Satellite-borne array-fed multi-beam reflector antenna beam compensation method based on genetic algorithm

Abstract

The application relates to a satellite-borne array-fed multi-beam reflector antenna beam compensation method based on a genetic algorithm, which comprises the following steps: establishing a mathematical model between a feed source amplitude and phase of a satellite-borne array-fed multi-beam antenna, a deformation model and beam pointing error and gain loss; based on the genetic algorithm, an optimization model of antenna beam compensation is established; the optimization model of antenna beam compensation is solved; until the beam pointing error and gain loss meet a convergence condition, an optimal solution of the feed source amplitude and phase is obtained; finally, the optimal solution of the feed source amplitude and phase is brought into the mathematical model, the beam pointing and gain of the deformed satellite-borne array-fed multi-beam reflector antenna are corrected, and the accurate compensation of the beam performance of the satellite-borne array-fed multi-beam reflector antenna is realized. The application can effectively reduce the interference between the same polarization and different frequency beams, and the lossless constraint ensures the consistency of the energy before and after the compensation; the compensation method is simple to implement, and the beam compensation precision is high.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite communications, and in particular to a beam compensation method for a satellite-borne array-fed multi-beam mesh reflector antenna. Background Art

[0002] Spaceborne array-fed reflector antennas are primarily used for signal transmission between satellites and the ground. Long transmission distances require precise beam pointing by the spaceborne antennas. Due to extreme temperatures, microgravity, and repeated deployments, spaceborne array-fed reflector antennas can experience both overall and local deformation. This deformation can degrade beam pointing and gain performance, significantly impacting communications and even causing signal transmission mission failure. Furthermore, this performance degradation becomes more pronounced with increasing operating frequency. To ensure that the beam achieves the desired electrical performance specifications, such as gain and pointing, specialized beam compensation technologies are required.

[0003] Beam compensation methods for reflector antenna systems are mainly divided into two types: mechanical adjustment and electrical adjustment. In terms of mechanical adjustment, the papers "Shape control of reconfigurable antenna reflector: Concepts and strategies" and "APhysics-Guided Coordinated Distributed MPC Method for Shape Control of an Antenna Reflector" proposed shape adjustment methods to address the deterioration of beam pointing and gain performance. This type of method changes the shape of the satellite-borne reflector antenna by adjusting the rope tension, thereby optimizing the beam pointing and gain performance. However, since the shape adjustment method requires additional mechanical structure and energy, this method is difficult to implement on orbit. The electrical adjustment method optimizes the beam pointing and gain performance by modifying the amplitude and phase of each unit of the feed array. It does not require mechanical adjustment and is easier to compensate on orbit.

[0004] In the paper "Novel Array-Feed Distortion Compensation Techniques for Reflector Antennas," Y. Rahmat-Samii et al. use the complex conjugate of the focal plane field to re-excite the array feed and electrically compensate for deformed reflector antennas. While CFM compensation is fast, it is less effective for reflector beams with large profile errors, and the beam cannot be fully corrected. Therefore, a beam compensation method that is both simple to adjust and accurate is needed.

[0005] It can be seen that there are still difficulties in on-orbit mechanical adjustment of satellite-borne array-fed reflector antennas in terms of beam compensation, as well as the problem of poor beam compensation capability of electrical compensation methods. Summary of the Invention

[0006] The purpose of the present invention is to make up for the shortcomings of the existing technology and provide a genetic algorithm-based satellite-borne array-fed multi-beam reflector antenna beam compensation method that optimizes and adjusts the amplitude and phase of the array feed source, effectively compensates for the deterioration of beam pointing and gain caused by the deformation of the antenna reflector surface, and improves the performance of the satellite communication system.

[0007] To achieve the above object, the present invention adopts a technical solution: a method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm, comprising the following steps:

[0008] Step 1: Based on the deformation model of the satellite-borne array-fed multi-beam reflector antenna and the physical optics method, a mathematical model is established between the feed amplitude and phase of the satellite-borne array-fed multi-beam antenna, the deformation model, the beam pointing error, and the gain loss;

[0009] Step 2: Based on the obtained mathematical model, a model of the orthogonality and losslessness conditions of the feed is established; then, using the amplitude and phase of the feed as design variables, minimizing beam pointing and gain loss as optimization goals, and the orthogonality and losslessness condition models of the feed as constraints, an optimization model for antenna beam compensation is established based on a genetic algorithm.

[0010] Step 3: Solve the optimization model of antenna beam compensation until the beam pointing error and gain loss meet the convergence conditions and obtain the optimal solution of feed amplitude and phase;

[0011] Step 4: The optimal solution of the feed amplitude and phase is brought into the mathematical model to correct the deformed beam pointing and gain of the satellite-borne array-fed multi-beam reflector antenna, thereby achieving accurate compensation of the beam performance of the satellite-borne array-fed multi-beam reflector antenna.

[0012] Furthermore, the mathematical model between the feed amplitude and phase, deformation model, beam pointing error and gain loss of the satellite-borne array-fed multi-beam antenna established in step 1 is:

[0013]

[0014] Where, is the far-field pattern containing beam pointing error and gain loss information, j is the imaginary unit, represents the normal unit vector of any point on the reflecting surface, represents the incident magnetic field of the array feed on the surface of the reflector, represents the distance from the source to the field, S is the deformed surface model of the satellite-borne array-fed multi-beam reflector antenna, σ is the integration unit, is the unit dyad, is a unit vector dyadic vector, k is the free space wave number, and η=120π is the free space wave impedance.

[0015] Furthermore, the step 2 is specifically as follows:

[0016] Step 21: Establish the orthogonality and losslessness conditional model of the feed. The orthogonality of the shared feed is to reduce the interference between the beams i and l with the same polarization but different frequencies, and is expressed by the absolute value of the Hermitian inner product of the shared feed. Then, the orthogonality conditional model of the feed g1(X i )for:

[0017]

[0018] Where M represents the number of feeds shared by beam i and beam l, a n，i represents the amplitude of the nth feed participating in forming beam i, represents the phase of the nth feed participating in forming beam i. Beam i and beam l represent two beams with the same polarization but different frequencies. The symbol |●| is an absolute value operator.

[0019] At the same time, the losslessness is to ensure the consistency of the energy required before and after optimization, so the losslessness condition model of the feed source g2(X i )for:

[0020]

[0021] Where N represents the number of feeds required to form beam u;

[0022] Step 22: Based on the genetic algorithm, establish an optimization model for beam compensation, using the amplitude and phase of the feed as the design variables X i , with the beam pointing error f1(X i ) and gain loss f2(X i ) is minimized as the optimization goal, and the orthogonality condition model g1(X i ) and lossless condition model g2(X i ) as a constraint condition, the optimization model expression of antenna beam compensation is established as follows:

[0023]

[0024] In the formula, the design variable a 1，i …a N，i represents the amplitude of the N feeds participating in forming beam i, represents the phase of the N feeds involved in forming beam i, and N represents the number of feed units required to form a beam; P in the objective function i The value is the deviation of the beam pointing, P0 is the threshold of the beam pointing deviation, G i represents the loss gain, and G0 represents the loss gain threshold.

[0025] Furthermore, the step three is specifically as follows:

[0026] The convergence condition of the optimization model of antenna beam compensation is set as and Where k is the kth iteration step in the optimization design, ε q represents the maximum threshold of the relative error of beam pointing, ε f Indicates the accuracy value of the convergence of the gain loss function; P i The value is the deviation of the beam pointing, P0 is the threshold of the beam pointing deviation, G i represents the gain of loss;

[0027] When the convergence condition is met, the iteration is stopped and the optimal solution of the feed amplitude and phase is obtained as the design variable X i , which is the feed source amplitude and phase that effectively compensates for the beam pointing error and gain loss, and the corresponding beam pointing error and gain loss of the satellite-borne array-fed multi-beam reflector antenna are minimized.

[0028] The beneficial effects of the present invention are as follows: the present invention proposes a method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm (GA). The genetic algorithm optimization model established by the method uses the amplitude and phase of the feed source as design variables, minimizes the beam pointing error and gain loss as optimization goals, and uses the orthogonality and losslessness of the feed source as constraints. In particular, the orthogonality constraint is used to effectively reduce the interference between beams of the same polarization but different frequencies, and the losslessness constraint ensures the consistency of energy before and after compensation. By solving the optimization model, the amplitude and phase of the array feed source can be obtained, thereby achieving accurate compensation for the deteriorated beam performance of the satellite-borne array-fed multi-beam reflector antenna. The method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm proposed by the present invention is simple to implement, has high beam compensation accuracy, and has important practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flow chart of the method provided by the present invention;

[0030] Figure 2 Deformation cloud map of satellite-borne array-fed multi-beam reflector antenna;

[0031] Figure 3This is a schematic diagram of the feed arrangement of a 20-feed, 4-beam, dual-frequency, dual-polarization array;

[0032] Figure 4 This is a comparison diagram of the ideal beam, degraded beam, and beam after genetic algorithm compensation. DETAILED DESCRIPTION

[0033] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0034] To address the difficulties of on-orbit mechanical adjustment and high-precision compensation for existing satellite-borne array-fed multi-beam reflector antennas, the present invention provides a beam compensation method for satellite-borne array-fed multi-beam reflector antennas based on a genetic algorithm. This method establishes a beam compensation optimization model based on the genetic algorithm and obtains the required compensation feed source amplitude and phase by solving the optimization model. The obtained feed source amplitude and phase can achieve high-precision compensation of the satellite-borne array-fed multi-beam reflector antenna beam, so that its beam pointing error and gain loss meet the requirements. To achieve the above objectives, the present invention provides the following specific embodiments:

[0035] Example 1: Figure 1 As shown, a beam compensation method for a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm includes the following steps:

[0036] S01. Based on the deformation model of the satellite-borne array-fed multi-beam reflector antenna and the physical optics method, a mathematical model is established between the feed amplitude and phase, deformation model, beam pointing error, and gain loss of the satellite-borne array-fed multi-beam antenna:

[0037]

[0038] Where, is the far-field pattern containing beam pointing error and gain loss information, j is the imaginary unit, represents the normal unit vector of any point on the reflecting surface, represents the incident magnetic field of the array feed on the surface of the reflector, represents the distance from the source to the field, S is the deformed surface model of the satellite-borne array-fed multi-beam reflector antenna, σ is the integration unit, is the unit dyad, is a unit vector dyadic vector, k is the free space wave number, and η=120π is the free space wave impedance.

[0039] S02. Based on the obtained mathematical model, the orthogonality and losslessness conditional models of the feed are established. The orthogonality of the shared feed is to reduce the interference between the beams i and l with the same polarization but different frequencies, and is expressed by the absolute value of the Hermitian inner product of the shared feed. Then, the orthogonality conditional model of the feed g1(X i )for:

[0040]

[0041] Where M represents the number of feeds shared by beam i and beam l, a n，i represents the amplitude of the nth feed participating in forming beam i, represents the phase of the nth feed participating in forming beam i. Beam i and beam l represent two beams with the same polarization but different frequencies. The symbol |●| is an absolute value operator.

[0042] At the same time, the losslessness is to ensure the consistency of the energy required before and after optimization, so the losslessness condition model of the feed source g2(X i )for:

[0043]

[0044] Where N represents the number of feeds required to form beam i;

[0045] S03. Based on the genetic algorithm, an optimization model for beam compensation is established, with the amplitude and phase of the feed as the design variables X i , with the beam pointing error f1(X i ) and gain loss f2(X i ) is minimized as the optimization goal, and the orthogonality condition model g1(X i ) and lossless condition model g2(X i ) as a constraint condition, the optimization model expression of antenna beam compensation is established as follows:

[0046]

[0047] In the formula, the design variable a 1，i …a M，i represents the amplitude of the N feeds participating in forming beam i, represents the phase of the N feeds involved in forming beam i, and N represents the number of feed units required to form a beam; P in the objective function i The value is the deviation of the beam pointing, P0 is the threshold of the beam pointing deviation, G i represents the loss gain, and G0 represents the loss gain threshold.

[0048] S04. Set the convergence condition of the optimization model of antenna beam compensation to and Where k is the kth iteration step in the optimization design, ε q represents the maximum threshold of the relative error of beam pointing, ε f Indicates the accuracy value of the convergence of the gain loss function; P i The value is the deviation of the beam pointing, P0 is the threshold of the beam pointing deviation, G i represents the gain of loss;

[0049] When the convergence condition is met, the iteration is stopped and the optimal solution of the feed amplitude and phase is obtained as the design variable X i , which is the feed source amplitude and phase that effectively compensates for the beam pointing error and gain loss, and the corresponding beam pointing error and gain loss of the satellite-borne array-fed multi-beam reflector antenna are minimized.

[0050] S05. The optimal solution of the feed source amplitude and phase is brought into the mathematical model to correct the deformed beam pointing and gain of the satellite-borne array-fed multi-beam reflector antenna, thereby achieving accurate compensation of the beam performance of the satellite-borne array-fed multi-beam reflector antenna.

[0051] like Figures 2 to 4 The advantages of the present invention can be further illustrated by the following simulation experiments:

[0052] 1. Simulation parameters:

[0053] The aperture D of a certain satellite-borne array-fed multi-beam reflector antenna is 10m, the focal diameter ratio is 0.6, the offset relative to the reflector is 0.5D, the operating frequency is 2 / 2.1GHz, and the feed source is a dual-frequency x / y dual-polarization 4-color 4-beam multiplexing array feed source. Figure 3 As shown, the feed source uses an array conical horn with 7 units per beam, arranged in a hexagonal shape, with a unit spacing of 0.1m and a radius of 0.05m.

[0054] Given the reflection surface error, Figure 2 As shown, the corresponding antenna pattern is Figure 4 As shown by Figure 4 It can be seen that the antenna's four beam pointing errors are 0.36°, 0.35°, 0.37°, and 0.34°; the gain losses are 0.38 dB, 0.27 dB, 0.34 dB, and 0.24 dB, requiring beam compensation.

[0055] The number of feed sources for each beam is 7, so the design variable is set to a vector of [1×14]. The optimization model parameters of the antenna beam compensation are assigned, and the population size is set to 50, the crossover ratio is 0.8, the mutation probability is 0.2, and the convergence condition ε is set to 1. q and ε f 10 respectively -3 and 10-5 Based on this parameter, the genetic algorithm method is used to solve the optimization models of the four beam compensations one by one.

[0056] 2. Simulation results:

[0057] The values ​​of beam pointing and gain are shown in Table 1:

[0058] Table 1 Comparison of compensation effects of CFM and genetic algorithm optimization models

[0059]

[0060] As can be seen from the data in the table, the beam compensation method proposed in the present invention can correct the beam pointing to an error of 0° for all four beams. Beam one, beam two, beam three, and beam four can all correct the gain to 43.81dB, 43.46dB, 43.54dB, and 43.83dB, which are all improvements compared to the degraded beams' 43.66dB, 43.34dB, 43.36dB, and 43.66dB. The optimized four beams can also ensure that the gain loss is reduced while ensuring correct pointing. However, the beam compensation effect of CFM is not very ideal. The beam pointing errors of beam two, beam three, and beam four cannot be corrected to 0°, and are 0.02°, 0.02°, and 0.03°, respectively. Moreover, the gains of the four beams after CFM correction do not exceed the beam gains after genetic algorithm compensation.

[0061] In addition to beam pointing and gain as electrical performance analysis, it is also necessary to pay attention to the orthogonality index of the shared feed, which is used to represent the interference between beams of the same polarization but different frequencies. Orthogonality is expressed in the absolute value table of the Hermitian inner product, as shown in Table 2:

[0062] Table 2 Comparison of common feed orthogonality after CFM and genetic algorithm compensation

[0063]

[0064]

[0065] Using the CFM method, the absolute values ​​of the Hermitian inner product of the common feeds for beams 1 and 2 are 0.0062, and the absolute values ​​of the Hermitian inner product of the common feeds for beams 3 and 4 are 0.0022. Using the genetic algorithm, the absolute values ​​of the Hermitian inner product of the common feeds for beams 1 and 2 are 0.0015, and the absolute values ​​of the Hermitian inner product of the common feeds for beams 3 and 4 are 0.0012.

[0066] 3. Result analysis:

[0067] Conclusion 1: The ideal beam, degraded beam, and beam compensated by genetic algorithm are plotted on a graph for comparison, as shown in the figure below. Figure 3 As shown in the figure, the dashed line represents the ideal beam, the dotted line represents the degraded beam, and the solid line represents the compensated beam. Each line type has four contour lines, each representing one of the four beams. When the reflective surface deteriorates, both the beam pointing and gain degrade. However, after correction using the genetic algorithm, the -3dB contour of the beam essentially coincides with the ideal beam, demonstrating effective compensation. Furthermore, compared to CFM, the genetic algorithm compensated beam pointing is more precise and has lower gain loss.

[0068] Conclusion 2: When performing multi-beam compensation, the absolute value of the Hermitian inner product of the shared feed after compensation by the genetic algorithm method is smaller than the compensation result of the CFM method, indicating that the interference between beams of the same polarization but different frequencies is smaller after compensation by the genetic algorithm method.

[0069] Conclusion 3: The simulation data show that the compensated beam pointing and gain loss as well as the compensation efficiency results meet the expected goals, and the feasibility and effectiveness of the theory and method proposed in this invention have been verified.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for beam compensation of a spaceborne array-fed multi-beam reflector antenna based on a genetic algorithm, characterized in that: The steps include: Step 1: Based on the deformation model of the satellite-borne array-fed multi-beam reflector antenna and the physical optics method, a mathematical model is established between the feed amplitude and phase of the satellite-borne array-fed multi-beam antenna, the deformation model, the beam pointing error, and the gain loss; Step 2: Based on the obtained mathematical model, a model of the orthogonality and losslessness conditions of the feed is established. Then, using the amplitude and phase of the feed as design variables, minimizing beam pointing and gain loss as optimization goals, and the orthogonality and losslessness condition models of the feed as constraints, an optimization model for antenna beam compensation is established based on a genetic algorithm. The specific steps include: Step 21: Establish the orthogonality and losslessness condition model of the feed source. The orthogonality of the shared feed source is to reduce the loss of the same polarization but different frequency beams. and The interference between them is expressed by the absolute value of the Hermitian inner product of the shared feed, then the orthogonality condition model of the feed is: for: ， Where, M Represents beam Sum beam The number of shared feeds, Indicates participation in beam forming No. The amplitude of the feed, Indicates participation in beam forming No. The phase of the feed, beam Sum beam Represents two beams with the same polarization but different frequencies. The symbol |●| is the absolute value operator. At the same time, the losslessness is to ensure the consistency of the energy required before and after optimization, so the losslessness condition model of the feed source is for: ， in, N Indicates beamforming need N Feeds; Step 22: Based on the genetic algorithm, establish an optimization model for beam compensation, using the amplitude and phase of the feed as design variables. , with beam pointing error and gain loss The optimization goal is to minimize the feed source orthogonality condition model. and lossless conditional models As a constraint condition, the optimization model expression of antenna beam compensation is established as follows: ， In the formula, the design variables Indicates participation in beam forming of N The amplitude of the feed, Indicates participation in beam forming of N The phase of the feed, Indicates the number of feed units required to form a beam; in the objective function The value is the deviation of the beam pointing, is the threshold of beam pointing deviation, represents the gain of loss, The threshold value indicating loss of gain; Step 3: Solve the optimization model of antenna beam compensation until the beam pointing error and gain loss meet the convergence conditions and obtain the optimal solution of feed amplitude and phase; Step 4: The optimal solution of the feed amplitude and phase is brought into the mathematical model to correct the deformed beam pointing and gain of the satellite-borne array-fed multi-beam reflector antenna, thereby achieving accurate compensation of the beam performance of the satellite-borne array-fed multi-beam reflector antenna.

2. The method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm according to claim 1, wherein: The mathematical model between the feed amplitude and phase, deformation model, beam pointing error and gain loss of the satellite-borne array-fed multi-beam antenna established in step 1 is: ， Where, is the far-field pattern containing information on beam pointing error and gain loss, j is the imaginary unit, represents the normal unit vector of any point on the reflecting surface, represents the incident magnetic field of the array feed on the surface of the reflector, S is the deformed surface model of the satellite-borne array-fed multi-beam reflector antenna. is the integration unit, is the unit dyad, is a unit vector The duo is the free space wave number, is the free space wave impedance.

3. The method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm according to claim 1 or 2, wherein: The step three is specifically as follows: The convergence condition of the optimization model of antenna beam compensation is set as and ,in k To optimize the design k Iteration step, represents the maximum threshold of the relative error of beam pointing, Indicates the accuracy value of the convergence of the gain loss function; The value is the deviation of the beam pointing, is the threshold of beam pointing deviation, represents the gain of loss; When the convergence condition is met, the iteration is stopped and the optimal solution of the feed amplitude and phase is obtained as the design variable X i , which is the feed source amplitude and phase that effectively compensates for the beam pointing error and gain loss, and the corresponding beam pointing error and gain loss of the satellite-borne array-fed multi-beam reflector antenna are minimized.

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