An antenna cover - phased array system integration pattern synthesis method

Abstract

The application provides an antenna cover- phased array system integrated pattern synthesis method, which only changes the amplitude and phase value of the phased array unit feed to realize integrated synthesis of the pattern of the antenna cover- phased array system. Strictly taking into account the antenna cover effect makes the result more accurate, while reducing the measurement workload; when optimizing, the absolute gain of the antenna cover- phased array system is constrained to ensure that the actual radiation efficiency of the antenna cover- phased array system under the optimal overall excitation obtained after optimization is as high as possible; the traditional global optimization algorithm is improved, so that the iteration converges faster and the algorithm is more versatile; the mutual coupling effect of the cover phased array is considered, and the application has the advantages of high accuracy, high actual radiation efficiency, fast optimization speed and less required test data.

Description

Technical Field

[0001] This invention belongs to the field of radar antenna technology, and particularly relates to an integrated pattern synthesis method for an antenna radome-phased array system. Background Technology

[0002] Missiles, as indispensable weapons in modern high-tech local wars, are of paramount importance in terms of their precision strike capabilities. Radar systems, as a key factor influencing guidance capabilities, perform tasks such as detection and location by emitting electromagnetic waves into space and utilizing the electromagnetic waves scattered by the target. Among these, the antenna, as a crucial component of the radar system, bears the important task of transmitting and receiving electromagnetic waves. Faced with today's increasingly complex electromagnetic environment, radar antennas in guidance systems must meet even higher performance requirements. Due to their high gain, narrow beamwidth, and the ability to electrically scan the beam, phased array antennas have become a hot topic in the current front-end design of radar systems.

[0003] Radomes, acting as barriers to protect antenna arrays from environmental influences, are widely used in various missile-borne radars and wireless communication systems. The introduction of radomes improves the stability and reliability of antenna operation, extends the lifespan of the antenna system, and also improves the aerodynamic shape of missile-borne phased array antennas. However, on the other hand, the introduction of the radome structure interferes with and affects the electromagnetic characteristics of the phased array antenna, leading to a decrease in its performance. The reflection, absorption, and scattering of electromagnetic waves by the radome shell cause the maximum gain of the radome-phased array system to be lower than that of the phased array antenna without a radome under normal circumstances. The radome's blocking of electromagnetic waves and its phase insertion can not only raise the sidelobe level of the phased array antenna but also cause beam broadening and an increase in the zero-depth level of the differential beam. Furthermore, when the radome and phased array antenna are tightly coupled, the coupling between antenna elements and between elements and the radome is very significant, resulting in severe distortion of the antenna pattern and causing the entire phased array to operate in a mismatched state. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing an integrated pattern synthesis method for an antenna radome-phased array system.

[0005] This invention provides an integrated pattern synthesis method for an antenna radome-phased array system, comprising:

[0006] The first target antenna element of the phased array is excited with a unit voltage, and the remaining antenna elements are all short-circuited to obtain the short-circuit current at the port of each antenna element and the active element radiation pattern of the first target antenna element.

[0007] The mutual admittance of the first target antenna element port to the second target antenna element port is determined based on the unit voltage excitation of the first target antenna element and the short-circuit current of the second target antenna element port.

[0008] Construct the admittance matrix of all antenna elements based on the mutual admittance of the first target antenna element port to the second target antenna element port;

[0009] Multiple complex voltage values ​​are obtained as unit excitations for each unit, and the unit excitations of all excitation units are used as the current overall excitation.

[0010] Under the current overall excitation, the active input admittance of the first target antenna element port is determined based on the mutual admittance of the second target antenna element port to the first target antenna element port;

[0011] The input power of the first target antenna element port is determined based on the active input admittance of the first target antenna element port and the element excitation of the first target antenna element port.

[0012] Traverse all antenna element ports and determine the total input power of all antenna element ports based on the input power of the first target antenna element port;

[0013] Under the current overall excitation, the total radiated electric field of the radome-phased array system is determined based on the active element radiation pattern of the first target antenna element;

[0014] The final gain of the radome-phased array system is determined based on the total radiated electric field of the radome-phased array system.

[0015] The fitness function value is determined based on the final gain corresponding to the current overall stimulus. An improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function value is minimized, thus obtaining the optimal overall stimulus.

[0016] Further, the step of constructing the admittance matrix of all antenna elements based on the mutual admittance of the first target antenna element port to the second target antenna element port includes:

[0017] Construct the expression for the admittance matrix [Y] of all antenna elements:

[0018]

[0019] Among them, Y mn Let n be the mutual admittance of the nth antenna element port to the mth antenna element port, where n = 1, 2, ..., N; m = 1, 2, ..., N; and N is the total number of antenna elements in the radome-phased array system.

[0020] Further, determining the active input admittance of the first target antenna element port based on the mutual admittance of the second target antenna element port to the first target antenna element port under the current overall excitation includes:

[0021] The active input admittance of the first target antenna element port is calculated using the following formula:

[0022]

[0023] Among them, Y1 n Y is the active input admittance of the nth antenna element port; N is the total number of antenna elements in the radome-phased array system; nm Let w be the mutual admittance between the port of the m-th antenna element and the port of the n-th antenna element; m The element excitation for the m-th antenna element; w n This is the element excitation for the nth antenna element.

[0024] Further, determining the input power of the first target antenna element port based on the active input admittance of the first target antenna element port and the element excitation of the first target antenna element port includes:

[0025] The input power at the port of the first target antenna element is calculated using the following formula:

[0026]

[0027] Where Pn is the input power at the port of the nth antenna element; Re represents the real part of the complex number; Y1 n w is the active input admittance of the nth antenna element port; n This is the element excitation for the nth antenna element; |·| represents the magnitude.

[0028] Further, the step of traversing all antenna element ports and determining the total input power of all antenna element ports based on the input power of the first target antenna element port includes:

[0029] Calculate the total input power of all antenna element ports using the following formula:

[0030]

[0031] Where P is the total input power of all antenna element ports; N is the total number of antenna elements in the radome-phased array system; Re represents taking the real part of the complex number; Y1 n w is the active input admittance of the nth antenna element port; n This is the element excitation for the nth antenna element; |·| represents the magnitude.

[0032] Furthermore, determining the total radiated electric field of the radome-phased array system based on the active element radiation pattern of the first target antenna element under the current overall excitation includes:

[0033] The total radiated electric field of the radome-phased array system can be calculated using the following formula.

[0034]

[0035] Where W = [w1, w2, ..., w n ,…,w N ] represents the current overall excitation; N represents the total number of antenna elements in the radome-phased array system; w n This is the element excitation for the nth antenna element; This is the radiation pattern of the active element of the nth antenna element; in spherical coordinates, elevation angle θ and azimuth angle are used. It indicates the direction of propagation of radiated electromagnetic waves.

[0036] Furthermore, determining the final gain of the radome-phased array system based on the total radiated electric field of the radome-phased array system includes:

[0037] Calculate the final gain of the radome-phased array system using the following formula.

[0038]

[0039] in, The total radiated electric field of the radome-phased array system; in spherical coordinates, the elevation angle θ and azimuth angle are used. Indicates the direction of propagation of radiated electromagnetic waves; W = [w1, w2, ..., w n ,…,w N ] represents the current overall excitation; η represents the wave impedance in vacuum; r represents the distance from the midpoint to the origin in the spherical coordinate system; and P represents the total input power of all antenna element ports.

[0040] Further, the step of determining the fitness function value based on the final gain corresponding to the current overall stimulus, and optimizing the current overall stimulus using an improved simulated annealing algorithm until the fitness function value is minimized to obtain the optimal overall stimulus, includes:

[0041] The indicators for the integrated radiation pattern and the maximum gain of the radome-phased array system under the current overall excitation with equal amplitude and in phase are obtained. The indicators include the maximum radiation direction of the radiation pattern, the sidelobes of the radiation pattern, the maximum gain of the radiation pattern, the null depth of the difference radiation pattern, the null position of the difference radiation pattern, and the sidelobes of the difference radiation pattern.

[0042] The range of expected absolute gain values ​​for the radome-phased array system after optimization is determined based on the maximum gain of the radome-phased array system under the current overall excitation with equal amplitude and phase, and the maximum gain of the radiation pattern.

[0043] The expected absolute gain range, expected sum and difference pattern shape, sum and difference sidelobes, and difference pattern zero depth determine the sum and difference pattern and the set of acceptable patterns for the difference pattern.

[0044] The final gain of the radome-phased array system is obtained from the set of acceptable radiation patterns based on the sum and difference patterns and the current overall excitation W. The absolute difference between the values ​​determines the expression for the fitness function (W) to be optimized:

[0045]

[0046] in, The absolute difference between the gain pattern of the radome-phased array system and the two templates under the current overall excitation W:

[0047]

[0048] in, This represents the lower boundary of the acceptable set of radiation patterns. The upper boundary of the acceptable pattern set; using pitch angle θ and azimuth angle in spherical coordinates. Indicates the direction of propagation of radiated electromagnetic waves;

[0049] An improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function Fitness(W) reaches its minimum value, thus obtaining the optimal overall stimulus.

[0050] Furthermore, the improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function (W) reaches its minimum value, thus obtaining the optimal overall stimulus, including:

[0051] Before the iteration cycle begins, determine the initial temperature T, the temperature decrease coefficient β, the maximum number of iterations M1 in the inner loop, and the maximum number of iterations M2 in the outer loop; initialize the current global stimulus W, and assign the randomly generated current global stimulus W to the local optimal solution W. local With the global optimal solution W best The corresponding fitness function Fitness(W) is assigned to the local minimum fitness function Fitness_local and the global minimum fitness function Fitness_best.

[0052] In the inner loop case, W' is generated within the neighborhood of the current global stimulus W, and the fitness function Fitness(W') corresponding to W' is calculated. The value of W' is determined by the following formula:

[0053]

[0054] Where ΔW is the change in the overall excitation; j is the imaginary unit; rand r1 rand r2 …rand rN with rand i1 rand i2 …rand iN These are two relatively independent sets of random numbers belonging to the range [0,1]; rand rN rand is the random variation of the real part of the excitation of the Nth unit. iN R is the random variation of the imaginary part of the excitation of the Nth unit; step The iteration step size is given, and the normalized modulus of W' ranges from (0,1].

[0055] Set the difference in adaptive function values ​​as ΔF = Fitness(W') - Fitness(W), and use the Metropolis criterion to determine whether to update the current overall stimulus to W':

[0056] 1) If ΔF≤0, then update the current global excitation to W', let W=W', and update the local optimum W. local =W';

[0057] 2) If ΔF > 0, and the following acceptance probabilities are met, then W and W local All updated to W':

[0058]

[0059] Where, k B K is the Boltzmann constant. B =1.380649×10 -23 δ is a random number with a value in the range [0,1), and exp represents an exponential operation with the natural constant e as the base.

[0060] 3) If none of the above conditions are met, then maintain the current global excitation W and the current local optimum W. local constant;

[0061] The inner loop terminates when the number of iterations reaches the maximum number of iterations M1 or when the change in the fitness function value within L consecutive steps is less than a preset threshold.

[0062] max(Fitness(W),…,Fitness(WL ))-min(Fitness(W),…,Fitness(W) L ))<ε;

[0063] Among them, W L ε is the updated solution after the inner loop reaches step L, determined by the Metropolis criterion; ε is the maximum acceptable change in the fitness function value.

[0064] In the case of external circulation, if the internal circulation termination condition is met, the internal circulation terminates, and the system enters the external circulation; the local optimal solution W at the current temperature T is compared. local and the global optimal solution W best The magnitude of the adaptive function value:

[0065] 1) If Fitness(W) local )≤Fitness(W best ), then W best Updated to W local ;

[0066] 2) If Fitness(W) local > Fitness (W) best If W is maintained, then W will remain unchanged. best constant;

[0067] If we start from the m2th outer loop iteration and iterate through M consecutive outer loop iterations, then Fitness(W) best When the value of ) does not change significantly, change the iteration step size R. step , making R step Gradually reduce to the target value:

[0068] Value(m2) = abs(Fitness(W) local )-Fitness(W best )) / abs(Fitness(W best ));

[0069] max(Value(m2),…,Value(m2+20))<0.2;

[0070] R step1 =R step -0.02, R step ≥0.1;

[0071] When the outer loop reaches the maximum number of iterations M2 or the Fitness(W) condition is met... best If the value of ) is less than the preset convergence value, the outer loop terminates; if the termination conditions for all outer loops are not met, the current temperature T is decreased to βT, and W is initialized to W. bestThen return to the beginning of the inner loop and repeat the iterative calculation until all loop termination conditions are met; if all outer loop termination conditions are met, then output the obtained overall optimal excitation solution W. best .

[0072] This invention provides an integrated radiation pattern synthesis method for a radome-phased array system. It achieves integrated radiation pattern synthesis of the radome-phased array system by only changing the amplitude and phase values ​​of the phased array element feeds. Strictly considering the radome effect improves accuracy and reduces measurement workload. During optimization, the absolute gain of the radome-phased array system is constrained to ensure that the actual radiation efficiency of the radome-phased array system under the optimal overall excitation is as high as possible after optimization. The traditional global optimization algorithm is improved, resulting in faster iterative convergence and greater algorithm versatility. This invention considers the mutual coupling effect of the radome-phased array, offering advantages such as high accuracy, high actual radiation efficiency, fast optimization speed, and less required test data. Attached Figure Description

[0073] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 A flowchart of an integrated pattern synthesis method for an antenna radome-phased array system provided in an embodiment of the present invention;

[0075] Figure 2 This is a schematic diagram of the radome-phased array system structure provided in an embodiment of the present invention;

[0076] Figure 3 This is a schematic diagram of the radiation pattern (E plane) provided in an embodiment of the present invention;

[0077] Figure 4 for Figure 3 The corresponding normalized amplitude distribution of the optimal overall excitation;

[0078] Figure 5 for Figure 3 The corresponding normalized phase distribution diagram of the optimal global excitation;

[0079] Figure 6 This is a schematic diagram of the differential orientation pattern (E plane) provided in an embodiment of the present invention;

[0080] Figure 7 for Figure 6 The corresponding normalized amplitude distribution of the optimal overall excitation;

[0081] Figure 8 for Figure 6 The corresponding normalized phase distribution diagram of the optimal overall excitation. Detailed Implementation

[0082] 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 skilled in the art without creative effort are within the scope of protection of the present invention.

[0083] like Figure 1 As shown, this embodiment of the invention provides an integrated pattern synthesis method for an radome-phased array system, comprising:

[0084] Step 101: Excite the first target antenna element of the phased array with a unit voltage, and short-circuit all the remaining antenna elements to obtain the short-circuit current at the port of each antenna element and the active element radiation pattern of the first target antenna element.

[0085] The radome-phased array system comprises N antenna elements, and the entire array can be viewed as an N-port network; in this embodiment, N = 100. The nth antenna element is excited by a unit voltage (i.e., the element excitation w of the nth antenna element). n =1), at which point the remaining antenna elements are short-circuited. Subsequently, a fast and efficient hybrid method combining the volume-surface integral equation (VSIE) and the modified surface integration (MSI) method is used to obtain the short-circuit current I at the port of each antenna element (i.e., the center feed point of the half-wavelength dipole). m And the short-circuit active radiation pattern of the nth antenna element (active element radiation pattern) Both VSIE and MSI are accelerated using the Multi-Level Fast Multipole Algorithm (MLFMA).

[0086] Step 102: Determine the mutual admittance of the first target antenna unit port to the second target antenna unit port based on the unit voltage excitation of the first target antenna unit and the short-circuit current of the second target antenna unit port.

[0087] Based on the element excitation w of the current nth antenna element n Solve for the mutual admittance Y between port n and port m. mn :

[0088]

[0089] That is, the value of the mutual admittance is numerically the short-circuit current value at the antenna element port (i.e., the center feed point of the half-wavelength dipole).

[0090] Step 103: Construct the admittance matrix of all antenna elements based on the mutual admittance of the first target antenna element port to the second target antenna element port.

[0091] Construct the expression for the admittance matrix [Y] of all antenna elements (i.e., the entire radome-phased array system with 100 ports):

[0092]

[0093] Among them, Y mn Let n be the mutual admittance of the nth antenna element port to the mth antenna element port, where n = 1, 2, ..., N; m = 1, 2, ..., N; and N is the total number of antenna elements in the radome-phased array system.

[0094] Step 104: Obtain multiple complex voltages as unit excitations for each unit, and use the unit excitations of all excitation units as the current overall excitation.

[0095] One hundred complex voltage values ​​are randomly selected as element excitations for 100 elements, with the magnitude of each element excitation not exceeding 1, i.e., |w|. n |≤1. 100 complex voltages constitute the current overall excitation W, W=[w1,w2,…,w… n ,…,w 100 ].

[0096] Step 105: Under the current overall excitation, determine the active input admittance of the first target antenna element port based on the mutual admittance of the second target antenna element port to the first target antenna element port.

[0097] For example, the active input admittance of the first target antenna element port is calculated according to the following formula:

[0098]

[0099] Among them, Y1 n Y is the active input admittance of the nth antenna element port; N is the total number of antenna elements in the radome-phased array system; nm Let w be the mutual admittance between the port of the m-th antenna element and the port of the n-th antenna element; m The element excitation for the m-th antenna element; w n This is the element excitation for the nth antenna element.

[0100] Step 106: Determine the input power of the first target antenna element port based on the active input admittance of the first target antenna element port and the element excitation of the first target antenna element port.

[0101] For example, the input power of the first target antenna element port is calculated according to the following formula:

[0102]

[0103] Where Pn is the input power at the port of the nth antenna element; Re represents the real part of the complex number; Y1 n w is the active input admittance of the nth antenna element port; n This is the element excitation for the nth antenna element; |·| represents the magnitude.

[0104] Step 107: Traverse all antenna element ports and determine the total input power of all antenna element ports based on the input power of the first target antenna element port.

[0105] For example, the total input power of all antenna element ports is calculated according to the following formula:

[0106]

[0107] Where P is the total input power of all antenna element ports.

[0108] Step 108: Under the current overall excitation, determine the total radiated electric field of the radome-phased array system based on the active element radiation pattern of the first target antenna element.

[0109] For example, the total radiated electric field of the radome-phased array system is calculated according to the following formula.

[0110]

[0111] in, This is the radiation pattern of the active element of the nth antenna element; in spherical coordinates, elevation angle θ and azimuth angle are used. Indicates the direction of propagation of radiated electromagnetic waves; the elevation angle θ ranges from 0 to 180 degrees; the azimuth angle... The range is 0-360 degrees.

[0112] Step 109: Determine the final gain of the radome-phased array system based on the total radiated electric field of the radome-phased array system.

[0113] For example, the final gain of the radome-phased array system is calculated according to the following formula.

[0114]

[0115] Where η is the wave impedance in vacuum, which is taken as 120π in this embodiment; r represents the distance parameter in spherical coordinates, that is, the distance from the field point to the origin. In this embodiment, the far field is calculated, so r should be as large as possible.

[0116] Step 1010: Determine the fitness function value based on the final gain corresponding to the current overall stimulus, and optimize the current overall stimulus using an improved simulated annealing algorithm until the fitness function value is minimized, thus obtaining the optimal overall stimulus.

[0117] For example, this step includes obtaining the indices of the integrated radiation pattern and the maximum gain of the radome-phased array system under the current integrated excitation with equal amplitude and phase. The indices include the maximum radiation direction of the radiation pattern, the sidelobes of the radiation pattern, the maximum gain of the radiation pattern, the null depth of the difference radiation pattern, the null position of the difference radiation pattern, and the sidelobes of the difference radiation pattern.

[0118] Based on the current overall excitation of equal amplitude and in phase (i.e., the element excitation w of each antenna element) n =1) The maximum gain of the radome-phased array system and the maximum gain of the radiation pattern G max Determine the range of expected absolute gain values ​​for the radome-phased array system after optimization.

[0119] The absolute gain of the radome-phased array system is constrained to ensure that the actual radiation efficiency of the optimized array is as high as possible. This constraint is manifested as follows: the maximum value of the lower boundary of the acceptable radiation pattern set is the maximum actual gain G calculated when the radome-phased array system is excited by a uniformly excited, in-phase system. max and the acceptable maximum gain drop G in the design specifications. drop To determine, specifically G max -G drop -cos(α); G max and G drop All units are dB. α is the target scanning angle, in degrees. The expected absolute gain range is set to [G]. max -G drop G max ].

[0120] The acceptable set of patterns for the sum and difference patterns is determined based on the expected absolute gain range, the expected sum and difference pattern shapes, the sum pattern sidelobes, and the difference pattern zero depth.

[0121] The final gain of the radome-phased array system is obtained from the set of acceptable radiation patterns based on the sum and difference patterns and the current overall excitation W. The absolute difference between the values ​​determines the expression for the fitness function (W) to be optimized:

[0122]

[0123] in, The absolute difference between the gain pattern of the radome-phased array system and the two templates under the current overall excitation W:

[0124]

[0125] in, This represents the lower boundary of the acceptable set of radiation patterns. This represents the upper boundary of the acceptable set of directional patterns.

[0126] An improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function Fitness(W) reaches its minimum value, thus obtaining the optimal overall stimulus.

[0127] The traditional Simulated Annealing (SA) algorithm first multiplies the overall excitation by the dot product of all short-circuited active radiation patterns in the antenna array to obtain the array's realizable radiation pattern, and then determines the upper and lower boundaries of the acceptable radiation pattern set based on its range. This process is quite complex and lacks flexibility when there are many scan angles, so an improvement is proposed. Since the optimization objective of the integrated radiation pattern synthesis of the radome-phased array system is to minimize the sidelobe level of the sum pattern and increase the null depth of the difference pattern while ensuring the absolute gain is as large as possible, the maximum values ​​of the upper and lower boundaries of the acceptable radiation pattern set are determined by the expected absolute gain range of the radome-phased array system, assuming that the shape of the acceptable radiation pattern set of the sum pattern is determined to be a rectangular pulse function and the shape of the acceptable radiation pattern set of the difference pattern is determined to be two adjacent rectangular pulses. The height of the rectangular pulse is determined by the radiation pattern sidelobe index, and the maximum radiation direction index and the difference pattern null position index correspond to the top center point of a single rectangular pulse and the midpoint of the connecting line segment between adjacent rectangular pulses, respectively.

[0128] The Improved Simulated Annealing (ISA) algorithm simplifies the process of determining the upper and lower boundaries of the acceptable pattern set compared to the traditional ISA algorithm. Since the optimization objective of overall array pattern synthesis is to minimize the sidelobe level of the sum pattern and increase the zero depth of the difference pattern while maximizing the absolute gain, the maximum values ​​of the upper and lower boundaries of the acceptable pattern set are determined by the expected absolute gain range of the system, provided that the shape of the acceptable sum pattern set is determined to be a rectangular pulse function and the acceptable difference pattern set is determined to be two adjacent rectangular pulses.

[0129] Both the ISA and SA algorithms have a logical structure of two-layer iterative loops. The main improvement of ISA is the introduction of an adaptive iteration step size. The iteration step size, which is a fixed value in the SA algorithm, is adaptively improved to ensure that when the value of Fitness(W) does not change significantly after M consecutive iterations, the iteration step size automatically decreases, avoiding "leaps" to the optimal solution and accelerating the iteration convergence speed. The process of obtaining the optimal overall stimulus is as follows:

[0130] Before the iteration cycle begins, determine the initial temperature T, the temperature decrease coefficient β, the maximum number of iterations M1 in the inner loop, and the maximum number of iterations M2 in the outer loop; initialize the current global stimulus W, and assign the randomly generated current global stimulus W to the local optimal solution W. local With the global optimal solution W best The corresponding fitness function Fitness(W) is then assigned to the local minimum fitness function Fitness_local and the global minimum fitness function Fitness_best.

[0131] In the inner loop case, a new global stimulus W' is generated in the neighborhood of the current global stimulus W, and the fitness function Fitness(W') corresponding to W' is calculated. The value of W' is determined by the following formula:

[0132]

[0133] Where ΔW is the change in the overall excitation; j is the imaginary unit; rand r1 rand r2 …rand rN with rand i1 rand i2 …rand iN These are two sets of relatively independent random numbers belonging to the range [0,1]. This indicates that the amplitude and phase changes of the unit excitation are independent of each other, and the changes in unit excitation between units are also independent of each other; rand rN rand is the random variation of the real part of the excitation of the Nth unit. iN R is the random variation of the imaginary part of the excitation of the Nth unit; step The iteration step size is [0.3, 0.6] in this embodiment; the normalized modulus of W' ranges from (0, 1).

[0134] Set the difference in adaptive function values ​​as ΔF = Fitness(W') - Fitness(W), and use the Metropolis criterion to determine whether to update the current overall stimulus to W':

[0135] 1) If ΔF≤0, then update the current global excitation to W', let W=W', and update the local optimum W.local =W'.

[0136] 2) If ΔF > 0, and the following acceptance probabilities are met, then W and W local All updated to W':

[0137]

[0138] Where, k B K is the Boltzmann constant. B =1.380649×10 -23 δ is a random number with a value in the range [0,1), and exp represents the exponential operation with the natural constant e as the base.

[0139] 3) If none of the above conditions are met, then maintain the current global excitation W and the current local optimum W. local constant.

[0140] The inner loop terminates when the number of iterations reaches the maximum number of iterations M1 or when the change in the fitness function value within L consecutive steps is less than a preset threshold.

[0141] max(Fitness(W),…,Fitness(W L ))-min(Fitness(W),…,Fitness(W) L ))<ε.

[0142] Among them, W L ε is the updated solution after the inner loop reaches step L, determined by the Metropolis criterion; ε is the maximum acceptable change in the fitness function value.

[0143] In the case of external circulation, if the internal circulation termination condition is met, the internal circulation terminates, and the system enters the external circulation; the local optimal solution W at the current temperature T is compared. local and the global optimal solution W best The magnitude of the adaptive function value:

[0144] 1) If Fitness(W) local )≤Fitness(W best ), then W best Updated to W local .

[0145] 2) If Fitness(W) local > Fitness (W) best If W is maintained, then W will remain unchanged. best constant.

[0146] If we start from the m2th outer loop iteration and iterate through M consecutive outer loop iterations, then Fitness(W)best When the value of ) does not change significantly, change the iteration step size R. step , making R step Gradually reduce to the target value:

[0147] Value(m2) = abs(Fitness(W) local )-Fitness(W best )) / abs(Fitness(W best )).

[0148] max(Value(m2),…,Value(m2+20))<0.2.

[0149] R step1 =R step -0.02, R step ≥0.1.

[0150] When the outer loop reaches the maximum number of iterations M2 or the Fitness(W) condition is met... best If the value of ) is less than the preset convergence value, the outer loop terminates; if the termination conditions for all outer loops are not met, the current temperature T is decreased to βT, and W is initialized to W. best Then return to the beginning of the inner loop and repeat the iterative calculation until all loop termination conditions are met; if all outer loop termination conditions are met, then output the obtained overall optimal excitation solution W. best .

[0151] like Figure 2 As shown, the proposed phased array antenna model is a 10×10 half-wave dipole array with X-polarization and an element spacing of 12.5 mm along both the X and Y directions. This phased array antenna is located 0.25λ0 (6.25 mm, where λ0 is the free-space wavelength) above a circular PEC ground plane with a diameter of 200 mm, and operates at a frequency of 12 GHz. The proposed single-layer parabolic radome has a diameter and height of 225.06 mm and 222.81 mm, respectively, with a wall thickness varying from 5.01 mm at the top to 2.53 mm at the bottom. The relative permittivity of the radome is 3.5, and the loss tangent is 0.015. (c) is a three-dimensional view of the radome-phased array system, (a) is a bottom view of (c), and (b) is a side sectional view of (c).

[0152] like Figure 3 , Figure 4 and Figure 5 The figures shown are the gain pattern (E-plane) of the radome-phased array system and the normalized amplitude and phase distribution of the corresponding optimal overall excitation, respectively. Figure 3The acceptable radiation pattern set is and the radiation pattern. The maximum value of the upper boundary of the set is determined by the actual absolute gain of the radome-phased array system, and the shape is determined to be similar to a rectangular pulse function.

[0153] Figure 3 In the acceptable pattern set, the maximum value of the lower boundary is the maximum value of the actual gain G on the E-plane calculated when the system is excited by a global system with equal amplitude and in-phase excitation. max The requirement for G to decrease gain drop (G here) drop =1dB) to determine, specifically G max -G drop -cos(α), in dB. Where α is the target scanning angle (here α=5), in degrees.

[0154] like Figure 6 , Figure 7 and Figure 8 The figures shown are the gain pattern (E-plane) of the radome-phased array system and the normalized amplitude and phase distribution of the corresponding optimal overall excitation, respectively. Figure 4 The acceptable pattern set is the difference pattern, and the maximum value of the upper boundary of the set is determined by the actual absolute gain of the system. The shape is determined as two adjacent rectangular pulse functions.

[0155] Figure 6 In the above, the maximum value of the upper boundary of the set is the actual maximum gain G on the E-plane calculated when the system is subjected to equal-amplitude and in-phase global excitation. max The requirement for G to decrease gain drop (G here) drop =0.5dB) to determine, specifically G max -G drop -cos(α)-3, in dB. Where α is the target scanning angle (here α=5), in degrees.

[0156] like Figure 3 and Figure 6 As shown, the integrated radiation pattern synthesis method for radome-phased array system proposed in this invention considers the mutual influence of the organic whole, constrains the absolute gain of the radome-phased array system, and can ultimately optimize the expected radiation pattern of the radome-phased array system.

[0157] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

Claims

1. A method for integrating the radiation pattern of a radome-phased array system, characterized in that, include: The first target antenna element of the phased array is excited with a unit voltage, and the remaining antenna elements are all short-circuited to obtain the short-circuit current at the port of each antenna element and the active element radiation pattern of the first target antenna element. The mutual admittance of the first target antenna element port to the second target antenna element port is determined based on the unit voltage excitation of the first target antenna element and the short-circuit current of the second target antenna element port. Construct the admittance matrix of all antenna elements based on the mutual admittance of the first target antenna element port to the second target antenna element port; Multiple complex voltage values ​​are obtained as unit excitations for each unit, and the unit excitations of all excitation units are used as the current overall excitation. Under the current overall excitation, the active input admittance of the first target antenna element port is determined based on the mutual admittance of the second target antenna element port to the first target antenna element port; The input power of the first target antenna element port is determined based on the active input admittance of the first target antenna element port and the element excitation of the first target antenna element port. Traverse all antenna element ports and determine the total input power of all antenna element ports based on the input power of the first target antenna element port; Under the current overall excitation, the total radiated electric field of the radome-phased array system is determined based on the active element radiation pattern of the first target antenna element; The final gain of the radome-phased array system is determined based on the total radiated electric field of the radome-phased array system. The fitness function value is determined based on the final gain corresponding to the current overall stimulus. An improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function value is minimized, thus obtaining the optimal overall stimulus. The step of determining the fitness function value based on the final gain corresponding to the current overall stimulus, and optimizing the current overall stimulus using an improved simulated annealing algorithm until the fitness function value is minimized to obtain the optimal overall stimulus, includes: The indicators for the integrated radiation pattern and the maximum gain of the radome-phased array system under the current overall excitation with equal amplitude and in phase are obtained. The indicators include the maximum radiation direction of the radiation pattern, the sidelobes of the radiation pattern, the maximum gain of the radiation pattern, the null depth of the difference radiation pattern, the null position of the difference radiation pattern, and the sidelobes of the difference radiation pattern. The range of expected absolute gain values ​​for the radome-phased array system after optimization is determined based on the maximum gain of the radome-phased array system under the current overall excitation with equal amplitude and phase, and the maximum gain of the radiation pattern. The expected absolute gain range, expected sum and difference pattern shape, sum and difference sidelobes, and difference pattern zero depth determine the sum and difference pattern and the set of acceptable patterns for the difference pattern. Based on the acceptable set of sum and difference directional patterns and the current overall excitation. W The final gain of the radome-phased array system obtained The absolute difference between them determines the fitness function to be optimized. Fitness ( W The expression for ) is: ； in, In order to provide overall incentives W The absolute difference between the gain pattern of the lower radome-phased array system and the two templates: ； in, This represents the lower boundary of the acceptable set of radiation patterns. The upper boundary of the acceptable pattern set; pitch angle is used in spherical coordinates. θ and azimuth Indicates the direction of propagation of radiated electromagnetic waves; An improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function is optimized. Fitness ( W The minimum value is obtained to achieve the optimal overall incentive.

2. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The step of constructing the admittance matrix of all antenna elements based on the mutual admittance of the first target antenna element port to the second target antenna element port includes: Construct the admittance matrix of all antenna elements expression: ； in, Y mn For the first n The antenna element port is paired with the first m The mutual admittance of each antenna element port n =1,2,…, N ; m =1,2,…, N ; N This represents the total number of antenna elements in the radome-phased array system.

3. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The step of determining the active input admittance of the first target antenna element port based on the mutual admittance of the second target antenna element port to the first target antenna element port under the current overall excitation includes: The active input admittance of the first target antenna element port is calculated using the following formula: ； in, For the first n Active input admittance of each antenna element port; N This represents the total number of antenna elements in the radome-phased array system. Y nm For the first m The antenna element port is paired with the first n Mutual admittance of each antenna element port; w m For the first m Unit excitation of each antenna element; w n For the first n Unit excitation of each antenna element.

4. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The step of determining the input power of the first target antenna element port based on the active input admittance of the first target antenna element port and the element excitation of the first target antenna element port includes: The input power at the port of the first target antenna element is calculated using the following formula: ； in, P n For the first n The input power of each antenna element port; Re represents taking the real part of the complex number; For the first n Active input admittance of each antenna element port; w n For the first n The element excitation of an antenna element; |·| represents the modulus.

5. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The step of traversing all antenna element ports and determining the total input power of all antenna element ports based on the input power of the first target antenna element port includes: Calculate the total input power of all antenna element ports using the following formula: ； in, P Total input power to all antenna unit ports; N The total number of antenna elements in the radome-phased array system; Re represents taking the real part of the complex number; For the first n Active input admittance of each antenna element port; w n For the first n The element excitation of an antenna element; |·| represents the modulus.

6. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The determination of the total radiated electric field of the radome-phased array system under the current overall excitation, based on the active element radiation pattern of the first target antenna element, includes: The total radiated electric field of the radome-phased array system can be calculated using the following formula. : ； in, W =[ w 1, w 2,…, w n ,…, w N This serves as the current overall incentive. N This represents the total number of antenna elements in the radome-phased array system. w n For the first n Unit excitation of each antenna element; For the first n The radiation pattern of the active element of each antenna element; using elevation angle in spherical coordinates. θ and azimuth It indicates the direction of propagation of radiated electromagnetic waves.

7. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The determination of the final gain of the radome-phased array system based on the total radiated electric field of the radome-phased array system includes: Calculate the final gain of the radome-phased array system using the following formula. : ； in, The total radiated electric field of the radome-phased array system; elevation angle is used in spherical coordinates. θ and azimuth Indicates the direction of propagation of radiated electromagnetic waves; W =[ w 1, w 2,…, w n ,…, w N This serves as the current overall incentive. The wave impedance in a vacuum; r This is the distance from the midpoint of the spherical coordinate system to the origin. P This represents the total input power to all antenna element ports.

8. The integrated pattern synthesis method for a radome-phased array system according to claim 1, characterized in that, The improved simulated annealing algorithm is used to optimize the current overall stimulus until the fitness function is optimized. Fitness ( W The optimal overall excitation is obtained by minimizing the value of ), which includes: Determine the starting temperature before the iteration cycle begins. T Temperature drop coefficient β Maximum number of iterations in the inner loop M 1 and the maximum number of iterations in the outer loop M 2; Initialize the current overall incentive W The current overall incentive will be randomly generated. W Assigned to the local optimal solution W local With the global optimal solution W best and its corresponding fitness function Fitness ( W The value of ) is assigned to the local minimum fitness function. Fitness_local With the global minimum fitness function Fitness_best ; Under the internal circulation scenario, with the current overall incentive W Generate new global incentives within the neighborhood. W' and calculate W' Corresponding fitness function Fitness ( W' ), W' The value is determined by the following formula: ； in, This represents the change in overall incentives; j The imaginary unit; and These are two sets of relatively independent random numbers belonging to the range [0,1]. For the first N The random variation of the real part of the unit excitation; For the first N The random variation of the imaginary part of each unit excitation; The iteration step size is the normalized value. W' The modulus range is (0,1]; Set the difference between the adaptive function values ​​to Δ F = Fitness ( W' )- Fitness ( W The Metropolis criterion is used to determine whether to update the current overall incentive. W' : 1) If Δ F If ≤0, then update the current overall incentive to W' ,make W=W' And update the local optimum. W local =W' ; 2) If Δ F＞ 0, under the following acceptance probability conditions, W and W local All updated to W' : ； in, k B Boltzmann's constant, k B = 1.380649×10 -23 , For a random number taking values ​​in the range [0,1), exp represents a natural constant. e Index-based operations; 3) If none of the above conditions are met, then maintain the current overall incentive. W and the current local optimum W local constant; When the number of inner loop iterations reaches the maximum number of iterations. M 1 or satisfying continuity L If the change in the fitness function value within a step is less than a preset threshold, the inner loop terminates. max( Fitness ( W ),…, Fitness ( W L )) - my( Fitness ( W ),…, Fitness ( W L ))< ε ; in, W L For the inner loop to proceed to the th L The solution is updated after being evaluated using the Metropolis criterion at each step; ε This is the maximum acceptable change in the fitness function value. In external circulation mode, if the internal circulation termination condition is met, the internal circulation terminates, and the system enters external circulation mode; compare the current temperature. T Local optimal solution W local and the global optimal solution W best The magnitude of the adaptive function value: 1) If Fitness ( W local )≤ Fitness ( W best ), then W best Updated to W local ; 2) If Fitness ( W local > Fitness ( W best If so, then maintain W best constant; If from the first m Start with the second external circulation, continuously M After the second iteration of the outer loop Fitness ( W best When the value of ) does not change significantly, change the iteration step size. R step ,make R step Gradually reduce to the target value: Value( m 2)=abs( Fitness ( W local )- Fitness ( W best )) / abs( Fitness ( W best )); max(Value( m 2),…,Value( m 2+20))<0.2; R step1 = R step -0.02 ， R step ≥0.1； When the outer loop reaches the maximum number of iterations M 2 or satisfy Fitness ( W best If the value of ) is less than the preset convergence value, the outer loop terminates; if the termination conditions for all outer loops are not met, the current temperature is set to 0. T Descending to βT At the same time, initialize W=W best Then return to the beginning of the inner loop and repeat the iterative calculation until all loop termination conditions are met; if all outer loop termination conditions are met, then output the obtained overall optimal excitation solution. W best .

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