A Design Method of Phased Array Subarray Considering the Collaboration of Electric Control Parameters

Abstract

The present invention belongs to the field of information science and technology, and proposes a phased array sub-array design method considering the coordination of electronic control parameters. The method includes: 1) determining the radiation performance of the phased array sub-array to be designed, and defining binary selection variables to control the subordination relationship between array elements and sub-arrays; 2) introducing an auxiliary function to express the binary selection variables as a function of a new design variable χ; 3) continuousizing the new design variable χ so that the optimization design can be carried out efficiently; 4) constructing a penalty function for the new design variable χ; 5) establishing an optimization design model. By constructing a reasonable parametric model, the present invention transforms the phased array sub-array design problem into an unconstrained continuous problem, which is suitable for solving by gradient-based algorithms. By simultaneously optimizing the sub-array clustering variables and the electronic control parameters, the sub-array design problem is solved without reducing the feasible region.

Description

Technical Field

[0001] The present invention relates to the field of information science and technology, and in particular to a phased array sub-array design method considering the coordination of electronic control parameters. Background Art

[0002] Phased array antennas are widely used in communications, military and other fields. Generally speaking, the performance of phased array antennas is closely related to the number of array elements. The more array elements a phased array antenna has, the stronger its ability to control the radiation beam. Each array element of a traditional phased array antenna requires a set of transceiver components to feed it to control the feeding phase and feeding amplitude of this array element. When the number of array elements of a phased array antenna increases, the increase in transceiver components will bring about the problem of complex feeding network and sharply increased cost. In a phased array antenna, the array elements are grouped, and the array elements in each group are fed by a set of electronically controlled components to form a phased array sub-array. Phased array sub-arrays can effectively reduce costs and reduce the complexity of the feeding network while ensuring the radiation performance of the antenna.

[0003] The design problem of phased array subarrays is a difficult combinatorial optimization problem. The main difficulties are the following two points: 1) For a given number of array elements and the number of subarrays to be divided, even if the number of array elements and subarrays is small, there are too many feasible subarray combinations, that is, the solution space is very large; 2) This type of problem is a highly non-convex problem. The existing phased array subarray design methods include the design method based on the polynomial theory pointed out in Irregular Subarray Tiling via Heuristic Iterative Convex Relaxation Programming, and the design method based on the excitation matching strategy theory pointed out in A Fast Graph-Searching Algorithm Enabling the Efficient Synthesis of Sub-Arrayed Planar Monopulse Antennas. These methods are all solved after reducing the original feasible solution space, which may lose some subarray configurations with excellent performance. In addition, the above methods basically use intelligent algorithms to solve the problem. When solving such highly non-convex problems, intelligent algorithms have slow convergence speed and poor optimization ability. Moreover, for large-scale problems, intelligent algorithms are almost difficult to solve. This problem becomes more difficult when considering the coordinated design of electronic control parameters and sub-array configuration.

[0004] Therefore, the present invention studies a phased array sub-array design method considering the coordination of electronic control parameters. By constructing a reasonable parameterized model, this method transforms the phased array sub-array design problem into an unconstrained continuous problem, which is suitable for solving by gradient-based algorithms. By simultaneously optimizing the sub-array clustering variables and electronic control parameters, the sub-array design problem is solved without reducing the feasible solution space. Summary of the Invention

[0005] The object of the present invention is to provide a phased array sub-array design method considering the coordination of electronic control parameters in view of the deficiencies of the prior art.

[0006] To achieve the above object of the invention, the technical solution of the present invention is as follows:

[0007] A phased array sub-array design method considering the coordination of electronic control parameters, comprising the following steps:

[0008] Step 1: According to the radiation performance of the phased array sub-array to be designed, such as synthesizing a low sidelobe pencil beam, a shaped beam, etc., establish the following optimization model:

[0009]

[0010] Wherein, w is the subordinate relationship between the phased array elements and the sub-arrays; Ψ is the radiation performance objective function for synthesizing the phased array sub-array to be designed; AF is the radiation directivity coefficient of the phased array antenna:

[0011]

[0012] N is the total number of elements of the phased array, Q is the number of sub-arrays to be partitioned; w n , n , q , qn , n , q , qn , qn (n = 1,..., N; q = 1,..., Q) is a binary selection variable, w qn = 1 means that the nth element is partitioned into the qth sub-array, w qn = 0 means that the nth element is not partitioned into the qth sub-array; the feeding phase ψ of the sub-array q and the feeding amplitude I of the sub-array q are design variables, x n , y n , z n is the position of the element center in the phased array in the space rectangular coordinate system; (θ, φ) is the elevation angle and azimuth angle in the spherical coordinate system, j is the imaginary unit, and k is the wave number;

[0013] Step 2: Since any element is fed and excited by at most one electronic control component, for any element, introduce an auxiliary function to make the binary selection variable satisfy the constraint

[0014] The auxiliary function is:

[0015] where χ s ∈{-1, 1} (3)

[0016]

[0017] Q w = ceil(log2Q) (5)

[0018] The feeding phase ψ q , the feeding amplitude I q and χ s (s = 1, ..., Q w ) are new design variables; ξ qs is the coefficient of the variable χ s ; ceil is the ceiling function;

[0019] Step 3: The value of the design variable χ s in Step 2 is a discrete value of -1 or 1. Continuize the value of the design variable χ s so that χ s ∈[-1, 1];

[0020] Step 4: When χ s takes an intermediate value other than {-1, 1}, the design result will have a sub-array partition situation that does not meet the actual physical meaning. Add a penalty term to the objective function Ψ to make χ s tend to {-1, 1} during the optimization design process; the penalty term is:

[0021] f(χ) = ∑(1 - χ·χ) (6)

[0022] Step 5: Substitute the penalty term in Step 4 into the optimization model, define the minimization of the objective function Ψ, and the constraint condition is that the new design variables satisfy the upper and lower limits. Establish the final optimization model as follows:

[0023]

[0024] where p is the penalty factor;

[0025] Step 6: Calculate the first-order derivatives of the objective function Ψ in the final optimization model with respect to the new design variables ψ q , I q and χ s . Use the gradient algorithm to update the design variables, and determine the phased array sub-array configuration, feeding phase, and feeding amplitude according to the obtained design variable results.

[0026] In Step 5, the established optimization model is a two-layer optimization during the optimization solution process. The inner layer optimizes χ, ψ, and I, and the outer layer optimizes and updates the penalty factor. The penalty factor p starts from 0 and increases. The increasing strategy is p = 2 i(i = 1,...m), where i is the number of loops for outer layer optimization, and m is the maximum number of loops for outer layer optimization. The maximum number of loops for outer layer optimization is taken as 10.

[0027] Compared with the prior art, the present invention has achieved the following beneficial effects:

[0028] (1) The present invention provides a phased array sub - array design method considering the coordination of electronic control parameters. Different from the existing methods, the position information of each element is applied in the optimization design process, and there is no requirement for the arrangement form of the elements. Therefore, this method is not limited to planar uniform phased arrays.

[0029] (2) The present invention provides a phased array sub - array design method considering the coordination of electronic control parameters. The phased array sub - array design problem is transformed into an unconstrained continuous problem, which is suitable for solving by gradient - based algorithms.

[0030] (3) The present invention provides a phased array sub - array design method considering the coordination of electronic control parameters. By simultaneously optimizing the sub - array clustering variables and electronic control parameters, excellent sub - array configurations can be obtained without reducing the feasible solution space. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram showing the subordination relationship between the binary selection variable - controlled elements and sub - arrays in the present invention;

[0032] Figure 2 It is a schematic diagram showing the arrangement of elements of the phased array to be designed in Embodiment 1;

[0033] Figure 3 It is a schematic diagram showing the distribution of 32 sub - arrays in Embodiment 1, and the numbers represent the sub - array numbers to which the elements are assigned;

[0034] Figure 4 It is the radiation normalized direction pattern of the 32 - sub - array phased array in Embodiment 1;

[0035] Figure 5 It is a schematic diagram showing the distribution of sub - arrays with different numbers of sub - arrays in Embodiment 1; among them, (a) is a schematic diagram showing the distribution of 4 sub - arrays, (b) is a schematic diagram showing the distribution of 8 sub - arrays, (c) is a schematic diagram showing the distribution of 16 sub - arrays, and (d) is a schematic diagram showing the distribution of 64 sub - arrays; the numbers represent the sub - array numbers to which the elements are assigned. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0037] Note that the terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0038] The present invention proposes a phased array sub-array design method considering the coordination of electrical control parameters. The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0039] Embodiment 1

[0040] In this embodiment, it is considered to design a planar phased array sub-array, and the phased array antenna to be designed is a uniform full array antenna with one element. The feeding phases of each sub-array are selected as design variables, and the feeding amplitudes of each sub-array are equal, that is, the amplitudes do not participate in the design. The radiation performance objective function is set to minimize the sidelobe level of the pencil beam. The main radiation direction of the pencil beam is that both the elevation angle and the azimuth angle are 0°. The sidelobe region is set as: the azimuth angle range is from 0° to 360°, and the elevation angle range is from 12° to 90°. The element arrangement of the phased array antenna to be designed is shown in Figure 2 as shown.

[0041] Step 1: Determine that the number of elements of the phased array antenna structure to be designed is 144, as shown in Figure 2 as shown. The number of sub-arrays is set to 32. Define a binary selection variable w qn ∈{0, 1} to control the subordinate relationship between the elements and the sub-arrays. At this time, the radiation direction coefficient calculation formula of the phased array antenna is:

[0042]

[0043] where the binary variable w qn (n = 1,..., 144; q = 1,..., 32), the feeding phase ψ of the sub-array q . x n , y n are the positions of the elements in the phased array in the space rectangular coordinate system;

[0044] Step 2: Since any element is fed and excited by at most one set of electrical control components, there must be a constraint This constraint is difficult to strictly satisfy during the optimization process. Therefore, an auxiliary function is introduced, and for each element, there is:

[0045] where χ s ∈{-1, 1} (6)

[0046] wq expressed as a new variable χ s function, the constraints described in this step can be automatically and strictly satisfied. At this time, the feeding phase ψ q and χ s (s = 1,..., 5) are new design variables;

[0047] Step 3: For the new design variable χ s in Step 2 above, the value can only be -1 or 1. Since discrete variables are difficult to handle in the optimization process, the values of the discrete variables are made continuous. At this time, χ s ∈[-1, 1], and the optimization design can proceed smoothly;

[0048] Step 4: When χ s in Step 3 above takes an intermediate value other than {-1, 1}, the design result will show a sub-array partition situation that does not meet the actual physical meaning. Therefore, a penalty term is added to the objective function to force χ s to gradually tend to {-1, 1} during the optimization design process. The penalty function is;

[0049] f(χ) = ∑(1 - χ·χ) (7)

[0050] Step 5: Put the penalty function in Step 4 above into the optimization formulation, define the objective function as the minimum, and the constraint condition is that the design variables satisfy the upper and lower limits. The optimization model is established as follows:

[0051]

[0052] where Φ is the objective function and p is the penalty factor.

[0053] Step 6: Calculate the first-order derivative of the objective function with respect to the design variables, and use the sequential quadratic programming algorithm to update the design variables to complete the design of the phased array sub-array, and obtain the radiation performance parameter table of the designed phased array sub-array.

[0054] Table 1 Radiation performance parameter table of phased array sub-arrays under different numbers of sub-arrays

[0055]

[0056] The above is only the preferred embodiment of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A design method for a phased array sub - array considering the coordination of electronic control parameters, characterized in that, The phased subarray design method includes the following steps: Step 1: According to the radiation performance of the phased subarray to be designed, establish the following optimization model: where w is the subordination relationship between the phased array elements and the subarray; Ψ is the radiation performance objective function for synthesizing the phased subarray to be designed; AF is the radiation directivity coefficient of the phased array antenna: N is the total number of array elements of the phased array, and Q is the number of sub - arrays to be divided; w qn (n = 1,..., N; q = 1,..., Q) is a binary selection variable, w qn = 1 means that the nth array element is divided into the qth sub - array, w qn = 0 means that the nth array element is not divided into the qth sub - array; the feeding phase ψ q and the feeding amplitude I q of the sub - array are design variables, x n , y n , z n are the positions of the array element centers in the phased array in the space rectangular coordinate system; (θ, φ) are the elevation angle and azimuth angle in the spherical coordinate system, j is the imaginary unit, and k is the wave number; Step 2: For any array element, introduce an auxiliary function and make the binary selection variable satisfy the constraint The auxiliary function is: Q w = ceil(log2Q) (5) Feed phase ψ q , feed amplitude I q and χ s (s = 1, ..., Q w ) are new design variables; ξ qs is the coefficient of variable χ s ; ceil is the ceiling function; Step 3: The design variable χ in Step 2 s takes discrete values of -1 or 1. Continuize the value of the design variable χ s so that χ s ∈[-1, 1]; Step 4: χ in Step 3 s When taking an intermediate value other than {-1, 1}, add a penalty term to the objective function Ψ to make χ s tend to {-1, 1} during the optimization design process; the penalty term is: f(χ) = ∑(1 - χ·χ) (6) Step 5: Substitute the penalty term in Step 4 into the optimization model, define the minimization of the objective function Ψ, and the constraint condition is that the newly designed variables satisfy the upper and lower limits, and establish the final optimization model as follows: where p is the penalty factor; Step 6: Calculate the first-order derivatives of the objective function Ψ in the final optimized model with respect to the new design variables ψ q , I q and χ s , update the design variables using the gradient algorithm, and determine the phased array subarray configuration, feeding phase, and feeding amplitude according to the obtained design variable results.

2. The design method for a phased array sub - array considering the coordination of electronic control parameters according to claim 1, characterized in that, In the said step 5, the penalty factor p increases starting from 0, and the increasing strategy is p = 2 i (i = 1,...m), where m is not greater than 10.

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