Directional diagram self-adaptive real-time zero setting method for large-scale arbitrary geometric array

Abstract

The invention discloses an adaptive real-time zero setting method for a directional diagram of a large-scale arbitrary geometric array, relates to the field of array antenna directional diagram synthesis, and aims to solve the problems of insufficient directional diagram null forming precision and overhigh comprehensive calculation complexity of a large-scale irregular array in a dynamic interference environment. The method comprises the following technical steps: firstly, establishing a directional diagram unified expression of any geometric array, and providing general modeling for different topologies; secondly, deducing an excitation analytic solution in the target direction when the directivity coefficient is maximum, and laying a foundation for constructing a beam base with directional enhancement capability; then, the directional diagram is expressed as a linear combination of a preset beam base, and the calculation dimension is reduced; then, a beam space manifold vector used for multi-direction null control is constructed to support null constraint accurate expression; and finally, deducing an excitation analytic solution of adaptive zero setting of the directional diagram in the beam space to realize rapid reconstruction. The method has the characteristics of analysis and non-iteration, microsecond-level zero setting adjustment can be completed on a conventional platform, and the method has real-time performance, structural adaptability and high-precision directional diagram performance.

Description

Technical Field

[0001] The present invention relates to the field of array antenna synthesis, and in particular to a method for adaptive real-time nulling of directional patterns of large-scale arbitrary geometric arrays. Background Art

[0002] In complex electromagnetic environments, simply optimizing the directivity coefficient or gain of the array pattern is no longer sufficient to meet the comprehensive multi-dimensional performance requirements of practical engineering applications. In particular, in key systems such as radar detection, electronic countermeasures, and intelligent communications, array antennas must not only achieve efficient directional radiation in the target direction, but also form deep nulls in the interference direction to effectively suppress the adverse effects of non-target signals and enemy interference sources. In addition, in a dynamic interference environment, the location of the interference source is significantly time-varying and unpredictable. The array antenna system must have good real-time adaptive adjustment capabilities to achieve continuous tracking and suppression of time-varying interference. Traditional static pattern design methods generally lack the ability to respond to environmental changes and are unable to meet the above application requirements. Therefore, how to achieve real-time and high-precision null formation in multiple specified directions while ensuring the stability of the main beam performance has become a key technical issue that needs to be urgently addressed in high-performance array antenna systems.

[0003] In the pattern synthesis problem of large-scale irregular arrays, real-time nulling presents even more severe technical challenges. On the one hand, with the substantial increase in the number of array elements, pattern modeling requires processing high-dimensional array manifolds, significantly increasing the computational burden. In regular array structures, the pattern can typically be quickly solved using efficient numerical algorithms such as the Fast Fourier Transform, thereby reducing computational complexity. However, in irregular arrays, due to the lack of periodicity and symmetry in the array element distribution, the pattern cannot be converted into a Fourier series form. The calculation must rely on direct matrix operations, and the computational complexity increases linearly with the number of array elements. Furthermore, pattern synthesis for irregular arrays involves not only pattern construction but also the joint optimization of the excitation parameters of a large number of elements. The large number of variables makes the optimization problem high-dimensional, non-convex, and strongly coupled, severely limiting its real-time solution capability. Therefore, large-scale irregular arrays face the dual challenges of high computational complexity and large optimization dimensions when performing pattern adaptive nulling, making it difficult to meet the stringent real-time and stability requirements of complex application scenarios. In summary, there is an urgent need to develop an efficient, scalable, and real-time synthesis method for directional patterns of irregular structures to achieve rapid response and precise control of dynamic interference, thereby promoting the application of array synthesis technology in actual complex electromagnetic environments.

[0004] Chinese patent 201710206959.4 discloses a radar array sum and difference beam pattern optimization method based on a convex optimization algorithm. The basic idea of ​​this method is to transform the sum and difference beam pattern optimization problem of the radar circular array into a convex optimization problem. By constructing a suitable objective function and constraints, and with the help of the convex optimization toolkit in MATLAB, the optimal array excitation weights are obtained. This method can effectively reduce the sidelobe level in the pattern and form a deep null, thereby improving the interference suppression performance of the radar system. Compared with traditional random optimization algorithms (such as genetic algorithms and simulated annealing algorithms), this method has higher computational efficiency. However, since it essentially relies on the numerical optimization solution process, it is difficult to adapt to the real-time zeroing requirements of the pattern of large-scale arrays under the condition of limited computing resources.

[0005] Chinese patent 201711024309.4 discloses an adaptive beamforming method based on deepening nulling of a uniform linear array. This method uses a uniform linear array as the signal receiving model and performs singular value decomposition on the autocorrelation matrix of the antenna array received signal, thereby expanding the interference subspace to enhance the interference signal power. Subsequently, the improved interference subspace matrix and the desired signal direction vector are combined to calculate the optimal excitation weights for adaptive beamforming after deepening nulling. This method can effectively overcome the problems of insufficient nulling depth and position offset of the directional pattern caused by interference power fluctuations in traditional technologies, thereby improving the accuracy of interference suppression. However, this method is only applicable to uniform linear arrays and is difficult to directly apply to array systems with irregular array element distribution or complex structure, limiting its promotion in various practical engineering scenarios.

[0006] Chinese patent CN202311803656.2 discloses a method for nulling the main lobe of a large-scale array shaped beam. This method is based on the beam scanning characteristics of a phased array. By superimposing multiple point beams pointing in different directions and adjusting the weights of each beam, the target pattern is shaped and constructed and nulled. Due to the low overall computational complexity, it can be run on an embedded system and has a certain real-time processing capability. It is suitable for beamforming and nulling tasks of low-complexity large-scale arrays. However, the weight adjustment of this method depends on the feedback correction of the nulling position, that is, by comparing the deviation between the actual nulling position and the expected position in the current pattern, the weight is iteratively updated, so the nulling accuracy depends on the number of iterations. If the nulling control accuracy needs to be improved, not only the number of iterations needs to be increased, but also the additional calculation of the nulling position verification needs to be introduced, resulting in an increase in the overall computational overhead, which limits its applicability in application scenarios where both high real-time performance and high precision are equally important. Summary of the Invention

[0007] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to propose a real-time adaptive nulling method for directional patterns applicable to large-scale arbitrary geometric arrays.

[0008] The technical approach of this invention is to introduce the concept of beam space modeling and represent the array pattern as a linear combination of a finite number of beam basis functions, thereby significantly reducing the dimensionality and complexity of pattern calculation. On this basis, combined with the numerical pattern synthesis technology used in adaptive array processing, an efficient beam space mapping mechanism is further constructed. Ultimately, an analytical solution for the excitation corresponding to the adaptive nulling of the pattern is obtained. The technical solution of this invention includes the following steps:

[0009] Step 1: Provide a mathematical expression for the array pattern applicable to any geometric array.

[0010] Step 2: derive the analytical solution of focused beam excitation applicable to arbitrary geometric arrays;

[0011] Step 3: introduce the beam basis function expansion representation of the array pattern;

[0012] Step 4, constructing a beam space manifold vector for adaptive zeroing of the pattern;

[0013] Step 5: Provide the analytical solution of the excitation corresponding to the adaptive nulling of the directional pattern in the beam space.

[0014] The present invention has the following advantages and beneficial effects:

[0015] a) This invention boasts superior real-time performance. By constructing preset beamspace basis functions and employing analytical methods to solve for excitations, the high computational overhead of iterative optimization in the high-dimensional array element excitation space is effectively avoided, significantly reducing overall computational complexity. On conventional computing platforms, microsecond-level zeroing adjustments can be achieved, fully meeting the real-time control requirements in high-speed dynamic interference environments.

[0016] b) This invention possesses excellent structural adaptability. Relying on beamspace mapping to solve the excitation vector, it eliminates the need for customized adjustments to the specific array structure. It demonstrates excellent pattern synthesis capabilities on complex platforms, including cylindrical conformal arrays, demonstrating its broad adaptability to large-scale arrays of arbitrary geometry.

[0017] c) This method achieves excellent pattern accuracy. It can accurately achieve deep nulling in multiple specified interference directions, effectively suppressing interfering signals while ensuring that the main beam is precisely pointed in the preset direction and maintaining good directivity. This fully demonstrates the effectiveness and robustness of the proposed method in high-precision pattern synthesis tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0019] Figure 1 It is a flowchart of the overall process of the array synthesis method involved in the present invention;

[0020] Figure 2 Schematic diagram of the structure of a 16×16 element cylindrical conformal array in an embodiment of the present invention;

[0021] Figure 3 is a three-dimensional schematic diagram of the main polarization pattern of the array obtained by synthesis in an embodiment of the present invention;

[0022] Figure 4 Schematic cross-sectional view of the main polarization pattern of the array obtained by synthesis in an embodiment of the present invention. DETAILED DESCRIPTION

[0023] Before describing any embodiment of the present invention in detail, it should be understood that the application of the present invention is not limited to the details of the structure shown in the following description or the accompanying drawings. The present invention may adopt other embodiments and may be implemented or carried out in various ways. Based on the embodiments of the present invention, all other embodiments obtained by ordinary skill in the art without making creative improvements are within the scope of protection of the present invention.

[0024] like Figure 1 As shown, the present invention includes the following steps:

[0025] 1) First, a mathematical expression for the array pattern applicable to arbitrary geometric arrays is given.

[0026] Consider an N-element array antenna with arbitrary geometry. The Cartesian coordinates of the n-th element in the array coordinate system are expressed as (x n ,y n ,z n ). In the observation direction The array pattern can be expressed as

[0027]

[0028] This expression serves as the mathematical modeling basis of the present invention. The meanings of the physical quantities in the formula are as follows:

[0029] a) The unit pattern of the nth unit reflects its radiation directivity and coupling characteristics, which can usually be obtained through full-wave electromagnetic simulation or actual measurement;

[0030] b)w n is the complex excitation of the nth unit;

[0031] c) is the position vector of the nth unit in the three-dimensional Cartesian coordinate system, and its specific form is in The unit vector representing its direction, and is the unit vector in the direction of the coordinate axis;

[0032] d) is the wave vector related to the spatial direction, and its specific form is

[0033] in is the wave number in free space and c is the speed of light.

[0034] 2) Secondly, an analytical solution for focused beam excitation applicable to arbitrary geometric arrays is derived.

[0035] In order to enhance the energy concentration of the main beam in space, the present invention introduces the directivity coefficient as an optimization index to improve the radiation gain and signal power utilization efficiency in the target direction. The directivity coefficient is defined as follows:

[0036]

[0037] It can be expressed in the following generalized Rayleigh quotient form:

[0038]

[0039] The matrices and vectors in the formula are defined as follows:

[0040]

[0041] w=[w1,w2,…,w N ] H (4d) For the nth unit in The complex directional response in the direction, which reflects the radiation gain and phase delay characteristics of the unit in this direction, is defined as According to the properties of the generalized Rayleigh quotient, when formula (3) reaches its maximum value, that is, the target direction When the directivity coefficient is the largest, the corresponding excitation analytical solution is

[0042]

[0043] 3) Subsequently, the beam basis function expansion representation of the array pattern is introduced.

[0044] The basic idea of ​​beam space array synthesis is to map the original high-dimensional array element excitation to a lower-dimensional beam coefficient space through a predefined set of beam basis functions, thereby significantly reducing the computational complexity and improving the flexibility of pattern optimization. In this framework, the array pattern can be expressed as a weighted linear combination of a set of beam basis functions, where the weight coefficients are used to control the contribution of each beam basis function. Based on this idea, the present invention further rewrites the array pattern expression (1) as

[0045]

[0046] in, represents the kth predefined beam, is the array element excitation corresponding to the beam, c k is the weighting coefficient of the beam. Equation (6) shows that the array pattern can be regarded as a linear combination of K beam basis functions. By adjusting the beam weighting coefficient, the radiation characteristics of the pattern can be flexibly controlled. Define the following beam space manifold vector and beam coefficient vector:

[0047]

[0048] Based on formula (7) The vector inner product representation of The beam space manifold vector can be written as

[0049]

[0050] Among them, W BB =[w (1) ,w (2) ,…,w (K) ] is the excitation matrix corresponding to the beam basis (BB). Combined with formula (6), the array pattern can be expressed as

[0051]

[0052] According to the above formula, it is obvious that the excitation corresponding to the directional pattern obtained by the weighted linear combination of beam basis functions is

[0053] w sol =W BB c (11) This expression shows that in the beam space method, although the array element excitation vector w sol It is no longer directly used as an optimization variable, but it can still be optimized through the coefficient vector c through the mapping matrix W BB This means that array synthesis is actually performed in the beam space rather than the original array element excitation space, significantly reducing the dimensionality of the optimization problem and improving computational efficiency.

[0054] 4) Then, construct a beam space manifold vector for adaptive nulling of the pattern.

[0055] Aiming at the problem of adaptive formation of nulling of array pattern, the present invention constructs beam space basis function with good focusing ability based on the maximum solution of directivity coefficient in formula (5). Specifically, considering that the solution has stronger directional focusing characteristics in the main lobe area, the corresponding target direction is selected. And K-1 preset interference directions or directions where nulls are expected to form (where k = 1, 2, ..., K-1), construct the corresponding focused beam, and use this as the basis function set of the beam space. This gives K beam bases, which are used to achieve mainlobe enhancement and multi-directional nulling control. To mathematically describe the beam basis construction method, the following array manifold submatrix is ​​defined:

[0056]

[0057] Combined with formula (5), the excitation matrix corresponding to the beam basis can be expressed as

[0058]

[0059] Substituting the above formula into formula (9), we can obtain the beam space manifold vector under the defined beam basis:

[0060]

[0061] where Q -H =Q -1 , which is because Q is a symmetric positive definite matrix. So far, the mathematical modeling of the array pattern in beam space has been completed.

[0062] 5) Finally, the analytical solution of the excitation corresponding to the adaptive nulling of the directional pattern in beam space is given.

[0063] In order to facilitate the numerical solution, the angle space Perform discrete sampling, select M discrete sampling points, and define the full airspace sampling set and the null region sampling set as follows: On this basis, the present invention combines the numerical pattern synthesis technology in adaptive array processing to achieve adaptive null formation of the array pattern. The core idea of ​​the numerical pattern synthesis method is to minimize the weighted total power of the entire pattern while ensuring the gain in the target direction, thereby achieving control of the sidelobe area. In the beam space method, the optimization problem can be described as

[0064]

[0065] Among them, F targetTarget direction The expected pattern value on is theoretically only used as a scaling factor and does not affect the relative shape of the pattern regardless of its value; For direction Based on formula (10), the problem can be further written as

[0066]

[0067] In order to simplify the formula expression, we define as well as In order to ensure the physical interpretability of the optimization solution, it is advisable to set F target Take the direction pattern value of the focused fundamental beam in the target direction at this point Right now:

[0068]

[0069] This setting ensures that the optimized directional pattern is consistent with the selected beam basis in the target direction, and on this basis, the null area is precisely controlled to suppress strong interference signals.

[0070] In the adaptive array processing framework, the weight factor Dynamic adjustment is performed and a clear physical meaning is given in the optimization model, namely the power of virtual interference. In addition, in order to improve the robustness of the optimization solution, the present invention additionally introduces the Gaussian white noise power Based on this, the minimization problem is reformulated as follows:

[0071]

[0072] To further simplify the problem, define the covariance matrix of the array:

[0073]

[0074] Where I is the identity matrix, represents the interference to noise ratio of the mth virtual interference. So far, the optimization problem can be reformulated as

[0075]

[0076] This problem is a quadratic optimization problem with equality constraints and can be solved using the Lagrange multiplier method. The beam coefficients corresponding to the optimal solution are expressed as follows:

[0077]

[0078] Equation (21) is an analytical solution, and its control of the pattern depends entirely on the interference-to-noise ratio ξ in the covariance matrix R mThe value of directly determines the degree of penalty imposed on the corresponding angle point during the optimization process. In the application scenario of null formation, strong constraints should be imposed on the null area in the optimization objective, while no restrictions should be imposed on other areas. To this end, the interference-to-noise ratio of the virtual interference can be defined as:

[0079]

[0080] Among them, Γ NL is the desired depth of the null (e.g., setting Γ NL =-50dB) to ensure that the signal in the target direction can be effectively suppressed; η is the adjustment factor used to control the weight of the penalty term. Proper selection of η (such as η = 50) can ensure that the null sink reaches a sufficient depth while avoiding numerical instability and improving the robustness of the optimization solution. c0 is the initial reference solution, set to

[0081]

[0082] This initial solution corresponds to all interference weights ξ in the covariance matrix R m = 0, which is the optimal solution assuming no interference. Based on formula (22), for the null direction have Then the covariance matrix R can be simplified to

[0083]

[0084] With the original covariance matrix In comparison, the simplified covariance matrix R Null The dimension of R is only (K-1)×(K-1), where K<<M. This dimension compression significantly reduces the scale of matrix operations required in subsequent processing. Null Substituting into equation (21) and combining it with equation (11), we can obtain the excitation analytical solution corresponding to the adaptive nulling of the directional pattern based on the beam space:

[0085]

[0086] In summary, the present invention is based on analytical derivation from the construction of beam basis functions to the solution of excitation, without relying on iterative optimization. By pre-storing beam basis functions, the null-forming process can be completed efficiently in the beam space, avoiding complex optimization directly in the high-dimensional array element excitation space. With the help of beam space mapping, this method significantly reduces the computational dimension and makes matrix operations extremely efficient. Under conventional computing resource conditions, the present invention can complete the null-forming adjustment in microseconds, with excellent real-time performance and computational stability. The overall flow chart of the array synthesis method involved in the present invention is as follows: Figure 1 shown.

[0087] Example:

[0088] In order to verify the effectiveness of the proposed large-scale arbitrary geometric array pattern adaptive real-time nulling method, this embodiment selects a cylindrical conformal array with actual structural characteristics as the verification object, and uses HFSS software to perform full-wave electromagnetic simulation to evaluate the applicability of the proposed method under actual complex array structure. The array consists of 16×16 array elements, with a structure as follows Figure 2 As shown, the unit uses a U-shaped slot loaded patch antenna with an operating frequency of 10 GHz, mounted on a substrate made of Rogers RT / duroid5880 dielectric material (relative dielectric constant of 2.2). The array size parameters are as follows: α = 60°, R = 233, L = 15, L P =9,L S =6,W=15,W P =10.5,W S =6.5,s=0.5,D=6,d=1,H=3.175,h=1 (unit: mm). The observation angle range is set to θ∈[-180°,180°], To achieve full coverage of the spherical space. The θ component of all active unit patterns is extracted through simulation and Component data, based on Ludwig's third definition, further synthesize the main polarization component data, that is, For this conformal array, the Y direction is set as the main polarization direction.

[0089] The array integration task requirements are as follows: the main beam is deflected to It is required to form deep nulls at the interference directions (60°, 0°), (-60°, 45°) and (120°, 90°). Set the Gaussian white noise power to Based on formula (25), the array excitation can be directly obtained analytically, and the array main polarization pattern can be generated accordingly to verify the comprehensive effect. Figure 3 A three-dimensional schematic diagram of the main polarization pattern of the resulting array is shown, showing that the main beam is precisely pointed in the preset direction, with a directivity coefficient of 26.05dBi. Figure 4 The direction diagram is and The distribution of the three typical sections shows that the three set interference directions all achieved deep nulling successfully, verifying the nulling control accuracy of the proposed method. In addition, the total computational time of the array synthesis is only 4.6×10 -5 The experimental platform was a desktop computer equipped with an Intel i7-11700K (3.6GHz) processor and 128GB of memory. These results demonstrate the high adaptability and superior real-time performance of the proposed method under complex beam configurations.

Claims

1. A method for adaptive real-time nulling of the directional pattern of large-scale arbitrary geometric arrays, characterized by: The steps include: Step 1: Provide a mathematical expression for the array pattern applicable to any geometric array. Step 2: derive the analytical solution of focused beam excitation applicable to arbitrary geometric arrays; Step 3: introduce the beam basis function expansion representation of the array pattern; Step 4, constructing a beam space manifold vector for adaptive zeroing of the pattern; Step 5: Provide the analytical solution of the excitation corresponding to the adaptive nulling of the directional pattern in the beam space.

2. The method for adaptive real-time nulling of the directional pattern of a large-scale arbitrary geometric array according to claim 1, characterized in that: In step 1, the mathematical expression of the array pattern of any geometric array is in, represents the unit direction diagram of the nth unit, w n is the complex excitation of the nth unit, is the position vector of the nth unit in the three-dimensional Cartesian coordinate system, is the wave vector associated with the spatial direction.

3. The method for adaptive real-time nulling of directional patterns of large-scale arbitrary geometric arrays according to claim 1, characterized in that: In step 2, the analytical solution of focused beam excitation for an arbitrary geometric array is expressed as The matrices and vectors in the formula are defined as follows: in=[in1,in2,…,in N ] H Among them, w opt When the array pattern is in the target direction The solution corresponding to the excitation w when the directivity coefficient on reaches its maximum value; For the nth unit in Complex directional response in direction.

4. The method for adaptive real-time nulling of the directional pattern of a large-scale arbitrary geometric array according to claim 1, characterized in that: In step 3, the beam basis function of the array pattern is expanded as The matrices and vectors in the formula are defined as follows: c=[c1,c2,…,c K ] T IN BB =[in (1) ,In (2) ,…,In (K) ] in, represents the kth predefined beam, w (k) is the array element vector corresponding to the beam, c k is the weighting coefficient of the beam.

5. The method for adaptive real-time nulling of the directional pattern of a large-scale arbitrary geometric array according to claim 1, characterized in that: In step 4, the beam space manifold vector for adaptive zeroing of the pattern is expressed as Where A sub is the array manifold submatrix, defined as follows: in, It is the preset interference direction or the direction where a null is expected to be formed.

6. The method for adaptive real-time nulling of directional patterns of large-scale arbitrary geometric arrays according to claim 1, characterized in that: In step 5, the excitation analytical solution corresponding to the adaptive zeroing of the pattern in the beam space is expressed as Where F target Target direction The expected pattern value on is set to R Null The simplified covariance matrix is ​​defined as follows: in, is the Gaussian white noise power, I is the unit matrix; ξ k is the interference-to-noise ratio of the kth virtual interference, defined as follows: Among them, Γ NL is the expected depth of the null sink, η is the adjustment factor; c0 is the initial reference solution, set to

Images