Spaceborne array feed multi-beam reflector antenna beam compensation method based on genetic algorithm

Abstract

The invention relates to a satellite-borne array-fed multi-beam reflector antenna beam compensation method based on a genetic algorithm, and the method comprises the steps: building a mathematical model between the amplitude and phase of a feed source of a satellite-borne array-fed multi-beam antenna, a deformation model and a beam pointing error and gain loss, building an optimization model of antenna beam compensation based on the genetic algorithm, and carrying out the beam compensation of the satellite-borne array-fed multi-beam antenna. And solving the optimization model of antenna beam compensation until the beam pointing error and the gain loss meet the convergence condition to obtain the optimal solutions of the amplitude and the phase of the feed source, finally substituting the optimal solutions of the amplitude and the phase of the feed source into the mathematical model, and correcting the beam pointing and the gain of the deformed satellite-borne array feed multi-beam reflector antenna. Therefore, accurate compensation of the beam performance of the satellite-borne array-fed multi-beam reflector antenna is realized. According to the invention, the interference between beams with the same polarization and different frequencies can be effectively reduced, the consistency of energy before and after compensation is ensured without loss constraint, the compensation method is simple and convenient to implement, and the beam compensation precision is high.

Description

Technical Field

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

[0002] Satellite-borne array-fed reflector antennas are mainly used for signal transmission between satellites and the ground. Long transmission distances require precise beam pointing of airborne antennas. Due to extreme temperatures, microgravity environments, and repeated deployments, satellite-borne array-fed reflector antennas will experience overall and local deformations. The deformation of satellite-borne array-fed reflector antennas will lead to deterioration of beam pointing and gain performance, greatly affecting communications and even causing signal transmission mission failures. In addition, as the operating frequency increases, this performance degradation will become more significant. In order to ensure that the beam can achieve the predetermined electrical performance indicators such as gain and pointing, it is necessary to study specialized beam compensation technologies.

[0003] The beam compensation methods of 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 is to change the shape of the satellite-borne reflector antenna by adjusting the rope tension to optimize 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. No mechanical adjustment is required, and on-orbit compensation is easier.

[0004] In the article "Novel Array-Feed Distortion Compensation Techniques for Reflector Antennas" published by Y.Rahmat-Samii et al., the complex conjugate of the focal plane field is used to re-excite the array feed source to electrically compensate the deformed reflector antenna. The CFM compensation speed is very fast, but the compensation effect is poor for the reflector beam with large surface errors, and the beam cannot be completely corrected. Therefore, it is necessary to propose a beam compensation method that is easy to adjust and accurate.

[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 deficiencies of the prior art and provide a genetic algorithm-based satellite-based 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 technical solution adopted by the present invention is: 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: According to the deformation model of the satellite-borne array-fed multi-beam reflector antenna, a mathematical model between the feed source amplitude and phase, the deformation model, the beam pointing error and the gain loss of the satellite-borne array-fed multi-beam antenna is established based on the physical optics method;

[0009] Step 2: Based on the obtained mathematical model, establish the orthogonality and losslessness condition model of the feed source; then, take the amplitude and phase of the feed source as design variables, take beam pointing and gain loss minimization as optimization goals, take the orthogonality and losslessness condition model of the feed source as constraints, and establish the optimization model of antenna beam compensation based on 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: Substitute the optimal solution of feed source amplitude and phase 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 source 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] In the formula, 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 reflective surface, represents the incident magnetic field of the array feed on the reflector surface, represents the distance from the source point to the field, S is the deformed surface model of the satellite-borne array-fed multi-beam reflector antenna, σ is the integral unit, is the unit vector, is the unit vector is the vector of free space, k is the wave number in free space, and η=120π is the wave impedance in free space.

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

[0016] Step 21, establish the orthogonality and lossless condition model of the feed source. The orthogonality of the shared feed source 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 source. Then, the orthogonality condition model of the feed source g1(X i )for:

[0017]

[0018] Where M represents the number of common feed sources for 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, and 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 means that N feeds are required to form beam u;

[0022] Step 22: 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:

[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 beam pointing, P0 is the threshold of beam pointing deviation, G i represents the loss gain, and G0 represents the threshold of the loss gain.

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

[0026] The convergence condition of the optimization model for 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 gain loss function convergence; P i The value is the deviation of beam pointing, P0 is the threshold of 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. 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 satellite-borne array-fed multi-beam reflector antenna based on genetic algorithm (GA). The genetic algorithm optimization model established by the method takes the amplitude and phase of the feed source as design variables, takes minimization of beam pointing error and gain loss as optimization goals, and takes 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 different frequencies with the same polarization, 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, and accurate compensation for the deteriorated beam performance of the satellite-borne array-fed multi-beam reflector antenna can be achieved. The satellite-borne array-fed multi-beam reflector antenna beam compensation method based on 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 diagram 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 in conjunction with 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] In order to solve the problems of difficult on-orbit mechanical adjustment and high-precision compensation of 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 genetic algorithms. The method establishes a beam compensation optimization model based on the genetic algorithm, and obtains the feed source amplitude and phase required for compensation by solving the optimization model. The feed source amplitude and phase obtained by solving can achieve high-precision compensation of the beam of the satellite-borne array-fed multi-beam reflector antenna, so that its beam pointing error and gain loss meet the requirements. To achieve the above purpose, the present invention provides the following specific implementation methods:

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

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

[0037]

[0038] In the formula, 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 reflective surface, represents the incident magnetic field of the array feed on the reflector surface, represents the distance from the source point to the field, S is the deformed surface model of the satellite-borne array-fed multi-beam reflector antenna, σ is the integral unit, is the unit vector, is the unit vector is the vector of free space, k is the wave number in free space, and η=120π is the wave impedance in free space.

[0039] S02. According to the obtained mathematical model, the orthogonality and lossless condition model of the feed is 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 condition model of the feed g1(X i )for:

[0040]

[0041] Where M represents the number of common feed sources for 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, and 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 means that N feeds are 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 beam pointing, P0 is the threshold of beam pointing deviation, G i represents the loss gain, and G0 represents the threshold of the loss gain.

[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 gain loss function convergence; P i The value is the deviation of beam pointing, P0 is the threshold of 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. 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 As shown, 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 satellite-borne array-fed multi-beam reflector antenna is 10m, the focal diameter ratio is 0.6, the relative reflector offset 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 cone horn with 7 units per beam, which are 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 The corresponding antenna pattern is shown as Figure 4 As shown by Figure 4 It can be seen that the pointing errors of the four beams of the antenna are 0.36°, 0.35°, 0.37° and 0.34°; the gain losses are 0.38dB, 0.27dB, 0.34dB and 0.24dB, and beam compensation is required.

[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 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 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] It can be seen from the data in the table that the beam compensation method proposed in the present invention can correct the beam pointing of all four beams to an error of 0°, and beam one, beam two, beam three and beam four can correct the gain to 43.81dB, 43.46dB, 43.54dB and 43.83dB, which are all improved compared to the 43.66dB, 43.34dB, 43.36dB and 43.66dB of the deteriorated beams. The four optimized beams can ensure that the gain loss is reduced while ensuring the 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; and the gains of the four beams after CFM correction do not exceed the beam gains after genetic algorithm compensation.

[0061] In addition to the electrical performance analysis of beam pointing and gain, we also need to pay attention to the orthogonality index of the shared feed source to indicate 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 value of the Hermitian inner product of the common feeds of beams 1 and 2 is 0.0062, and the absolute value of the Hermitian inner product of the common feeds of beams 3 and 4 is 0.0022. Using the genetic algorithm, the absolute value of the Hermitian inner product of the common feeds of beams 1 and 2 is 0.0015, and the absolute value of the Hermitian inner product of the common feeds of beams 3 and 4 is 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 Figure 3 As shown in the figure. The dashed line is the ideal beam, the dotted line is the degraded beam, and the solid line is the compensated beam. Each line type has four contour lines representing four beams. After the reflector surface deteriorates, the beam pointing and gain are deteriorated, but after correction by the genetic algorithm method, the -3dB contour line of the beam can basically coincide with the ideal beam, and the compensation effect is good. Compared with CFM, the beam pointing is more accurate and the gain loss is lower after compensation by the genetic algorithm method.

[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 principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on genetic algorithm, characterized in that: The steps include: Step 1: According to the deformation model of the satellite-borne array-fed multi-beam reflector antenna, a mathematical model between the feed source amplitude and phase, the deformation model, the beam pointing error and the gain loss of the satellite-borne array-fed multi-beam antenna is established based on the physical optics method; Step 2: Based on the obtained mathematical model, establish the orthogonality and losslessness condition model of the feed source; then, take the amplitude and phase of the feed source as design variables, take beam pointing and gain loss minimization as optimization goals, take the orthogonality and losslessness condition model of the feed source as constraints, and establish the optimization model of antenna beam compensation based on genetic algorithm; 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: Substitute the optimal solution of feed source amplitude and phase 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 as claimed in claim 1, characterized in that: The mathematical model between the feed source 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: In the formula, 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 reflective surface, represents the incident magnetic field of the array feed on the reflector surface, represents the distance from the source point to the field, S is the deformed surface model of the satellite-borne array-fed multi-beam reflector antenna, σ is the integral unit, is the unit vector, is the unit vector is the vector of free space, k is the wave number in free space, and η=120π is the wave impedance in free space.

3. The method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on genetic algorithm according to claim 1, characterized in that: The step 2 is specifically as follows: Step 21, establish the orthogonality and lossless condition model of the feed source. The orthogonality of the shared feed source 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 source. Then, the orthogonality condition model of the feed source g1(X i )for: Where M represents the number of common feed sources for 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, and the symbol |●| is an 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 g2(X i )for: Where N means that N feeds are required to form beam i; Step 22: 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: 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 beam pointing, P0 is the threshold of beam pointing deviation, G i represents the loss gain, and G0 represents the threshold of the loss gain.

4. The method for beam compensation of a satellite-borne array-fed multi-beam reflector antenna based on a genetic algorithm according to any one of claims 1 to 3, characterized in that: The step three is specifically as follows: The convergence condition of the optimization model for 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 gain loss function convergence; P i The value is the deviation of beam pointing, P0 is the threshold of beam pointing deviation, G i 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. The corresponding beam pointing error and gain loss of the satellite-borne array-fed multi-beam reflector antenna are minimized.

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