An optimal beam analytical method for a heterogeneous array antenna

Abstract

The application discloses an optimal beam analytical method of a heterogeneous array antenna, and comprises the following steps: for any form of the heterogeneous array antenna, a mapping relationship between a subarray and an array element is expressed by a binary correlation function; the overall excitation of the heterogeneous array is expressed in the form of the correlation function and the excitation of the subarray to be optimized; the total directional diagram of the heterogeneous array is calculated by the superposition theorem of a field, and then the directivity coefficient / gain is calculated; the directivity coefficient / gain is converted into a generalized Rayleigh quotient form; the subarray excitation weight of the optimal directivity coefficient / gain focusing beam is derived based on the extreme value property of the Rayleigh quotient, and the corresponding theoretical optimal value is obtained; the calculated subarray excitation is multiplied by the correlation function, so that the overall excitation distribution of the heterogeneous array is obtained. The method can realize the optimal beam analytical solution of any form of the heterogeneous array antenna, and has excellent calculation efficiency while ensuring accuracy.

Description

Technical Field

[0001] This invention relates to the field of beamforming for array antennas, and more specifically to an optimal beam analysis method for heterogeneous array antennas. Background Technology

[0002] With the rapid development of wireless communication technology, traditional antenna arrays using single-structure unit arrays are no longer sufficient to meet the urgent needs of high-performance wireless information systems for multi-functional integration, ultra-wideband intelligence, and low-cost miniaturization. To address this limitation, heterogeneous array antennas offer an effective solution. There are two main implementation methods: one is to directly use antenna units of different structures or sizes for arraying; the other is to array the same type of antenna units through differentiated subarray division. This design not only effectively alleviates the contradiction between aperture size, operating bandwidth, and radiation efficiency, but also significantly improves grating lobe suppression performance in the high-frequency band. Furthermore, the subarray division-based implementation method, while ensuring overall radiation performance, can also significantly reduce the number of transmit and receive channels, thereby effectively reducing system hardware costs.

[0003] Directivity and gain, as core indicators for evaluating the performance of array antennas, have fundamental guiding significance for the design and optimization of heterogeneous array antennas. Directivity is defined as the ratio of the power density in the direction of maximum main lobe to the average power density in the entire space, given the same total radiated power. It characterizes the concentration of radiated energy, i.e., the theoretical focusing capability of the antenna in the direction of maximum radiation, without considering power loss caused by port impedance mismatch. Gain is defined as the ratio of the power density in the direction of maximum main lobe to the average power density in the entire space, given the same input power. It more accurately characterizes the overall radiation utilization efficiency of the antenna in a specific direction.

[0004] In-depth analysis of the theoretical limits of gain and directivity coefficient of array antennas has dual significance. Firstly, it provides a performance benchmark for evaluating heterogeneous array designs. Due to differences in element types or subarray partitioning, heterogeneous arrays exhibit more complex electromagnetic characteristics. Calculating the theoretical limits allows for the evaluation of the fundamental performance of heterogeneous array antenna designs, thereby guiding array parameter optimization. Secondly, theoretical limit analysis provides a fundamental reference for beamforming. Clearly defining the theoretical limits of gain and directivity coefficients helps designers set reasonable beamforming targets, avoiding the pursuit of performance indicators that exceed physical limits, thus determining feasible technical routes from the early stages of design.

[0005] In the prior art:

[0006] In 2017, Yang Jing, in her paper "Optimal Directivity Synthesis of Arbitrary Arrays with Cross-Polarization and Sidelobe Constraints," proposed an analytical solution method based on the Rayleigh quotient for solving the optimal directivity coefficient problem of traditional arrays under unconstrained conditions. This method transforms the matrix representation of the directivity coefficients into a generalized Rayleigh quotient form and, utilizing the extremum property of the Rayleigh quotient and the Lagrange multiplier method, derives the analytical solution for the excitation weights to achieve optimal directional focusing, thus obtaining the theoretical limit of the directivity coefficients. Building on this, in 2023, Xiao Fan, in his paper "Rapid Calculation of Gain Pattern and Subarray Partitioning Technology for Phased Array Antennas," similarly used the extremum property of the Rayleigh quotient to derive the analytical solution and theoretical limit of the optimal gain of traditional arrays under unconstrained conditions. However, the above analytical methods are all based on the assumption of traditional uniform arrays and have not yet addressed the case of heterogeneous antenna arrays. In particular, for heterogeneous arrays constructed through differentiated subarray partitioning, which are fed using combined subarrays, existing analytical methods cannot be applied. Therefore, how to establish an analytical theory for optimal beamforming based on the structural characteristics of heterogeneous arrays still needs further in-depth research. Summary of the Invention

[0007] The purpose of this invention is to solve the problem that existing optimal beam analysis solutions cannot be applied to heterogeneous arrays. It proposes an optimal beam analysis method for heterogeneous array antennas. This method is applicable to heterogeneous arrays that directly use unit antennas of different structures or sizes for arraying, as well as heterogeneous arrays that use the same type of antenna units for arraying through differentiated subarray division. It can achieve a focused beam with optimal directivity and optimal gain.

[0008] An optimal beam analysis method for heterogeneous array antennas includes the following steps:

[0009] Step 1: For any form of heterogeneous array antenna, use a binary correlation function to describe whether any array element belongs to a certain subarray, thereby establishing the mapping relationship between subarrays and array elements;

[0010] Step 2: Multiply the correlation function with the subarray excitation to be optimized, and express the overall excitation of the heterogeneous array as a linear combination of subarray excitations;

[0011] Step 3: Calculate the total radiation pattern of the heterogeneous array using the superposition theorem of fields, and then calculate the directional coefficients / gain;

[0012] Step 4: Express the directivity coefficient / gain as a matrix expression for the element pattern, correlation function, and subarray excitation, and transform it into the generalized Rayleigh quotient form;

[0013] Step 5: Based on the extreme value property of Rayleigh quotient, derive the subarray excitation weights of the optimal directional coefficient / gain, and obtain the corresponding theoretical optimal values.

[0014] Step 6: Multiply the calculated subarray excitations by the correlation function to obtain the overall excitation distribution of the heterogeneous array.

[0015] Furthermore, in step 1, it is assumed that the heterogeneous array has N array elements, which are numbered as follows: There are M subarrays operating simultaneously. Here, a subarray refers to a collection of antenna elements fed by the same radio frequency channel, which are numbered as follows: The binary associative function is expressed as

[0016] (1)

[0017] Furthermore, in step 2, using a binary correlation function, the overall excitation of the heterogeneous array is expressed as follows:

[0018] (2)

[0019] in, This represents the excitation of the nth array element. This represents the excitation of the m-th subarray.

[0020] Furthermore, in step 3, assuming the heterogeneous array is placed in the xoy plane, its total radiation pattern can be represented as the sum of the radiation patterns of M subarrays.

[0021] (3)

[0022] in, , , This represents the free-space beam at the operating frequency f. This indicates the position of the nth array element. This represents the radiation pattern of the active element of the nth array element.

[0023] By defining the directional coefficient and gain, the heterogeneous array can be positioned at the pointing angle. The directivity coefficient and actual gain at a given point can be written as:

[0024] (4)

[0025] (5)

[0026] in, This is the free-space wave impedance.

[0027] Furthermore, in step 4, the directional coefficients and gain are rewritten in the form of generalized Rayleigh quotients through matrix representation.

[0028] (6)

[0029] (7)

[0030] in, The subarray excitation matrix L is defined as follows: The active element radiation pattern matrix is ​​defined as follows: , .

[0031] Furthermore, in step 5, by utilizing the extreme value property of the Rayleigh quotient, the subarray excitation under optimal directional beam is obtained.

[0032] (8)

[0033] At this point, the theoretical limit of the directionality of the heterogeneous array is...

[0034] (9)

[0035] Subarray excitation under optimal gain beam

[0036] (10)

[0037] At this point, the theoretical limit of the gain of the heterogeneous array is...

[0038] (11)

[0039] Furthermore, in step 6, the calculated optimal directional subarray excitation and optimal gain subarray excitation are multiplied by the correlation function to obtain the optimal directional and optimal gain beam excitation weights of the heterogeneous array.

[0040] (12)

[0041] (13)

[0042] in, This represents the overall excitation of the heterogeneous array.

[0043] The advantages of this invention are:

[0044] 1. This invention transforms the optimization problem of the directional coefficients and gain of heterogeneous arrays into a generalized Rayleigh quotient form and derives an analytical solution using the Lagrange multiplier method. Compared to convex optimization methods that require iterative solutions, this method eliminates the need for multiple numerical calculations, resulting in higher computational efficiency and facilitating engineering implementation and real-time applications.

[0045] 2. This invention uses the product of a binary correlation function and the subarray excitation to uniformly express the excitation distribution of heterogeneous arrays. The resulting analytical expression is applicable not only to heterogeneous arrays composed of units with different structures or sizes, but also to heterogeneous arrays constructed using differentiated subarray partitioning methods. It is also compatible with traditional array antennas, thus possessing wide applicability.

[0046] 3. This invention not only provides analytical solutions for the excitation of a focused beam with optimal directivity and gain, but also obtains the theoretical limits of the corresponding directivity coefficient and gain. These theoretical values ​​provide clear benchmarks for the performance evaluation of heterogeneous array antennas, helping to set reasonable performance targets in the design process, avoid unrealistic pursuit of physical limits, and improve design efficiency and feasibility. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the optimal beam resolution method for a heterogeneous array antenna according to the present invention.

[0048] Figure 2 This is a schematic diagram of the heterogeneous array antenna layout in an embodiment of the present invention;

[0049] Figure 3 This is the antenna element model used in the heterogeneous array in the embodiments of the present invention;

[0050] Figure 4 This is the optimal directional focusing beam in the embodiment of the present invention. Directional coefficient diagram of cross section and uv surface directional coefficient diagram.

[0051] Figure 5 This is the excitation amplitude and phase distribution diagram of the optimal directional focusing beam of the heterogeneous array in this embodiment of the invention.

[0052] Figure 6 This is the optimal gain focusing beam in the embodiment of the present invention. Cross-sectional gain pattern and uv-plane gain pattern.

[0053] Figure 7 This is the excitation amplitude and phase distribution diagram of the heterogeneous array optimal gain focusing beam in this embodiment of the invention. Detailed Implementation

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments given are not intended to limit the present invention. The present invention can adopt other embodiments and can be implemented or performed in various ways. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative improvements are within the scope of protection of the present invention.

[0055] This invention includes the following steps:

[0056] Step 1: For a heterogeneous array antenna with N elements, number the elements as follows: There are M subarrays operating simultaneously. Here, a subarray refers to a collection of antenna elements fed by the same radio frequency channel, which are numbered as follows: The binary associative function is expressed as

[0057] (1)

[0058] Step 2: Using binary correlation functions, the overall excitation of the heterogeneous array is expressed as follows:

[0059] (2)

[0060] in, This represents the excitation of the nth array element. This represents the excitation of the m-th subarray.

[0061] Step 3: The heterogeneous array is placed in the xoy plane, and its overall radiation pattern can be represented as the sum of the radiation patterns of M subarrays.

[0062] (3)

[0063] in, , , This represents the free-space beam at the operating frequency f. This indicates the position of the nth array element. This represents the radiation pattern of the active element of the nth array element.

[0064] By defining the directional coefficient and gain, the heterogeneous array can be positioned at the pointing angle. The directivity coefficient and actual gain at a given point can be written as:

[0065] (4)

[0066] (5)

[0067] in, This is the free-space wave impedance.

[0068] Step 4: Rewrite the directional coefficients and gain into the form of a generalized Rayleigh quotient using matrix representation.

[0069] (6)

[0070] (7)

[0071] in, The subarray excitation matrix L is defined as follows: The active element radiation pattern matrix is ​​defined as follows: , .

[0072] Step 5: Using the extreme value property of the Rayleigh quotient, obtain the subarray excitation under optimal directional beam.

[0073] (8)

[0074] At this point, the theoretical limit of the directionality of the heterogeneous array is...

[0075] (9)

[0076] Subarray excitation under optimal gain beam

[0077] (10)

[0078] At this point, the theoretical limit of the gain of the heterogeneous array is...

[0079] (11)

[0080] Step 6: Multiply the calculated optimal directional subarray excitation and optimal gain subarray excitation by the correlation function to obtain the optimal directional and optimal gain beam excitation weights of the heterogeneous array.

[0081] (12)

[0082] (13)

[0083] in, This represents the overall excitation of the heterogeneous array.

[0084] The specific implementation of the optimal beam analysis method for heterogeneous array antennas proposed in this invention can be further given through the following simulation examples and results:

[0085] Taking an aperture multiplexing heterogeneous array placed on the xoy plane as an example, the specific layout is as follows: Figure 1 As shown, heterogeneous subarray A (dark gray) is composed of a single antenna element, and the element form is as follows: Figure 2 The Vivaldi antenna shown has an element spacing of [missing information]. Heterogeneous subarray B (light gray) uses an O-tetromino type subarray for combining based on the same antenna elements. Considering that the broadband characteristics of the Vivaldi antenna depend on the periodic structure, to more accurately reflect its actual radiation performance in an array environment, a 7×7 uniform planar array composed of these elements is simulated. The radiation pattern of the active element at 20 GHz is extracted from the central element and used as the radiation pattern of the elements in heterogeneous subarrays A and B. Based on this, the analytical solution derived in this invention and traditional convex optimization numerical methods are used to optimize the directivity coefficient and gain of the array normal. Figure 3 and Figure 5 Simulation results for the directivity coefficient and gain in the xoz plane were compared. The analytical solution proposed in this paper is consistent with the results of the convex optimization method, with a directivity coefficient of 28.65 dBi and a normal gain of 28.78 dBi in both cases. As can be seen from the uv-plane radiation pattern, both methods achieve effective focusing in the normal direction. Figure 4 and Figure 6 The excitation amplitude and phase distributions of the optimal directivity and optimal gain beams are presented respectively. Numerical simulation results show that the analytical solution is completely consistent with the results obtained by the traditional convex optimization method, which fully demonstrates that the optimal beam analytical method proposed in this invention has important theoretical guiding significance for the engineering practice of heterogeneous array antennas.

Claims

1. An optimal beam resolution method for a heterogeneous array antenna, comprising the following steps: Step 1: For any form of heterogeneous array antenna, use a binary correlation function to describe whether any array element belongs to a certain subarray, thereby establishing the mapping relationship between subarrays and array elements; Step 2: Multiply the correlation function with the subarray excitation to be optimized, and express the overall excitation of the heterogeneous array as a linear combination of subarray excitations; Step 3: Calculate the total radiation pattern of the heterogeneous array using the superposition theorem of fields, and then calculate the directional coefficients / gain; Step 4: Express the directivity coefficient / gain as a matrix expression for the element pattern, correlation function, and subarray excitation, and transform it into the generalized Rayleigh quotient form; Step 5: Based on the extreme value property of Rayleigh quotient, derive the subarray excitation weights of the optimal directional coefficient / gain, and obtain the corresponding theoretical optimal values. Step 6: Multiply the calculated subarray excitations by the correlation function to obtain the overall excitation distribution of the heterogeneous array.

2. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 1, assume the heterogeneous array has N elements, which are numbered as follows: There are M subarrays operating simultaneously. Here, a subarray refers to a collection of antenna elements fed by the same radio frequency channel, which are numbered as follows: The binary associative function is expressed as 。 3. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 2, using the binary correlation function, the overall excitation of the heterogeneous array is expressed as: ； in, This represents the excitation of the nth array element. This represents the excitation of the m-th subarray.

4. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 3, assuming the heterogeneous array is placed in the xoy plane, its total radiation pattern can be represented as the sum of the radiation patterns of M subarrays. ； in, , , This represents the free-space beam at the operating frequency f. This indicates the position of the nth array element. This represents the radiation pattern of the active element of the nth array element.

5. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 3, by defining the directional coefficient and gain, the heterogeneous array at the pointing angle... The directivity coefficient and actual gain at a given point can be written as: ； ； in, This is the free-space wave impedance.

6. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 4, the directional coefficients and gains are rewritten in the form of generalized Rayleigh quotients through matrix representation. ； ； in, The subarray excitation matrix L is defined as follows: The active element radiation pattern matrix is ​​defined as follows: , .

7. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 5, the subarray excitation under optimal directional beam is obtained by utilizing the extreme value property of the Rayleigh quotient. ； At this point, the theoretical limit of the directionality of the heterogeneous array is... ； Subarray excitation under optimal gain beam ； At this point, the theoretical limit of the gain of the heterogeneous array is... 。 8. The optimal beam analysis method for a heterogeneous array antenna according to claim 1, characterized in that: In step 6, the calculated optimal directional subarray excitation and optimal gain subarray excitation are multiplied by the correlation function to obtain the optimal directional and optimal gain beam excitation weights of the heterogeneous array. ； ； in, This represents the overall excitation of the heterogeneous array.

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