Large-scale array phase-only fast beamforming method based on alternating direction multiplier method and application of large-scale array phase-only fast beamforming method

Abstract

According to the large-scale array phase-only fast beam forming method based on the alternating direction multiplier method and the application thereof, the AEP of each unit is extracted by establishing a small array, and then the extracted AEP of each unit of a sub-array is approximately equivalent to the AEP of other units of a target large array through a sub-array extrapolation calculation method; then the method is substituted into the algorithm, and the comprehensive applicability of the directional diagram is improved; setting an upper and lower bound constraint function and an auxiliary variable of directional diagram synthesis, introducing parameters such as a scale factor and a Lagrange multiplier, and constructing a directional diagram synthesis mathematical expression and an augmented Lagrange function; iteratively updating the auxiliary variable, the scale factor, the feed phase of each unit of the antenna array and the value of the Lagrange multiplier, and solving the equation to obtain a phase-only comprehensive result; the method is applied to design of a matched feed network, and an antenna array is combined to construct a feed network and antenna array integrated model; according to the invention, rapid beamforming of a large-scale array is realized, the influence of a mutual coupling effect on array performance is avoided, and the speed and precision of beamforming are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of array antennas, and in particular relates to a large-scale array phase-only fast beamforming method based on an alternating direction multiplier method and an application thereof. Background Art

[0002] Phase-only beamforming adjusts the phase of each element in the antenna array so that the signal interferes constructively in a specific direction to enhance the signal strength, and interferes destructively in other directions to reduce signal radiation, thereby forming a directional beam. Phase-only beamforming technology is widely used in special applications such as radar and satellite communications. For example, in radar systems, phase-only beamforming technology can form a null in the interference direction to improve the radar's anti-interference ability and detection accuracy. At present, the research on phase-only weighted beamforming technology mainly uses intelligent evolutionary algorithms and traditional optimization algorithms for beamforming. Intelligent evolutionary algorithms have large computational complexity, long computational time, slow convergence speed, difficult parameter adjustment, and high hardware requirements. The results of traditional optimization algorithms are strongly dependent on the initial value and fall into local optimal solutions in complex nonlinear problems. Research on large-scale array phase-only weighted beamforming methods that take into account mutual coupling is of great significance for solving the problem of slow beamforming and large errors in scenarios such as radar detection, wireless communication, and intelligent antenna systems.

[0003] In antenna array design, synthesizing the radiation pattern of array antennas while considering mutual coupling is an important topic and a major problem in the field of antennas. The mutual coupling between antenna elements may affect the beam shape, gain and radiation power of the array antenna, thereby limiting the accuracy and effectiveness of the array in practical applications. On the one hand, for the problem of phase-weighted beamforming only, most of the existing phase-weighted beamforming methods do not consider the impact of mutual coupling between array elements on the performance of the antenna array. When synthesizing, it is assumed that each array element is in an ideal state or mutual coupling is considered by simulation software based on numerical algorithms such as the method of moments and the finite element method. However, once the scale is too large, it will take a lot of time or even be impossible to calculate due to the limited computing power of current PCs. On the other hand, the existing phase-weighted beamforming methods have high computational complexity and are limited by different coupling conditions, and the algorithm has poor applicability. Researching large-scale array phase-weighted fast beamforming methods and phase-weighted beamforming methods that take into account mutual coupling is of great significance for solving the problem of errors between beamforming and theory in practical engineering applications.

[0004] The patent application with application publication number CN116362107A discloses a method for calculating the phase-only weighted cosecant square pattern of a radar simulated annealing algorithm. The method establishes a basic signal model for calculating the phase of the cosecant square pattern by a simulated annealing algorithm; encodes the phase weighting to construct a population of multiple individual solutions; calculates the fitness value corresponding to any individual solution in the population; sorts the population individual solutions according to the calculated fitness value to obtain the optimal fitness value and the optimal individual solution; and mutates the population individual solutions according to a preset mutation strategy, updates the optimal fitness value and the optimal individual solution, and completes annealing; decodes based on the obtained optimal fitness value and the optimal individual solution to obtain the phase weighting. However, the simulated annealing algorithm based on this method has high computational complexity, requires a large number of iterations and evaluations, and has a large computational overhead, especially in large-scale antenna array optimization, which may lead to long-term calculations. And it lacks precision. Although a better solution can be found, because it is based on random search, the result may not be the global optimal solution, but only an approximate optimal solution. Moreover, this method does not consider the influence of mutual coupling effects between units on array antennas in actual engineering, which limits the accuracy and effectiveness of the array in practical applications and makes it difficult to meet the needs of beamforming in actual engineering. Therefore, it is not suitable for a wide range of beamforming scenarios. Summary of the invention

[0005] In order to overcome the deficiencies of the above-mentioned prior art, the purpose of the present invention is to propose a large-scale array phase-only fast beamforming method based on the alternating direction multiplier method and its application, by establishing a small array, that is, a subarray of the target large array to simulate and extract the AEP of each unit, and then through the subarray extrapolation calculation method based on the AEP theory, the AEP of each unit of the extracted subarray is approximately equivalent to the AEP of other units of the target large array, thereby avoiding matrix operations in the calculation process, and converting the radiation field calculation problem of the large array into an AEP calculation problem of a small array, effectively reducing the amount of calculation and reducing the difficulty of implementation; then the AEP of each unit of the large array obtained after the equivalence is brought into the algorithm to improve the accuracy of the beamforming. Improve the applicability of beamforming, and solve the fast beamforming of large-scale arrays through the subarray method; by introducing the proportional factor, improve the algorithm freedom and reduce the restrictions on beamforming; combine the classic ADMM algorithm and BFGS algorithm to calculate the feeding phase and select the most suitable phase according to the phase-only beamforming target to further improve the speed and accuracy of beamforming; design the matching feeding network according to the optimized phase, and then design the integrated model of the feeding network antenna array in combination with the antenna array to obtain the radiation pattern after phase-only synthesis, so as to improve the speed and accuracy of beamforming and improve its versatility, with the advantages of high conversion curve, good robustness, simple and efficient calculation process.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A large-scale array phase-only fast beamforming method based on an alternating direction multiplier method specifically comprises the following steps:

[0008] Step 1: Get the antenna element of each antenna element in the antenna array subarray Set the sampling angle domain range Get the M antenna elements in the M-element subarray respectively Wherein, p = 1, 2, ..., P, P is the number of sampling points in azimuth, (m = 1, 2 ... M), M is the number of sub-array elements;

[0009] Step 2: Use the small array, i.e. the AEP of each unit of the M-element subarray obtained in step 1, to approximate the AEP of each unit of the N-element target large array. N is the number of target large array elements (N>M);

[0010] Step 3: Construct the corresponding angle domain range The desired upper limit of the radiated power of a dimension 1×P With the expected lower limit

[0011] Step 4: Combine the N-element target large array obtained in step 2 with each unit and the desired upper limit of the radiated power in step 3 With the expected lower limit Construct the mathematical expression of phase-only weighted beamforming;

[0012] Step 5: Introduce the penalty parameter ρ and the Lagrangian multiplier λ, and establish the augmented Lagrangian function L(μ, φ, Z, λ) based on the mathematical expression of phase-only weighted beamforming obtained in step 4:

[0013]

[0014] in, represents the real part, represents the imaginary part, and denote the Lagrange multipliers of the real and imaginary parts of the constraints, respectively;

[0015] Step 6: According to the augmented Lagrangian function L(μ,φ,Z,λ) obtained in step 5, set the maximum number of iterations T and the auxiliary variable Z n , proportional factor μ, antenna array element feeding phase φ n , Lagrange multiplier λ n The initial value of μ(t), φ n (t) According to the initial value μ(t), φn (t) Iterate and solve the current auxiliary variables separately Proportional factor μ(t+1), antenna array element feeding phase φ n (t+1) and the Lagrange multiplier matrix

[0016] Step 7. Define auxiliary variables The residual Determine whether the residual meets the iteration termination condition. If it does, output the phase φ n If it is not satisfied, return to step 6 to continue the iteration, and retain the feeding phase φ of each unit of the antenna array in the tth iteration t , t=1,2,...,T, T represents the maximum number of iterations, according to the feeding phase φ t With the feeding amplitude A n Get the directional pattern data E of only phase beamforming t .

[0017] The specific method of step 1 is:

[0018] Set the sampling angle domain range Get the M antenna elements in the M-element subarray respectively It is expressed as follows:

[0019] E m =[E1,E2,...,E m ,...,E M ]

[0020] Where, (m=1,2…M), M is the number of sub-array elements, E m is the AEP of the mth antenna element, which is a two-dimensional matrix with dimension 1×P, p=1,2,...,P, P is the number of azimuth sampling points and is expressed as follows:

[0021]

[0022] in, Indicates that the mth antenna unit is Directional pattern data of the direction, It is the pth azimuth variable in the directional pattern sampling angle domain.

[0023] The specific method of step 2 is:

[0024] The M-element subarray is divided into a central unit, a unit on the left side of the center, and a unit on the right side of the center. The subarray AEP is extrapolated equivalently. The AEP of the unit on the left side of the subarray center is equivalent to replacing the AEP of 1 to (M-1) / 2 units on the left side of the N-element target large array. The AEP of the unit on the right side of the subarray center is equivalent to replacing the AEP of N-(M+1) / 2+2 to N units on the right side of the target array. The AEP of the subarray center unit is equivalent to replacing the AEP of (M+1) / 2 to N-(M+1) / 2+1 units in the middle of the target array. After the AEP of the target array is equivalently replaced, spatial phase compensation is performed to finally obtain the radiation field of the target array. The calculation formula is as follows:

[0025]

[0026] in, represents the radiation field of the left unit of the subarray, represents the radiation field of the central unit of the subarray, represents the radiation field of the right unit of the subarray, i=(M+1) / 2~N-(M+1) / 2+1 represents the middle unit, and y=N-(M+1) / 2+2~N represents the right unit;

[0027] Each unit in a large array of N-element targets It is expressed as follows:

[0028] E n =[E1,E2,...,E n ,...,E N ]

[0029] Among them, E n is the AEP of the nth antenna element, which is a two-dimensional matrix with dimension 1×P and is expressed as follows:

[0030]

[0031] in, Indicates that the nth antenna element is Directional pattern data of the direction.

[0032] The corresponding angle domain range is constructed in step 3 The desired upper limit U of the radiated power with dimension 1×P is expressed as follows:

[0033]

[0034] in, Indicated in The desired upper limit of the directed radiated power, is the pth azimuth variable in the directional pattern sampling angle domain;

[0035] Construct the corresponding angle domain range The expected lower limit L of the radiated power of dimension 1×P is expressed as follows:

[0036]

[0037] in, Indicated in The desired lower limit of the directed radiated power, is the pth azimuth variable in the directional pattern sampling angle domain;

[0038] At p = 1, ... P1, Set to the antenna main lobe angle area;

[0039] At p = 1, ... P2, Set to the antenna sidelobe angle area;

[0040] Where P = P1 + P2; the expected upper limit of the radiated power With the expected lower limit Customize settings for users.

[0041] The specific method of step 4 is:

[0042] Introduce the proportional factor μ and define the auxiliary variables: Among them, A n Indicates the feeding amplitude of each unit of the antenna array, φ n Indicates the feeding phase of each unit of the antenna array, n=1,2,...N, N indicates the number of antenna array units, [] T represents transpose, [] H represents conjugate transpose;

[0043] Combining auxiliary variables and the desired upper limit of the radiated power in step 3 With the expected lower limit The mathematical expression for phase-only weighted beamforming is established as:

[0044]

[0045] Step 6 describes the initial value μ(t), φ n (t) Iterate to solve for the current auxiliary variable Proportional factor μ(t+1), antenna array element feeding phase φ n (t+1) and the Lagrange multiplier matrix The specific method is:

[0046] 6.1) Iterate to solve the current auxiliary variable The formula is as follows:

[0047]

[0048] in, represents the expected upper limit of radiated power, Indicates the expected lower limit of radiation power, arg() indicates the phase angle, To ignore the expression of the terms irrelevant to Z in the augmented Lagrangian function L(μ,φ,Z,λ), it is expressed as follows:

[0049]

[0050] Among them, ρ represents the penalty parameter, represents the radiation field of N antenna elements, A=[A1,A2,...,A n ,...,A N ] represents the feed amplitude of each unit of the target N-element antenna array, φ=[φ1,φ2,...,φ n ,...,φ N ] represents the feeding phase of each unit of the target N-element antenna array, [] T represents transpose;

[0051] 6.2) Iterate to solve the current proportional factor μ(t+1) and the feed phase φ of each element of the antenna array n (t+1), as follows:

[0052] 6.2.1) Define two auxiliary functions W(φ) and H(φ) respectively:

[0053]

[0054]

[0055] Among them, ρ represents the penalty parameter, represents the radiation field of N antenna elements, A represents the feeding amplitude of each element of the target N-element antenna array, φ represents the feeding phase of each element of the target N-element antenna array, [] H represents the conjugate transpose, [] * represents taking the complex conjugate;

[0056] 6.2.2) Use two auxiliary functions W(φ) and H(φ) to construct the following nonlinear optimization problem:

[0057]

[0058] 6.2.3) When φ is given, the scale factor μ is expressed as follows using two auxiliary functions W(φ) and H(φ):

[0059]

[0060] The following nonlinear optimization problem is constructed:

[0061]

[0062] The BFGS algorithm is introduced to update the value of the feeding phase φ of each unit. The current feeding phase φ(t+1) of the antenna array is obtained through the MATLAB function "fminunc", which is expressed as follows:

[0063]

[0064] Among them, φ(t) is the feeding phase of each unit before updating, and fminunc is a MATLAB function used to solve the minimum value of nonlinear multivariate function;

[0065] 6.2.4) Update the proportional factor μ according to the current feeding phase φ(t+1) to obtain the current proportional factor μ(t+1):

[0066]

[0067] 6.3) Iteratively solve the current Lagrange multiplier The value of is as follows:

[0068]

[0069] in and They represent the Lagrange multipliers of the real part and imaginary part of the constraint obtained in the current iteration respectively.

[0070] In step 7, auxiliary variables are defined The residual ΔZ is expressed as follows:

[0071]

[0072] Among them, ΔZ is the introduced auxiliary variable, is the expression after ignoring the irrelevant terms with Z in the augmented Lagrangian function L(μ,φ,Z,λ).

[0073] The determination of whether the residual meets the iteration termination condition in step 7 is: ΔZ≤Δor t+1=T

[0074] Wherein, Δ is the residual set by the user, t=1,2,...,T, and T represents the maximum number of iterations. The feeding phase φ of each element of the antenna array for the tth iteration in step 7 is t , which is expressed as follows:

[0075] φ t =[φ t,1 ,φ t,2 ,...,φt,n ,...,φ t,N ] T

[0076] According to the feeding phase φ t With the feeding amplitude A n Get the corresponding directional pattern data E t , which is expressed as follows:

[0077]

[0078] Among them, ρ represents the penalty parameter, E t represents the total radiated field of an N-element target array, represents the radiation field of N antenna elements, A n Indicates the feed amplitude of each unit of the target N-element antenna array, φ t,n represents the feeding phase of the nth antenna element in the tth iteration.

[0079] A supporting feed network for a large-scale array phase-only fast beamforming method based on an alternating direction multiplier method, and a feed network-antenna array integrated model of the feed network combined with a Vivaldi antenna array are used to accurately control the radiation pattern.

[0080] The feeding network adopts a 1-to-n Wilkinson power divider, that is, from one input port, n output ports are formed by m-times of bisection; it includes a dielectric layer 2, the front and back sides of the dielectric layer 2 are respectively covered with a microstrip line 1 and a metal ground 3, the starting end of the microstrip line 1 is the input port, the microstrip line 1 is bisectioned m times to form n output ports, and 2 m =n, m is a positive integer, 1≤m≤6; a chip resistor 8 is connected between every two output ports; the phase required for each branch is obtained according to the length difference of each microstrip line in the binary division process; the Vivaldi antenna unit includes a feed balun 4, a dielectric plate 5 and a radiation surface 6, the feed balun 4 and the radiation surface 6 are respectively covered on the front and back of the dielectric plate 5, the microstrip line 1 with the same material specifications is connected to the feed balun 4, the dielectric layer 2 is connected to the dielectric plate 5, and the metal ground 3 is connected to the radiation surface 6 to form an integrated model of the feed network antenna array; a number of non-metallic through holes 7 are punched in the model for fixing the integrated model during actual measurement.

[0081] Compared with the prior art, the present invention has the following advantages:

[0082] First, the present invention optimizes the phase of the array antenna by taking into account the mutual coupling of the large-scale array phase-only fast beamforming method, which can achieve efficient and accurate beam control of large-scale arrays. Compared with traditional amplitude-phase beamforming, this method greatly simplifies the hardware design, reduces the complexity and cost of the system, and compared with traditional amplitude control, this method has lower power consumption and wider application scenarios.

[0083] Second, the present invention simulates and extracts the AEP of each unit by establishing a small array, that is, a subarray of the target large array, and then uses a subarray extrapolation calculation method based on AEP theory to approximate the AEP of each unit of the extracted subarray to the AEP of other units of the target large array, thereby avoiding matrix operations in the calculation process and converting the radiation field calculation problem of the large array into an AEP calculation problem of a small array, effectively reducing the amount of calculation and the difficulty of implementation. It can solve the influence of mutual coupling effects on array performance, avoid array performance being different from expectations, improve the accuracy of the algorithm in practical applications, increase the robustness of the system, and use the subarray method to solve the rapid beamforming of large-scale arrays.

[0084] Third, the present invention improves the algorithm freedom by introducing the proportional factor μ, and calculates the feeding phase through the classic ADMM algorithm and the BFGS algorithm, avoiding the adjustment of algorithm parameters, greatly simplifying the calculation process, improving the calculation accuracy and efficiency, and solving the problem of sensitivity to the initial value of the parameter.

[0085] Fourthly, the present invention has constructed an integrated structure of a feed network antenna array based on the phase obtained after optimization and completed the processing of the physical object, and implemented a phase-only fast beamforming method for a large-scale array taking mutual coupling into account.

[0086] In summary, the present invention has the advantages of high accuracy, good robustness, simple and efficient calculation, and can be used for phase-only fast beamforming of large-scale arrays. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 It is a flow chart for implementing the present invention.

[0088] Figure 2 This is a flow chart for implementing subarray extrapolation of the present invention.

[0089] Figure 3 is an array structure diagram of the neutron array of the present invention, wherein: Figure 3 (a) is the top view of the array. Figure 3 (b) is a bottom view of the array.

[0090] Figure 4 is an array structure diagram of the target large array in the present invention, wherein: Figure 4 (a) is the top view of the array. Figure 4 (b) is a bottom view of the array.

[0091] Figure 5 This is an integrated structure diagram of the feed network antenna array in the present invention, wherein: Figure 5 (a) The integrated structure diagram of the feed network antenna array for sidelobe null generation. Figure 5(b) is the integrated structure diagram of the feed network antenna array for beam broadening. Figure 5 (c) is the integrated structure diagram of the feeding network antenna array that generates multiple main lobes.

[0092] Figure 6 The comparison diagram of the radiation patterns of the 32-element array in the θ=90° plane under different methods of the present invention is shown.

[0093] Figure 7 This is a diagram of the phase-weighted beamforming result for sidelobe generation nulling in the present invention, where: Figure 7 (a) is the result diagram obtained by calculating the optimized excitation through the subarray extrapolation method in MATLAB. Figure 7 (b) is the simulation result obtained by inputting the optimized excitation into the HFSS array. Figure 7 (c) is the structural diagram of the integrated feed network antenna array based on the optimized excitation design obtained through HFSS simulation. Figure 7 (d) is a comparison of the results obtained by the above three methods. Figure 7 (f) is the residual curve of the optimization process.

[0094] Figure 8 This is a diagram showing the result of beam broadening and phase-weighted beamforming in the present invention, where: Figure 8 (a) is the result diagram obtained by calculating the optimized excitation through the subarray extrapolation method in MATLAB. Figure 8 (b) is the simulation result obtained by inputting the optimized excitation into the HFSS array. Figure 8 (c) is the structural diagram of the integrated feed network antenna array based on the optimized excitation design obtained through HFSS simulation. Figure 8 (d) is a comparison of the results obtained by the above three methods. Figure 8 (f) is the residual curve of the optimization process.

[0095] Fig. 9 This is a result diagram of multiple main lobe phase-only weighted beamforming in the present invention, where: Fig. 9 (a) is the result diagram obtained by calculating the optimized excitation through the subarray extrapolation method in MATLAB. Fig. 9 (b) is the simulation result obtained by inputting the optimized excitation into the HFSS array. Fig. 9 (c) is the structural diagram of the integrated feed network antenna array based on the optimized excitation design obtained through HFSS simulation. Fig. 9 (d) is a comparison of the results obtained by the above three methods. Fig. 9 (f) is the residual curve of the optimization process. DETAILED DESCRIPTION

[0096] In order to more clearly describe the scheme and effect of the present invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without creative work should all fall within the scope of protection of the present invention.

[0097] It should be noted that the step numbers in the specification and claims of the present invention are only for the purpose of clearly describing the implementation scheme of the present invention and facilitating understanding, and the order of the step numbers is not limited.

[0098] Reference Figure 1 , the process of this example is as follows:

[0099] A large-scale array phase-only fast beamforming method based on an alternating direction multiplier method specifically comprises the following steps:

[0100] Step 1: Get the antenna element of each antenna element in the antenna array subarray Set the sampling angle domain range Get the M antenna elements in the M-element subarray respectively Wherein, p = 1, 2, ..., P, P is the number of sampling points in azimuth, (m = 1, 2 ... M), M is the number of sub-array elements;

[0101] The antenna array, such as Figure 3 As shown, Figure 3 (a) is the array radiation surface, Figure 3 (b) is a feed balun, including 7 Vivaldi antenna units with a center frequency of 10 GHz. These 7 antenna units are evenly arranged along the y-axis with a spacing of d = 0.016m to form a 1×7 uniform linear array, where the phase center of unit No. 1 is located at point 0;

[0102] This step is to obtain the antenna element of each antenna element in the antenna array through simulation software. The implementation is as follows:

[0103] Set the sampling angle domain range Get the M antenna elements in the M-element subarray respectively It is expressed as follows:

[0104] E m =[E1,E2,...,E m ,...,E M ]

[0105] Where, (m=1,2…M), M is the number of sub-array elements, E mis the AEP of the mth antenna element, which is a two-dimensional matrix with dimension 1×P, p=1,2,...,P, P is the number of azimuth sampling points and is expressed as follows:

[0106]

[0107] in, Indicates that the mth antenna unit is Directional pattern data of the direction, It is the pth azimuth variable in the directional pattern sampling angle domain.

[0108] Step 2: Use the small array, i.e. the AEP of each unit of the M-element subarray obtained in step 1, to approximate the AEP of each unit of the N-element target large array. N is the number of target large array elements (N>M);

[0109] The M-element subarray is divided into a central unit, a unit on the left side of the center, and a unit on the right side of the center. The subarray AEP is extrapolated equivalently. The AEP of the unit on the left side of the subarray center is equivalent to replacing the AEP of 1 to (M-1) / 2 units on the left side of the N-element target large array. The AEP of the unit on the right side of the subarray center is equivalent to replacing the AEP of N-(M+1) / 2+2 to N units on the right side of the target array. The AEP of the subarray center unit is equivalent to replacing the AEP of (M+1) / 2 to N-(M+1) / 2+1 units in the middle of the target array. After the AEP of the target array is equivalently replaced, spatial phase compensation is performed to finally obtain the radiation field of the target array. The calculation formula is as follows:

[0110]

[0111] in, represents the radiation field of the left unit of the subarray, represents the radiation field of the central unit of the subarray, represents the radiation field of the right unit of the subarray, i=(M+1) / 2~N-(M+1) / 2+1 represents the middle unit, and y=N-(M+1) / 2+2~N represents the right unit;

[0112] Each unit in a large array of N-element targets It is expressed as follows:

[0113] E n =[E1,E2,...,E n ,...,E N ]

[0114] Among them, E n is the AEP of the nth antenna element, which is a two-dimensional matrix with dimension 1×P and is expressed as follows:

[0115]

[0116] in, Indicates that the nth antenna element is Directional pattern data of the direction.

[0117] Step 3: Construct the corresponding angle domain range The desired upper limit of the radiated power of a dimension 1×P With the expected lower limit

[0118] It is expressed as follows:

[0119]

[0120] in, Indicated in The desired upper limit of the directed radiated power, is the pth azimuth variable in the directional pattern sampling angle domain;

[0121] Construct the corresponding angle domain range The expected lower limit L of the radiated power of dimension 1×P is expressed as follows:

[0122]

[0123] in, Indicated in The desired lower limit of the directed radiated power, is the pth azimuth variable in the directional pattern sampling angle domain;

[0124] At p = 1, ... P1, Set to the antenna main lobe angle area;

[0125] At p = 1, ... P2, Set to the antenna sidelobe angle area;

[0126] Where P = P1 + P2; the expected upper limit of the radiated power With the expected lower limit Customize settings for users.

[0127] Step 4: Combine the N-element target large array obtained in step 2 with each unit and the desired upper limit of the radiated power in step 3 With the expected lower limit Construct the mathematical expression of phase-only weighted beamforming;

[0128] Introduce the proportional factor μ and define the auxiliary variables: Among them, A n Indicates the feeding amplitude of each unit of the antenna array, φ nIndicates the feeding phase of each unit of the antenna array, n=1,2,...N, N indicates the number of antenna array units, [] T represents transpose, [] H represents conjugate transpose;

[0129] Combining auxiliary variables and the desired upper limit of the radiated power in step 3 With the expected lower limit The mathematical expression for phase-only weighted beamforming is established as:

[0130]

[0131] Step 5: Introduce the penalty parameter ρ and the Lagrangian multiplier λ, and establish the augmented Lagrangian function L(μ, φ, Z, λ) based on the mathematical expression of phase-only weighted beamforming obtained in step 4:

[0132]

[0133] in, represents the real part, represents the imaginary part, and denote the Lagrange multipliers of the real and imaginary parts of the constraints, respectively;

[0134] Step 6: According to the augmented Lagrangian function L(μ,φ,Z,λ) obtained in step 5, set the maximum number of iterations T and the auxiliary variable Z n , proportional factor μ, antenna array element feeding phase φ n , Lagrange multiplier λ n The initial value of μ(t), φ n (t) According to the initial value μ(t), φ n (t) Iterate and solve the current auxiliary variables separately Proportional factor μ(t+1), antenna array element feeding phase φ n (t+1) and the Lagrange multiplier matrix

[0135] The specific method is:

[0136] 6.1) Iterate to solve the current auxiliary variable The formula is as follows:

[0137]

[0138] in, represents the expected upper limit of radiated power, Indicates the expected lower limit of radiation power, arg() indicates the phase angle, To ignore the expression of the terms irrelevant to Z in the augmented Lagrangian function L(μ,φ,Z,λ), it is expressed as follows:

[0139]

[0140] Among them, ρ represents the penalty parameter, represents the radiation field of N antenna elements, A=[A1,A2,...,A n ,...,A N ] represents the feed amplitude of each unit of the target N-element antenna array, φ=[φ1,φ2,...,φ n ,...,φ N ] represents the feeding phase of each unit of the target N-element antenna array, [] T represents transpose;

[0141] 6.2) Iterate to solve the current proportional factor μ(t+1) and the feed phase φ of each element of the antenna array n (t+1), as follows:

[0142] 6.2.1) Define two auxiliary functions W(φ) and H(φ) respectively:

[0143]

[0144] Among them, ρ represents the penalty parameter, represents the radiation field of N antenna elements, A represents the feeding amplitude of each element of the target N-element antenna array, φ represents the feeding phase of each element of the target N-element antenna array, [] H represents the conjugate transpose, [] * represents taking the complex conjugate;

[0145] 6.2.2) Use two auxiliary functions W(φ) and H(φ) to construct the following nonlinear optimization problem:

[0146]

[0147] 6.2.3) When φ is given, the scale factor μ is expressed as follows using two auxiliary functions W(φ) and H(φ):

[0148]

[0149] The following nonlinear optimization problem is constructed:

[0150]

[0151] The BFGS algorithm is introduced to update the value of the feeding phase φ of each unit. The current feeding phase φ(t+1) of the antenna array is obtained through the MATLAB function "fminunc", which is expressed as follows:

[0152]

[0153] Among them, φ(t) is the feeding phase of each unit before updating, and fminunc is a MATLAB function used to solve the minimum value of nonlinear multivariate function;

[0154] 6.2.4) Update the proportional factor μ according to the current feeding phase φ(t+1) to obtain the current proportional factor μ(t+1):

[0155]

[0156] 6.3) Iteratively solve the current Lagrange multiplier The value of is as follows:

[0157]

[0158] in and They represent the Lagrange multipliers of the real part and imaginary part of the constraint obtained in the current iteration respectively.

[0159] Step 7. Define auxiliary variables The residual ΔZ is expressed as follows:

[0160]

[0161] Among them, ΔZ is the introduced auxiliary variable, This is the expression after ignoring the terms irrelevant to Z in the augmented Lagrangian function L(μ,φ,Z,λ);

[0162] Determine whether the residual meets the iteration termination condition, which is: ΔZ≤Δor t+1=T

[0163] Wherein, Δ is the residual set by the user, t=1,2,...,T, T represents the maximum number of iterations. The feeding phase φ of each element of the antenna array for the tth iteration in step 7 is t , which is expressed as follows:

[0164] φ t =[φ t,1 ,φ t,2 ,...,φ t,n ,...,φ t,N ] T

[0165] According to the feeding phase φt With the feeding amplitude A n Get the corresponding directional pattern data E t , which is expressed as follows:

[0166]

[0167] Among them, ρ represents the penalty parameter, E t represents the total radiated field of an N-element target array, represents the radiation field of N antenna elements, A n Indicates the feed amplitude of each unit of the target N-element antenna array, φ t,n Indicates the feeding phase of the nth antenna unit in the tth iteration. If it satisfies, the output phase φ n If it is not satisfied, return to step 6 to continue the iteration, and retain the feeding phase φ of each unit of the antenna array in the tth iteration t , t=1,2,...,T, T represents the maximum number of iterations, according to the feeding phase φ t With the feeding amplitude A n Get the directional pattern data E of only phase beamforming t .

[0168] A supporting feed network for a large-scale array phase-only fast beamforming method based on an alternating direction multiplier method, and a feed network-antenna array integrated model of the feed network combined with a Vivaldi antenna array are used to accurately control the radiation pattern.

[0169] The feeding network adopts a 1-to-32 Wilkinson power divider, that is, 32 output ports are formed from one input port through 5 times of bisection; it includes a dielectric layer 2, the front and back sides of the dielectric layer 2 are respectively covered with a microstrip line 1 and a metal ground 3, the thickness of the dielectric layer 2 is 0.5 mm, and the microstrip line 1 includes an input port and thirty-two output ports, which are first divided into one into two, then two into four, then four into eight, then eight into sixteen, and finally sixteen into thirty-two. A chip resistor 8 is welded between every two output ports, for a total of thirty-one 100Ω chip resistors; the phase required for each branch is obtained by setting the length difference of each microstrip line in the binary process; 32 Vivaldi antenna units are used, and the Vivaldi antenna unit includes a feed balun 4, a dielectric plate 5 and a radiation surface 6. The feed balun 4 and the radiation surface 6 are respectively covered on the front and back of the dielectric plate 5. The thickness of the dielectric plate 5 is 0.5mm. The microstrip line 1 with the same material specifications is connected to the feed balun 4, the dielectric layer 2 is connected to the dielectric plate 5, and the metal ground 3 is connected to the radiation surface 6 to form an integrated model of the feed network antenna array; a number of non-metallic through holes 7 are punched in the model to fix the integrated model. The integrated model of the feed network antenna array is as follows Figure 5The integrated radiation pattern of the feed network antenna array after phase beamforming is obtained by simulation software such as HFSS. If the simulation results meet the standards, the actual object is processed according to the integrated model of the feed network antenna array.

[0170] The effect of the present invention can be further illustrated by the following simulation experiment.

[0171] 1. Simulation Experiment Conditions

[0172] Using Ansys HFSS simulation software, 7 Vivaldi antenna units and 32 Vivaldi antenna units are set, and the feeding phase of each antenna unit is 0°. These 7 Vivaldi antenna units and 32 Vivaldi antenna units are evenly arranged along the y-axis with a spacing of d=0.016m to form 1×7 and 1×32 uniform linear arrays, where the phase center of unit No. 1 is located at 0, and the operating frequency is 10GHz;

[0173] 2. Simulation experiment content

[0174] Simulation experiment 1: Under the above experimental conditions, the method of the present invention is used to perform the subarray extrapolation calculation based on the AEP idea to generate the radiation pattern of the antenna array. In this simulation experiment, the feeding phase of 32 antenna units is set to 0°, and the feeding amplitude of 32 antenna units is set to 1W. Figure 6 As shown, it is a comparison diagram of the radiation patterns of the 32-element array in the θ=90° plane under different methods in the present invention.

[0175] Simulation experiment 2: Under the above experimental conditions, the method of the present invention is used to perform phase-weighted beamforming with sidelobe null generation. An array pattern is generated with the main lobe pointing to θ=90° and the side lobes suppressed below -16dB, and a -45dB deep null is generated at [35°~40°]. The main lobe area is [-4°~4°], and the side lobe areas are [-90°~-5°], [5°~34°] and [41°~90°]. Figure 7 As shown, Figure 7 (a) is the phase optimized by MATLAB algorithm, and the array radiation pattern is calculated by subarray extrapolation calculation method based on AEP idea. Figure 7 (b) To input the feed amplitude and phase into Figure 4 The antenna array radiation pattern obtained from the HFSS antenna array shown, Figure 7 (c) is designed according to the feeding amplitude and phase. Figure 5 The feed network antenna array shown is integrated to obtain the passive integrated antenna array radiation pattern. Figure 7 (d) is a comparison of the antenna array radiation patterns obtained by the three methods. Figure 7(f) is the residual curve of the algorithm optimization iterative process. Figure 7 It can be seen that the phase-weighted beamforming proposed by the present invention can accurately achieve sidelobe generation nulling. The integrated model of the feed network antenna array in this experiment is as follows: Figure 5 (a) shown.

[0176] Simulation experiment 3: Under the above experimental conditions, the phase-weighted beamforming method of the present invention is used to perform beam broadening. An array pattern with a 26° wide flat-top beam and sidelobe suppression below -15dB is generated. The main lobe area is [-13° to 13°] and the upper and lower limits of the radiation power are set for the main lobe area, which are 0.35dB and -0.35dB respectively. The side lobe areas are [-90° to -14°] and [14° to 90°]. Figure 8 As shown, Figure 8 (a) is the phase optimized by MATLAB algorithm, and the array radiation pattern is calculated by subarray extrapolation calculation method based on AEP idea. Figure 8 (b) To input the feed amplitude and phase into Figure 4 The antenna array radiation pattern obtained from the HFSS antenna array shown, Figure 8 (c) is designed according to the feeding amplitude and phase. Figure 5 The feed network antenna array shown is integrated to obtain the passive integrated antenna array radiation pattern. Figure 8 (d) is a comparison of the antenna array radiation patterns obtained by the three methods. Figure 8 (f) is the residual curve of the algorithm optimization iterative process. Figure 8 It can be seen that the phase-weighted beamforming proposed in the present invention can accurately achieve beam broadening. The integrated model of the feed network antenna array in this experiment is as follows: Figure 5 (b) as shown.

[0177] Simulation experiment 4: Under the above experimental conditions, the method of the present invention is used to perform phase-weighted beamforming of multiple main lobes. An array radiation pattern with two main lobes and side lobes suppressed below -14dB is generated. The main lobe points are θ=-23° and θ=23°, respectively. The main lobe areas are [-28°~-18°] and [18°~28°], and the side lobe areas are [-90°~-29°], [-17°~17°] and [29°~90°]. Fig. 9 As shown, Fig. 9 (a) is the phase optimized by MATLAB algorithm, and the array radiation pattern is calculated by subarray extrapolation calculation method based on AEP idea. Fig. 9 (b) To input the feed amplitude and phase into Figure 4 The antenna array radiation pattern obtained from the HFSS antenna array shown, Fig. 9(c) is designed according to the feeding amplitude and phase. Figure 5 The feed network antenna array shown is integrated to obtain the passive integrated antenna array radiation pattern. Fig. 9 (d) is a comparison of the antenna array radiation patterns obtained by the three methods. Fig. 9 (f) is the residual curve of the algorithm optimization iterative process. Fig. 9 It can be seen that the present invention can accurately realize phase-weighted beamforming of multiple main lobes. The integrated model of the feed network antenna array in this experiment is as follows: Figure 5 (c) As shown. Compared with the traditional amplitude and phase beamforming for planar arrays, the present invention simulates and extracts the AEP of each unit by establishing a small array (a subarray of the target large array), and then uses the subarray extrapolation calculation method based on the AEP theory to approximate the AEP of each unit of the extracted subarray to the AEP of other units of the target large array, thereby avoiding matrix operations in the calculation process and converting the radiation field calculation problem of the large array into an AEP calculation problem of a small array, effectively reducing the amount of calculation and the difficulty of implementation. The AEP of each unit of the large array obtained after the equivalence is then brought into the algorithm to improve the applicability of beamforming, and the fast beamforming of large-scale arrays is solved by the subarray method. By introducing a proportional factor, the algorithm's degree of freedom is increased and the restrictions on beamforming are reduced. The feed phase is calculated by combining the classic ADMM algorithm and the BFGS algorithm and the most suitable phase is selected according to the phase-only beamforming target, further improving the beamforming speed and accuracy. According to the optimized phase design, the matching feeding network is designed. Combined with the antenna array, an integrated model of the feeding network and antenna array is designed to obtain the radiation pattern after phase synthesis only. A large-scale array phase-only fast beamforming method based on the alternating direction multiplier method and its implementation are completed.

Claims

1. A large-scale array phase-only fast beamforming method based on alternating direction multiplier method, characterized in that: The specific steps include: Step 1: Obtain the AEP E of each antenna element in the antenna array subarray m : Set the sampling angle domain range Get the AEP of the M antenna elements in the M-element subarray respectively Wherein, p = 1, 2, ..., P, P is the number of sampling points in azimuth, (m = 1, 2 ... M), M is the number of sub-array elements; Step 2: Use the small array, i.e. the AEP of each unit of the M-element subarray obtained in step 1, to approximate the AEP of each unit of the N-element target large array. N is the number of target large array elements (N>M); Step 3: Construct the corresponding angle domain range The desired upper limit of the radiated power of a dimension 1×P With the expected lower limit Step 4: Combine the AEP of each unit of the N-element target large array obtained in step 2 and the desired upper limit of the radiated power in step 3 With the expected lower limit Construct the mathematical expression of phase-only weighted beamforming; Step 5: Introduce the penalty parameter ρ and the Lagrangian multiplier λ, and establish the augmented Lagrangian function L(μ, φ, Z, λ) based on the mathematical expression of phase-only weighted beamforming obtained in step 4: in, represents the real part, represents the imaginary part, and denote the Lagrange multipliers of the real and imaginary parts of the constraints, respectively; Step 6: According to the augmented Lagrangian function L(μ,φ,Z,λ) obtained in step 5, set the maximum number of iterations T and the auxiliary variable Z n , proportional factor μ, antenna array element feeding phase φ n , Lagrange multiplier λ n The initial value of μ(t), φ n (t) According to the initial value μ(t), φ n (t) Iterate and solve the current auxiliary variables separately Proportional factor μ(t+1), antenna array element feeding phase φ n (t+1) and the Lagrange multiplier matrix Step 7. Define auxiliary variables The residual Determine whether the residual meets the iteration termination condition. If it does, output the phase φ n If it is not satisfied, return to step 6 to continue the iteration, and retain the feeding phase φ of each unit of the antenna array in the tth iteration t , t=1,2,...,T, T represents the maximum number of iterations. According to the residual ΔZ of the auxiliary variable, the feeding phase φ corresponding to the minimum residual is selected. t , according to the feeding phase φ t With the feeding amplitude A n Get the directional pattern data E of only phase beamforming t .

2. According to claim 1, a large-scale array phase-only fast beamforming method based on alternating direction multiplier method is characterized in that: The specific method of step 1 is: Set the sampling angle domain range Get the AEP of the M antenna elements in the M-element subarray respectively It is expressed as follows: THE m =[E1,E2,...,E m ,...,THE M ] Where, (m=1,2…M), M is the number of sub-array elements, E m is the AEP of the mth antenna element, which is a two-dimensional matrix with dimension 1×P, p=1,2,...,P, P is the number of azimuth sampling points and is expressed as follows: in, Indicates that the mth antenna element is Directional pattern data of the direction, It is the pth azimuth variable in the directional pattern sampling angle domain.

3. According to claim 1, a large-scale array phase-only fast beamforming method based on alternating direction multiplier method is characterized in that: The specific method of step 2 is: The M-element subarray is divided into a central unit, a unit on the left side of the center, and a unit on the right side of the center. The subarray AEP is extrapolated equivalently. The AEP of the unit on the left side of the subarray center is equivalent to replacing the AEP of 1 to (M-1) / 2 units on the left side of the N-element target large array. The AEP of the unit on the right side of the subarray center is equivalent to replacing the AEP of N-(M+1) / 2+2 to N units on the right side of the target array. The AEP of the subarray center unit is equivalent to replacing the AEP of (M+1) / 2 to N-(M+1) / 2+1 units in the middle of the target array. After the AEP of the target array is equivalently replaced, spatial phase compensation is performed to finally obtain the radiation field of the target array. The calculation formula is as follows: in, represents the radiation field of the left unit of the subarray, represents the radiation field of the central unit of the subarray, represents the radiation field of the right unit of the subarray, i=(M+1) / 2~N-(M+1) / 2+1 represents the middle unit, and y=N-(M+1) / 2+2~N represents the right unit; AEP of each unit in a large array of N-element targets It is expressed as follows: THE n =[E1,E2,...,E n ,...,THE N ] Among them, E n is the AEP of the nth antenna element, which is a two-dimensional matrix with dimension 1×P and is expressed as follows: in, Indicates that the nth antenna element is Directional pattern data of the direction.

4. According to claim 1, a large-scale array phase-only fast beamforming method based on alternating direction multiplier method is characterized in that: The corresponding angle domain range is constructed in step 3 The desired upper limit U of the radiated power with dimension 1×P is expressed as follows: in, Indicated in The desired upper limit of the directed radiated power, is the pth azimuth variable in the directional pattern sampling angle domain; Construct the corresponding angle domain range The expected lower limit L of the radiated power of dimension 1×P is expressed as follows: in, Indicated in The desired lower limit of the directed radiated power, is the pth azimuth variable in the directional pattern sampling angle domain; At p = 1, ... P1, Set to the antenna main lobe angle area; At p = 1, ... P2, Set to the antenna sidelobe angle area; Where P = P1 + P2; the expected upper limit of the radiated power With the expected lower limit Customize settings for users.

5. According to claim 1, a large-scale array phase-only fast beamforming method based on alternating direction multiplier method is characterized in that: The specific method of step 4 is: Introduce the proportional factor μ and define the auxiliary variables: Among them, A n Indicates the feeding amplitude of each unit of the antenna array, φ n Indicates the feeding phase of each unit of the antenna array, n=1,2,...N, N indicates the number of antenna array units, [] T represents transpose, [] H represents conjugate transpose; Combining auxiliary variables and the desired upper limit of the radiated power in step 3 With the expected lower limit The mathematical expression for phase-only weighted beamforming is established as:

6. According to the large-scale array phase-only fast beamforming method based on the alternating direction multiplier method in claim 1, it is characterized in that the initial value in step 6 is μ(t), φ n (t) Iterate to solve for the current auxiliary variable Proportional factor μ(t+1), antenna array element feeding phase φ n (t+1) and the Lagrange multiplier matrix The specific method is: 6.1) Iterate to solve the current auxiliary variable The formula is as follows: in, represents the expected upper limit of radiated power, Indicates the expected lower limit of radiation power, arg() indicates the phase angle, To ignore the expression of the terms irrelevant to Z in the augmented Lagrangian function L(μ,φ,Z,λ), it is expressed as follows: Among them, ρ represents the penalty parameter, represents the radiation field of N antenna elements, A=[A1,A2,...,A n ,...,A N ] represents the feed amplitude of each unit of the target N-element antenna array, φ=[φ1,φ2,...,φ n ,...,φ N ] represents the feeding phase of each unit of the target N-element antenna array, [] T represents transpose; 6.2) Iterate to solve the current proportional factor μ(t+1) and the feed phase φ of each element of the antenna array n (t+1), as follows: 6.2.1) Define two auxiliary functions W(φ) and H(φ) respectively: in, ρ represents the penalty parameter, represents the radiation field of N antenna elements, A represents the feeding amplitude of each element of the target N-element antenna array, φ represents the feeding phase of each element of the target N-element antenna array, [] H represents the conjugate transpose, [] * represents taking the complex conjugate; 6.2.2) Use two auxiliary functions W(φ) and H(φ) to construct the following nonlinear optimization problem: 6.2.3) When φ is given, the scale factor μ is expressed as follows using two auxiliary functions W(φ) and H(φ): The following nonlinear optimization problem is constructed: The BFGS algorithm is introduced to update the value of the feeding phase φ of each unit. The current feeding phase φ(t+1) of the antenna array is obtained through the MATLAB function "fminunc", which is expressed as follows: Among them, φ(t) is the feeding phase of each unit before updating, and fminunc is a MATLAB function used to solve the minimum value of nonlinear multivariate function; 6.2.4) Update the proportional factor μ according to the current feeding phase φ(t+1) to obtain the current proportional factor μ(t+1): 6.3) Iteratively solve the current Lagrange multiplier The value of is as follows: in and They represent the Lagrange multipliers of the real part and imaginary part of the constraint obtained in the current iteration respectively.

7. According to claim 1, a large-scale array phase-only fast beamforming method based on alternating direction multiplier method is characterized in that: In step 7, auxiliary variables are defined The residual ΔZ is expressed as follows: Among them, ΔZ is the introduced residual, is the expression after ignoring the irrelevant terms with Z in the augmented Lagrangian function L(μ,φ,Z,λ).

8. According to claim 1, a large-scale array phase-only fast beamforming method based on alternating direction multiplier method is characterized in that: The determination of whether the residual satisfies the iteration termination condition in step 7 is: ΔZ≤Δor t+1=T; Where Δ is the residual set by the user, t = 1, 2, ..., T, T represents the maximum number of iterations, and the feed phase φ of each element of the antenna array at the tth iteration is t , which is expressed as follows: f t =[φ t,1 ,f t,2 ,...,f t,n ,...,f t,N ] T According to the feeding phase φ t With the feeding amplitude A n Get the corresponding directional pattern data E t , which is expressed as follows: Among them, ρ represents the penalty parameter, E t represents the total radiated field of an N-element target array, represents the radiation field of N antenna elements, A n Indicates the feed amplitude of each unit of the target N-element antenna array, φ t,n represents the feeding phase of the nth antenna element in the tth iteration.

9. A supporting feeding network for a large-scale array phase-only fast beamforming method based on an alternating direction multiplier method as described in any one of claims 1 to 8, and an integrated model of a feeding network antenna array in which the feeding network is combined with a Vivaldi antenna array, for precisely controlling the radiation pattern.

10. The integrated model of the feed network antenna array according to claim 9, characterized in that: The feeding network adopts a 1-to-n Wilkinson power divider, that is, from one input port, n output ports are formed by m-fold division; it comprises a dielectric layer (2), the front and back sides of the dielectric layer (2) are respectively covered with a microstrip line (1) and a metal ground (3), the starting end of the microstrip line (1) is the input port, the microstrip line (1) is formed by m-fold division to form n output ports, and 2 m =n, m is a positive integer, 1≤m≤6; a chip resistor (8) is connected between every two output ports; the phase required for each branch is obtained by setting the length difference of each microstrip line (1) in the binary process; the Vivaldi antenna unit comprises a feeding balun (4), a dielectric plate (5) and a radiating surface (6); the feeding balun (4) and the radiating surface (6) are respectively covered on the front and back of the dielectric plate (5); the microstrip line (1) and the feeding balun (4) with the same material specifications are spliced, the dielectric layer (2) and the dielectric plate (5) are spliced, and the metal ground (3) and the radiating surface (6) are spliced ​​to form an integrated model of the feeding network antenna array; a plurality of non-metallic through holes (7) are punched on the integrated model for installation and fixation of the integrated model during actual measurement.

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