Weight-constrained array antenna shaped beam gain optimization method and device

Abstract

The invention discloses a weight-constrained array antenna shaped beam gain optimization method and device, and the method comprises the steps: setting an array structure and target shaped beam parameters according to a set target; according to the relational expression of the weight and the directivity coefficient, constructing a shaped beam maximization directivity coefficient weight optimization model; obtaining an initial array weight according to the main lobe width of the target beam; solving and optimizing variables in the optimization model through an alternating direction multiplier method to obtain an optimization result, calculating an original error of the variables according to the result, and obtaining a maximum value of the original error through calculation; comparing the original error with a set error threshold, if the original error is smaller than the set error threshold, stopping iteration, and outputting a final array element weight; and if the original error is not smaller than the set error threshold, iteratively calculating the original error until a set iteration frequency is reached, and outputting a final array element weight. According to the invention, the main lobe gain can be improved and the amplitude dynamic range ratio can be reduced while the beam shape is satisfied.

Description

Technical Field

[0001] The present invention relates to the technical field of array antenna optimization design, and in particular to a method and device for optimizing the gain of an array antenna shaped beam with constrained weights. Background Art

[0002] Phased array technology has been widely used in fields such as communications, sonar, navigation, and unmanned driving. In different application fields, the requirements for array beam shapes vary. For example, if a longer effective range is required, a pencil beam is usually used; if the effective range is relatively short, but the effective airspace range is large, a wide beam is usually used. In order to achieve different beam shapes, the signals of a single antenna (i.e., array element) in the array can be amplitude- and phase-weighted, thereby changing the synthetic ratio of electromagnetic waves in space. Appropriate amplitude- and phase weighting can often improve the beam performance of the antenna array and provide support for subsequent signal processing such as target detection and recognition. Therefore, the development of a beamforming method with fast optimization speed and good beam performance is of great significance for the application of antenna arrays.

[0003] At present, there are many parameters that need to be considered when implementing beamforming, mainly including main lobe gain, side lobe level, and dynamic range ratio of weight amplitude. Given the desired beam, solving the weight is a typical inverse problem, which is usually solved by optimization algorithm. Among them, the methods with a wide range of applications include SDR method using semi-definite relaxation strategy. The weights obtained by the above method can form the desired beam shape, but the two important parameters of amplitude dynamic range ratio and main lobe gain are ignored in the optimization process. In the actual phased array system, the main lobe gain is related to the ability of the effective range, while the amplitude dynamic range ratio affects the difficulty of hardware implementation.

[0004] Therefore, in beamforming, how to improve the main lobe gain and reduce the amplitude dynamic range ratio while satisfying the beam shape is of great practical significance. Summary of the invention

[0005] To this end, the present invention provides a method and device for optimizing the shaped beam gain of an array antenna with constrained weights. The idea of ​​the alternating direction multiplier method is adopted to split the expression of the directivity coefficient. By means of variable substitution, the main lobe gain fluctuation, side lobe level and weight dynamic range are constrained, ultimately achieving the effect of improving the shaped beam gain under multiple constraints.

[0006] In order to achieve the above object, the present invention provides the following technical solution: a method for optimizing the gain of an array antenna shaped beam with constrained weights, comprising:

[0007] According to the set target, set the array structure and target shaped beam parameters;

[0008] According to the relationship between weight and directivity coefficient, a weight optimization model for shaped beam maximization directivity coefficient is constructed;

[0009] Acquiring initial array weights according to a target beam main lobe width in the target shaped beam parameters;

[0010] The variables in the shaped beam maximization directivity coefficient weight optimization model are solved and optimized by an alternating direction multiplier method to obtain an optimization result;

[0011] According to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation;

[0012] The original error is compared with a set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output; if the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

[0013] As a preferred scheme for a constrained weight array antenna shaped beam gain optimization method, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

[0014] As a preferred solution of a method for optimizing the gain of an array antenna shaped beam with constrained weights, in the process of constructing the weight optimization model for maximizing the directivity coefficient of the shaped beam, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through an auxiliary variable method and an augmented Lagrange multiplier method; the multivariable model is the weight optimization model for maximizing the directivity coefficient of the shaped beam;

[0015] The expression of the shaped beam maximization directivity coefficient weight optimization model is:

[0016]

[0017] st1≤|q m | 2 ≤a mll

[0018] |p s |≤a sll

[0019] ||x|| 2 =1

[0020] L ω ≤|vn |≤U ω

[0021] m=1,2,…,M

[0022] s=1,2,…,S

[0023] n=1,2,…,N

[0024]

[0025] A q =[a(θ1),…,a(θ m ),…,a(θ M )]

[0026] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0027] p=[p1,…,p s ,…,p S ] T

[0028] q=[q1,…,q m ,…,q M ] T

[0029] In the formula, the superscript T represents the transposition operation; the superscript H represents the conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the beam total power scaling factor; q is the beam main lobe electric field strength; p is the beam side lobe electric field strength; x is the beam total electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe region; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; Lω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

[0030] As an optimal solution for the array antenna shaped beam gain optimization method with constrained weights, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

[0031] As a preferred solution of a method for optimizing the gain of an array antenna shaped beam with a weight constraint, the expression of the original error is:

[0032]

[0033] In the formula, k is the number of iterations.

[0034] The present invention also provides a device for optimizing the shaped beam gain of an array antenna with a constraint weight. The method for optimizing the shaped beam gain of an array antenna with a constraint weight is based on the above method, comprising:

[0035] An array parameter setting module is used to set the array structure and target shaped beam parameters according to the set target;

[0036] A shaped beam maximization directivity coefficient weight optimization model construction module is used to construct a shaped beam maximization directivity coefficient weight optimization model according to a relationship between the weight and the directivity coefficient;

[0037] An initial array weight acquisition module is used to acquire initial array weights according to the target beam main lobe width in the target shaped beam parameters;

[0038] A variable solving and optimization module is used to solve and optimize the variables in the shaped beam maximization directivity coefficient weight optimization model by an alternating direction multiplier method to obtain an optimization result;

[0039] An original error maximum value calculation module is used to calculate the original error of the variable according to the optimization result; and obtain the original error maximum value by calculation according to the original error;

[0040] The final array element weight acquisition module is used to compare the original error with the set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output; if the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

[0041] As a preferred solution for a constrained weight array antenna shaped beam gain optimization device, in the array parameter setting module, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

[0042] As a preferred solution of an array antenna shaped beam gain optimization device with constrained weights, in the shaped beam maximization directivity coefficient weight optimization model construction module, in the process of constructing the shaped beam maximization directivity coefficient weight optimization model, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through an auxiliary variable method and an augmented Lagrange multiplier method; the multivariable model is the shaped beam maximization directivity coefficient weight optimization model;

[0043] The expression of the shaped beam maximization directivity coefficient weight optimization model is:

[0044]

[0045] st1≤|q m | 2 ≤a mll

[0046] |p s |≤a sll

[0047] ||x|| 2 =1

[0048] L ω ≤|v n |≤U ω

[0049] m=1,2,…,M

[0050] s=1,2,…,S

[0051] n=1,2,…,N

[0052]

[0053] A q =[a(θ1),…,a(θ m ),…,a(θ M )]

[0054] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0055] p=[p1,…,p s ,…,p S ] T

[0056] q=[q1,…,q m ,…,q M ] T

[0057] In the formula, the superscript T represents the transposition operation; the superscript H represents the conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the beam total power scaling factor; q is the beam main lobe electric field strength; p is the beam side lobe electric field strength; x is the beam total electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe region; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

[0058] As a preferred solution of an array antenna shaped beam gain optimization device with constrained weights, in the variable solution optimization module, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

[0059] As a preferred solution of an array antenna shaped beam gain optimization device with a constrained weight, in the original error maximum value calculation module, the expression of the original error is:

[0060]

[0061] In the formula, k is the number of iterations.

[0062] The present invention has the following advantages: according to the set target, the array structure and the target shaped beam parameters are set; according to the relationship between the weight and the directivity coefficient, a shaped beam maximization directivity coefficient weight optimization model is constructed; according to the target beam main lobe width in the target shaped beam parameters, the initial array weight is obtained; the variables in the shaped beam maximization directivity coefficient weight optimization model are solved and optimized by the alternating direction multiplier method to obtain the optimization result; according to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation; the original error is compared with the set error threshold, if the original error is less than the set error threshold, the iterative calculation is stopped, and the final array element weight is output; if the original error is not less than the set error threshold, the original error is iteratively calculated until the set number of iterations is reached, and the final array element weight is output. The present invention adopts the idea of ​​the alternating direction multiplier method, first splits the expression of the directivity coefficient, and then constrains the main lobe gain fluctuation, side lobe level and weight dynamic range by variable substitution, and finally achieves the effect of improving the shaped beam gain under multiple constraints. The present invention improves the gain of the shaped beam, and at the same time controls the maximum main lobe gain fluctuation, the highest side lobe level and the weight dynamic range to be less than the preset threshold. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0064] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with the technology. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantial technical significance. Any structural modification, change in proportion or adjustment of size shall still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0065] Figure 1 A schematic flow chart of a method for optimizing array antenna shaped beam gain with a constraint weight provided in Embodiment 1 of the present invention;

[0066] Figure 2Schematic diagram of array initial weights and normalized directions in a possible embodiment provided in Embodiment 1 of the present invention; wherein (a) is a schematic diagram of array initial weight amplitude distribution; (b) is a schematic diagram of array initial weight phase distribution; (c) is a schematic diagram of array initial normalized direction pattern;

[0067] Figure 3 A schematic diagram of a curve showing a change in the original error versus the number of iterations in a possible embodiment provided in Embodiment 1 of the present invention;

[0068] Figure 4 An array pattern obtained by optimizing the iterative convex optimization method, the semi-positive definite relaxation method and the method of the present invention in a possible embodiment provided in Embodiment 1 of the present invention;

[0069] Figure 5 A schematic diagram of the weight amplitude and weight phase distribution obtained after optimization using the iterative convex optimization method, the semi-positive definite relaxation method and the method of the present invention in a possible embodiment provided in Embodiment 1 of the present invention; wherein (a) is a schematic diagram of the weight amplitude distribution; (b) is a schematic diagram of the weight phase distribution;

[0070] Figure 6 This is a schematic diagram of the architecture of an array antenna shaped beam gain optimization device with constrained weights provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0071] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0072] Example 1

[0073] See also Figure 1 Embodiment 1 of the present invention provides a method for optimizing the gain of an array antenna shaped beam with a constrained weight, comprising the following steps:

[0074] S1. Set the array structure and target shaped beam parameters according to the set target;

[0075] S2. According to the relationship between the weight and the directivity coefficient, a weight optimization model for maximizing the directivity coefficient of the shaped beam is constructed;

[0076] S3, acquiring initial array weights according to the target beam main lobe width in the target shaped beam parameters;

[0077] S4, solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by an alternating direction multiplier method to obtain an optimization result;

[0078] S5. According to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation;

[0079] S6. Compare the original error with a set error threshold. If the original error is less than the set error threshold, stop iterative calculation and output the final array element weight. If the original error is not less than the set error threshold, iteratively calculate the original error until a set number of iterations is reached, and output the final array element weight.

[0080] In this embodiment, in step S1, the array structure and target shaped beam parameters are set according to the set target;

[0081] Specifically, according to the set target, set the array structure and target shaped beam parameters. Input the number of array elements N, the array element spacing d, the main lobe spatial range [κ1, κ2], the side lobe spatial range [κ3, κ4], the target main lobe gain fluctuation upper bound α mll , target sidelobe level upper limit α sll And the dynamic range of the target weight amplitude [L ω ,U ω ].

[0082] The spatial range of the shaped beam is expressed by an angle, where -90<κ1<κ2<90, -90<κ3<κ4<90, and κ3<κ1<κ2<κ4.

[0083] The dynamic range ratio of the weight amplitude refers to the ratio of the maximum amplitude to the minimum amplitude of the weight, that is:

[0084]

[0085] The dynamic range of the preset weight amplitude [L ω ,U ω ] is usually determined according to the following formula:

[0086]

[0087] U ω =γ·L ω

[0088] Where, L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

[0089] In this embodiment, in step S2, a shaped beam maximizing directivity coefficient weight optimization model is constructed according to a relationship between the weight and the directivity coefficient;

[0090] Specifically, a weight optimization model for shaped beam maximization directivity coefficient is established. First, the original single variable model is established according to the relationship between the weight and the directivity coefficient, and then the auxiliary variable method and augmented Lagrange multiplier method are used to rewrite the original model into a multivariable model;

[0091] A weight optimization model for shaped beam maximization directivity coefficient is established; the optimization model of the original single variable is as follows:

[0092]

[0093] stη≤|a H (θ m )ω|≤a mll η

[0094] |a H (θ s )ω|≤a sll η

[0095] ω H Gω=1

[0096] L ω ≤|ω n |≤U ω

[0097] m=1,2,…,M

[0098] s=1,2,…,S

[0099] n=1,2,…,N

[0100] Where η represents the minimum gain within the main lobe range; M, S, and N represent the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements, respectively. Assume that the wavelength is λ, and:

[0101] a(θ)=[a1(θ),a2(θ),…,a n (θ)…,a N (θ)] T

[0102]

[0103] δ i,j =|ij|d

[0104] 1≤i≤N,1≤j≤N

[0105] Rewrite the original single-variable optimization model into a multi-variable optimization model;

[0106]

[0107] st1≤|q m| 2 ≤a mll

[0108] |p s |≤a sll

[0109] ||x|| 2 =1

[0110] L ω ≤|v n |≤U ω

[0111] m=1,2,…,M

[0112] s=1,2,…,S

[0113] n=1,2,…,N

[0114]

[0115] A q =[a(θ1),…,a(θ m ),…,a(θ M )]

[0116] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0117] p=[p1,…,p s ,…,p S ] T

[0118] q=[q1,…,q m ,…,q M ] T

[0119] In the formula, the superscript T represents the transposition operation; the superscript H represents the conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ vare the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the beam total power scaling factor; q is the beam main lobe electric field strength; p is the beam side lobe electric field strength; x is the beam total electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe region; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

[0120] In this embodiment, in step S3, the initial array weights are obtained according to the target beam main lobe width in the target shaped beam parameters;

[0121] Specifically, the initial array weight ω0 is determined according to the target beam main lobe width:

[0122]

[0123] Where c0 is a parameter that varies with the desired beam shape, and its value range is c0∈[0,1].

[0124] In this embodiment, in step S4, the variables in the shaped beam maximization directivity coefficient weight optimization model are solved and optimized by an alternating direction multiplier method to obtain an optimization result;

[0125] Specifically, each variable is optimized in turn based on the alternating direction multiplier method. First, the variables in the shaped beam maximization directivity coefficient weight optimization model in step S2 are divided into two variable blocks, and then the original optimization problem is transformed into two sub-problems; then the two sub-problems are solved in turn;

[0126] The two variable blocks are {q, p, x, v} and {m, x, ω}, and all variables have closed-form expressions.

[0127] 1. Solve the variable block {q,p,x,v}. At the kth (k≥1) iteration,

[0128]

[0129]

[0130] 2. Solve the variable block {m,x,ω}. At the kth (k≥1) iteration,

[0131] ω (k) =(K·K H ) -1 ·K·y

[0132]

[0133] ω (k) =(K·K H ) -1 ·K·y

[0134]

[0135] f m =v (k) -ρ (k-1) χ v (k-1)

[0136]

[0137] Update the penalty factor and dual variable:

[0138] ρ (k) =c1·ρ (k-1)

[0139]

[0140] In this embodiment, in step S5, the original error of the variable is calculated based on the optimization result; and the maximum value of the original error is obtained by calculation based on the original error;

[0141] Specifically, the expression of the original error is:

[0142]

[0143] In the formula, k is the number of iterations.

[0144] In this embodiment, in step S6, the original error is compared with a set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output; if the original error is not less than the set error threshold, the original error is iteratively calculated until the set number of iterations is reached, and the final array element weight is output.

[0145] Specifically, the original error is compared with a preset error threshold. If the error is less than the threshold, the iteration is stopped and the final array element weight is output; otherwise, steps S4 and S5 are repeated until the preset maximum number of iterations is reached.

[0146] In a possible embodiment, a specific example of array antenna shaped beam gain optimization is provided as follows:

[0147] T1, given array structure and multi-beam range;

[0148] Specifically, set the number of array elements N = 32 and the array element spacing Main lobe spatial range [-10°, 10°], side lobe spatial range [-15°, 15°], expected main lobe gain fluctuation upper bound α mll =10 0.2 / 10 , the upper limit of the expected sidelobe level α sll =10 -30 / 10 and the expected dynamic range ratio of the weight amplitude is 5.63, so L ω =0.8769, U ω =4.9370. In addition, a null region is set within the angle [35°, 40°], and the null depth is -60 dB.

[0149] T2, shaped beam maximization directivity coefficient weight optimization model;

[0150] Specifically,

[0151]

[0152] st1≤|q m | 2 ≤a mll

[0153] |p s |≤a sll

[0154] ||x|| 2 =1

[0155] L ω ≤|v n |≤U ω

[0156] m=1,2,…,M

[0157] s=1,2,…,S

[0158] n=1,2,…,N

[0159]

[0160] Aq =[a(θ1),…,a(θ m ),…,a(θ M )]

[0161] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0162] Take the initial value ρ (0) =1,

[0163] T3, determine the initial array weight ω0 according to the target beam main lobe width;

[0164] Specifically,

[0165]

[0166] Among them, c0 takes The magnitude and phase distribution of the weights and the corresponding directions are as follows: Figure 2 shown.

[0167] T4. In the kth iteration, solve the two variable blocks {q,p,x,v} and {m,x,ω}. Get μ (k) ,x (k) ,q (k) ,p (k) ,x (k) ,v (k) ,ω (k) .

[0168] The value of c1 is:

[0169]

[0170] T5, calculating the original error after the kth iteration based on the result of step T4;

[0171] Specifically,

[0172]

[0173] T6. If Or if k>10000, the iteration stops and the final weight ω is output. (k) Otherwise, return to step T4 and perform the k+1th iteration. The logarithm of the original error of all iterations is as follows: Figure 3 As shown in the figure, it can be seen that the method of the present invention has good convergence. After no more than 10,000 iterations, the error is reduced to 10 -8 the following.

[0174] like Figure 4As shown, it can be seen that both the semi-definite relaxation method and the method of the present invention can achieve the same main lobe gain of 6.82 dBi, with a main lobe gain fluctuation of 0.2 dB, while the gain of the iterative convex optimization method is only 6.08 dBi, and the gain fluctuation is much greater than that of the method of the present invention, which is 1.4 dB.

[0175] like Figure 5 As shown, after calculation, the amplitude dynamic range ratios of the three methods are 5.63, 437.74 and 5.63 respectively. By comparison, it can be seen that the amplitude dynamic range of the weights optimized by the present invention reaches the minimum value.

[0176] Main lobe gain minimum Sidelobe level Zero Depth Weighted Dynamic Range Ratio Solution time Iterative Convex Optimization Method 6.08dBi -17.53dB -22.27dB 5.63 12.41 seconds Semidefinite relaxation method 6.82dBi -30dB -60dB 437.74 55.03 seconds Method of the present invention 6.82dBi -30dB -60dB 5.63 3.53 seconds

[0177] Table 1 Performance of different methods

[0178] As shown in Table 1, the performance comparison of the three methods under the same computing environment shows that, under the premise of achieving the same gain, the solution speed of the present invention is increased by 3.5 times and 15 times respectively compared with the existing methods.

[0179] In summary, the present invention sets the array structure and target shaped beam parameters according to the set target; constructs a shaped beam maximizing directivity coefficient weight optimization model according to the relationship between the weight and the directivity coefficient; obtains the initial array weight according to the target beam main lobe width in the target shaped beam parameters; solves and optimizes the variables in the shaped beam maximizing directivity coefficient weight optimization model by the alternating direction multiplier method to obtain the optimization result; calculates and obtains the original error of the variable according to the optimization result; obtains the maximum value of the original error by calculation according to the original error; compares the original error with the set error threshold, if the original error is less than the set error threshold, stops the iterative calculation and outputs the final array element weight; if the original error is not less than the set error threshold, iteratively calculates the original error until the set number of iterations is reached, and outputs the final array element weight. The present invention adopts the idea of ​​the alternating direction multiplier method, first splits the expression of the directivity coefficient, and then constrains the main lobe gain fluctuation, side lobe level and weight dynamic range by variable substitution, and finally achieves the effect of improving the shaped beam gain under multiple constraints. The present invention improves the gain of the shaped beam, and at the same time controls the maximum main lobe gain fluctuation, the highest side lobe level and the weight dynamic range to be less than the preset threshold.

[0180] It should be noted that the method of the embodiment of the present disclosure can be performed by a single device, such as a computer or a server. The method of the present embodiment can also be applied in a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present disclosure, and the multiple devices will interact with each other to complete the described method.

[0181] It should be noted that the above describes some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0182] Example 2

[0183] See also Figure 6 Embodiment 2 of the present invention further provides an array antenna shaped beam gain optimization device with constrained weights, comprising:

[0184] Array parameter setting module 001, used to set array structure and target shaped beam parameters according to set targets;

[0185] The module 002 for constructing a shaped beam maximizing directivity coefficient weight optimization model is used to construct a shaped beam maximizing directivity coefficient weight optimization model according to a relationship between the weight and the directivity coefficient;

[0186] An initial array weight acquisition module 003 is used to acquire initial array weights according to the target beam main lobe width in the target shaped beam parameters;

[0187] The variable solving and optimizing module 004 is used to solve and optimize the variables in the shaped beam maximizing directivity coefficient weight optimization model by using an alternating direction multiplier method to obtain an optimization result;

[0188] The original error maximum value calculation module 005 is used to calculate the original error of the variable according to the optimization result; and obtain the original error maximum value by calculation according to the original error;

[0189] The final array element weight acquisition module 006 is used to compare the original error with the set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output; if the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

[0190] In this embodiment, in the array parameter setting module 001, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

[0191] In this embodiment, in the shaped beam maximizing directivity coefficient weight optimization model construction module 002, in the process of constructing the shaped beam maximizing directivity coefficient weight optimization model, according to the relationship between the weight and the directivity coefficient, the original single variable model is constructed; the original single variable model is rewritten into a multivariable model through the auxiliary variable method and the augmented Lagrange multiplier method; the multivariable model is the shaped beam maximizing directivity coefficient weight optimization model;

[0192] The expression of the shaped beam maximization directivity coefficient weight optimization model is:

[0193]

[0194] st1≤|q m | 2 ≤a mll

[0195] |p s |≤a sll

[0196] ||x|| 2 =1

[0197] L ω ≤|v n |≤U ω

[0198] m=1,2,…,M

[0199] s=1,2,…,S

[0200] n=1,2,…,N

[0201]

[0202] A q =[a(θ1),…,a(θ m ),…,a(θM )]

[0203] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0204] p=[p1,…,p s ,…,p S ] T

[0205] q=[q1,…,q m ,…,q M ] T

[0206] In the formula, the superscript T represents the transposition operation; the superscript H represents the conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the beam total power scaling factor; q is the beam main lobe electric field strength; p is the beam side lobe electric field strength; x is the beam total electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe region; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

[0207] In this embodiment, in the variable solution optimization module 004, in the process of solving and optimizing the variables in the shaped beam maximizing directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting the solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

[0208] In this embodiment, in the original error maximum value calculation module 005, the expression of the original error is:

[0209]

[0210] In the formula, k is the number of iterations.

[0211] It should be noted that the information interaction, execution process and other contents between the modules of the above-mentioned system are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown above in the present application, and will not be repeated here.

[0212] Example 3

[0213] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code for an array antenna shaped beam gain optimization method with a constrained weight is stored. The program code includes instructions for executing embodiment 1 or any possible implementation method of the array antenna shaped beam gain optimization method with a constrained weight.

[0214] The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more available media. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0215] Example 4

[0216] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0217] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a constrained weight array antenna shaped beam gain optimization method of embodiment 1 or any possible implementation method thereof.

[0218] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor implemented by reading software codes stored in a memory. The memory can be integrated in the processor or can be located outside the processor and exist independently.

[0219] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium, or transmitted from a computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center.

[0220] Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing system, they can be concentrated on a single computing system, or distributed on a network composed of multiple computing systems, and optionally, they can be implemented by a program code executable by a computing system, so that they can be stored in a storage system and executed by the computing system, and in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

[0221] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made on the basis of the present invention. Therefore, these modifications or improvements made on the basis of not departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A method for optimizing the gain of an array antenna shaped beam with constrained weights, characterized in that: include: According to the set target, set the array structure and target shaped beam parameters; According to the relationship between weight and directivity coefficient, a weight optimization model for shaped beam maximization directivity coefficient is constructed; Acquiring initial array weights according to a target beam main lobe width in the target shaped beam parameters; The variables in the shaped beam maximization directivity coefficient weight optimization model are solved and optimized by an alternating direction multiplier method to obtain an optimization result; According to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation; Compare the original error with a set error threshold, and if the original error is less than the set error threshold, stop iterative calculation and output the final array element weight; If the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

2. The method for optimizing the gain of an array antenna shaped beam with constrained weights according to claim 1, characterized in that: The array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

3. The method for optimizing the gain of an array antenna shaped beam with constrained weights according to claim 2, characterized in that: In the process of constructing the shaped beam maximizing directivity coefficient weight optimization model, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through the auxiliary variable method and the augmented Lagrange multiplier method; the multivariable model is the shaped beam maximizing directivity coefficient weight optimization model; The expression of the shaped beam maximization directivity coefficient weight optimization model is: s.t.1≤|q m | 2 ≤a mll |p s |≤a sll ||x|| 2 ＝1 L ω ≤|v n |≤U ω m=1,2,…,M s=1,2,…,S n=1,2,…,N A q =[a(θ1),…,a(θ m ),…,a(θ M )] A p =[a(θ1),…,a(θ s ),…,a(θ S )] p=[p1,…,p s ,…,p S ] T q=[q1,…,q m ,…,q M ] T In the formula, the superscript T represents the transposition operation; the superscript H represents the conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables respectively; M, S, and N are the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements respectively; μ is the weight scaling factor; x is the total beam power scaling factor; q is the electric field strength of the main lobe of the beam; p is the electric field strength of the side lobe of the beam; and x is the total electric field strength of the beam; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe region; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

4. The method for optimizing the shaped beam gain of an array antenna with constrained weights according to claim 3, characterized in that: In the process of solving and optimizing the variables in the shaped beam maximizing directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

5. The method for optimizing the shaped beam gain of an array antenna with constrained weights according to claim 4, characterized in that: The expression of the original error is: In the formula, k is the number of iterations.

6. A device for optimizing the shaped beam gain of an array antenna with a constraint weight, using a method for optimizing the shaped beam gain of an array antenna with a constraint weight as claimed in any one of claims 1 to 5, characterized in that: include: An array parameter setting module is used to set the array structure and target shaped beam parameters according to the set target; A module for constructing a shaped beam maximizing directivity coefficient weight optimization model, which is used to construct a shaped beam maximizing directivity coefficient weight optimization model according to a relationship between the weight and the directivity coefficient; An initial array weight acquisition module is used to acquire initial array weights according to the target beam main lobe width in the target shaped beam parameters; A variable solving and optimization module is used to solve and optimize the variables in the shaped beam maximization directivity coefficient weight optimization model by an alternating direction multiplier method to obtain an optimization result; An original error maximum value calculation module is used to calculate the original error of the variable according to the optimization result; and obtain the original error maximum value by calculation according to the original error; A final array element weight acquisition module is used to compare the original error with a set error threshold, and if the original error is less than the set error threshold, stop iterative calculation and output the final array element weight; If the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

7. The device for optimizing array antenna shaped beam gain with constrained weights according to claim 6, characterized in that: In the array parameter setting module, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

8. The device for optimizing the gain of an array antenna shaped beam with constrained weights according to claim 7, characterized in that: In the shaped beam maximization directivity coefficient weight optimization model construction module, in the process of constructing the shaped beam maximization directivity coefficient weight optimization model, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through the auxiliary variable method and the augmented Lagrange multiplier method; the multivariable model is the shaped beam maximization directivity coefficient weight optimization model; The expression of the shaped beam maximization directivity coefficient weight optimization model is: s.t.1≤|q m | 2 ≤a mll |p s |≤a sll ||x|| 2 ＝1 L ω ≤|v n |≤U ω m=1,2,…,M s=1,2,…,S n=1,2,…,N A q =[a(θ1),…,a(θ m ),…,a(θ M )] A p =[a(θ1),…,a(θ s ),…,a(θ S )] p=[p1,…,p s ,…,p S ] T q=[q1,…,q m ,…,q M ] T In the formula, the superscript T represents the transposition operation; the superscript H represents the conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables respectively; M, S, and N are the number of spatial sampling within the main lobe range, the number of spatial sampling within the side lobe range, and the number of array elements respectively; μ is the weight scaling factor; x is the total beam power scaling factor; q is the electric field strength of the main lobe of the beam; p is the electric field strength of the side lobe of the beam; and x is the total electric field strength of the beam; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe region; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

9. The device for optimizing the gain of an array antenna shaped beam with constrained weights according to claim 8, characterized in that: In the variable solution optimization module, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

10. The device for optimizing array antenna shaped beam gain with constrained weights according to claim 9, characterized in that: In the original error maximum value calculation module, the expression of the original error is: In the formula, k is the number of iterations.

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