Beamforming method, apparatus, device and medium for polarized time modulation array

Abstract

This application belongs to the field of beamforming technology, and relates to a method, apparatus, device, and medium for beamforming a polarization-time modulation array. The method includes: obtaining a polarization-time modulation array model and acquiring the weighting coefficients of each harmonic; based on polarization null space theory, transforming a quadratic constrained quadratic programming optimization problem into an equivalent second-order cone programming problem and solving it to obtain the optimal fundamental excitation weights; obtaining the constraint relationship between the optimal fundamental excitation weights and the phase state conduction duration, and obtaining the range of values ​​for the phase state conduction duration; performing synchronous optimization within the range of values ​​for the phase state conduction duration to obtain the optimal conduction duration and the optimal phase selection sequence, thereby determining the remaining conduction time; and performing modulation based on the optimal conduction duration and the remaining conduction time to form the beam of the polarization-time modulation array. This application can significantly improve the efficiency and numerical stability of beamforming.

Description

Technical Field

[0001] This application relates to the field of beamforming technology, and in particular to beamforming methods, apparatus, devices and media for polarization time modulation arrays. Background Technology

[0002] Array beamforming is a core technology of modern wireless communication systems. Its goal is to form a high-gain beam in a specific spatial direction by adjusting the complex weighting coefficients of each array element, while generating low-gain sidelobes.

[0003] In practical engineering applications, beamforming design often needs to satisfy a variety of complex constraints, including main lobe pointing constraints, side lobe level constraints, and polarization characteristic constraints. These constraints can usually be expressed as a combination of linear equations and quadratic inequality constraints, forming a quadratic constrained quadratic programming (QCQP) problem.

[0004] In existing technologies, the common approach to solving such beam optimization problems is to transform the original problem into a second-order cone programming (SOCP) or semi-definite programming (SDP) problem, and then solve it.

[0005] However, while the above method can guarantee global optimality, it has the following drawbacks:

[0006] (1) High computational complexity: The solution complexity is ,in To optimize variable dimensions, the computational burden becomes very heavy when the array size is large; (2) Large memory requirements: When solving directly, it is necessary to store a large number of Hessian matrices and constraint matrices; (3) Poor numerical stability: If the generated constraint matrix is ​​ill-conditioned, the numerical stability of the direct solution cannot be guaranteed.

[0007] In polarization array systems, when jointly optimizing the horizontal and vertical polarization components, the dimensionality of the optimization variables increases exponentially, making the aforementioned problems more prominent. Summary of the Invention

[0008] Therefore, it is necessary to provide a beamforming method, apparatus, device, and medium for a polarization time modulation array to address the aforementioned technical problems, which can form an ultra-low sidelobe beam and significantly improve the efficiency and numerical stability of beamforming.

[0009] Beamforming methods for polarization-time modulation arrays include: Obtain the polarization time modulation array model, and obtain the weighting coefficients of each harmonic based on the array steering vector and polarization vector; Based on the beam pointing constraints in the spatial and polarization domains, the polarization ratio constraints of the main lobe, the energy and stability constraints of the sidelobes, the ultra-low sidelobe energy constraints in the joint domain, and the minimum energy constraints, a quadratic constraint quadratic programming optimization problem is established. Based on the polarization null space theory, the polarization ratio constraints of the main lobe are transformed, and then the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, which is then solved to obtain the optimal fundamental excitation weights. The constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration is obtained to determine the range of values ​​for the phase state conduction duration. Using the conduction duration and phase selection sequence as a set of gene parameters of the chromosome, the objective function is to minimize the deviation between the sidelobe level of each harmonic and the desired sidelobe level, and the fitness function is to use the sum of the absolute differences between the highest harmonic level and the desired harmonic level. A genetic algorithm is used to perform synchronous optimization within the range of values ​​for the phase state conduction duration to obtain the optimal conduction duration and the optimal phase selection sequence, so as to determine the remaining conduction time. Modulation is performed based on the optimal conduction duration and the remaining conduction time to form the beam of the polarization time modulation array.

[0010] In one embodiment, based on the polarization null space theory, the polarization ratio constraint of the main lobe is transformed, including: Based on the polarization null space theory, a weighted vector is obtained from the constraint matrix to transform the polarization ratio constraint of the main lobe into the form of a constraint matrix and a weighted vector:

[0011] In the formula, for The conjugate transpose of . For the constraint matrix, It is the fundamental wave weighted vector.

[0012] In one embodiment, obtaining the weighted vector based on the constraint matrix includes: Perform column pivoting QR decomposition on the constraint matrix to obtain the decomposition vector; Based on the decomposition vectors, the orthogonal basis matrix of the polarization null space is obtained; Based on the orthogonal basis matrix of the polarization null space, we obtain the weighted vector that satisfies the polarization constraint.

[0013] In one embodiment, column-pivoted QR decomposition is performed on the constraint matrix to obtain a decomposition vector, including:

[0014] In the formula, for The conjugate transpose of . For the constraint matrix, Let be the permutation matrix. It is an orthogonal matrix. It is an upper triangular matrix.

[0015] In one embodiment, a quadratic constrained quadratic programming optimization problem is established based on beam pointing constraints in the spatial and polarization domains, main lobe polarization ratio constraints, sidelobe energy and stability constraints, ultra-low sidelobe energy constraints in the joint domain, and minimum energy constraints, including:

[0016] In the formula, This is a quadratic programming optimization problem with quadratic constraints. The fundamental wave weighting vector, For the new optimization variables after dimensionality reduction, for The conjugate transpose of . for The conjugate transpose of . for The conjugate transpose of . The horizontally polarized fundamental wave weighting vector. The weighted vector for the vertically polarized fundamental wave. For polarization steering vector, As the guide vector, The polarization ratio of the main lobe of the fundamental wave beam. This represents the maximum power gain of the sidelobes of the vertical polarization component of the fundamental beam. This represents the maximum power gain of the fundamental wave beam sidelobes. The fundamental wave beam pointing angle, To describe the polarization argument of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization phase angle of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization argument of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, For the angular spatial sampling points of the fundamental wave beam sidelobe region, For the angle set of the sidelobe region of the fundamental wave beam, Jones vector parameter set to describe the sidelobe polarization state of the fundamental beam. This is the power threshold for the fundamental wave beam transmission.

[0017] In one embodiment, the quadratic constrained quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, including:

[0018] In the formula, For the new optimization variables after dimensionality reduction, To obtain the real part, To obtain the imaginary part, for The conjugate transpose of . for The conjugate transpose of . for The conjugate transpose of . For the orthogonal basis matrix of the polarization null space, This is the vertical polarization constraint matrix. For polarization steering vector, As the guide vector, The fundamental wave beam pointing angle, To describe the polarization argument of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization phase angle of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization argument of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, For the angular spatial sampling points of the fundamental wave beam sidelobe region, For the angle set of the sidelobe region of the fundamental wave beam, Jones vector parameter set to describe the sidelobe polarization state of the fundamental beam. This represents the maximum power gain of the sidelobes of the vertical polarization component of the fundamental beam. This represents the maximum power gain of the fundamental wave beam sidelobes. This is the power threshold for the fundamental wave beam transmission.

[0019] In one embodiment, a polarization-time modulation array model is obtained, and the weighting coefficients of each harmonic are derived based on the array steering vector and the polarization vector, including: Obtain the polarization time modulation array model, and derive the polarization steering vector based on the array steering vector and the polarization vector; Based on the polarization steering vector, the far-field radiation of the polarization time modulation array model is expressed as a Fourier series expansion, and the far-field radiation vector is obtained. By performing a Fourier transform on the time modulation function of the far-field radiation vector, the weighting coefficients of each harmonic are obtained.

[0020] A beamforming device for a polarization time modulation array, comprising: The first module is used to obtain the polarization time modulation array model and obtain the weighting coefficients of each harmonic based on the array steering vector and polarization vector. The second module is used to establish a quadratic constraint quadratic programming optimization problem based on beam pointing constraints in the spatial and polarization domains, polarization ratio constraints of the main lobe, energy and stability constraints of the sidelobe, ultra-low sidelobe energy constraints in the joint domain, and minimum energy constraints. Based on the polarization null space theory, the polarization ratio constraint of the main lobe is transformed, and then the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, which is then solved to obtain the optimal fundamental excitation weight. The third module is used to obtain the constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration, and to obtain the value range of the phase state conduction duration. Using the conduction duration and phase selection sequence as a set of gene parameters of the chromosome, the objective function is to minimize the deviation between the sidelobe level of each harmonic and the desired sidelobe level, and the fitness function is to use the sum of the absolute differences between the highest harmonic level and the desired harmonic level. A genetic algorithm is used to perform synchronous optimization within the value range of the phase state conduction duration to obtain the optimal conduction duration and the optimal phase selection sequence, so as to determine the remaining conduction time. The fourth module is used to modulate the beam of the polarization time modulation array based on the optimal conduction duration and the remaining conduction time.

[0021] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the above-described method.

[0022] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0023] The beamforming method, apparatus, device, and medium of the aforementioned polarization time modulation array robustly constructs a constrained null space through column pivoting QR decomposition with column exchange, reducing the high-dimensional QCQP problem to a low-dimensional SOCP problem. Then, a convex optimization method is used to solve the array fundamental weighting, and a genetic algorithm is used to suppress harmonic energy (harmonic level). This avoids getting trapped in local optima or consuming a lot of time, thereby ensuring the formation of ultra-low sidelobe beams and significantly improving the efficiency and numerical stability of beamforming.

[0024] Specifically, it has the following technical effects: (1) By reducing the dimensionality of the optimization variables from the polarization null space, the dimensionality of the optimization variables is reduced from... Down to This reduces the complexity of SOCP solution from Reduce to ,in To constrain the number of beams, the optimization complexity was significantly reduced, and the optimization efficiency was greatly improved, thereby increasing the beamforming efficiency.

[0025] (2) By using column pivot QR decomposition (the linear equation system is obtained through polarization constraints, and the coefficient matrix of the linear equation system is decomposed by QR), numerical instability caused by small pivots is avoided during the solution process. The solution can still be solved stably under ill-conditioned constraints, and the numerical stability is significantly enhanced.

[0026] (3) Using polarized null space for sparse storage replacement information significantly reduces memory consumption (memory usage is reduced by about 40%); after dimensionality reduction, the size of the optimization problem is reduced, further reducing memory requirements.

[0027] (4) By using the grouping column principal component strategy, the polarization structure is fully utilized to maintain the physical separability of the horizontal and vertical polarization components, so that the optimization results are more in line with engineering practice. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating a beamforming method for a polarization time modulation array in one embodiment. Figure 2 This is a schematic diagram of a polarization time modulation array in one embodiment; Figure 3 This is a simulation of the fundamental wave pattern in a specific embodiment; Figure 4 This is a schematic diagram of a +1st harmonic beam (the sideband beam with the highest energy) in a specific embodiment; Figure 5 A comparison of the +1st harmonic and fundamental wave beams in a specific embodiment (when the main lobe polarization angle is 60 degrees and the polarization phase angle is 90 degrees); Figure 6 This is a normalized phase state timing diagram of the H array in a specific embodiment; Figure 7 This is a normalized phase state timing diagram of the V array in a specific embodiment; Figure 8 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0030] Furthermore, the use of terms such as "first" and "second" in this application is for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of those features. In the description of this application, "multiple sets" means at least two sets, such as two sets, three sets, etc., unless otherwise explicitly specified.

[0031] In this application, unless otherwise expressly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two elements or the interaction between two elements, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0032] Furthermore, the technical solutions of the various embodiments of this application can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by this application.

[0033] This application provides a beamforming method for a polarization time modulation array, such as... Figure 1 The flowchart shown, in one embodiment, includes: Step 101: Obtain the polarization time modulation array model, and obtain the weighting coefficients of each harmonic based on the array steering vector and polarization vector.

[0034] Specifically: Obtain the polarization time modulation array model, and derive the polarization steering vector based on the array steering vector and the polarization vector; Based on the polarization steering vector, the far-field radiation of the polarization time modulation array model is expressed as a Fourier series expansion, and the far-field radiation vector is obtained. By performing a Fourier transform on the time modulation function of the far-field radiation vector, the weighting coefficients of each harmonic are obtained.

[0035] More specifically: Obtain the polarization-time modulation array model, such as Figure 2 The 2-bit dual-polarization time modulation array shown is composed of N One dual-polarized array antenna ( N The system consists of one array element, one beamforming network, one duplexer, one waveform generator, and one digital-to-analog converter; the beamforming network consists of 2...N 2-way power splitter N It consists of a 2-bit time modulation module and a field programmable gate array (FPGA); the 2-bit time modulation module includes four single-pole double-throw RF switches and multiple fixed delay lines; the state of the four single-pole double-throw RF switches is controlled by the FPGA, so that the antenna presents four phase states, namely 0 degrees, 90 degrees, 180 degrees and 270 degrees. Based on the polarization-time modulation array model, when the beam pointing angle (fundamental wave beam pointing angle) is At that time, the array steering vector is obtained:

[0036] in,

[0037] In the formula, For array guide vector, From an airspace perspective, It is a complex number. For the first The position of each array element ( ), The fundamental wave beam pointing angle, The wavelength of electromagnetic waves, At the speed of light, The frequency of electromagnetic waves, The number of array elements; Based on the polarization-time modulation array model, electromagnetic wave polarization is described by the Jones number, resulting in the polarization vector:

[0038] In the formula, The polarization vector, This is the polarization angle (the polarization angle of the Jones parameter). It is a complex number. This is the polarization phase angle (the polarization phase angle of the Jones parameter). Based on the array steering vector and polarization vector, the polarization steering vector of the dual-polarization array is obtained:

[0039] In the formula, For polarization steering vector, It is a 2x1 polarization vector. The guide vector is a 2x1 array. This is the Kronecker product. For the number of array elements, The polarization angle, It is a complex number. This is the polarization phase angle; Based on the polarization steering vector and considering periodic modulation, the far-field radiation of the polarization-time modulation array model can be expressed as a Fourier series expansion, yielding the far-field radiation vector:

[0040] in,

[0041] In the formula, For far-field radiation vector, From an airspace perspective, The polarization angle, For polarization phase angle, For time, The frequency of electromagnetic waves, For the first Each array element, For the number of array elements, For the first in the array The time modulation function of each array element This is the time modulation function for the horizontal polarization channel. This is the time modulation function for the vertical polarization channel. It is the polarization steering vector; For a 2-bit polarization time modulation array, the time modulation function of the horizontal and vertical polarization channels of each element can be expressed as: Where H represents horizontal polarization and V represents vertical polarization. It is possible in state (1, j , -1, - j Switching between states, determined by the start time of each state. and duration definition:

[0042] In the formula, The time modulation function for the horizontal and vertical polarization channels of each array element. It is a complex number. For the modulation period, For time, The start time for each state, The duration of each state, Choose 1, 2, 3, 4; By performing a Fourier transform on the time modulation function of the far-field radiation vector, the weighting coefficients of each harmonic are obtained:

[0043] in,

[0044] In the formula, For the first The weighting coefficients of each array element, For the first The weighting coefficients of the horizontal polarization channels of each array element For the first The weighting coefficients of the vertical polarization channels of each array element; For the first The weighting coefficients of the horizontal and vertical polarization channels of each array element. H represents horizontal polarization, and V represents vertical polarization; For the first The time modulation functions of the horizontal and vertical polarization channels of each array element; The harmonic order is... The frequency is time-modulated. In particular, the fundamental frequency ( The equivalent element weighting coefficients of ) are:

[0045] In the formula, The equivalent array element weighting coefficients of the fundamental wave; The equivalent weighting (excitation) for each array element can be rewritten as follows: , It can be viewed as an array of weighted arrays.

[0046] In this step, the weighting coefficients of each harmonic are obtained based on the polarization time modulation array model.

[0047] Step 102: Based on the beam pointing constraints in the spatial and polarization domains, the polarization ratio constraints of the main lobe, the energy and stability constraints of the sidelobes, the ultra-low sidelobe energy constraints in the joint domain, and the minimum energy constraints, a quadratic constraint quadratic programming optimization problem is established. Based on the polarization null space theory, the polarization ratio constraints of the main lobe are transformed, and then the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, which is then solved to obtain the optimal fundamental excitation weight.

[0048] Specifically: Based on the beam pointing constraints in the spatial and polarization domains, the polarization ratio constraints of the main lobe, the energy and stability constraints of the sidelobe, the ultra-low sidelobe energy constraints in the joint domain, and the minimum energy constraints, a quadratic constrained quadratic programming optimization problem is established. Based on the polarization null space theory, a weighted vector is obtained from the constraint matrix to transform the polarization ratio constraint of the main lobe into the form of a constraint matrix and a weighted vector. Then, the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem. The optimal fundamental excitation weights are obtained by solving the second-order cone programming problem.

[0049] More specifically: Based on the polarization-time modulation array model, the fundamental weighting vector of the dual-polarization-time modulation array is:

[0050] in,

[0051]

[0052] In the formula, The fundamental wave weighting vector, The horizontally polarized fundamental wave weighting vector. The weighted vector for the vertically polarized fundamental wave. Indicates the first N The zeroth-order horizontally polarized fundamental weighted vector of each array element Indicates the first N The zeroth-order vertical polarization fundamental wave weighted vector of each array element; Based on the beam pointing constraints in the spatial and polarization domains, the polarization ratio constraints of the main lobe, the energy and stability constraints of the sidelobe, the ultra-low sidelobe energy constraints in the joint domain, and the minimum energy constraints, combined with the fundamental wave weighting vector of the dual-polarization time-modulated array, a quadratic constrained quadratic programming optimization problem is established:

[0053] In the formula, This is a quadratic programming optimization problem with quadratic constraints. This indicates beam pointing constraints in the spatial and polarization domains. This indicates the polarization ratio constraint of the main lobe. This indicates the constraints on sidelobe energy and stability. This indicates the ultra-low sidelobe energy constraint in the joint domain. This represents the minimum energy constraint; The fundamental wave weighting vector, For the new optimization variables after dimensionality reduction, for The conjugate transpose of . for The conjugate transpose of . for The conjugate transpose of . The horizontally polarized fundamental wave weighting vector. The weighted vector for the vertically polarized fundamental wave. For polarization steering vector, As the guide vector, The polarization ratio of the main lobe of the fundamental wave beam. This represents the maximum power gain of the sidelobes of the vertical polarization component of the fundamental beam. This represents the maximum power gain of the fundamental wave beam sidelobes. The fundamental wave beam pointing angle, To describe the polarization argument of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization phase angle of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization argument of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, For the angular spatial sampling points of the fundamental wave beam sidelobe region, For the angle set of the sidelobe region of the fundamental wave beam, Jones vector parameter set to describe the sidelobe polarization state of the fundamental beam. This is the fundamental wave beam transmit power threshold; The aforementioned quadratic constrained quadratic programming optimization problem is a convex quadratic constrained quadratic programming problem (QCQP problem). The computational complexity of directly solving this problem is O(n log n). ,in N Indicates the number of array elements. L The number of constraints is indicated by the need for dense sampling in both the spatial and polarization domains to control the sidelobes. L The size is very large, resulting in a heavy computational burden; Based on the polarization null space theory, a weighted vector is obtained from the constraint matrix to transform the polarization ratio constraint of the main lobe into the form of a constraint matrix and a weighted vector:

[0054] in,

[0055] When polarization constraints are At that time,

[0056] In the formula, for The conjugate transpose of . For the constraint matrix, The fundamental wave weighting vector; for The conjugate transpose of . Choose a matrix for horizontal polarization. for The conjugate transpose of . Choose a matrix for vertical polarization; The process of obtaining the weighted vector based on the constraint matrix includes: performing column-pivoting QR decomposition on the constraint matrix to obtain the decomposition vector; and obtaining the orthogonal basis matrix of the polarization null space based on the decomposition vector. Depend on Chinese correspondence (Constructed from column vectors of zero diagonal elements); based on the orthogonal basis matrix of the polarization null space, we obtain the weighted vectors that satisfy the polarization constraints:

[0057]

[0058]

[0059] In the formula, for The conjugate transpose of . For the constraint matrix, Let be the permutation matrix. It is an orthogonal matrix. It is an upper triangular matrix; For the orthogonal basis matrix of the polarization null space, for rank, It is the fundamental wave weighting vector (which satisfies the polarization constraint and is also the optimal fundamental wave excitation weight of the array). For the new optimization variables after dimensionality reduction, For complex numbers; The polarization ratio constraint of the main lobe is transformed into a constraint matrix and a weighted vector. Then, by utilizing the property that the complex modulus constraint and the vector norm constraint can be equivalently transformed into a second-order cone constraint, the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem.

[0060] In the formula, For the new optimization variables after dimensionality reduction, To obtain the real part, To obtain the imaginary part, for The conjugate transpose of . for The conjugate transpose of . for The conjugate transpose of . For the orthogonal basis matrix of the polarization null space, This is the vertical polarization constraint matrix. For polarization steering vector, As the guide vector, The fundamental wave beam pointing angle, To describe the polarization argument of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization phase angle of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization argument of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, For the angular spatial sampling points of the fundamental wave beam sidelobe region, For the angle set of the sidelobe region of the fundamental wave beam, Jones vector parameter set to describe the sidelobe polarization state of the fundamental beam. This represents the maximum power gain of the sidelobes of the vertical polarization component of the fundamental beam. This represents the maximum power gain of the fundamental wave beam sidelobes. This is the fundamental wave beam transmit power threshold; For the second-order cone programming problem, the interior-point method is used to obtain the optimal fundamental excitation weights of the array. .

[0061] In this step, a quadratic constraint quadratic programming optimization problem is established based on five different constraints to form a high-gain, polarization-controllable main lobe in a specified direction and achieve an ultra-low level in the sidelobe region (i.e., generate an ultra-low sidelobe fundamental wave). Based on this, the polarization ratio constraint of the main lobe is transformed according to the polarization null space theory. This transformation automatically satisfies the original polarization constraint. Then, the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem and solved to reduce computational complexity.

[0062] Step 103: Obtain the constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration to obtain the range of values ​​for the phase state conduction duration; using the conduction duration and phase selection sequence as a set of gene parameters of the chromosome, with the objective function being to minimize the deviation between the sidelobe level of each harmonic and the desired sidelobe level, and the fitness function being the sum of the absolute differences between the highest harmonic level and the desired harmonic level, a genetic algorithm is used to perform synchronous optimization within the range of values ​​for the phase state conduction duration to obtain the optimal conduction duration and the optimal phase selection sequence, so as to determine the remaining conduction time.

[0063] Specifically: Obtain the constraint relationship between the optimal fundamental excitation weight and the conduction duration of the phase state (including: complex phase properties, the sum of the four phase durations equals the normalized modulation period):

[0064]

[0065] In the formula, The equivalent weight (excitation) for each array element (i.e., the optimal fundamental excitation weight for each array element). Based on the constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration, the range of values ​​for the phase state conduction duration is obtained (i.e., (the range of values). With conduction duration and phase selection sequence (For a 2-bit array, there are 24 possible phase combinations) These are used as a set of genetic parameters for a chromosome. The objective function is to minimize the deviation between the sidelobe level of each harmonic and the desired sidelobe level (i.e., the fitness function is the sum of the absolute differences between the highest harmonic level and the desired harmonic level). A genetic algorithm is employed to determine the conduction duration in each phase state. Within the range of values ​​for conduction duration and phase selection sequence Synchronization optimization is performed to obtain the optimal conduction duration and the optimal phase selection sequence, in order to determine the remaining conduction time; The fitness function is:

[0066] In the formula, For the first The highest level of the first harmonic, For the desired harmonic level, It represents the harmonic order.

[0067] In this step, after obtaining the optimal fundamental excitation weight, the conduction duration of each phase state within each array element is further optimized in order to reduce the power level of the harmonic beam while maintaining the main lobe energy.

[0068] Step 104: Modulate according to the optimal conduction duration and the remaining conduction time to form the beam of the polarization time modulation array.

[0069] The modulation process described in this step is existing technology and will not be elaborated upon here.

[0070] The beamforming method for the aforementioned polarization time modulation array robustly constructs a constrained null space through column pivoting QR decomposition with column exchange, reducing the high-dimensional QCQP problem to a low-dimensional SOCP problem. Then, a convex optimization method is used to solve the array fundamental weighting, and a genetic algorithm is used to suppress harmonic energy (harmonic level). This avoids getting trapped in local optima or consuming a lot of time, thus ensuring the formation of ultra-low sidelobe beams and significantly improving the efficiency and numerical stability of beamforming.

[0071] Specifically, it has the following technical effects: (1) By reducing the dimensionality of the optimization variables from the polarization null space, the dimensionality of the optimization variables is reduced from... Down to This reduces the complexity of SOCP solution from Reduce to ,in To constrain the number of beams, the optimization complexity was significantly reduced, and the optimization efficiency was greatly improved, thereby increasing the beamforming efficiency.

[0072] (2) By using column pivot QR decomposition (the linear equation system is obtained through polarization constraints, and the coefficient matrix of the linear equation system is decomposed by QR), numerical instability caused by small pivots is avoided during the solution process. The solution can still be solved stably under ill-conditioned constraints, and the numerical stability is significantly enhanced.

[0073] (3) Using polarized null space for sparse storage replacement information significantly reduces memory consumption (memory usage is reduced by about 40%); after dimensionality reduction, the size of the optimization problem is reduced, further reducing memory requirements.

[0074] (4) By using the grouping column principal component strategy, the polarization structure is fully utilized to maintain the physical separability of the horizontal and vertical polarization components, so that the optimization results are more in line with engineering practice.

[0075] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0076] In a specific embodiment, simulation verification was performed. Taking a dual-polarized array with an array size of 30×2 as an example, the main lobe pointing is 10 degrees, the polarization amplitude is 60 degrees, the polarization phase is 90 degrees, the constrained sidelobe level is less than -20dB, and the null level is less than -40dB.

[0077] like Figure 3 The simulated fundamental wave pattern shown shows that the beam energy reaches its peak at the direction of the main lobe beam (polarization angle of 60 degrees and spatial angle of 10 degrees); at a polarization angle of 60 degrees, the sidelobe gain does not exceed -40dB; in other regions, the sidelobe gain does not exceed -18dB.

[0078] After obtaining the fundamental wave beam with ultra-low sidelobes, it is also necessary to optimize the sideband energy, such as... Figure 4 The schematic diagram of the +1st harmonic beam (the sideband beam with the highest energy) shows that after optimization of the sideband, the sideband energy is low in the spatial-polarization domain, not exceeding -30dB.

[0079] like Figure 5 The diagram shows a comparison between the +1st harmonic and the fundamental wave beam (when the main lobe polarization angle is 60 degrees and the polarization phase angle is 90 degrees).

[0080] like Figure 6 The normalized phase state timing diagram of the H array shown is as follows: Figure 7 The normalized phase state timing diagram of the V array shown can be used to illustrate the duration of different phase states for each antenna element.

[0081] This application also provides a beamforming apparatus for a polarization time modulation array, which in one embodiment includes: a first module, a second module, a third module, and a fourth module, wherein: The first module is used to obtain the polarization time modulation array model and obtain the weighting coefficients of each harmonic based on the array steering vector and polarization vector. The second module is used to establish a quadratic constraint quadratic programming optimization problem based on beam pointing constraints in the spatial and polarization domains, polarization ratio constraints of the main lobe, energy and stability constraints of the sidelobe, ultra-low sidelobe energy constraints in the joint domain, and minimum energy constraints. Based on the polarization null space theory, the polarization ratio constraint of the main lobe is transformed, and then the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, which is then solved to obtain the optimal fundamental excitation weight. The third module is used to obtain the constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration, and to obtain the value range of the phase state conduction duration. Using the conduction duration and phase selection sequence as a set of gene parameters of the chromosome, the objective function is to minimize the deviation between the sidelobe level of each harmonic and the desired sidelobe level, and the fitness function is to use the sum of the absolute differences between the highest harmonic level and the desired harmonic level. A genetic algorithm is used to perform synchronous optimization within the value range of the phase state conduction duration to obtain the optimal conduction duration and the optimal phase selection sequence, so as to determine the remaining conduction time. The fourth module is used to modulate the beam of the polarization time modulation array based on the optimal conduction duration and the remaining conduction time.

[0082] Specific limitations regarding the beamforming device for the polarization-time modulation array can be found in the limitations of the beamforming method for the polarization-time modulation array above, and will not be repeated here. Each module in the above device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the operations corresponding to each module.

[0083] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 8 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a beamforming method for a polarization time modulation array. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0084] Those skilled in the art will understand that Figure 8 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0085] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the method described above.

[0086] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0087] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0088] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0089] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0090] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended application documents.

Claims

1. A beamforming method for a polarization time modulation array, characterized in that, include: Obtain the polarization time modulation array model, and obtain the weighting coefficients of each harmonic based on the array steering vector and polarization vector; Based on the beam pointing constraints in the spatial and polarization domains, the polarization ratio constraints of the main lobe, the energy and stability constraints of the sidelobe, the ultra-low sidelobe energy constraints in the joint domain, and the minimum energy constraints, a quadratic constrained quadratic programming optimization problem is established. Based on the polarization null space theory, the polarization ratio constraint of the main lobe is transformed, and then the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, which is then solved to obtain the optimal fundamental excitation weight. Obtain the constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration, and obtain the range of values ​​for the phase state conduction duration; Using conduction duration and phase selection sequence as a set of gene parameters of chromosome, minimizing the deviation between the sidelobe level of each harmonic and the desired sidelobe level as the objective function, and the sum of the absolute differences between the highest harmonic level and the desired harmonic level as the fitness function, a genetic algorithm is used to simultaneously optimize within the range of the conduction duration of the phase state to obtain the optimal conduction duration and the optimal phase selection sequence, so as to determine the remaining conduction time. Modulation is performed based on the optimal conduction duration and the remaining conduction time to form the beam of the polarization time modulation array.

2. The beamforming method for a polarization time modulation array according to claim 1, characterized in that, Based on the polarization null space theory, the polarization ratio constraint of the main lobe is transformed, including: Based on the polarization null space theory, a weighted vector is obtained from the constraint matrix to transform the polarization ratio constraint of the main lobe into the form of a constraint matrix and a weighted vector: In the formula, for The conjugate transpose of . For the constraint matrix, It is the fundamental wave weighted vector.

3. The beamforming method for a polarization time modulation array according to claim 2, characterized in that, The weighted vectors are obtained from the constraint matrix, including: Perform column pivoting QR decomposition on the constraint matrix to obtain the decomposition vector; Based on the decomposition vectors, the orthogonal basis matrix of the polarization null space is obtained; Based on the orthogonal basis matrix of the polarization null space, we obtain the weighted vector that satisfies the polarization constraint.

4. The beamforming method for a polarization time modulation array according to claim 3, characterized in that, Perform column-pivoting QR decomposition on the constraint matrix to obtain the decomposition vector, including: In the formula, for The conjugate transpose of . For the constraint matrix, Let be the permutation matrix. It is an orthogonal matrix. It is an upper triangular matrix.

5. The beamforming method for a polarization time modulation array according to any one of claims 1 to 4, characterized in that, Based on beam pointing constraints in the spatial and polarization domains, polarization ratio constraints of the main lobe, sidelobe energy and stability constraints, ultra-low sidelobe energy constraints in the joint domain, and minimum energy constraints, a quadratic constrained quadratic programming optimization problem is established, including: In the formula, This is a quadratic programming optimization problem with quadratic constraints. The fundamental wave weighting vector, For the new optimization variables after dimensionality reduction, for The conjugate transpose of . for The conjugate transpose of . for The conjugate transpose of . The horizontally polarized fundamental wave weighting vector. The weighted vector for the vertically polarized fundamental wave. For polarization steering vector, As the guide vector, The polarization ratio of the main lobe of the fundamental wave beam. This represents the maximum power gain of the sidelobes of the vertical polarization component of the fundamental beam. This represents the maximum power gain of the fundamental wave beam sidelobes. The fundamental wave beam pointing angle, To describe the polarization argument of the Jones vector, which represents the polarization state of the main lobe of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization argument of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, For the angular spatial sampling points of the fundamental wave beam sidelobe region, For the angle set of the sidelobe region of the fundamental wave beam, Jones vector parameter set to describe the sidelobe polarization state of the fundamental beam. This is the power threshold for the fundamental wave beam transmission.

6. The beamforming method for a polarization time modulation array according to any one of claims 1 to 4, characterized in that, The quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, including: In the formula, For the new optimization variables after dimensionality reduction, To obtain the real part, To obtain the imaginary part, for The conjugate transpose of . for The conjugate transpose of . for The conjugate transpose of . For the orthogonal basis matrix of the polarization null space, This is the vertical polarization constraint matrix. For polarization steering vector, As the guide vector, The fundamental wave beam pointing angle, To describe the polarization argument of the Jones vector, which represents the polarization state of the main lobe of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the polarization state of the fundamental beam's main lobe, To describe the polarization argument of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, To describe the polarization phase angle of the Jones vector, which represents the sidelobe polarization state of the fundamental beam, For the angular spatial sampling points of the fundamental wave beam sidelobe region, For the angle set of the sidelobe region of the fundamental wave beam, Jones vector parameter set to describe the sidelobe polarization state of the fundamental beam. This represents the maximum power gain of the sidelobes of the vertical polarization component of the fundamental beam. This represents the maximum power gain of the fundamental wave beam sidelobes. This is the power threshold for the fundamental wave beam transmission.

7. The beamforming method for a polarization time modulation array according to any one of claims 1 to 4, characterized in that, Obtain the polarization-time modulation array model, and based on the array steering vector and polarization vector, obtain the weighting coefficients for each harmonic, including: Obtain the polarization time modulation array model, and derive the polarization steering vector based on the array steering vector and the polarization vector; Based on the polarization steering vector, the far-field radiation of the polarization time modulation array model is expressed as a Fourier series expansion, and the far-field radiation vector is obtained. By performing a Fourier transform on the time modulation function of the far-field radiation vector, the weighting coefficients of each harmonic are obtained.

8. A beamforming apparatus for a polarization time modulation array, characterized in that, include: The first module is used to obtain the polarization time modulation array model and obtain the weighting coefficients of each harmonic based on the array steering vector and polarization vector. The second module is used to establish a quadratic constraint quadratic programming optimization problem based on the beam pointing constraints in the spatial and polarization domains, the polarization ratio constraints of the main lobe, the energy and stability constraints of the sidelobe, the ultra-low sidelobe energy constraints in the joint domain, and the minimum energy constraints. Based on the polarization null space theory, the polarization ratio constraint of the main lobe is transformed, and then the quadratic constraint quadratic programming optimization problem is transformed into an equivalent second-order cone programming problem, which is then solved to obtain the optimal fundamental excitation weight. The third module is used to obtain the constraint relationship between the optimal fundamental excitation weight and the phase state conduction duration, and to obtain the range of values ​​for the phase state conduction duration. Using conduction duration and phase selection sequence as a set of gene parameters of chromosome, minimizing the deviation between the sidelobe level of each harmonic and the desired sidelobe level as the objective function, and the sum of the absolute differences between the highest harmonic level and the desired harmonic level as the fitness function, a genetic algorithm is used to simultaneously optimize within the range of the conduction duration of the phase state to obtain the optimal conduction duration and the optimal phase selection sequence, so as to determine the remaining conduction time. The fourth module is used to modulate the beam of the polarization time modulation array based on the optimal conduction duration and the remaining conduction time.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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