A channel power equalization subarray division method applied to a satellite-borne transmitting phased array

Abstract

The application discloses a channel power equalization subarray division method applied to a satellite-borne transmitting phased array and belongs to the satellite-borne transmitting phased array technology.The application can obtain the highest EIRP under the same array aperture while reducing the sidelobe and does not need to optimize the amplitude and phase of the subarray level, thereby reducing the optimization complexity.Meanwhile, the application can realize the accurate division of the array surface under a specific channel number.The method can provide a certain amplitude freedom degree while ensuring the full channel power input through the power equalization strategy of the subarray level, can reduce the sidelobe while ensuring the EIRP, and can be effectively applied to the satellite transmitting phased array.

Description

Technical Field

[0001] This invention relates to spaceborne phased array technology, and more particularly to a method for dividing the channel power into equal-mode arrays for use in spaceborne phased arrays. Background Technology

[0002] In low-Earth orbit satellite communication systems, onboard phased arrays need to achieve global coverage through wide-angle scanning. However, traditional phased arrays have a large number of channels, posing challenges related to space and heat dissipation. To address this issue, irregular subarray technology has emerged, becoming a research hotspot in the field of array integration due to its significant cost reduction advantage. Irregular subarray technology, by scrambling the phase center and arranging the array irregularly, can reduce the number of array channels (transceiver components) while suppressing grating lobes. In the irregular subarray partitioning method of planar phased arrays, the subarray forms mainly include overlapping subarrays and non-overlapping subarrays. Non-overlapping subarrays are further divided into multi-dominant (adjacent subarrays) and non-adjacent subarray forms.

[0003] For example, with Taking a planar phased array antenna as an example, along Directional unit spacing is The number of array elements is ,along Directional unit spacing is The number of array elements is Then the far-field radiated electric field of the phased array antenna is:

[0004] (1)

[0005] In the formula, Representative unit radiation pattern, Representing the The excitation amplitude and phase of each unit, The imaginary unit, For the first The excitation phase of each unit, , Represents spherical coordinate system to The mapping of coordinate systems, where, These are the pitch angle and the azimuth angle, respectively. , Represents wavelength.

[0006] The far-field directivity coefficient can be defined as:

[0007] (2)

[0008] in, Indicates the desired beam direction.

[0009] Equations (1) and (2) can both be simplified to matrix form.

[0010] (3)

[0011] (4)

[0012] in , Antenna gain can be expressed as:

[0013] (5)

[0014] in, This represents the antenna's radiation efficiency. for The abbreviation, considering the antenna element as an ideal point source radiation efficiency The equivalent isotropic radiated power (EIRP) of the array can be expressed as:

[0015] (6)

[0016] Currently, the optimization problem of subarrays can be solved using subarray rotation algorithms or maximum entropy model algorithms, specifically as follows:

[0017] The optimization problem of subarray rotation algorithm for subarray partitioning can be described as:

[0018] (7)

[0019] in, Represents the main lobe region. Represents the sidelobe region. This represents the number of sub-formations on the battle surface. Representing the Number of phase centers in a row, Representing the Number of phase centers of the column, This is a preset constant.

[0020] Solving this problem using a subarray rotation algorithm yields the result of partitioning non-adjacent subarrays. By performing excitation amplitude and phase synthesis on the partitioned result, the following pattern synthesis problem can be established:

[0021] (8)

[0022] in, Represents the predefined peak sidelobe level. Representing the sidelobe region, this problem is a typical second-order cone programming problem, which can be solved using the interior point method.

[0023] However, in the subarray rotation algorithm, non-adjacent subarrays need to undergo amplitude and phase optimization after the array surface partitioning solution, which will cause a sharp drop in EIRP. At the same time, the dynamic range of the excitation amplitude will also affect the radiation efficiency of the array, resulting in a decrease in gain and thus a deterioration in EIRP.

[0024] The optimization model for irregular subarray arrangement based on the maximum entropy principle can be described as follows:

[0025] (9)

[0026] in, This represents the theoretical upper limit of array information entropy. and Representing the first Line number Number of phase centers on the column, The total number of array subarrays is determined using a genetic algorithm. After obtaining the array surface partitioning results, excitation amplitude and phase optimization is performed. The optimization problem is as follows:

[0027] (10)

[0028] in, As slack variables, For a predefined standard radiation pattern, The matrix L2 norm represents the problem, which is a typical second-order cone programming problem and can be solved using the interior point method.

[0029] However, in this solution method, after the array is divided, the amplitude and phase need to be optimized, which will cause the EIRP to drop sharply. At the same time, the dynamic range of the excitation amplitude will also affect the radiation efficiency of the array, resulting in a decrease in gain and thus a deterioration of EIRP. Summary of the Invention

[0030] This invention proposes a channel power equalization subarray partitioning method for spaceborne phased arrays. Based on a hybrid subarray form with channel power control, it only uses array topology optimization, avoiding the problem of reduced equivalent omnidirectional radiation power caused by amplitude and phase optimization. This invention can control the number of array channels, and compared with existing methods, it can achieve higher equivalent omnidirectional radiation power in the scanning spatial domain.

[0031] The technical solution adopted in this invention is: a method for dividing the channel power equalization array of a phased array for spaceborne transmission, which includes the following steps:

[0032] The optimization problem of array surface partitioning for constructing a spaceborne phased array:

[0033] (11)

[0034] The subarray types of the array include: unit subarray, double subarray and quadruple subarray; the double subarray and quadruple subarray include a variety of arrangement forms. This is a binary integer variable; 0 indicates that the current subarray is not selected for placement on the array, and 1 indicates that the current subarray is selected for placement on the array. h represents the total number of possible subarray arrangements. For amplitude-constrained slack variables, For phase-constrained slack variables, L represents the possible arrangements of all types of subarrays on the plane, and L represents the total number of array elements on the array surface (i.e., the array size). For the preset expected amplitude distribution, and Indicates azimuth angle and The expected phase distribution at the maximum scanning angle under the cross section. This indicates the preset number of channels. Representing the Seed array, in which, 1 represents a single subarray, 2 represents a two-column subarray, and 3 represents a four-column subarray. Representing the first on the field The minimum number of subarrays; Z is the set of integers.

[0035] The optimization problem is solved using a solver, and the array partitioning result is obtained based on the solution.

[0036] Based on the array surface division results, the far-field electric field and equivalent isotropic radiation power of the array are calculated; and the beam scanning of the array is achieved through phase modulation of the subarray level. For example, the far-field electric field and equivalent isotropic radiation power (EIRP) of the array are calculated directly through formulas (3) and (6); in this invention, beam synthesis in the desired target direction is achieved through phase modulation of the subarray level, thereby realizing the beam scanning of the array, wherein the phase modulation of the subarray level is obtained according to the traditional method of compensating for the relative path difference in the target direction.

[0037] Furthermore, the arrangement of the two-unit subarrays adopts a linear arrangement, including horizontal and vertical arrangements; the arrangement of the four-unit subarrays includes: 2×2 square array, L-shaped structure, T-shaped structure, staggered structure and linear arrangement.

[0038] Furthermore, the average channel power allocation within each element of each subarray is as follows:

[0039] (12)

[0040] in, Let be the amplitude of the s-th subarray. For input channel power, Let be the number of elements contained within the s-th subarray. Let be the phase of the s-th subarray. Let be the propagation constant. Let be the phase center position of the s-th subarray. Let be the scanning pointing angle of the s-th subarray.

[0041] Meanwhile, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the channel power equalization array partitioning method for spaceborne phased arrays provided by the present invention.

[0042] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program / instructions thereon, characterized in that the computer program / instructions, when executed by a processor, implement the steps of a channel power equalization array partitioning method applied to a spaceborne transmission phased array.

[0043] The technical solution provided by this invention brings at least the following beneficial effects:

[0044] This invention can reduce sidelobes while ensuring full-channel power output, achieving the highest EIRP for the same array aperture (array size). It also eliminates the need for amplitude and phase optimization at the subarray level, reducing optimization complexity. Furthermore, it enables precise array division with a specific number of channels. The proposed method, through a subarray-level power equalization strategy, provides a certain degree of amplitude freedom while ensuring full-channel power input, reducing sidelobes while maintaining EIRP, and can be effectively applied to phased arrays for satellite launches. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of the launch channel;

[0047] Figure 2 The diagram shows the subarray division, where (2a) is a schematic diagram of the satellite-borne phased array scanning; and (2b) is a schematic diagram of the channel power equalization subarray structure.

[0048] Figure 3 This is a schematic diagram of the 16×16 array division result;

[0049] Figure 4 A comparison of EIRP array arrangements with scanning angle for the same number of channels;

[0050] Figure 5 The normalized radiation pattern and subarray amplitude and phase distribution are shown below; where (5a) is the normalized radiation pattern scanned to (35°, 0°); (5b) is the normalized radiation pattern scanned to (55°, 0°); (5c) is the amplitude distribution scanned to (35°, 0°); (5d) is the amplitude distribution scanned to (55°, 0°); (5e) is the phase distribution scanned to (35°, 0°); and (5f) is the phase distribution scanned to (55°, 0°).

[0051] Figure 6 The graph shows the variation of EIRP with scanning angle for different cross sections;

[0052] Figure 7 This is a schematic diagram showing the EIRP variation with scanning angle for different channel numbers. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be described in detail and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Generally, the components of the embodiments of the present invention described and shown in the accompanying drawings can be arranged and designed using different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the present invention.

[0054] Existing methods for partitioning sparse arrays and irregular subarrays mostly focus on two aspects: array structure optimization and amplitude / phase control. First, the topology of the entire array surface is optimized, and then the amplitude and phase are calculated based on the current array surface. This approach can reduce array sidelobes and improve scanning performance. However, because the array excitation amplitude is reduced after sidelobe control, it significantly affects the equivalent isotropic radiation power of the array scan. To address this issue, this invention proposes a channel power-equalized subarray partitioning method for spaceborne phased arrays. This method uses a hybrid subarray configuration with channel power control, employing only array topology optimization to avoid the decrease in equivalent isotropic radiation power caused by amplitude / phase optimization.

[0055] like Figure 1As shown, the equivalent isotropic radiated power (EIRP) is a core indicator of spaceborne phased arrays, determined by the array's input power and gain. Due to satellite resource and power consumption constraints, full-channel output spaceborne phased arrays generate significant heat, substantially impacting satellite resource consumption. To comprehensively consider the power consumption and performance of spaceborne phased arrays, subarray technology has emerged. However, existing methods require further amplitude and phase optimization of the array surfaces after subarray division. Although amplitude and phase optimization can reduce array sidelobes and improve directivity, it significantly affects channel power.

[0056] like Figure 2 As shown in (2a), the onboard phased array used in low Earth orbit satellites usually needs to achieve global coverage. Its coverage angle can be calculated from the altitude above the ground, and the calculation formula is as follows:

[0057] (13)

[0058] in, The elevation angle scan coverage area of ​​the phased array for spaceborne launch. It is the Earth's radius (approximately 6371 km). This refers to the altitude of a low-Earth orbit satellite above the Earth's surface. Taking low Earth orbit satellites as an example (LEO satellite orbital distance) (Unit: km), its scanning coverage requirement is .

[0059] Figure 2 (2b) in the figure refers to the channel power equalization subarray proposed in the embodiment of the present invention, which includes single-unit subarray, double-unit subarray and quadruple-unit subarray. The channel power is evenly distributed among the units in the subarray. The specific calculation formula is as follows:

[0060] (14)

[0061] in, Let be the amplitude of the s-th subarray. For input channel power, Let be the number of elements contained within the s-th subarray. Let be the phase of the s-th subarray. Let be the phase center position of the s-th subarray. The scanning angle.

[0062] like Figure 2As shown in (2b), a single-unit subarray consists of only one unit, a two-unit subarray consists of two units, and a four-unit subarray consists of four units. The two-unit subarray is arranged linearly, either horizontally or vertically. The four-unit subarray can have various arrangement forms, such as a 2×2 square matrix, an L-shaped matrix (e.g., three units vertically and one horizontally), a T-shaped matrix, a staggered matrix (two units in each of the two columns, but the two columns are not aligned), and linear matrices in different directions.

[0063] To achieve precise array division, and simultaneously make the amplitude of array division fit the desired amplitude distribution. The optimization problem can be established as

[0064] (15)

[0065] in, This is a binary integer variable, where "0" represents not selecting the current subarray to place on the array, and "1" represents selecting the current subarray to place on the array. h is the total number of possible subarray arrangements (i.e., the dimension of the solution set). Represents the amplitude constraint slack variable. Represents the phase-constrained relaxation variable. This represents all possible arrangements of subarrays of all types on the plane. For the preset expected amplitude distribution, and Represents azimuth angle and The expected phase distribution at the maximum scanning angle under the cross section. This represents the preset number of channels. Representing the Seed array, in which, 1 represents a single subarray, 2 represents a two-column subarray, and 3 represents a four-column subarray. Representing the first on the field The minimum number of subarrays is typically set to 1, but can also be any integer less than L. This problem is an integer programming problem, an NP-hard problem, and an approximate solution can be obtained by using the branch and bound algorithm in the existing commercial solver GUROBI.

[0066] The embodiments of the present invention are based on Taking a spaceborne planar phased array as an example, the satellite orbital altitude is ,like Figure 2 As shown, the power is divided into three subarrays with equal distribution across the channels, and the desired amplitude is determined by a discrete Taylor distribution. The relative path difference is the desired phase distribution. and The partitioning results are as follows Figure 3 As shown.

[0067] Figure 4This demonstrates that the method proposed in the embodiments of the present invention can achieve scanning range Achieving stable EIRP within the system, with 50% of the channels ( The array is divided into 128 subarrays. The proposed method achieves a higher EIRP across the entire scanning range than existing domino-based and non-adjacent subarray methods. The average peak sidelobe levels across the entire scanning range are -15.8003 dB (proposed method), -15.6468 dB (non-adjacent subarray), and -15.5699 dB (domino subarray). The proposed method achieves the highest EIRP. On average across the entire scanning range, the proposed method is 6.4550 dB higher than the non-adjacent subarray and 4.5141 dB higher than the domino subarray.

[0068] Figure 5 The normalized radiation pattern and amplitude-phase distribution of the method proposed in this embodiment of the invention are shown at scanning angles of (35°, 0°) and (55°, 0°). The EIRP variation in different azimuth planes is as follows. Figure 6 As shown.

[0069] To further verify the performance of the proposed method, it is extended to... Further verification of the array surface, such as Figure 7 As shown, the method proposed in this embodiment of the invention can achieve good EIRP scanning performance under different channel number controls.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0071] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for partitioning the channel power equalization matrix of a phased array applied to a spaceborne transmission phased array, characterized in that, Includes the following steps: The optimization problem of array surface partitioning for constructing a spaceborne phased array: The subarray types of the array include: unit subarray, double subarray and quadruple subarray; the double subarray and quadruple subarray include a variety of arrangement forms. This is a binary integer variable; 0 indicates that the current subarray is not selected for placement on the array, and 1 indicates that the current subarray is selected for placement on the array. h represents the total number of possible subarray arrangements. For amplitude-constrained slack variables, For phase-constrained slack variables, L represents the possible arrangements of all types of subarrays on the plane, and L represents the total number of array elements on the array surface. For the preset expected amplitude distribution, and Indicates azimuth angle and The expected phase distribution at the maximum scanning angle under the cross section. This indicates the preset number of channels. Representing the Seed array, in which, 1 represents a single subarray, 2 represents a two-column subarray, and 3 represents a four-column subarray. Representing the first on the field The minimum number of subarrays; The optimization problem is solved using a solver, and the array partitioning result is obtained based on the solution. Based on the array surface division results, the far-field electric field and equivalent isotropic radiated power of the array are calculated; and beam scanning of the array is achieved through phase modulation of the subarray level.

2. The method for dividing the channel power into equal-mode arrays for use in spaceborne phased arrays as described in claim 1, characterized in that, The arrangement of the two subarrays adopts a linear arrangement, including both horizontal and vertical linear arrangements.

3. The method for dividing the channel power into equal-mode arrays for use in spaceborne phased arrays as described in claim 1, characterized in that, The arrangement of four subarrays includes: 2×2 square array, L-shaped structure, T-shaped structure, staggered structure and linear arrangement.

4. The method for dividing the channel power into equal-mode arrays for use in spaceborne phased arrays as described in claim 1, characterized in that, The average channel power distribution within each element of each subarray is as follows: in, Let be the amplitude of the s-th subarray. For input channel power, Let be the number of elements contained within the s-th subarray. Let be the phase of the s-th subarray. Let be the propagation constant. Let be the phase center position of the s-th subarray. Let be the scanning pointing angle of the s-th subarray.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 4.

6. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 11 to 4.

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