Conformal polarization array transmit beamforming algorithm based on accumulated parameter iteration

Abstract

The present application relates to radar communication technology, disclose a kind of based on cumulative parameter adjustment iteration's conformal polarization array transmit beam shaping algorithm.The present application is based on MVDR criterion to obtain the analytical solution of transmission weight vector, then based on matrix inversion rule to obtain weight vector iterative recurrence formula, the optimal analytical solution of real adjustment parameter in each step iteration is obtained by mathematical derivation, finally the transmit beam pattern that satisfies performance requirement is obtained.This method is low in operation amount, good in convergence, at the same time, makes the conformal polarization array transmit beam pattern satisfy main beam pointing and polarization constraint, and effectively reduces peak sidelobe level and peak cross-polarization level, and can form deep recess in specific angle range.In addition, the method is especially suitable for large-scale array beam shaping.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar communication, and particularly relates to a transmit beamforming technology of a conformal polarization array. BACKGROUND

[0002] Compared with a traditional planar array, a polarization conformal array can be flexibly attached to a carrier surface, has advantages of easy installation, small constraint by the carrier, wide angle coverage range, and the like, and has a wider application prospect and practical value. However, the non-planar and anisotropic characteristics of the polarization conformal array lead to a high peak sidelobe level and serious cross polarization of the transmit pattern of the conformal array, and the beamforming algorithm applied to the traditional planar array cannot directly optimize the pattern of the conformal array. Therefore, it is an important research topic to perform beamforming on the transmit pattern of the conformal array.

[0003] In recent years, convex optimization theory has become a popular direction of patternforming algorithm. Fuchs B and the like construct a convex optimization problem to realize constraint on the main beam pointing direction, the peak sidelobe level, and the polarization parameter of the conformal array, but do not constrain the cross polarization, and the algorithm needs to use a CVX tool package in the process of solving the optimal weight vector, which has a large amount of calculation and a long calculation running time. (See document: Fuchs B, Fuchs J J. Optimal polarization synthesis of arbitrary arrays with focused power pattern[J]. IEEE Transactions on Antennas and Propagation, 2011, 59(12): 4512-4519.) Compared with the convex optimization algorithm, the transmit beamforming algorithm (PWOPD) of the conformal array based on pre-weighted orthogonal projection decomposition does not need to solve a convex optimization problem and has the advantage of easy parameter setting, but when applied to a large array, the algorithm still has a certain amount of calculation and needs to spend a long time to obtain a satisfactory pattern result.

[0004] Therefore, it is of great significance to design a conformal array transmit beam weight vector to quickly and effectively perform beamforming on the transmit beam pattern, so that the conformal array meets specific requirements of the expected transmit pattern, such as the main beam pointing direction, polarization constraint, peak sidelobe level, cross polarization level, formation of a notch within a specified range, and the like. SUMMARY

[0005] The applicant analyzes the advantages and disadvantages of the existing transmit beamforming algorithms of the conformal polarization array, and the existing algorithms have a long time-consuming phenomenon under multiple constraint conditions. In view of this, the present application provides a transmit beamforming algorithm of a conformal polarization array based on cumulative parameter adjustment iteration, to solve the problems in the existing method.

[0006] The technical scheme provided by the application is specifically a conformal polarization array transmitting beam shaping algorithm based on cumulative parameter adjustment iteration, which comprises the following steps:

[0007] Step 1) A conformal polarization array model is established by comprehensively considering the carrier shielding effect and the inconsistency of the element directional diagram.

[0008] Step 2) Based on the signal power of the main polarization direction and the cross polarization direction and , the main polarization direction steering vector and the cross polarization direction steering vector are obtained.

[0009] Step 3) In order to ensure that the main beam is aligned and the cross polarization level at the main beam pointing direction is as low as possible, the initial weight is set based on the MVDR criterion as follows:

[0010]

[0011] Here,

[0012] Step 4) Based on the minimum signal power at , the optimal adaptive weight w * is obtained by combining the maximum output signal-to-noise ratio criterion as follows:

[0013]

[0014] Where is the normalized noise plus interference covariance matrix, β i is the transmit directional diagram adjustment point power, is the adjustment point steering vector, and g is co or x according to whether the to-be-adjusted directional diagram is the main polarization component or the cross polarization component.

[0015] Step 5) The optimal weight is further expressed by applying the matrix inversion rule as follows:

[0016]

[0017] Where the adjustment parameter μ is a real number, and satisfies:

[0018]

[0019] Step 6) Based on the construction idea of the optimal weight, the adjustment direction of the kth iteration k-1 of the weight vector w can be expressed as:

[0020] ​

[0021] Where, μ k Adjust the parameters for the real number to be determined;

[0022] Step 7) Determine μ for the weight vector update in step k. k ;

[0023] The normalized response at point can be expressed as:

[0024]

[0025] If Adjust the level at the desired level ρ k It needs to satisfy the following formula:

[0026]

[0027] In addition, the response change between two adjacent pattern controls should be as small as possible. In summary, μ k Solving this problem is equivalent to solving the following optimization problem:

[0028]

[0029]

[0030] Step 8) Solve the above optimization problem to obtain the optimal weight vector for the k-th iteration.

[0031]

[0032] Step 9) When the final transmission pattern satisfies the desired constraints or the number of iterations reaches its maximum, terminate the iteration and obtain the optimal transmission weight vector w. T* To achieve beamforming;

[0033] This invention discloses a beamforming algorithm for the transmit pattern of a conformal polarized array. Combining cumulative parameter tuning iteration, this invention proposes a simple and effective single-point array pattern control method. The invention provides an analytical expression for the transmit weight vector, performs cumulative parameter tuning iteration on it, and flexibly designs and selects real-valued parameters in each iteration to achieve rapid pattern optimization.

[0034] The beneficial effects of this invention are that, while having low computational complexity and good convergence, it enables the conformal polarization array transmission pattern to satisfy the main beam pointing and polarization constraints, effectively reduces the peak sidelobe level and peak cross-polarization level, and can form a deep dip within a specific angular range. Furthermore, the proposed method is particularly suitable for large-scale array beamforming. Attached Figure Description

[0035] Figure 1 Flowchart of the method of the present invention, i.e. the abstract figure;

[0036] Figure 2 Schematic of the hemispherical conformal polarized array of the present invention;

[0037] Figure 3 Total pattern of the initial transmit beam;

[0038] Figure 4 Main polarization direction pattern of the initial transmit beam;

[0039] Figure 5 Cross polarization direction pattern of the initial transmit beam;

[0040] Figure 6 Initial transmit beam Component elevation profile pattern;

[0041] Figure 7 Initial transmit beam Component azimuth profile pattern;

[0042] Figure 8 Total pattern of the transmit beam of the proposed algorithm under linear polarization;

[0043] Figure 9 Main polarization direction pattern of the transmit beam of the proposed algorithm under linear polarization;

[0044] Figure 10 Cross polarization direction pattern of the transmit beam of the proposed algorithm under linear polarization;

[0045] Figure 11 Transmit beam of the proposed algorithm under linear polarization Component elevation profile pattern;

[0046] Figure 12 Transmit beam of the proposed algorithm under linear polarization Component azimuth profile pattern;

[0047] Figure 13 Total pattern of the transmit beam of the proposed algorithm under circular polarization;

[0048] Figure 14 Main polarization direction pattern of the transmit beam of the proposed algorithm under circular polarization;

[0049] Figure 15 Cross polarization direction pattern of the transmit beam of the proposed algorithm under circular polarization;

[0050] Figure 16 Transmit beam of the proposed algorithm under circular polarization Component elevation profile pattern;

[0051] Figure 17 Transmit beam of the algorithm under circular polarization Component azimuth dimension profile pattern direction. DETAILED DESCRIPTION

[0052] The specific embodiments of the present application and working principles will be further described in detail below in combination with the drawings.

[0053] In order to better describe, first, the following definitions are made:

[0054] Peak cross-polarization level (Cross-polarization level): the cross-polarization component level value based on the normalization of the main polarization pattern, the expression is as follows:

[0055]

[0056] Wherein, is the level of the cross-polarization component, is the level of the main polarization direction of the transmitted signal. The value of CPI represents the degree of antenna polarization close to the main polarization, in order to ensure that the antenna polarization is the main polarization, we hope that the smaller the CPI value is, the better.

[0057] The specific embodiments of the present application will be described in detail below in combination with the drawings of the specification. As Figure 1 shown in the flow chart of the conformal polarization array transmit beam shaping algorithm based on cumulative parameter adjustment iteration, it specifically includes the following steps:

[0058] Step 1, set the total number of conformal polarization array elements as N, considering the characteristics of the conformal array, according to the local pattern of the array element, establish a conformal polarization array model. Here the azimuth angle is set as and the elevation angle is set as θ∈[0,π / 2].

[0059] Step 2, according to the array model, get and direction of the steering vector.

[0060]

[0061]

[0062] Wherein, the element position of the nth element is (x n ,y n ,z n ), the signal wavelength is λ,

[0063]

[0064] Step 3, according to the main polarization parameters (γ co ,ηco and cross-polarization parameter (γ) x ,η x ), thus obtaining the expressions for the steering vectors of the main polarization direction and the cross-polarization direction:

[0065]

[0066]

[0067] Step 4: To ensure the main beam is aligned and the cross-polarization level at the main beam pointing point is as low as possible, the optimization problem of the initial weight vector is expressed as follows:

[0068]

[0069]

[0070] Based on the MVDR criterion, the initial weights are obtained as follows: Since the normalization factor α1 does not affect the shape of the final pattern, we ignore it.

[0071] Step 5, based on The signal power is minimized at the point where the maximum output signal-to-interference-plus-noise ratio (SINR) is reached, yielding the optimal adaptive weight vector. Applying the matrix inversion rule, the optimal weights can be expressed as:

[0072]

[0073] Further expressed as:

[0074]

[0075]

[0076] Where, β i express The interference-to-noise ratio in the direction is adjusted by adjusting the pattern of the main polarization component when g is co and by adjusting the pattern of the cross-polarization component when g is x.

[0077] Step 6: As can be seen from Step 5, we can change the real parameter μ. The directional pattern response at a given weight vector w k-1 If adjustment is needed To obtain a desired value from the normalized pattern response at a given point, we can construct the expression for the k-th weight vector as follows:

[0078]

[0079] Step 7: Given the weight vector w k-1 Define the angle of the k-th adjustment. The direction is relative to The normalized power pattern of the direction is:

[0080]

[0081] Here, we consider the angle in the k-1th iteration pattern that deviates most from the expected pattern as

[0082] Step 8, adjust μ k So that the kth adjustment polar The level value at the point satisfies the expected level value ρ k That is

[0083]

[0084] The above μ k Is not unique, but we need to choose a suitable μ k To better control the pattern; here we choose μ k The optimal solution according to the criterion of minimizing the response change controlled by the pattern between the two iterations. The pattern change between the two iterations can be measured by:

[0085]

[0086] In summary, the solution of μ k Converts to solving the following conditional extremum problem:

[0087]

[0088] Let the Lagrange multiplier be λ, construct the cost function and let its gradient be 0 to get:

[0089]

[0090] Bring it into the constraint, and based on the following equations, solve to get (λ * +λ)1、(λ * +λ)2:

[0091] 4χ 2 α-8χβκ+16κ 2 const+[-β 2 α+4α 2 const](λ * +λ) 2 +[-4β 2 κ+16καconst](λ * +λ)

[0092] Here,

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] Therefore, μ k The feasible solutions are as follows:

[0099]

[0100]

[0101] We start from (μ) k )1 and (μ k Select from )2 such that F(μ) k The parameter with the smallest value is used as the optimal adjustment parameter for the k-th iteration. The weight vector for the k-th iteration can be expressed as:

[0102] Step 9: Terminate the iteration when the final transmission pattern meets the expected constraints or the number of iterations reaches the termination iteration number, thus realizing transmission beamforming.

[0103] To make the objectives, technical solutions, and technical effects of this invention clearer, a simulation experiment is conducted to provide a more detailed description of the invention.

[0104] This experiment simulates the conformal polarization array transmit beamforming (CTI) algorithm based on cumulative parameter tuning iteration. In the simulation, the array is a lower hemisphere, the array elements are matrix microstrip antennas with radius R = 6λ, the arc length between adjacent rings is l = 0.5λ, and the spacing between adjacent array elements in the same ring is d. c =0.5λ, total number of array elements 933. The transmitted signal is a narrowband signal with a wavelength λ = 1. Signal transmission direction. The range of each angle is defined as follows:

[0105] The main lobe angle range is

[0106] The concave angle range is 1.

[0107] The concave angle range 2 is

[0108] Considering both linear and circular polarization, the methods used for comparison include the alternating projection algorithm (AP) under the same simulation conditions and the initial transmit beam pattern that only performs spatial steering vector phase supplementation weighting.

[0109] Simulation Experiment 1: In this simulation, the initial transmitted beam pattern is simulated with only spatial steering vector phase supplementation weighting. Figures 3 to 7 These are the initial transmitted beam pattern, main polarization pattern, and cross-polarization pattern, respectively. Component elevation profile transmitted beam diagram Component azimuth profile transmitted beam pattern.

[0110] Simulation Experiment 2: In this simulation, the polarization mode is considered to be linear polarization, and the principal polarization is set as the vertical polarization component. η co =0), cross-polarization is set as the horizontal polarization component (γ). x =0, η x =0), the optimized transmit pattern cross-polarization level should be below -28dB, the peak sidelobe level should be below -25dB, and the concave region level should be below -47dB. Both the AP algorithm and the CTI algorithm are iterated 1500 times. Figures 8 to 12 These are the overall transmit beam pattern, main polarization pattern, and cross-polarization pattern after CTI algorithm optimization. Component elevation profile transmitted beam diagram Component azimuth profile transmitted beam pattern. Performance parameters of AP and CTI algorithms are shown in Table 1.

[0111] Table 1. Algorithm performance parameters under linear polarization

[0112]

[0113] Simulation Experiment 3: In this simulation, the polarization mode is considered to be circular polarization, and the main polarization is set to left-hand circular polarization. Cross-polarization is set to right-hand circular polarization The optimized transmit pattern should have a cross-polarization level below -26dB, a peak sidelobe level below -24dB, and a concave region level below -45dB. Both the AP algorithm and the CTI algorithm are iterated 1500 times. Figures 13 to 17 These are the overall transmit beam pattern, main polarization pattern, and cross-polarization pattern after CTI algorithm optimization. Component elevation profile transmitted beam diagram Component azimuth profile transmitted beam pattern. Performance parameters of AP and CTI algorithms are shown in Table 2.

[0114] Table 2 Algorithm performance parameters under circular polarization

[0115]

[0116]

[0117] In summary, as can be seen from the tables and simulation figures above, the CTI algorithm can significantly improve the performance of the conformal array transmit pattern, achieving the specific requirements of the desired pattern: polarization constraint, main lobe pointing, peak cross-polarization level, peak sidelobe level, wide notch, etc. While the AP algorithm outperforms the CTI algorithm in peak sidelobe level and cross-polarization level, it is less effective in polarization constraint, and the level in the notch region is significantly higher than that of the CTI algorithm. Overall, the performance of the two algorithms is similar. Furthermore, the CTI algorithm not only achieves a higher output signal-to-noise ratio but also runs faster and has wider applicability.

[0118] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated otherwise, may be replaced by other equivalent or similar alternative features. All disclosed features, or steps in all methods or processes, except for mutually exclusive features and / or steps, may be combined in any way. Any non-essential additions or substitutions made by those skilled in the art based on the technical features of the present invention shall fall within the protection scope of the present invention.

Claims

1. A conformal polarization array transmit beamforming algorithm based on cumulative parameter tuning iteration, characterized in that, Includes the following steps: Step 1) Set the total number of elements N of the conformal polarization array. The array elements are respectively in and The element radiation pattern is used to establish a conformal array model based on the local radiation pattern of the array elements. Here, the angle θ∈[0,π / 2] is the pitch angle. It is the azimuth angle; Step 2) Based on The steering vectors in the direction yield steering vectors for the main polarization direction and the cross-polarization direction: in, λ is the signal wavelength, (x n ,y n ,z n () represents the position of the nth array element. n = 1, ..., N, (γ co ,η co ) and (γ x ,η x These are the main polarization parameter and the cross-polarization parameter, respectively. Step 3) Construct the MVDR beamformer to obtain the initial weight vector Step 4) Combine the initial weight vector to make The signal power is minimized at this point, thus obtaining the optimal adaptive transmission weights: Step 5) Simplify and decompose the emission weight vector to obtain: As can be seen from the above formula, we can control it by adjusting μ. The radiation pattern response at point μ is a real-valued adjustment parameter, expressed as follows: Step 6) shows that we can achieve this by adding... The initial weight w T,0 It became w * Based on this idea, given the weight vector w k-1 The kth adjustment angle and the corresponding expected level ρ k The weight vector at step k can be written as: The remaining question is how to find the appropriate parameter μ. k To achieve the given requirements; to provide information about μ based on the expected requirements. k Mathematical model: here This indicates that the angle will be adjusted. Adjust the level at the desired level ρ k , This means minimizing the change in response between two consecutive pattern control operations; The optimal solution is obtained by applying the Lagrange multiplier method to the above equation. Where λ is a Lagrange multiplier, (λ * +λ)1 and (λ * +λ)2 is the equation 4χ 2 α - 8χβκ + 16κ 2 const + [-β 2 α + 4α 2 const](λ * + λ) 2 + [-4β 2 κ + 16καconst](λ * The solution of + λ) Step 7) Express the optimal weight vector for the k-th iteration as: Step 8) The iteration is terminated when the final transmission pattern meets the expected constraints or the number of iterations reaches the maximum, and the transmission beam pattern that meets the performance requirements is obtained.

2. The method as described in claim 1, characterized in that, In step 3), the conditional extremum problem of the MVDR beamformer can be expressed as follows: Solving the above optimization problem, we can obtain the initial solution as follows: Since the normalization factor α1 does not affect the final pattern shape, we ignore it.

3. The method as described in claim 1, characterized in that, In step 4), we set the radiation pattern to be adjusted as the main polarization component radiation pattern and the cross polarization component radiation pattern: when adjusting the main polarization component radiation pattern, we adjust the point guide vector. In this context, g is set to co, and the point steering vector will be adjusted when the cross-polarization component pattern is adjusted. Let g be x.

4. The method as described in claim 1, characterized in that, In step 6), we will determine the direction in the radiation pattern obtained in the (k-1)th iteration that deviates the most from the desired radiation pattern. Let this be the adjustment direction for the k-th iteration.

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