. ch {} represents the chance measure; It calculates the main lobe beam gain; It is a pre-defined confidence level, and its value is selected according to the decision-making needs; and The first u The normal angles of each sub-array (horizontal azimuth and elevation angles in the array coordinate system); and These are the azimuth and elevation angles in spherical coordinates for beamforming of a randomly distributed array; and These represent the 3dB beamwidth of the array element pattern in the subarray. The last two constraints describe that the angle by which the normal to the subarray participating in beam synthesis deviates from the beam synthesis direction of the random array should be less than half the beamwidth.

[0135] To effectively utilize the aforementioned uncertainty constraints to address the uncertainty problem in beam synthesis of randomly distributed array antennas, it is proposed to increase the number of sub-arrays (or elements) participating in beam synthesis. x As an interval random variable, its range of variation As the beam pointing angle changes, it can be determined (or inferred) based on prior simulation calculations. And the interval... The larger the value, the higher the confidence level in satisfying the constraints. Within the interval, x For random variables that satisfy a certain probability distribution. Thus, by determining the number of subarrays (or array elements). xBy understanding the range of values ​​and probability statistics of ξ, the uncertainty (random fuzzy performance or fuzzy random performance) of ξ can be described more accurately, thus reducing the computational complexity brought about by complex hybrid intelligent algorithms. Figure 5 This is the beam synthesis result of a randomly distributed array.

[0136] The above description is merely a specific embodiment of the present invention, providing a detailed description of the invention. Parts not covered herein are conventional techniques. However, the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for suppressing the spatial variation of the synthesized characteristics of randomly distributed array beams, characterized in that: The steps are as follows: Step 1: Determine the mission airspace beam scanning range; Step 2: Establish the mapping relationship between the coordinate system of each subarray and the random array polar coordinate system. Based on the mission spatial beam scanning range and the mapping relationship, select the subarray that meets the beam spatial coverage range. Step 3: For each beam arranged within the beam scanning range, perform beam synthesis based on the selected subarray. Step 4: Determine whether the synthesized beams meet the constraints. If yes, proceed to Step 6; otherwise, proceed to Step 5. Step 5: Adjust the number and distribution of subarrays, re-perform beam synthesis, and return to Step 4; Step 6: Output the beam synthesis result corresponding to the current beam; Step 7: Determine if there are other beams in the beam scanning range. If yes, proceed to Step 3; otherwise, proceed to Step 8. Step 8: Statistically analyze the subarray resource allocation results for different beams in the task.

2. The method according to claim 1, characterized in that: In step one, the azimuth range of the mission airspace beam scanning range is [ φ min , φ max The pitch angle range is [ θ min , θ max ].

3. The method according to claim 2, characterized in that: In step two, the process is as follows: The array distribution of a typical aircraft is modeled, which includes eight sub-arrays, and the beam space coverage range corresponding to different arrays is fixed. Select subarrays or combinations of subarrays that overlap with the mission's airspace beam coverage requirements. The complete coverage of the beam space where the mission is located is provided by I The beams are scanned at different times to achieve this, and the first beam is scanned at different times to achieve this. i (1≤ i ≤ I The beam synthesis results of each beam are optimized. The mapping relationship is established as follows: First, let the random array in polar coordinates be... i Azimuth-Pitch Angle of Each Beam Mapped to a random array Cartesian coordinate system x i , y i , z i Then transform to the Cartesian coordinate system of the subarray. Finally, it is transformed to the polar coordinate system of the subarray. ; and Let be the azimuth-elevation angles of the beam in the polar coordinate system of the random array, and satisfy . φ imin ≤ φ i ≤ φ imax , θ imin ≤ θ i ≤ θ imax ; x i , y i , z i These are the coordinate values ​​in the Cartesian coordinate system of the random array; The respective u The coordinate values ​​of each sub-array in the Cartesian coordinate system; The respective u Azimuth-elevation angles of individual array surfaces in polar coordinates; set up and These represent the azimuth and elevation dimensions of the array element patterns in the subarray, respectively, and the 3dB beamwidth. If the... u Each sub-array must satisfy the following conditions: （1） Then it is determined that the subarray can participate in beamforming; make Through statistics Within different variation ranges, the number of sub-arrays satisfying condition (1) on a certain array surface is determined to be greater than the minimum number of sub-arrays required for beamforming when the number of sub-arrays satisfying the condition is greater than the minimum number of sub-arrays required for beamforming. In this case, it is determined that the beam formed by the corresponding array surface can cover the spatial angle. .

4. The method according to claim 3, characterized in that: In step three, the beamforming process is as follows: Suppose that a randomly distributed array has U planar subarrays with normals pointing in different directions. The position of each subarray is randomly variable, and the direction of the normals of the subarray surfaces changes with the curvature of the aircraft surface. Each of the U subarray surfaces is a regular surface array composed of N*M array elements. For a uniformly fed area array, assuming the radar transmits a narrowband signal, the array antenna elements are arranged according to... d = λ 0 / 2 interval layout, λ 0= c / f 0; If we consider the first u The normal direction of each sub-array is ( φ ( u ), θ ( u )),when U A random array composed of subarrays needs to be positioned in the beam pointing direction ( φ i , θ i To form a beam, let the amplitude weighting coefficient of each subarray / element of the random array be... W ( φ i , θ i , u , m , n ); The antenna beam gain of a randomly distributed array can then be expressed as: (2) In the formula, ( φ i , θ i ) represents the pointing angle of the formed beam, which is an angle in spherical coordinates; U The number of sub-arrays; M and N These represent the number of rows and columns of array elements within each subarray; W ( φ i , θ i , u , m , n ) is in the direction of beamforming ( φ i , θ i ), sub-array u Element number in sub-array m and n The relevant weighting coefficients; α i ( u )and β i ( u ) are respectively with the first u The normal direction of each sub-array is ( φ ( u )and θ ( u )), beam pointing direction ( φ i , θ i The two associated angular parameters represent the direction in which the random array forms the beam ( ). φ i , θ i Transform to the first u Azimuth and elevation angles in each sub-array; For array antenna pattern design implemented using beam synthesis methods, the influence of sidelobes on beam gain cannot be ignored; If we set the normalized amplitude of the main lobe of the beam as... a 0, P The normalized amplitude of the larger sidelobe level is a p ( p =1,2,…, P Then the main lobe receiving and radiation efficiency of the array antenna can be expressed as: η p : （3） In the same sub-array cos[ α i ( u )] and cos[ β i ( u )] will not follow n and m If the equation changes, then equation (2) can be expressed as: （4）。 5. The method according to claim 4, characterized in that: In step four, the constraints include: 1) The beam gain of the random array beam synthesis is not less than G 0; 2) The maximum main lobe-to-side lobe ratio of random array beamforming is not less than a p0 .

6. The method according to claim 5, characterized in that: In step five, the process of adjusting the number of sub-arrays is as follows: When determining the number of subarrays participating in the synthesis, the constraint condition of the allowable range of beam gain variation is used as the verification and discrimination condition. The search interval of variables such as the number of subarrays participating in the beam synthesis is reduced by combining the bisection method to reduce the computational load of the algorithm. Assume the beam gain is a fixed value. ,as follows: （5） in, It depends on the beam pointing angle. The number of participating beam synthesizer subarrays changes; Solve equation (4) using the bisection method to make the direction The beam synthesis result on the beam has a beam gain of The process can be described as follows: (1) Step 1 Half-interval verification calculation Let the initial number of subarrays participating in beam synthesis be... To further narrow the range of values ​​for U, Divide into halves and calculate the midpoint of the number of subarrays. And order Perform beam synthesis or consult a table of beam synthesis results for the relevant array. Then, calculate the beam gain value based on the main lobe gain value obtained from the beam synthesis or table lookup results. ; (2) Step 2: Half-interval verification calculation like Then take ,make ; like Then take ,make ; Again Beam synthesis is performed, and then the main lobe gain value of the beam is obtained from the beam synthesis. Numerical values; iterating sequentially; ( k ) No. k Step-by-step half-interval verification calculation like Then take ,make ; like Then take ,make ; Again Beam synthesis is performed, and then the main lobe gain value of the beam is obtained from the beam synthesis. Until the condition is met: or number of iterations K The iterative calculation ends when the set value is exceeded. Through the above iterative process based on the bisection method, the range of the maximum possible variation of the number of subarrays that satisfy the main lobe beam gain under different scanning angle conditions can be obtained, and the subarray search range can be effectively reduced without reducing the reliability of the subarray number distribution. Because the subarray positions and normal directions of a randomly distributed array cause the subarray's operating state to be random, the beam synthesis results sometimes cannot fully meet the optimization objectives. Therefore, the beam synthesis results are optimized when the confidence level of the constraint conditions is not less than a pre-given confidence level. The problem of the beam with a specified gain changing with the beam pointing angle in this step is treated as a dynamic optimization allocation problem of subarray resources of a randomly distributed array and solved accordingly. use This indicates the deviation between the beam gain after beam synthesis and the expected value: （6） An uncertainty constraint for beam synthesis optimization can be expressed as follows: （7） In the formula, The number of subarrays participating in beam synthesis; Fuzzy variables are used to describe the number of units participating in pattern synthesis; For a pre-given confidence level The credibility of the number of subarrays / elements participating in pattern synthesis satisfying the constraints is not less than [a certain value]. The probability is not less than β ; Therefore, the fuzzy chance-constrained programming model for multi-faceted pattern synthesis is obtained as follows: （8） In the formula, It is a predetermined chance measure, representing the confidence and probability of satisfying the constraints; ch {} represents the chance measure; To effectively utilize equation (7) to address the uncertainty in beam synthesis of randomly distributed array antennas, the number of sub-arrays or array elements participating in beam synthesis is... ξ As an interval random variable, its range of variation The beam pointing angle varies, determined based on prior simulation calculations; the interval The larger the value, the higher the confidence level of satisfying the constraints; exist Within the interval, ξ For a random variable that satisfies a certain probability distribution; thus, by determining the number of sub-arrays... ξ The range of values ​​and probability statistics of ξ describe the uncertainty of ξ, thereby reducing the computational complexity brought about by complex hybrid intelligent algorithms.

7. The method according to claim 6, characterized in that: In step six, the output results include the following parameters: 1) Number of subarrays participating in beamforming ; 2) Beam main lobe gain ; 3) Reliability of beam synthesis results α Sum of probabilities β .

8. The method according to claim 7, characterized in that: In step seven, the constraints include: beam number. i Equal to the total number of beams covering the mission's airspace. I , i=I .

9. The method according to claim 8, characterized in that: In step eight, the output is as follows: 1) Beam pointing of different beams within the mission airspace coverage area; 2) Beam gain for each beam direction; 3) The number and distribution of subarrays required for each beam; 4) The credibility and probability of each beam.

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