Amplitude-phase coupling type antenna array initial excitation estimation method based on amplitude measurement
By establishing a signal model of amplitude-phase coupling characteristics in a dynamic metasurface antenna system and designing an optimized solution strategy, high-precision initial excitation estimation is achieved, solving the problems of insufficient estimation accuracy and poor adaptability in existing methods. This method is applicable to the calibration and performance compensation of dynamic metasurface antennas.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-16
- Publication Date
- 2026-04-14
AI Technical Summary
Existing initial excitation estimation methods based on amplitude measurement have poor adaptability and insufficient estimation accuracy in amplitude-phase coupled antenna arrays, especially in dynamic metasurface antenna systems where they cannot be effectively calibrated. Traditional methods do not fully consider the impact of amplitude-phase coupling on the power response model and have limited phase adjustment range.
By establishing an accurate signal model that includes amplitude-phase coupling characteristics, designing corresponding optimization solution strategies, and achieving high-precision initial excitation estimation based solely on amplitude measurement, nonlinear least squares optimization or linear estimation methods are employed. The power expression is constructed using the amplitude-phase coupling relationship, and the optimization problem is solved to estimate the initial excitation parameters.
It significantly improves the calibration accuracy of novel antenna systems such as dynamic metasurface antennas, adapts to amplitude-phase coupling characteristics, eliminates the dependence on the full phase adjustment range, is suitable for the calibration and performance compensation of dynamic metasurface antennas, and is compatible with antenna elements with limited phase shift range, thus enhancing its engineering applicability.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of antenna calibration technology, and more specifically, relates to an initial excitation estimation method for amplitude-phase coupled antenna arrays based on amplitude measurement. Background Technology
[0002] With the large-scale deployment of fifth-generation (5G) mobile communication technology and the deepening research on sixth-generation (6G) mobile communication technology, wireless communication systems are placing higher demands on the performance, integration, and energy efficiency of antenna arrays. Massive multiple-input multiple-output (MIMO) systems significantly improve system capacity and spectral efficiency by deploying a large number of antenna elements. However, traditional phased array antenna systems typically rely on independent radio frequency chains and phase adjustment modules, resulting in high hardware complexity, high power consumption, and high cost, which limits their practical application in large-scale deployments.
[0003] In recent years, Dynamic Metasurface Antennas (DMA), as an emerging hardware architecture, have attracted widespread attention due to their potential in realizing large-scale antenna arrays. DMA integrates phase modulation functionality into the metamaterial radiating element, dynamically adjusting the electromagnetic response of the element through external control signals (such as bias voltage), thus eliminating the need for traditional active phase shifters and complex feed networks. This structure not only reduces hardware complexity and manufacturing costs but also achieves compact, low-power large-scale antenna integration, and is considered one of the key technologies for realizing ultra-large-scale MIMO in future 6G systems.
[0004] However, DMA faces a key challenge in practical applications: its radiating elements often exhibit non-ideal amplitude changes when adjusting the phase, a phenomenon known as amplitude-phase coupling. This coupling characteristic stems from the structural design and control mechanism of the metamaterial elements, preventing the radiative response from independently controlling phase and amplitude like an ideal phase shifter. Furthermore, due to manufacturing errors, temperature drift, and device aging, the initial excitation (including amplitude and phase) of each DMA element deviates from the design values, thus affecting beamforming accuracy and system performance. Therefore, high-precision initial excitation estimation and calibration of the DMA array are crucial prerequisites for realizing its performance advantages.
[0005] Currently, estimation methods for the initial excitation of antenna arrays can be mainly divided into two categories: methods based on joint amplitude and phase measurements, and methods based solely on amplitude measurements. The former typically relies on equipment such as a vector network analyzer (VNA) to obtain complete complex signal information, achieving high accuracy, but it is costly and complex, making it unsuitable for rapid calibration of large-scale arrays. The latter, on the other hand, infers the excitation state of each element simply by measuring the amplitude information of the received signal, offering advantages such as simple equipment and ease of integration, making it more suitable for practical engineering applications.
[0006] Among estimation methods based solely on amplitude measurement, the most representative is the Rotating Element Electric Field Vector (REV) method. This method estimates the amplitude and relative phase of each element by sequentially rotating the phase of each array element and recording the received power change, using a sinusoidal power response relationship. Although the REV method is widely used in traditional phased arrays, its core assumption is that phase and amplitude can be independently controlled, and it requires array elements to have full-range (0°-360°) phase adjustment capability. However, DMA elements are limited by their physical structure and control mechanism, typically possessing only a limited phase adjustment range (e.g., 0°-180°), and exhibit significant amplitude-phase coupling, leading to a significant performance degradation of the traditional REV method in DMA systems.
[0007] To improve estimation efficiency, subsequent studies have proposed fast REV methods and their variants based on multiple phase states (such as 0°, 90°, 180°, and 270°), which achieve excitation estimation by constructing a system of linear equations. However, these methods still do not consider hardware limitations such as amplitude-phase coupling effects for optimization, resulting in large estimation errors and limited practicality in DMA systems.
[0008] In summary, existing amplitude measurement-based estimation methods have the following main problems when dealing with novel antenna systems with amplitude-phase coupling characteristics, such as DMA: 1) The impact of amplitude-phase coupling on the power response model was not fully considered; 2) Poor adaptability to the limited phase adjustment range of DMA units.
[0009] Therefore, there is an urgent need to develop a new calibration method that can adapt to the characteristics of DMA hardware and achieve initial excitation estimation based solely on amplitude measurement. Summary of the Invention
[0010] This invention addresses the problems of poor adaptability and insufficient estimation accuracy of existing initial excitation estimation methods in amplitude-phase coupled antenna arrays (especially DMA systems), and proposes an initial excitation estimation method based on amplitude measurement. This method establishes an accurate signal model incorporating amplitude-phase coupling characteristics and designs corresponding optimized solution strategies, enabling high-precision estimation of the initial excitation of array elements without requiring phase information.
[0011] According to the present invention, an array initial excitation estimation method based on amplitude measurement is provided, comprising the following steps: S1: Determine the amplitude-phase coupling relationship of any phase-tunable element in the antenna array. Based on the amplitude-phase coupling relationship, obtain the power expression of the antenna array at the receiving probe, and formalize the initial excitation estimation problem of the element into an optimization problem. S2: Apply multiple phase shifts to the unit and measure the received signal power corresponding to each phase shift; S3: Based on the received signal power obtained in step S2 and the amplitude-phase coupling relationship in step S1, solve the optimization problem in step S1 to obtain the initial excitation related parameters of the unit, and characterize the initial excitation state of the unit completely according to the initial excitation related parameters. S4: Replace the unit in step S1, and perform the initial excitation state estimation of all units of the antenna array in sequence according to the operations of steps S1-S3.
[0012] Preferably, step S1 specifically includes the following steps: S11: Configure the antenna array to include One phase-adjustable unit, unit The phase shift is denoted as The amplitude-phase coupling relationship is determined by measurement or simulation, and the amplitude-phase coupling relationship is denoted as... The unit Effective phase shift coefficient Described by the following model: (1) in, Is phase shift The amplitude response of the coupling, the phase shift of each element. The range of values is ,in The phase shift adjustment range of the unit. ; S12: Received signal at the receiving probe y Represented as: (2) in, It is the first The composite initial excitation of each unit, It is the first The actual initial excitation of each unit, including amplitude and phase , It is the coupling coefficient between the unit and the probe; S13: To estimate the unit of Keep the phase offset of the remaining units fixed at the reference value. Independently change the unit The phase shift is Different states ( In each state, the received signal in step S12 y Further expressed as : (3) in: Is phase shift The amplitude response of the coupling, Is phase shift The amplitude response of the coupling, It is a unit The synthesis field of all other units under the reference phase shift, yes phase, for The range; S14: Calculate the received signal at the probe. With its inner product, in each state, the power expression of the antenna array at the receiving probe is derived: (4) in: It is a unit The relative phase between the excitation and the rest of the composite field, yes The phase; S15: The initial excitation problem of the antenna is formulated as a nonlinear least squares problem (P1) to estimate the initial excitation parameters by minimizing the difference between the measured and theoretical values. : (5) in, This represents the measured received signal power. It is the first The phase shift of each unit is The received signal power measured at that time, This is the theoretical received signal power obtained according to equation (4); the phase shift group used in the measurement The corresponding coupling amplitude is , For the initial incentive magnitude, For the initial incentive magnitude, The initial excitation relative phase.
[0013] Preferably, in step S2, phase shifts are sequentially applied to the unit. Meanwhile, the phases of the remaining array elements are kept fixed at the reference value. Measure the corresponding received signal power .
[0014] Preferably, in step S3, the iterative estimation method is used to solve the nonlinear least squares problem (P1), which specifically includes the following steps: S31: is the parameter vector Set initial values ; S32: In the In the next iteration, the theoretical received signal power is calculated according to equation (4). ; S33: Calculate the residuals ; (6) S34: Calculate the Jacobian matrix The elements of each Jacobian matrix are calculated using the following formula: (7) S35: Calculate the parameter update amount using the following formula. : (8) in, It is the damping factor; S36: Update parameters ,judge Whether it is less than the preset threshold or has reached the maximum number of iterations; S37: If If the number of iterations is greater than or equal to the preset threshold or less than the maximum number of iterations, continue iterating according to steps S32-S36 until... If the number of iterations is less than the preset threshold or the maximum number of iterations is reached, the iteration ends and the result is output; if If the number of iterations is less than the preset threshold or greater than or equal to the maximum number of iterations, the iteration ends and the result is output. S38: Obtained through the following calculation relative phase : (9) It is the first The excitation of each unit in the initial phase shift The relative phase between the current and the initial array excitation of the antenna array; function Calculate points in Cartesian coordinate system Yizheng The angles between the axes, while also considering the correct quadrant in which the angles lie, are used to complete the initial excitation of the m-th element. The estimate.
[0015] Preferably, in step S3, the nonlinear least squares problem (P1) is solved using a linear estimation method, specifically including the following steps: S3-1: Using trigonometric identities The power expression in S14 is reformulated as follows: (10) S3-2: Order: (11) S3-3: Then The measurements constitute a system of linear equations. (12) S3-4: Transform the nonlinear least squares problem (P1) into a linear least squares problem (P2): (13) in, for The estimated vector; S3-5: According to the matrix The linear correlation between columns is used to classify the cases into Case 1, Case 2, Case 3, and Case 4, and the vector is adjusted accordingly. sum matrix Definition; Case 1: If Full column rank, parameters remain unchanged: (14) Scenario 2: If , If is any non-zero real number, then merge the matrices. The first and second columns, vectors sum matrix Adjusted to: (15) Scenario 3: If , If is any non-zero real number, then merge the matrices. Columns 2 and 3, vector sum matrix Adjusted to: (16) Scenario 4: If , If is any non-zero real number, then merge the matrices. Columns 2 and 4, vector sum matrix Adjusted to: (17) S3-6: Let and They represent the first time. Vector in this case sum matrix Adjustment items, among which The linear least squares problem (P2) in steps 3-4 is restated as (P3); (18) in, for The estimated vector, Sometimes, , Sometimes, ; S3-7: For each case, the optimal solution in step S3-6 (P3) is expressed as: (19) in, express The pseudo-inverse is defined as follows: ; S3-8: When the estimated vector is obtained , The elements corresponding to the unmerged columns can be obtained directly, while the elements corresponding to the merged columns are obtained by solving a system of quadratic equations consisting of the merging conditions and the following relationship: (20) For case 1, then ; For scenario 2, it is necessary to determine the merged elements. and The system of equations constructed is as follows: (twenty one) for and There are two possible solutions, expressed as follows: (twenty two) For case 3, the constructed system of equations is as follows: (twenty three) The solution to the system of equations is: (twenty four) For case 4, the constructed system of equations is: (25) The solution to the system of equations is: (26) S3-9: Determine the unknown vector Then, the amplitude of the initial excitation can be determined according to equation (11). and relative phase Its expression is (27) Preferably, L is greater than or equal to 3.
[0016] Preferably, the value of L is in the range of 4-8.
[0017] Preferably, the phase shift In [0, The surface is evenly distributed.
[0018] Preferably, the initial value of the parameter vector .
[0019] Preferably, the antenna array is a dynamic metasurface antenna array.
[0020] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: (1) This invention, for the first time, explicitly models and utilizes amplitude-phase coupling characteristics within an amplitude-only measurement framework, fundamentally solving the estimation error problem caused by model mismatch in existing methods. Specifically, traditional REV methods and other methods assume that the amplitude of the antenna element remains constant during phase adjustment, and its power expression is: However, for systems with amplitude-phase coupling characteristics, such as dynamic metasurface antennas, the amplitude varies with the phase, and the corresponding true power expression is shown in equation (4), where, Given a known amplitude-phase coupling relationship, this invention will... The power expression (4) is explicitly introduced to make the estimation process consistent with the actual hardware response, eliminating the systematic bias caused by neglecting amplitude-phase coupling. Simulation results show that the proposed method significantly improves the calibration accuracy.
[0021] (2) This invention gets rid of the dependence on the full phase adjustment range (0°-360°) and only requires a finite phase shift to achieve high-precision excitation estimation, effectively adapting to the hardware constraints of new antennas such as dynamic metasurface antennas.
[0022] Traditional REV methods require the cell to have full-phase scanning capability to form a complete sinusoidal power response curve for parameter fitting. This invention, based on a nonlinear least-squares optimization framework, only requires L arbitrarily distributed phase states (e.g., uniformly sampled within [0, 160°]) to uniquely determine the excitation parameters by solving an optimization problem (P1). This mechanism does not depend on specific phase points (e.g., 0°, 90°, 180°, 270°) and has no minimum requirement for the phase adjustment range; only the amplitude response is needed. Linear independence at the selected phase point is sufficient. Therefore, this method is suitable for antenna elements with limited phase shift range, solving the problem of inability to estimate phase due to insufficient phase range in existing technologies, and enhancing the engineering applicability of the method.
[0023] (3) The initial excitation estimation method based solely on amplitude measurement in this invention is applicable to antenna array systems with amplitude-phase coupling characteristics. This method can achieve initial excitation estimation of antenna elements without obtaining phase information, and is particularly suitable for calibration and performance compensation of dynamic metasurface antennas (DMA). It can also be extended to other reconfigurable antennas and smart metasurface systems with similar hardware constraints. Attached Figure Description
[0024] Figure 1 This is a schematic diagram of the measurement configuration for the initial excitation estimation of the present invention.
[0025] Figure 2 This is a schematic diagram of array signal field vector synthesis according to the present invention.
[0026] Figure 3 This is an example of the amplitude-phase coupling relationship of the unit in this invention.
[0027] Figure 4 The mean square error of the initial excitation and the number of phase offset states in this invention The relationship. Detailed Implementation
[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0029] I. Prerequisites and related assumptions 1. There exists a... An amplitude-phase coupled antenna array (such as DMA) consists of several adjustable elements, each of which can independently adjust its phase via an external control signal (such as a bias voltage).
[0030] 2. Amplitude-phase coupling relationship of array elements The relationships obtained through full-wave simulation, equivalent circuit modeling, or experimental calibration, such as the DMA of substrate integrated waveguide structures, typically follow the Lorentz constraint model. .
[0031] 3. The measurement system includes a probe antenna serving as the receiver, which is typically positioned in the far-field region along the normal direction of the array. The receiving equipment must have signal amplitude measurement capabilities, such as using a spectrum analyzer.
[0032] 4. The system controller can apply a preset phase offset to any specified cell in the array. At the same time, it can fix the phase of all other units to a common reference phase. .
[0033] II. Basic Steps 1. System Modeling: Based on the hardware characteristics of the target antenna array, determine its amplitude-phase coupling relationship through measurement or simulation. Based on the superposition relationship of unit fields, the theoretical received signal power is obtained as shown in equation (4). Furthermore, the initial excitation estimation problem is formalized into a nonlinear least squares optimization problem (P1).
[0034] 2. Amplitude Measurement: Phase offsets are sequentially applied to the target unit. Meanwhile, the phase of the remaining units remains fixed at the reference value. , usually choose If the amplitude response corresponding to that phase If the signal strength is close to zero, then another signal that can guarantee sufficient signal strength needs to be selected. Value; design a set containing Phase offset state Preferably, these phase values are within the phase shift range allowed by the hardware. Uniformly distributed within; record the corresponding received signal power. .
[0035] 3. Parameter solution: based on measured power Coupling relationship Solve the optimization problem (P1), which can be solved using any numerical optimization method applicable to nonlinear least squares problems, including step 3 in Example 1; or by transforming it into a linear least squares problem through parameter rearrangement using the method described in step 3 of Example 2. Further, using the initial excitation-related parameters obtained from solving the optimization problem (P1), calculate the initial excitation relative phase of the target unit relative to the entire array using the relative phase relationship. , and the initial incentive magnitude This allows for a complete characterization of the initial excitation state.
[0036] 4. Array traversal: Repeat steps 2-3 to complete the initial excitation estimation of all array elements in sequence.
[0037] The following are specific examples: Example 1 The core of this invention lies in constructing a measurement and estimation framework capable of accurately describing amplitude-phase coupling characteristics. The specific solution is as follows: 1) System Modeling Consider a A dynamic metasurface antenna (DMA) composed of tunable metamaterial radiating elements. Each element... Adjustable phase shift is denoted as Its effective phase shift coefficient is described by the following model: (29) in, Is phase shift The magnitude response of the coupling, in its specific form, is determined by the DMA hardware; for example, it could be... The Lorentz constraint form or other corresponding relationship determined by full-wave simulation or experimental measurements. Phase shift of each element. The range of values is ,in This refers to the phase shift adjustment range of the DMA. .
[0038] This invention considers as follows Figure 1 The measurement configuration is shown. In this measurement scenario, the received signal at the probe... for (30) in, It is the first The composite initial excitation of each unit, Yes, yes, the first The actual initial excitation of each unit (including amplitude) and phase , It is the coupling coefficient between the element and the probe. In the far field and in the direction of each element in the array... Figure 1 Under the assumption of consistency, it can be assumed that all Equal, at this time Directly reflects The relative value.
[0039] To estimate a specific unit of The phase shift of all other units is fixed as the reference value. (usually taken) ), independently change the unit The phase shift is Different states ( In each state, the received signal y is further represented as... (31) in: Is phase shift The amplitude response of the coupling, Is phase shift The amplitude response of the coupling, It is a unit The synthesis field of all other units under the reference phase shift, yes phase, for The range; To determine the first The array signal power received at the probe by each DMA unit at different phase shifts is calculated, and the inner product of the signal at the probe and the unit itself is calculated to derive the expression for the received signal power in each state. (32) in: It is a unit The relative phase between the excitation and the rest of the composite field ( and They are and (phase).
[0040] The core innovation of this model lies in the fact that each term explicitly includes the phase shift. and Related amplitude coefficient and This fully integrates the amplitude-phase coupling, a core hardware constraint of DMA, into the estimation problem.
[0041] Based on the above model and principles, the initial excitation problem of DMA is formulated as a nonlinear least squares problem, the objective of which is to estimate the initial excitation parameters by minimizing the difference between the measured and theoretical values. : (33) in, This represents the measured received signal power. It is the first The phase shift of each unit is The received signal power measured at that time, This is the theoretical received signal power obtained according to equation (32). The phase shift group used in the measurement... The corresponding coupling amplitude is .
[0042] 2) Amplitude measurement: Phase shifts are applied sequentially to the target array elements. Meanwhile, the phases of the remaining array elements are kept fixed at the reference value. Measure the corresponding received signal power .
[0043] 3) Parameter solution: To address the nonlinear least squares optimization problem described in (P1), this invention proposes an iterative estimation method based on the Levenberg-Marquardt (LM) algorithm. The specific iterative steps of the algorithm are as follows: S31: is the parameter vector Setting an initial value is preferred in this invention.
[0044] S32: In the In the next iteration, the theoretical received signal power is calculated according to (32).
[0045] S33: Calculate the residuals
[0046] (34) S34: Calculate the Jacobian matrix The elements of each Jacobian matrix are calculated using the following formula: (35) S35: Calculate the parameter update amount using the following formula. : (36) Among them, damping factor The trust region strategy is adaptively adjusted to achieve a balance between gradient descent (high stability) and Gauss-Newton method (fast convergence).
[0047] S36: Update parameters ,judge Whether it is less than the preset threshold or has reached the maximum number of iterations; S37: If If the number of iterations is greater than or equal to the preset threshold or less than the maximum number of iterations, continue iterating according to steps S32-S36 until... If the number of iterations is less than the preset threshold or the maximum number of iterations is reached, the iteration ends and the result is output; if If the number of iterations is less than the preset threshold or greater than or equal to the maximum number of iterations, the iteration ends and the result is output.
[0048] The parameter vector is obtained by completing the iteration. Then, the following calculation was performed to obtain... relative phase : (37) It is the first The excitation of each unit in the initial phase shift The relative phase between the current and the initial array excitation of the antenna array; function Calculate points in Cartesian coordinate system Yizheng The angles between the axes, while also considering the correct quadrant in which the angles lie, are used to complete the initial excitation of the m-th element. The estimate.
[0049] 4) Array traversal Repeat steps 2)-3) to complete the initial excitation estimation for all array elements in sequence.
[0050] Example 2 The core of this invention lies in constructing a measurement and estimation framework capable of accurately describing amplitude-phase coupling characteristics. The specific solution is as follows: 1) System Modeling Same as 1) System modeling in Example 1 2) Amplitude measurement: Same as 2) Amplitude measurement in Example 1.
[0051] 3) Parameter solution: To reduce computational complexity and avoid iteration, this invention transforms the optimization problem (P1) into a linear least squares problem through variable substitution and parameter reorganization, and proposes a low-complexity linear estimation method. By calculating the closed-form solution, iteration is avoided and complexity is reduced. The specific steps are as follows.
[0052] Using trigonometric identities The power expression (32) is rewritten as: (38) make: (39) but The measurements constitute a system of linear equations. (40) At this point, the nonlinear least squares problem (P1) used for initial excitation estimation is transformed into a linear least squares problem: (41) in, for The estimated vector.
[0053] want If a unique solution can be obtained, it must be a full column rank matrix. In the current construction method, the matrix... The first column (constant term), the third column ( ) and the fourth column ( These terms are usually not parallel because they represent different trigonometric function terms and constant terms, and However, by The determined second column depends on the characteristics of the DMA unit and may be linearly related to one of the other three columns, thus reducing the matrix... Rank.
[0054] To ensure the solvability of the least squares problem, we use the matrix... The linear correlation between columns is used to classify the cases and adjust accordingly. and Definition.
[0055] Case 1 (Full Rank): If Full column rank, parameters remain unchanged: (42) Case 2 (constant amplitude): If Then merge columns 1 and 2. and Adjusted to (43) Case 3 (Lorentz constraint): If Then merge columns 2 and 3. and Adjusted to (44) Case 4 (similar to Case 3): If Then merge columns 2 and 4. and Adjusted to (45) set up and They represent the first time. Vector in this case sum matrix Adjustment items, among which The least squares problem is reformulated as follows: (46) For each case, the optimal solution for (P3) can be expressed as: (47) in, for The estimated vector, Sometimes, , Sometimes, , express The pseudo-inverse is defined as follows: .
[0056] For case 1, i.e. The case of a full rank requires at least four measurements to solve. There are four unknowns. In other cases, due to column merging, The number of unknowns is reduced, and the minimum number of measurements required is reduced. The rank decreases to 3. This is the matrix with a lower rank compared to other cases. In contrast, the full-rank matrix in case 1 It typically has a higher condition number. This indicates that the estimate in case 1 is more sensitive to noise and other perturbations. Therefore, when the matrix When two columns are not perfectly parallel but have a strong linear correlation, they can be approximated as parallel, and a rank reduction approach can be used to improve stability at the expense of some accuracy. The choice depends on the measurement noise level and specific application requirements.
[0057] When the estimated vector is obtained , The elements corresponding to the unmerged columns can be obtained directly, while the elements corresponding to the merged columns are obtained by solving a system of quadratic equations consisting of the merging conditions and the following relationship: (48) For case 1, we have For case 2, the merged elements need to be determined. and The system of equations constructed is as follows: (49) for and There are two possible solutions, expressed as follows: (50) For case 3, the system of equations constructed is as follows: (51) The solution to the system of equations is: (52) For case 4, the system of equations constructed is as follows: (53) The solution to the system of equations is: (54) In cases 2, 3, and 4, due to the quadratic property of the equation, the solution by combining elements has two possible roots. However, in all three cases, by applying constraints... And the typical relationship obtained from the multi-unit characteristics of DMA. This can resolve the ambiguity of the solution and determine the unknown vector. Then, the amplitude of the initial excitation can be determined according to (39). and relative phase Its expression is (55) Among them, such as Figure 2 As shown, It is the first The excitation of each unit in the initial phase shift The relative phase between the current phase and the initial array excitation of the DMA. Calculate points in Cartesian coordinate system Yizheng The angle between the axes, while also considering the correct quadrant in which the angle lies. This completes the initial excitation. The estimate.
[0058] This linear estimation method avoids iteration, is more computationally efficient than the LM method, and has similar performance under certain configurations.
[0059] 4) Array traversal Repeat steps 2)-3) to complete the initial excitation estimation for all array elements in sequence.
[0060] Simulation results for Examples 1 and 2: 1. Simulation parameters Array structure: 16-element uniform area array, with an element spacing of half a wavelength.
[0061] Amplitude-phase coupling model: Amplitude-phase coupling relationship as follows Figure 3 As shown. The phase offset state used for measurement is in Select evenly within the range.
[0062] Initial excitation: The initial excitation amplitude of each unit is within dB is randomly distributed, with the initial phase at... The range is randomly distributed; Operating frequency: 2.45 GHz; Evaluation metrics: Statistical mean square error (MSE) of the estimation of the amplitude and relative phase of the initial excitation in 2000 independent Monte Carlo trials.
[0063] 2. Simulation data To evaluate the performance of the proposed method, under the same simulation conditions, the estimation results of the LM-IEE and LIEE-based estimation methods were compared with the estimation results of the classical rotating electric vector method (REV, which assumes that the amplitude response is constant in all phase states).
[0064] Under different estimation methods, the mean square error (MSE) of the initial excitation estimation varies with the number of phase states used in the measurement. The relationship of change is as follows Figure 4 As shown. Simulation results show that: (1) The estimation accuracy of the LM-IEE proposed in Embodiment 1 and the LIEE proposed in Embodiment 2 is significantly better than that of the traditional REV method. This verifies the importance of explicitly considering amplitude-phase coupling characteristics in the estimation model for improving accuracy.
[0065] (2) The estimation error of all methods increases with the number of phase states. The decrease due to the increase aligns with the intuitive expectation that more measurement data will lead to more accurate estimates. Considering the increase... This linearly increases measurement time and resource overhead, requiring a trade-off between estimation accuracy and measurement cost in practical system design. Based on the convergence trend of simulation curves, the optimal approach is... The value of is around 8, which can achieve a good balance between performance and complexity in this simulation scenario.
[0066] Simulation results demonstrate that the calibration framework for explicit modeling amplitude-phase coupling characteristics proposed in this invention can effectively overcome the limitations of traditional methods in novel antenna systems such as DMA, and provide a reliable solution for achieving high-precision initial excitation estimation.
[0067] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for estimating the initial excitation of an array based on amplitude measurement, characterized in that, Includes the following steps: S1: Determine the amplitude-phase coupling relationship of any phase-tunable element in the antenna array. Based on the amplitude-phase coupling relationship, obtain the power expression of the antenna array at the receiving probe, and formalize the initial excitation estimation problem of the element into an optimization problem. S2: Apply multiple phase shifts to the unit and measure the received signal power corresponding to each phase shift; S3: Based on the received signal power obtained in step S2 and the amplitude-phase coupling relationship in step S1, solve the optimization problem in step S1 to obtain the initial excitation related parameters of the unit, and characterize the initial excitation state of the unit completely according to the initial excitation related parameters. S4: Replace the unit in step S1, and perform the initial excitation state estimation of all units of the antenna array in sequence according to the operations of steps S1-S3.
2. The array initial excitation estimation method based on amplitude measurement as described in claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Configure the antenna array to include One phase-adjustable unit, unit The phase shift is denoted as The amplitude-phase coupling relationship is determined by measurement or simulation, and the amplitude-phase coupling relationship is denoted as... The unit Effective phase shift coefficient Described by the following model: (1) in, Is phase shift The amplitude response of the coupling, the phase shift of each element. The range of values is ,in The phase shift adjustment range of the unit. ; S12: Received signal at the receiving probe y Represented as: (2) in, It is the first The composite initial excitation of each unit, It is the first The actual initial excitation of each unit, including amplitude and phase , It is the coupling coefficient between the unit and the probe; S13: To estimate the unit of Keep the phase offset of the remaining units fixed at the reference value. Independently change the unit The phase shift is Different states ( In each state, the received signal in step S12 y Further expressed as : (3) in: Is phase shift The amplitude response of the coupling, Is phase shift The amplitude response of the coupling, It is a unit The synthesis field of all other units under the reference phase shift, yes phase, for The range; S14: Calculate the received signal at the probe. With its inner product, in each state, the power expression of the antenna array at the receiving probe is derived: (4) in: It is a unit The relative phase between the excitation and the rest of the composite field, yes The phase; S15: The initial excitation problem of the antenna is formulated as a nonlinear least squares problem (P1) to estimate the initial excitation parameters by minimizing the difference between the measured and theoretical values. : (5) in, This represents the measured received signal power. It is the first The phase shift of each unit is The received signal power measured at that time, This is the theoretical received signal power obtained according to equation (4); the phase shift group used in the measurement The corresponding coupling amplitude is , For the initial incentive magnitude, For the initial incentive magnitude, The initial excitation relative phase.
3. The array initial excitation estimation method based on amplitude measurement as described in claim 2, characterized in that, In step S2, phase shifts are sequentially applied to the unit. Meanwhile, the phases of the remaining array elements are kept fixed at the reference value. Measure the corresponding received signal power .
4. The array initial excitation estimation method based on amplitude measurement as described in claim 3, characterized in that, In step S3, the nonlinear least squares problem (P1) is solved using an iterative estimation method, specifically including the following steps: S31: is the parameter vector Set initial values ; S32: In the In the next iteration, the theoretical received signal power is calculated according to equation (4). ; S33: Calculate the residuals ; (6) S34: Calculate the Jacobian matrix The elements of each Jacobian matrix are calculated using the following formula: (7) S35: Calculate the parameter update amount using the following formula. : (8) in, It is the damping factor; S36: Update parameters ,judge Whether it is less than the preset threshold or has reached the maximum number of iterations; S37: If If the number of iterations is greater than or equal to the preset threshold or less than the maximum number of iterations, continue iterating according to steps S32-S36 until... If the number of iterations is less than the preset threshold or the maximum number of iterations is reached, the iteration ends and the result is output; if If the number of iterations is less than the preset threshold or greater than or equal to the maximum number of iterations, the iteration ends and the result is output. S38: Obtained through the following calculation relative phase : (9) It is the first The excitation of each unit in the initial phase shift The relative phase between the current and the initial array excitation of the antenna array; function Calculate points in Cartesian coordinate system Yizheng The angles between the axes, while also considering the correct quadrant in which the angles lie, are used to complete the initial excitation of the m-th element. The estimate.
5. The array initial excitation estimation method based on amplitude measurement as described in claim 3, characterized in that, In step S3, the nonlinear least squares problem (P1) is solved using a linear estimation method, specifically including the following steps: S3-1: Using trigonometric identities The power expression in S14 is reformulated as follows: (10) S3-2: Order: (11) S3-3: Then The measurements constitute a system of linear equations. (12) S3-4: Transform the nonlinear least squares problem (P1) into a linear least squares problem (P2): (13) in, for The estimated vector; S3-5: According to the matrix The linear correlation between columns is used to classify the cases into Case 1, Case 2, Case 3, and Case 4, and the vector is adjusted accordingly. sum matrix Definition; Case 1: If Full column rank, parameters remain unchanged: (14) Scenario 2: If , If is any non-zero real number, then merge the matrices. The first and second columns, vectors sum matrix Adjusted to: (15) Scenario 3: If , If is any non-zero real number, then merge the matrices. Columns 2 and 3, vector sum matrix Adjusted to: (16) Scenario 4: If , If is any non-zero real number, then merge the matrices. Columns 2 and 4, vector sum matrix Adjusted to: (17) S3-6: Let and They represent the first time. Vector in this case sum matrix Adjustment items, among which The linear least squares problem (P2) in steps 3-4 is restated as (P3); (18) in, for The estimated vector, Sometimes, , Sometimes, ; S3-7: For each case, the optimal solution in step S3-6 (P3) is expressed as: (19) in, express The pseudo-inverse is defined as follows: ; S3-8: When the estimated vector is obtained , The elements corresponding to the unmerged columns can be obtained directly, while the elements corresponding to the merged columns are obtained by solving a system of quadratic equations consisting of the merging conditions and the following relationship: (20) For case 1, then ; For scenario 2, it is necessary to determine the merged elements. and The system of equations constructed is as follows: (21) for and There are two possible solutions, expressed as follows: (22) For case 3, the constructed system of equations is as follows: (23) The solution to the system of equations is: (24) For case 4, the constructed system of equations is: (25) The solution to the system of equations is: (26) S3-9: Determine the unknown vector Then, the amplitude of the initial excitation can be determined according to equation (11). and relative phase Its expression is (27)。 6. The array initial excitation estimation method based on amplitude measurement as described in claim 2, characterized in that, The L is greater than or equal to 3.
7. The array initial excitation estimation method based on amplitude measurement as described in claim 2, characterized in that, The value of L is in the range of 4-8.
8. The array initial excitation estimation method based on amplitude measurement as described in claim 2, characterized in that, The phase shift In [0, The surface is evenly distributed.
9. The array initial excitation estimation method based on amplitude measurement as described in claim 4, characterized in that, The initial value of the parameter vector .
10. The array initial excitation estimation method based on amplitude measurement as described in claim 1, characterized in that, The antenna array is a dynamic metasurface antenna array.