CN114815436A - Mutual coupling compensation method of optical phased array elements based on neighborhood sampling principal component analysis - Google Patents

Abstract

The invention discloses a mutual-coupling compensation method for optical phased array elements based on neighborhood sampling principal component analysis, which includes two processes of dimensionality reduction and iteration. The dimensionality reduction includes the following steps: S1. S2, obtain the neighborhood sampling matrix X; S3, calculate the covariance matrix C of X; S4, calculate the eigenvalues and eigenvectors of C, and splicing the eigenvectors in rows to obtain matrix U; S5, eigenvalues from large To the small order, the eigenvectors in the U matrix are also sorted correspondingly, and the space transformation matrix P is obtained; S6, use the P matrix to multiply the voltage vector to the left to obtain a new vector

The iteration includes the following steps: S7, obtain the updated voltage vector and load it on the array element of the phased array; S8, collect the value J of the evaluation function, according to the change of the evaluation function δJ

Update the top K values of . The invention can greatly reduce the iterative dimension of the optimization process, improve the convergence speed, and improve the robustness of system operation.

Description

Mutual coupling compensation method of optical phased array elements based on neighborhood sampling principal component analysis

technical field

The invention belongs to the technical field of optical phased array control and adaptive optics optimization algorithm, in particular to a mutual coupling compensation method of optical phased array array elements based on neighborhood sampling principal component analysis.

Background technique

Optical phased arrays are ideal for non-mechanical beam deflection and are used in many fields, such as light detection and ranging, free-space communications, target tracking, and remote sensing. However, many optical phased arrays face the problem of mutual coupling between array elements, such as the lateral electric field of liquid crystal phased arrays, the thermal crosstalk of silicon-based phased arrays, etc. Deterioration of far-field deflection beam quality. These coupling problems caused by the device structure are difficult to solve only by improving the manufacturing process or materials. Therefore, the commonly used method is to compensate the phase difference through some iterative-based adaptive optimization algorithms, such as genetic algorithm, particle swarm algorithm, stochastic parallel gradient descent algorithm, etc. However, the iterative convergence rate of these algorithms decreases greatly as the number of array elements increases. This is because these iterative algorithms optimize each element of the phased array independently, so the dimension of the iterative variable is equal to the number of array elements, and it is very difficult to find the global optimal solution through the iterative method in high-dimensional space, and even It may fall into a local optimal solution and fail to complete the convergence. Therefore, the slow iterative convergence speed has become the main obstacle restricting the application of optimization algorithms in practical systems.

In order to improve the convergence speed of the optimization algorithm, there are three main methods at present. The first method is decoupling of array elements, that is, through numerical calculation, the coupling relationship between array elements is modeled, so as to strip out the influence of a single array element on the evaluation function. However, in the actual system, it is very difficult to accurately model the coupling relationship between the elements, so this method mostly stays at the theoretical level and is rarely applied in practical engineering. The second method is phase difference modeling, which is to model the phase difference of the system according to the phase difference theory, establish the relationship between the phase difference and the evaluation function, and then optimize the cause of the phase difference. This method can optimize the speed of the system, but the established model can only be applied to specific scenarios, different scenarios require different models, and it is difficult to accurately model the phase difference in some scenarios. The third method is machine learning modeling, which builds the error model of the phased array device through a large number of sample training, and then optimizes the device. But this approach requires a large number of samples for pre-training the model, and the model is not universal across different devices.

In general, there is still a lack of a practical algorithm that can perform adaptive iterative optimization and phase compensation for the phase error caused by the coupling problem between optical phased array elements, while ensuring fast convergence speed and supporting online operation. while taking into account the versatility.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a neighborhood sampling based neighborhood sampling that can greatly reduce the iterative dimension of the optimization process, avoid falling into the local optimal solution, improve the convergence speed, and improve the robustness of the system operation. Principal component analysis method for mutual coupling compensation of optical phased array elements.

The object of the present invention is achieved through the following technical solutions: a method for mutual coupling compensation of optical phased array elements based on neighborhood sampling principal component analysis, including two processes of dimensionality reduction and iteration, and the dimensionality reduction process includes the following steps:

其中N为相控阵的阵元总数；S1. According to the deflection target angle, through the phased array formula and the voltage-phase relationship, calculate the driving voltage corresponding to each array element of the phased array, and record the driving voltage of all the array elements as an N-dimensional column vector

where N is the total number of elements of the phased array;

将它们与

按列拼接，得到邻域采样矩阵

记为X，其中K为电压向量总数；S2. Set K-1 sampling points in a neighborhood of the target angle, and calculate the voltage vector corresponding to each sampling point

combine them with

Concatenate by column to get the neighborhood sampling matrix

Denoted as X, where K is the total number of voltage vectors;

S3, calculate the covariance matrix C=XX ^T of the neighborhood sampling matrix X;

S4. Calculate the eigenvalues of the covariance matrix C and the eigenvectors corresponding to the eigenvalues, and splicing the eigenvectors in rows to obtain the matrix U;

S5, sort the eigenvalues of the covariance matrix C from large to small, and also sort the eigenvectors in the U matrix correspondingly to obtain the space transformation matrix P;

对其进行空间变换，得到新的向量

S6. Use the P matrix to left multiply the voltage vector

space transform it to get a new vector

The iterative process includes the following steps:

的前K个维度施加随机微扰

对更新后的

使用空间变化矩阵P的逆矩阵进行反变换，得到更新后的电压向量

并将

加载到相控阵的阵元上；S7, yes

Apply random perturbations to the first K dimensions of

to the updated

Inverse transform using the inverse of the space-varying matrix P to get the updated voltage vector

and will

Loaded on the element of the phased array;

的前K个值进行更新，更新公式为：

其中

表示第n次迭代的数据，γ为迭代步长。S8. Collect the value J of the evaluation function, according to the change amount δJ of the evaluation function to

The first K values of , are updated, and the update formula is:

in

Indicates the data of the nth iteration, and γ is the iteration step size.

Further, the specific implementation method of step S1 is: the phased array formula refers to the relationship between the phase shift amount ΔΦ between adjacent array elements of the phased array and the target angle θ, that is, ΔΦ=2π/λ·dsinθ , where λ is the wavelength of the incident laser light, and d is the center-to-center spacing of the phased array elements; the voltage-phase relationship refers to the relationship curve between the phased array phasor ΔΦ and the driving voltage, which is measured experimentally and used for The phasor ΔΦ is mapped to a voltage value, and then the driving voltage required by each array element is obtained.

Further, a neighborhood of the target angle in the step S2 refers to the angular range of [θ-δθ, θ+δθ] centered on the target angle θ, where δθ satisfies: |sin(θ+δθ)- sin(θ)|<λ/(Nd), where λ is the wavelength of the incident laser light, and d is the center-to-center spacing of the phased array elements.

The beneficial effects of the present invention are as follows: the present invention extracts the structural information of the optical phased array through principal component analysis, approximates it with a small number of dimensions at the same time, and automatically conducts the driving voltage of the optical phased array element in a low-dimensional space by self-reporting. Adaptive optimization realizes the compensation of the phase difference caused by the mutual coupling of the antenna elements; on this basis, through multiple sampling in the neighborhood of the target angle, the coupling information in different dimensions is obtained, and the accuracy of the linear approximation is improved. It can greatly reduce the iterative dimension of the optimization process, avoid falling into the local optimal solution, improve the convergence speed, and improve the robustness of the system operation; at the same time, the algorithm does not depend on any specific device structure or application scenario, It can be applied to any phased array system with coupling problems between array elements, and has strong universality.

Description of drawings

FIG. 1 is a flow chart of a mutual coupling compensation method for optical phased array elements based on neighborhood sampling principal component analysis of the present invention.

Detailed ways

The technical solutions of the present invention are further described below with reference to the accompanying drawings.

As shown in Figure 1, a method for mutual coupling compensation of optical phased array elements based on neighborhood sampling principal component analysis of the present invention includes two processes of dimensionality reduction and iteration, wherein the dimensionality reduction process uses principal component analysis to extract optical The structure information of the phased array is obtained, and the space transformation matrix is generated by sorting the eigenvalues and eigenvectors, and it is approximated by a few dimensions in the new space, so as to reduce the dimension of the high-dimensional data; Multiple sampling in the neighborhood of the target angle to obtain coupling information in different dimensions and improve the accuracy of linear approximation; the iterative process adopts stochastic parallel gradient descent algorithm to iteratively optimize the dimensionality-reduced data, so as to optimize the optical phased array array. The phase error caused by the element mutual coupling is compensated.

The dimensionality reduction process only needs to be run once for the optimization of each target angle, and includes the following steps:

S1. According to the deflection target angle, through the phased array formula and the voltage-phase relationship, calculate the driving voltage corresponding to each array element of the phased array, and record the driving voltage of all the array elements as an N-dimensional column vector

where N is the total number of elements of the phased array;

The specific implementation method is: the phased array formula refers to the relationship between the phase shift amount ΔΦ between adjacent elements of the phased array and the target angle θ, that is, ΔΦ=2π/λ·dsinθ, where λ is the incident laser wavelength, d is the distance between the centers of the phased array elements; the voltage-phase relationship refers to the relationship curve between the phased array phasor ΔΦ and the driving voltage, which is measured by experiments and used to map the phasor ΔΦ as voltage value, and then obtain the driving voltage required by each array element.

将它们与

按列拼接，得到邻域采样矩阵

记为X，其中K为电压向量总数；目标角度的一个邻域是指以目标角度θ为中心，位于[θ-δθ，θ+δθ]的角度范围，其中δθ满足：|sin(θ+δθ)-sin(θ)|＜λ/(Nd)，其中λ为入射激光的波长，d为相控阵阵元中心间距。S2. Set K-1 sampling points in a neighborhood of the target angle, and calculate the voltage vector corresponding to each sampling point

combine them with

Concatenate by column to get the neighborhood sampling matrix

Denoted as X, where K is the total number of voltage vectors; a neighborhood of the target angle refers to the angular range of [θ-δθ, θ+δθ] centered on the target angle θ, where δθ satisfies: |sin(θ+δθ )-sin(θ)|<λ/(Nd), where λ is the wavelength of the incident laser, and d is the center-to-center spacing of the phased array elements.

S3. Calculate the covariance matrix C=XX ^T of the neighborhood sampling matrix X, and the superscript T means transposition. The obtained covariance matrix C is an N-dimensional real symmetric matrix, and its diagonal elements are the variances of each dimension of X. The diagonal elements are the covariance;

S4. Calculate the eigenvalues {λ ₁ , λ ₂ ... λ _N } of the covariance matrix C and the eigenvectors ξ ₁ , ξ ₂ ... ξ _N corresponding to the eigenvalues, and splicing the eigenvectors in rows to obtain the matrix U; From the properties of real symmetric matrices, C satisfies:

D = UCU ^T

where U is a matrix formed by splicing the eigenvectors of C as row vectors; D is a diagonal matrix, and the diagonal elements are each eigenvalue of C in turn, namely:

S5. Sort the eigenvalues {λ ₁ , λ ₂ ... λ _N } of the covariance matrix C from large to small, and also sort the eigenvectors in the U matrix correspondingly to obtain the spatial transformation matrix P, so that the higher the value is The eigenvector corresponding to the larger eigenvalue is placed in the higher row in the P matrix;

对其进行空间变换，得到新的向量

S6. Use the P matrix to left multiply the voltage vector

space transform it to get a new vector

相当于定义了这样一种空间变换，即将

的每个元素映射到这组新的基底上，新基底中每个维度上的值对应为

的每个元素。根据协方差矩阵C的定义，特征向量对应的特征值越大，代表该维度上数据的方差越大，其在空间变换后涵盖的信息量也越大。因此，通过对特征值进行排序，将信息量较大的特征向量对应的维度排到靠前的位置，实现对相控阵结构信息的线性近似，亦即保留了主要的信息；在迭代过程中只对这些维度进行优化，相较于直接对原始电压向量的N维空间进行优化，即为实现了降维；其余维度由于对应较小的特征值，因此涵盖的信息量较小，是相对次要的信息，予以忽略有助于提高优化的效率。The principle of the dimensionality reduction process of S1 to S6 is: the eigenvectors constitute a new set of orthogonal bases, and the matrix P is used to multiply the original voltage vector left in S6

It is equivalent to defining such a space transformation, namely

Each element of is mapped to this new set of bases, and the value of each dimension in the new base corresponds to

of each element. According to the definition of the covariance matrix C, the larger the eigenvalue corresponding to the eigenvector, the larger the variance of the data in this dimension, and the larger the amount of information it covers after spatial transformation. Therefore, by sorting the eigenvalues, the dimension corresponding to the eigenvectors with larger amount of information is arranged to the front, and the linear approximation of the phased array structure information is realized, that is, the main information is retained; in the iterative process Only these dimensions are optimized, compared to directly optimizing the N-dimensional space of the original voltage vector, which is to achieve dimensionality reduction; the remaining dimensions, because they correspond to smaller eigenvalues, cover a smaller amount of information, which is relatively inferior. The necessary information, ignoring it helps to improve the efficiency of optimization.

The present invention introduces neighborhood sampling in S2 because for the same optical phased array, different angles correspond to different voltage vectors, and the degree of mutual coupling between array elements is also different. Therefore, each additional voltage vector introduces new dimensional information into the PCA.

The covariance matrix C is an N-dimensional real symmetric square matrix, and its rank is equal to the number of sampling points K in the neighborhood, and is also equal to the number of non-zero eigenvalues; since the space transformation matrix is composed of eigenvectors, the more the number of sampling points K Larger, the more eigenvectors corresponding to the non-zero eigenvalues that can be obtained, the more accurate the approximation of the phased array structure information, but the slower the calculation speed. In practical applications, the number of sampling points should be selected reasonably, and a balance should be sought between accuracy and speed.

The iterative process needs to be run repeatedly until a preset convergence condition is reached, that is, to complete the optimization, the following steps are included:

的前K个维度施加随机微扰

对更新后的

使用空间变化矩阵P的逆矩阵进行反变换，得到更新后的电压向量

并将

加载到相控阵的阵元上；S7, yes

Apply random perturbations to the first K dimensions of

to the updated

Inverse transform using the inverse of the space-varying matrix P to get the updated voltage vector

and will

Loaded on the element of the phased array;

的前K个值进行更新，更新公式为：

其中

表示第n次迭代的数据，γ为迭代步长。评价函数，是指对当前远场光强分布状况的一个评价函数，常用的评价函数包括偏转效率、边模抑制比和主瓣半高全宽等，可根据实际需求进行选用。S8. Collect the value J of the evaluation function, according to the change amount δJ of the evaluation function to

The first K values of , are updated, and the update formula is:

in

Indicates the data of the nth iteration, and γ is the iteration step size. The evaluation function refers to an evaluation function for the current far-field light intensity distribution. Common evaluation functions include deflection efficiency, side mode suppression ratio, and full width at half maximum of the main lobe, which can be selected according to actual needs.

The iteration is stopped until the preset convergence condition is reached, such as the expected convergence value or the set number of iterations, or the change of the evaluation function caused by the perturbation reaches the set value, etc.

Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to assist readers in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (3)

1. The optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis is characterized by comprising two processes of dimensionality reduction and iteration, wherein the dimensionality reduction process comprises the following steps of:

s1, calculating the phase according to the target angle of deflection through a phased array formula and a voltage-phase relationControlling the driving voltage corresponding to each array element of the array, and recording the driving voltage of all the array elements as an N-dimensional column vector

Wherein N is the total number of array elements of the phased array;

s2, setting K-1 sampling points in one neighborhood of the target angle, and calculating the voltage vector corresponding to each sampling point

By mixing them with

Splicing according to columns to obtain a neighborhood sampling matrix

Marking as X, wherein K is the total number of the voltage vectors;

s3, calculating covariance matrix C of neighborhood sampling matrix X as XX ^T ；

S4, calculating the eigenvalue of the covariance matrix C and the eigenvector corresponding to the eigenvalue, and splicing the eigenvector according to rows to obtain a matrix U;

s5, sorting the eigenvalues of the covariance matrix C from large to small, and correspondingly sorting the eigenvectors in the U matrix to obtain a spatial transformation matrix P;

s6 left-multiplying voltage vector by P matrix

Carrying out space transformation on the vector to obtain a new vector

The iterative process comprises the steps of:

s7, pair

Front ofRandom perturbation applied in K dimensions

For updated

Performing inverse transformation by using an inverse matrix of the spatial variation matrix P to obtain an updated voltage vector

And will be

Loading to array elements of a phased array;

s8, collecting the value J of the evaluation function, and according to the change delta J pair of the evaluation function

The first K values are updated, and the updating formula is as follows:

wherein

Data representing the nth iteration, γ being the iteration step.

2. The optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis according to claim 1, wherein the step S1 is realized by the following specific method: the phased array formula is a relational expression between phase shift quantity delta phi between adjacent array elements of the phased array and a target angle theta, namely delta phi is 2 pi/lambda dsin theta, wherein lambda is the wavelength of incident laser, and d is the central distance between the phased array elements; the voltage-phase relation is a relation curve between phased array phase shift quantity delta phi and driving voltage, and is measured by experiments, and used for mapping the phase shift quantity delta phi into a voltage value so as to obtain the driving voltage required by each array element.

3. The method for compensating mutual coupling of array elements of an optical phased array based on neighborhood sampling principal component analysis according to claim 1, wherein one neighborhood of the target angle in the step S2 is an angle range centered on the target angle θ and located in [ θ - δ θ, θ + δ θ ], where δ θ satisfies: and | sin (theta + delta theta) -sin (theta) | < lambda/(Nd), wherein lambda is the wavelength of incident laser, and d is the central distance of the phased array elements.

Images