A method and system for pre-phase loaded sparse phased array synthesis

Abstract

The application discloses a kind of pre-phase loaded sparse phased array comprehensive design method and system, the present application is based on the expected beam requirement, first maximizes sparse rate under accurate feed phase, and selected unit is recovered to expected sparse rate;Subsequently, the dynamic range ratio of amplitude is minimized, to obtain the amplitude distribution of low dynamic range ratio;Then under rounding feed phase, pre-phase distribution is optimized, to preliminarily reduce side lobe;After amplitude and pre-phase meet the convergence condition, the state of phase shifter is optimized again, to further lower side lobe, obtain the phase shifter state distribution with lowest side lobe and its corresponding feed phase distribution.The present application overcomes the problem of high gain loss and high side lobe of traditional sparse phased array in low resolution phase control, reduces the gain loss of sparse array by using low dynamic range ratio amplitude control, reduces side lobe by loading low resolution phase control of pre-phase, saves chip by sparse array, thereby reduces complexity and reduces cost.

Description

Technical Field

[0001] This invention belongs to the field of phased array antenna technology, and specifically relates to a comprehensive design method and system for sparse phased arrays with pre-phase loading. It solves the problems of high sidelobes and high gain loss in traditional low-resolution phased sparse arrays, and reduces the complexity and cost of phased array antennas. Background Technology

[0002] Phased array antennas typically employ numerous high-resolution phase shifters to achieve high-gain, low-sidelobe beam scanning. However, the large number of high-resolution phase shifters also presents challenges in terms of complexity and cost, especially in large-scale arrays and above the millimeter-wave band. Replacing a full-scale high-resolution phased array with a sparse, low-resolution phased array while maintaining high gain and low sidelobe beam scanning capability can reduce complexity through the use of low-resolution phase shifters and lower costs by saving on chip count through sparse array placement. However, current low-resolution phased arrays still suffer from high gain loss and high sidelobe issues, which significantly limits their application scope. Summary of the Invention

[0003] Purpose of the invention: To address the problems in the prior art, the present invention aims to propose a comprehensive design method and system for sparse phased arrays with pre-phase loading. By jointly optimizing the excitation amplitude distribution, pre-phase distribution, and phase shifter state, high-gain and low-sidelobe beam scanning can be achieved, thereby reducing the complexity and cost of phased array antennas.

[0004] Technical Solution: To achieve the above objectives, this invention provides a method for synthesizing and designing sparse phased arrays with pre-phase loading, comprising the following steps:

[0005] Step 1: Input the maximum elevation angle θ of the desired beam pointing. Max The expected sparsity R′, expected sidelobes g′, expected half-power beamwidth h′, expected main lobe width l′, the number of phase shifters Q, and the number of pre-phase types P are used to comprehensively design the excitation amplitude w of the (m,n)th unit with the smallest sidelobes. mn Pre-phase Phase shifter status Make the sidelobe within the scanning range lower than the expected sidelobe g′;

[0006] Step 2: Maximizing sparsity under precise phase feeding Where M×N is the number of sparse phased array elements loaded with pre-phase, and ||·||0 represents the 0 norm;

[0007] Step 3: Select the retained cells and restore them to the expected sparsity R′. At this point, the excitation amplitude of the (m,n)th cell is w″. mn ;

[0008] Step 4: Under precise phase feeding, minimize the dynamic range ratio of the amplitude to obtain the amplitude distribution with a low dynamic range ratio. At this time, the excitation amplitude of the (m,n)th element is...

[0009] Step 5: Under rounding-off phase feeding, optimize the pre-phase distribution with the goal of minimizing sidelobes to initially reduce sidelobes and obtain the pre-phase distribution.

[0010] Step 6: Determine if the convergence condition is met. If the convergence condition is not met, return to Step 3. If the convergence condition is met, proceed to Step 7.

[0011] Step 7: Amplitude distribution obtained in step 4 And the pre-phase distribution obtained in step 5 Optimize the state of the phase shifter Further reducing the sidelobes yields the phase shifter state distribution with the lowest possible sidelobes.

[0012] Preferably, in step 1, the comprehensive design problem is expressed as:

[0013]

[0014]

[0015] R(w 11 ,w 12 ,…,w MN )=R′

[0016]

[0017]

[0018] in, Indicates the expected beam's elevation and azimuth angles; This represents the half-power beamwidth when the beam direction is (0°, 0°); This represents the main lobe width when the beam direction is (0°, 0°).

[0019] Preferably, in step 2, the constraint corresponding to the precise feed is expressed as:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] in, These represent the elevation and azimuth angles of the expected beam, respectively. These respectively represent the expected beam pointing direction. At that time, the expected beam pointing region, the region outside the half-power lobe width in the main lobe, and the radiation pattern of the region where the side lobes are located; h represents the half-power lobe width; l represents the main lobe width; α mn Indicates the feed phase of the (m,n)th cell; x mn y mn λ represents the x-coordinate and y-coordinate of the (m,n)th element, respectively; λ is the wavelength of the sparse phased array operating frequency in air.

[0027] Preferably, in step 2, the sparsity rate is maximized using the reweighted l1 norm method, and the optimization problem is expressed as:

[0028]

[0029]

[0030]

[0031]

[0032] (U0,V0)=(0,0)

[0033] sin 2 (h′ / 2)≤(U B 2 +V B 2 )≤sin 2 (l′ / 2)

[0034] sin 2 (l′ / 2)≤(U S 2 +V S 2 )≤(1+sinθ Max ) 2

[0035] Among them, w mn,k w mn,k+1 These represent the excitation amplitudes of the (m,n)th unit in the k-th and (k+1)-th iterations, respectively; ε is a very small positive number, and w will be less than ε in each iteration. mn,k Set to 0; For unit radiation pattern The expression in the sinusoidal coordinate system (U,V), (U0,V0), (U B V B ), (U S V S ) are respectively Representation in a sinusoidal coordinate system.

[0036] Preferably, in step 3, the selected and retained units are optimized using a swarm intelligence algorithm.

[0037] Preferably, in step 4, the optimization objective of minimizing the dynamic range ratio of the amplitude is expressed as:

[0038]

[0039] Among them, w″ Max and w″ Min They are {w″ 11 ,w″ 12 ,…,w″ MN The maximum and minimum values ​​among all non-zero elements in}.

[0040] As a preferred approach, the problem of pre-phase optimization is expressed as:

[0041]

[0042]

[0043] θ0∈{0°,Δθ0,Δθ0×2,…,θ Max}

[0044]

[0045] in, This indicates the quantized phase shifter state under rounded-off feed conditions. Indicates the incentive magnitude Pre-phase Phase shifter status The lower sidelobe, Δθ0, This is the quantization interval.

[0046] Preferably, in step 7, the problem of optimizing the phase shifter state is expressed as:

[0047]

[0048] in, Indicates the incentive magnitude Pre-phase Phase shifter status The lower side lobe.

[0049] Preferably, a swarm intelligence algorithm is used to optimize the pre-phase distribution in step 5 and the phase shifter state distribution in step 7.

[0050] Based on the same inventive concept, the present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when loaded onto the processor, implements the steps of a pre-phase sparse phased array synthesis design method.

[0051] Beneficial effects: Compared with the prior art, this invention proposes a comprehensive design method for sparse phased arrays with pre-phase loading. On the one hand, by using an amplitude distribution with a low dynamic range ratio, this invention makes the aperture surface electric field more uniform, thereby successfully reducing the gain loss caused by low-resolution phased arrays. On the other hand, by loading pre-phase, this invention makes the feeding phase of the low-resolution phased sparse array close to the phase of a precise feeding phase, thereby successfully overcoming the high sidelobes caused by low-resolution phased arrays. Compared with traditional phased arrays, this invention achieves high gain and low sidelobes close to a full-scale, precisely-fed array in a low-resolution phased sparse array. It not only reduces complexity by using low-resolution chips, but also saves chips and reduces costs through sparse array arrangement. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the overall steps of the method according to an embodiment of the present invention.

[0053] Figure 2 This is a structural schematic diagram of an embodiment of the present invention.

[0054] Figure 3 This is a schematic diagram of the array distribution in an embodiment of the present invention.

[0055] Figure 4 This is a schematic diagram of the traditional full-array amplitude distribution.

[0056] Figure 5 This is a schematic diagram of the amplitude distribution of the maximized sparsity obtained in step 2 of this embodiment of the invention.

[0057] Figure 6 This is a schematic diagram of the amplitude distribution of the recovery to the expected sparsity obtained in step 3 of the embodiment of the present invention.

[0058] Figure 7 This is a schematic diagram of the amplitude distribution of the minimized dynamic range ratio obtained in step 4 of this embodiment of the invention.

[0059] Figure 8 This is a schematic diagram of the pre-phase distribution obtained in step 5 of an embodiment of the present invention.

[0060] Figure 9This is the sparse phased array with pre-phase loading designed according to the embodiments of the present invention. Gain loss curves during scanning and their comparison graphs.

[0061] Figure 10 This is the sparse phased array with pre-phase loading designed according to the embodiments of the present invention. Sidelobe curves during scanning and their comparison images.

[0062] Figure 11 This is the sparse phased array with pre-phase loading designed according to the embodiments of the present invention. The half-power beamwidth (i.e., 3-dB beamwidth) curve during scanning and its comparison graph. Detailed Implementation

[0063] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0064] like Figure 1 As shown in the figure, this invention discloses a method for synthesizing sparse phased arrays with pre-phase loading. By jointly optimizing the excitation amplitude distribution, pre-phase distribution, and phase shifter states, it achieves high-gain and low-sidelobe beam scanning, thereby reducing the complexity and cost of the phased array antenna. To facilitate understanding of the specific implementation steps, the relevant technical background is first introduced:

[0065] For a sparse phased array with M×N elements and pre-phase loading, a Q-bit phase shifter is used to load P types of pre-phase {Y1,Y2,…,Y}. s ,…,Y P The operating wavelength is λ, and its structure is as follows: Figure 2 As shown, its array arrangement is as follows Figure 3 As shown, the radiation pattern of this array antenna is... It can be represented as

[0066]

[0067] Here θ is the pitch angle in free space and The azimuth angle in free space and For the unit radiation pattern; x mn Let y be the x-coordinate of the (m,n)th cell, where m = 1, 2, ..., M, n = 1, 2, ..., N; mn w is the ordinate of the (m,n)th cell; mn λ is the excitation amplitude of the (m,n)th unit; λ is the wavelength of the sparse phased array operating frequency in air; The prephase loaded for the (m,n)th element, Y sFor the s-th prephase, For the expected beam pointing The feed phase of the (m,n)th unit, θ0∈[0,θ Max ], θ Max The maximum elevation angle for the expected beam pointing. Feed phase. Determined by the expected beam direction The state of the (m,n)th Q-bit phase shifter Right now The phase shift interval of the Q-bit phase shifter. sparsity R(w) 11 ,w 12 ,…,w MN It can be defined as: R(w 11 ,w 12 ,…,w MN It depends only on the incentive magnitude w mn The distribution. The dynamic range of the amplitude is greater than that of D(w). 11 ,w 12 ,…,w MN It can be defined as: w Max and w Min They are {w 11 ,w 12 ,…,w MN The maximum and minimum values ​​of non-zero elements in}, D(w 11 ,w 12 ,…,w MN It depends only on the incentive magnitude w mn The distribution of the M×N element. Therefore, the radiation pattern of the pre-phased sparse phased array is determined only by the excitation amplitude w of the (m,n)th element. mn Pre-phase Phase shifter status Directional chart Side lobe Half-power beamwidth and main lobe width The same parameters are also determined only by w. mn , and

[0068] Directional chart Side lobe The calculation formula is:

[0069] here For the expected beam pointing At that time, the direction chart A series of maxima and satisfying

[0070] Directional chart half-power beamwidth The calculation formula is: here and All are within the main lobe and satisfy the following conditions: θ 3dB_Max ≥θ 3dB_Min .

[0071] Directional chart main lobe width The calculation formula is:

[0072] here and All are within the main lobe and satisfy the following conditions: and for The minimum value of .

[0073] We need to be at the maximum elevation angle θ of the expected beam pointing. Max Under the constraints of sparsity R′, normal half-power lobe width h′, and normal main lobe width l′, the minimum sidelobe w is synthesized. mn , and Make the side lobes within the scanning range As low as possible below the expected sidelobe g′, i.e.:

[0074]

[0075]

[0076] R(w 11 ,w 12 ,…,w MN )=R′

[0077]

[0078]

[0079] Based on the above design objectives, this invention discloses a method for synthesizing sparse phased arrays with pre-phase loading, which specifically includes the following steps:

[0080] Step 1: Input the maximum elevation angle θ of the desired beam pointing. MaxExpected sparsity R′, expected sidelobe g′, expected normal (i.e., Half-power beamwidth h′, expected normal main lobe width l′, number of phase shifters Q, and number of pre-phase types P;

[0081] Step 2: Maximize the sparsity R(w) under precise phase feeding. 11 ,w 12 ,…,w MN At this point, the excitation amplitude of the (m,n)th unit is w′. mn ;

[0082] Step 3: Select the retained cells and restore them to the expected sparsity R′. At this point, the excitation amplitude of the (m,n)th cell is w″. mn ;

[0083] Step 4: Under precise phase feeding, minimize the dynamic range ratio of the amplitude to obtain the amplitude distribution with a low dynamic range ratio. At this time, the excitation amplitude of the (m,n)th element is...

[0084] Step 5: Under rounding-off phase feeding, optimize the pre-phase distribution with the goal of minimizing sidelobes. To initially reduce the sidelobe;

[0085] Step 6: Determine if the convergence condition is met. If the convergence condition is not met, return to Step 3. If the convergence condition is met, proceed to Step 7.

[0086] Step 7: Amplitude distribution obtained in step 4 and the pre-phase distribution obtained in step 5 Next, optimize the state of the phase shifter. Further reducing the sidelobes yields the phase shifter state distribution with the lowest possible sidelobes. and its corresponding feed phase distribution

[0087] Furthermore, in step 2, under precise phase feeding, maximizing the sparsity ratio can be expressed as:

[0088] (w′ 11 ,w′ 12 ,…w′ MN )=R(w 11 ,w 12 ,…w MN )

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] here The region outside the half-power lobe width in the main lobe. This refers to the region where the secondary lobe is located.

[0096] Furthermore, in step 2, under precise phase feeding, maximizing the sparsity using the reweighted l1 norm method can be expressed as:

[0097]

[0098]

[0099]

[0100]

[0101] (U0,V0)=(0,0)

[0102] sin 2 (h′ / 2)≤(U B 2 +V B 2 )≤sin 2 (l′ / 2)

[0103] sin 2 (l′ / 2)≤(U S 2 +V S 2 )≤(1+sinθ Max ) 2

[0104] here For unit radiation pattern The expression in the sinusoidal coordinate system (U,V), w mn,k Let ε represent the excitation amplitude of the (m,n)th unit in the k-th iteration. ε is a very small positive number, preferably ε = 0.00001. In each iteration, w that is less than ε will be used. mn,k Setting it to 0 will achieve the maximum sparsity of the array.

[0105] Furthermore, in step 3, the selected and retained units can be optimized using swarm intelligence algorithms to minimize sidelobes while restoring the sparsity. For example, the Particle Swarm Optimization-Genetic Algorithm (PSO-GA) is preferred, restoring the expected sparsity R′, i.e., the excitation amplitude of all (m,n) units is w″ at this point. mn Satisfying R(w″) 11 ,w″ 12 ,…w″ MN )=R′.

[0106] Furthermore, in step 4, under precise phase feeding, the amplitude {w″ is minimized using a convex optimization algorithm. 11 ,w″ 12 ,…w″ MN The dynamic range ratio of} is used to obtain the amplitude distribution of low dynamic range ratio. It can be represented as:

[0107]

[0108]

[0109]

[0110]

[0111] (U0,V0)=(0,0)

[0112] sin 2 (h′ / 2)≤(U B 2 +V B 2 )≤sin 2 (l′ / 2)

[0113] sin 2 (l′ / 2)≤(U S 2 +V S 2 )≤(1+sinθ Max ) 2

[0114] Here w″ Max and w″ Min They are {w″ 11 ,w″ 12 ,…,w″ MN The maximum and minimum values ​​among all non-zero elements in}.

[0115] Furthermore, in step 5, the excitation amplitude adopts... The state of the phase shifter under rounding feed. Using a fixed quantization method and Discretization is required, with pitch angle θ0 at 5° intervals and azimuth angle... A 22.5° interval is preferred, that is:

[0116]

[0117]

[0118] θ0∈{0°,5°,…,θ Max}

[0119]

[0120] Furthermore, in step 6, the convergence condition is not unique; it can be preferably set to a change in sidelobe of less than 0.1 dB over 20 consecutive generations.

[0121] Furthermore, in step 7, after convergence in step 6, the amplitude distribution obtained in step 4... and the pre-phase distribution obtained in step 5 The state of the phase shifter is optimized using a swarm intelligence algorithm. Further suppressing the sidelobe, i.e.

[0122]

[0123] This swarm intelligence algorithm is not unique; the PSO-GA algorithm can be used as the preferred choice.

[0124] The design effects of this invention embodiment are illustrated below with specific examples. In this embodiment, the maximum beam elevation angle is 60°, the expected sparsity is 25%, the expected sidelobes are -21dB, the expected half-power beamwidth is 3.56°, the main lobe width is 7.76°, the phase shifter bit number is 2, the pre-phase type number is 4, and a 90° rotationally symmetrical array distribution is used. The distance between array elements is half a wavelength, i.e. The unit radiation pattern is In addition, a 6-bit conventional full array with the same sidelobes and half-power beamwidth and a 2-bit conventional sparse array with the same sidelobes, half-power beamwidth and sparsity are used as comparison examples, and their amplitude distributions are as follows: Figure 4 and Figure 6 As shown.

[0125] Step 1: Input the maximum elevation angle θ of the desired beam pointing. Max=60°, expected sparsity R = 0.25, expected sidelobe g′ = -21dB, expected normal half-power beamwidth h′ = 3.56°, expected normal main lobe width l′ = 7.76°, phase shifter bit number Q = 2 and prephase type number P = 4;

[0126] Step 2: Under precise phase feeding, maximize the sparsity R(w) using the reweighted l1 norm method. 11 ,w 12 ,…,w MN At this point, the excitation amplitude w′ of the (m,n)th unit is... mn like Figure 5 As shown.

[0127] Step 3: Select the retained cells and restore them to the expected sparsity R′. At this point, the excitation amplitude w″ of the (m,n)th cell is... mn like Figure 6 As shown;

[0128] Step 4: Under precise phase feeding, use a convex optimization algorithm to minimize the dynamic range ratio of the amplitude to obtain the amplitude distribution with a low dynamic range ratio. At this time, the excitation amplitude of the (m,n)th unit is... like Figure 7 As shown;

[0129] Step 5: Under rounding-off phase feeding, optimize the pre-phase distribution using the PSO-GA algorithm with the goal of minimizing sidelobes. To initially reduce sidelobes, the pre-phase distribution is as follows: Figure 8 As shown;

[0130] Step 6: Determine if the convergence condition is met. If the convergence condition is not met, return to step 3. If the convergence condition is met, proceed to step 7. The convergence condition is that the sidelobe change is less than 0.1dB for 20 consecutive generations.

[0131] Step 7: Amplitude distribution obtained in step 4 and the pre-phase distribution obtained in step 5 The state of the phase shifter is optimized using a swarm intelligence algorithm. Further reducing the sidelobes yields the phase shifter state distribution with the lowest possible sidelobes. and its corresponding feed phase distribution

[0132] In this embodiment of the invention, the four types of pre-phase sparse phased arrays synthesized by this invention, when using a 2-bit phase shifter, achieve sidelobes far lower than those of traditional 2-bit sparse arrays, and are close to those of traditional 6-bit full arrays. Figure 9As shown. Compared to a traditional 6-bit full array, the sparse phased array with four pre-phase loading methods synthesized in this invention only experiences a 2dB decrease in gain loss when using a 2-bit phase shifter, while the traditional 2-bit sparse array experiences a 3.5dB decrease in gain loss. Figure 10 As shown. Compared to a traditional 6-bit full array, the four types of pre-phase sparse phased arrays synthesized in this invention have almost identical 3-dB beamwidths when using 2-bit phase shifters, such as... Figure 11 As shown. Therefore, compared to sparse phased arrays with the same low resolution, the pre-phased sparse phased array synthesized in this invention can achieve smaller gain loss and lower sidelobes, while having a half-power beamwidth close to that of a fully phased array, thereby reducing the complexity and cost of the phased array.

[0133] Based on the same inventive concept, the present invention discloses a computer system including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the steps of a pre-phase sparse phased array synthesis design method.

[0134] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for synthesizing and designing a sparse phased array with pre-phase loading, characterized in that, Includes the following steps: Step 1: Input the maximum elevation angle θ of the desired beam pointing. Max The expected sparsity R′, expected sidelobes g′, expected half-power lobe width h′, expected main lobe width l′, the number of phase shifters Q, and the number of pre-phase types P are used to comprehensively design the excitation amplitude w of the (m,n)th unit with the smallest sidelobes. mn Pre-phase Phase shifter status Make the sidelobe within the scanning range lower than the expected sidelobe g′; Step 2: Maximizing sparsity under precise phase feeding Where M×N is the number of sparse phased array elements loaded with pre-phase, and ||·||0 represents the 0 norm; Step 3: Select the retained cells and restore them to the expected sparsity R′. At this point, the excitation amplitude of the (m,n)th cell is w″. mn ; Step 4: Under precise phase feeding, minimize the dynamic range ratio of the amplitude to obtain the amplitude distribution with a low dynamic range ratio. At this time, the excitation amplitude of the (m,n)th element is... Step 5: Under rounding-off phase feeding, optimize the pre-phase distribution with the goal of minimizing sidelobes to initially reduce sidelobes and obtain the pre-phase distribution. Step 6: Determine if the convergence condition is met. If the convergence condition is not met, return to Step 3. If the convergence condition is met, proceed to Step 7. Step 7: Amplitude distribution obtained in step 4 And the pre-phase distribution obtained in step 5 Optimize the state of the phase shifter Further reducing the sidelobes yields the phase shifter state distribution with the lowest possible sidelobes.

2. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, In step 1, the comprehensive design problem is expressed as: R(w 11 ,w 12 ,…,w MN )=R′ in, Indicates the expected beam's elevation and azimuth angles; This represents the half-power beamwidth when the beam direction is (0°, 0°); This represents the main lobe width when the beam direction is (0°, 0°).

3. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, In step 2, the constraint corresponding to the precise feed is expressed as follows: in, These represent the elevation and azimuth angles of the expected beam, respectively. These respectively represent the expected beam pointing direction. At that time, the expected beam pointing region, the region outside the half-power lobe width in the main lobe, and the radiation pattern of the region where the side lobes are located; h represents the half-power lobe width; l represents the main lobe width; α mn Indicates the feed phase of the (m,n)th cell; x mn y mn λ represents the x-coordinate and y-coordinate of the (m,n)th element, respectively; λ is the wavelength of the sparse phased array operating frequency in air.

4. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 3, characterized in that, In step 2, the sparsity rate is maximized using the reweighted l1 norm method. The optimization problem is expressed as: (U0,V0)=(0,0) that 2 (h′ / 2)≤(U B 2 +V B 2 )≤that 2 (l′ / 2) sin 2 (l′ / 2)≤(U S 2 +V S 2 )≤(1+sinθ Max ) 2 Among them, w mn,k w mn,k+1 These represent the excitation amplitudes of the (m,n)th unit in the k-th and (k+1)-th iterations, respectively; ε is a very small positive number, and w will be less than ε in each iteration. mn,k Set to 0; For unit radiation pattern The expression in the sinusoidal coordinate system (U,V), (U0,V0), (U B V B ), (U S V S ) are respectively Representation in a sinusoidal coordinate system.

5. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, In step 3, the selected and retained units are optimized using a swarm intelligence algorithm.

6. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, In step 4, the optimization objective of minimizing the dynamic range ratio of the amplitude is expressed as: Among them, w″ Max and w″ Min They are {w″ 11 ,w″ 12 ,…,w″ MN The maximum and minimum values ​​among all non-zero elements in}.

7. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, In step 5, the problem of pre-phase optimization is expressed as: θ0∈{0°,Δθ0,Δθ0×2,…,θ Max } in, This indicates the quantized phase shifter state under rounded-off feed conditions. Indicates the incentive magnitude Pre-phase Phase shifter status The lower sidelobe, Δθ0, This is the quantization interval.

8. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, In step 7, the problem of optimizing the phase shifter state is expressed as follows: in, Indicates the incentive magnitude Pre-phase Phase shifter status The lower side lobe.

9. The method for synthesizing and designing a sparse phased array with pre-phase loading according to claim 1, characterized in that, The pre-phase distribution in step 5 and the phase shifter state distribution in step 7 are optimized using a swarm intelligence algorithm.

10. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the steps of the pre-phase loading sparse phased array synthesis design method according to any one of claims 1-9.

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