A non-plane wave single-pulse angle measurement method

Abstract

Currently, for electromagnetic fields that do not satisfy the plane wave approximation, receiving beamforming algorithms may fail, and algorithms based on beamforming technology, such as sum-difference angle measurement algorithms, will therefore introduce errors. To overcome the shortcomings of existing technologies, this invention proposes a non-plane wave single-pulse angle measurement method. This method does not require prior knowledge of the incident electromagnetic field wavefront and can handle electromagnetic fields that do not satisfy the plane wave approximation due to unknown factors such as structured light or strong airflow disturbances in complex environments. It is also compatible with the classical case that satisfies the plane wave approximation. Only the current measurement value of the complex amplitude of the electromagnetic field needs to be input to output the angle measurement information at the current moment. No prior knowledge of the spatial distribution of the complex amplitude of the electromagnetic field is required, nor is prior information on the rough estimates of the azimuth and elevation angles of the electromagnetic field required.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, specifically relating to a non-plane wave single-pulse angle measurement method. Background Technology

[0002] Single-pulse angle measurement technology can quickly determine the azimuth and elevation angles of an incident electromagnetic wave signal source in free space. It has wide applications in 5G / 6G communication systems, including base station-user alignment, free-space assisted positioning, inter-satellite communication link alignment, free-space laser communication equipment alignment, and novel sensing technologies. Based on the receiving array, current single-pulse angle measurement techniques mainly include interferometry, sum-difference beamwidth comparison, and pattern matching algorithms. These methods all assume that the electromagnetic field being measured satisfies the plane wave approximation at the array, serving as the basis for the algorithm to form a specific directional receiving beam. If the received electromagnetic wave signal does not satisfy the plane wave approximation condition, and the wavefront phase spatial distribution is complex, the overlap integral between the received beam formed for the plane wave and the non-plane wave electromagnetic field will deviate significantly from the design value, introducing angle measurement errors.

[0003] Non-plane waves possess undeniable value and have an ever-growing number of applications. According to electromagnetic field propagation theory, as wireless communication carrier frequencies increase, beam divergence weakens, base stations become denser, and users are closer to them, making it increasingly difficult to satisfy the uniform plane wave approximation condition for the receiver. Furthermore, in recent years, structured light, represented by optical orbital angular momentum (OAM), has gained increasing attention in ultra-high-capacity optical communication and 3D imaging sensing. OAM modes can provide additional coded information dimensions, thus significantly improving the channel capacity of free-space optical communication. In addition, some structured lights have wave vector components perpendicular to the propagation direction, providing additional sensing dimensions. However, there is currently no systematic single-pulse angle measurement scheme applicable to arbitrary structured lights. Structured light single-pulse angle measurement cannot utilize existing technologies. Taking OAM as an example, the non-zero topological charge of the OAM mode is orthogonal to the plane wave mode, which in extreme cases can lead to zero output signal from the correctly pointed receiving beam, resulting in completely erroneous angle measurement results. On the other hand, factors such as airflow disturbances in harsh environments will disrupt the wavefront, introducing some non-plane wave components. Therefore, for electromagnetic fields that do not satisfy the plane wave approximation, current receiving beamforming algorithms may fail, and algorithms based on beamforming technology, such as sum-difference angle measurement algorithms, will therefore produce errors.

[0004] In summary, a general single-pulse angle measurement method that can handle non-plane wave cases is needed to meet the angle measurement requirements of incident electromagnetic waves with arbitrary unknown wavefront shapes. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention proposes a single-pulse angle measurement method applicable to non-plane wave cases. It requires no prior knowledge of the incident electromagnetic field wavefront and can handle electromagnetic fields that do not satisfy the plane wave approximation due to unknown factors such as structured light or strong airflow disturbances in complex environments. Furthermore, this invention is a compatible and universal method, also compatible with the classical case satisfying the plane wave approximation. It only requires inputting the current measurement value of the complex amplitude of the electromagnetic field to output the angle measurement information for that moment, eliminating the need for multiple measurements of the complex amplitude or long-term measurements. This method requires no prior knowledge of the spatial distribution of the complex amplitude of the electromagnetic field (e.g., whether it satisfies the plane wave approximation, or what form of structured light it is), and requires no prior information on the rough estimates of the azimuth and elevation angles of the electromagnetic field. Specifically, it includes the following steps:

[0006] 1. Preprocessing

[0007] The preprocessing process includes multi-channel digital array complex amplitude reception and analog-to-digital conversion (DAC) module to obtain the electromagnetic field complex amplitude. Based on the planar digital array for receiving the electromagnetic field to be measured, the input of this algorithm is the complex amplitude of the received electromagnetic field. Digital array elements need to be located on the same plane in order to define the array surface normal. Complex amplitude It is in functional form, where the parameters (x, y) are the coordinates of each array element in a Cartesian coordinate system on the two-dimensional plane containing the array surface. In particular, for the case where the array elements are spatially distributed on a rectangular grid, It can be simplified as a complex matrix. The output of the single-pulse angle measurement algorithm in this invention is the spatial angle between the propagation direction of the electromagnetic field to be measured and the normal of the digital array surface, which can be represented by the azimuth angle θ and the elevation angle η or their sine functions sinθ and sinη.

[0008] 2. Key point selection

[0009] On the plane containing the digital array, select N coordinate points (x1, y1), (x2, y2)...(x...). N ,y N These key points serve as crucial points in step 3 and subsequent calculations. The number of key points must satisfy N≥3. When computational resources are plentiful, more key points can be selected to improve the algorithm's robustness against noise interference. It should be noted that:

[0010] (a) To achieve better algorithm performance, the keypoint coordinates should avoid being collinear. Therefore, based on the idea of ​​linear regression, the Pearson correlation coefficient measure for this step is defined as follows:

[0011]

[0012] In the above formula, the average value of the coordinates of N coordinate points is shown below:

[0013]

[0014] A typical choice is as follows: if the measure in equation (1) satisfies |R Sq If |≤0.3, then the selected key point is more appropriate.

[0015] (b) The above N coordinate points may or may not coincide with the elements of the digital array, (x1,y1), (x2,y2)...(x N ,y N It can be taken on the array element or at certain coordinate points between array elements.

[0016] 3. Numerical Calculation of Orbital Angular Momentum (OAM)

[0017] Calculate the orbital angular momentum (OAM) values ​​L1, L2...L1, with the N key points selected in step 2 as reference centers. N The calculation method is the same for each keypoint. Let's take the m-th keypoint (x...) as an example. m ,y m Taking 1≤m≤N as an example, the OAM value calculation formula is as follows:

[0018]

[0019] In the above formula, C l The intensity of the l-th order OAM component is calculated using the following formula:

[0020]

[0021] In the formula, ∫∫ represents the full-plane integral. Formula (4) uses the electromagnetic field complex amplitude coordinate transformation, from a rectangular coordinate system with (0,0) as the origin to a coordinate system with complex amplitude. Transform into (x) m ,y m Complex amplitude in polar coordinates with origin Where r and φ are the polar axis and polar angle, respectively. Depending on the specific application scenario, M in general formula (3) can be taken as 5 to 10. The energy components of higher order OAM are weaker and can be ignored.

[0022] 4. Based on the coordinates of N key points (x1, y1), (x2, y2)...(x N ,y N ) and their corresponding OAM values ​​L1, L2...L N Using the z-axis coordinate as the basis, the spatial plane is obtained through fitting:

[0023] surf:L(x,y)=P 00+P 01 x+P 10 y (5)

[0024] The fitting method can be the least squares method, where P 00 ,P 01 ,P 10 These are the fitting parameters. If N = 3, the aforementioned plane can be directly obtained through three key points.

[0025] 5. Calculate the normal direction of the plane to obtain the spatial incident angle to be measured.

[0026] The single-pulse angle measurement result can be obtained from the plane fitting parameters in step 4:

[0027]

[0028] In the formula, λ is the wavelength of the electromagnetic wave to be measured.

[0029] The beneficial effects of this invention are as follows:

[0030] 1. Compared to interferometry, this method can handle non-planar wave electromagnetic fields such as structured light; compared to beamforming algorithms such as sum-difference beamforming, this method can not only handle non-planar wave electromagnetic fields such as structured light, but also does not require prior knowledge of the approximate direction of the target.

[0031] 2. Only the spatial distribution sampling of the electromagnetic field complex amplitude at the current moment needs to be input to output the angle measurement information at the current moment, without the need to measure the electromagnetic field complex amplitude multiple times or perform long-term measurement of the electromagnetic field complex amplitude.

[0032] 3. No prior knowledge of the spatial distribution of the complex amplitude of the electromagnetic field is required (e.g., whether the plane wave approximation is satisfied), and no rough values ​​of the azimuth and elevation angles of the electromagnetic field are known.

[0033] 4. It effectively utilizes the large amount of information that can be detected by a large-scale digital array. By deeply mining and processing the output information of the digital array, it can cope with scenarios where traditional single-pulse angle measurement algorithms (such as sum-difference beam angle measurement) may fail, such as orbital angular momentum beam angle measurement or other non-plane wave angle measurement.

[0034] 5. The main calculation steps of this method can be transformed into matrix multiplication and addition, which can be accelerated by parallel processing. Attached Figure Description

[0035] Figure 1 This is the flowchart for this method.

[0036] Figure 2 This is a use case diagram. Detailed Implementation

[0037] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] like Figure 1 and 2 As shown, after preprocessing such as analog-to-digital conversion, the multi-channel digital array complex amplitude receiver result is: Assuming the sampling points are located on a square grid, the complex amplitude can be represented as a complex matrix. The absolute value of the complex matrix (electromagnetic field amplitude) and the complex angle (electromagnetic field phase) are respectively as follows: Figure 2 (Top left) and Figure 2 As shown in the lower left corner. Figure 2 (Top left) Grayscale values ​​0-255 are proportional to the amplitude. Figure 2 In the lower left corner, grayscale values ​​of 0 to 255 correspond to phases of 0 to 2π.

[0039] The locations of 13×13 array elements within the central region of the digital array are selected as key points. These key points satisfy the requirement of linear independence of x and y coordinates. The key point locations are... Figure 2 (Lower left) within the dashed box.

[0040] Calculate the OAM value with each keypoint as the reference center. Corresponding to the number of keypoints, a total of 13 × 13 = 169 OAM values ​​are calculated. The similar OAM value calculation process is repeated 169 times, with no specific order required. Parallel processing is recommended if computing resources permit.

[0041] For each keypoint, the OAM calculation steps are 3.1 to 3.5. Taking the calculation of the OAM value l1 at the keypoint (x1, y1) as an example.

[0042] 3.1 Calculate the polar axis of all array elements at the key point (x1, y1):

[0043]

[0044] 3.2 Calculate the polar angles of all array elements relative to the key point (x1, y1):

[0045] φ(x,y)=arctan(y-y1,x-x1) (8)

[0046] In the formula, the arctan function is the inverse operation of the tangent.

[0047] 3.3 Electromagnetic Field Complex Amplitude Coordinate Transformation. Based on the polar axis and polar angle calculated in 3.1 and 3.2, the coordinates of all array elements are transformed from the complex amplitude coordinates with (0,0) as the origin to a Cartesian coordinate system. Convert to complex amplitude in polar coordinates with (x1, y1) as the origin Where r and φ are the polar axis and polar angle, respectively.

[0048] 3.4 Calculate the l-th order OAM component C corresponding to l = -M to M. l The value of C needs to be calculated. Assuming M = 5, we need to calculate 2M = 10 C values ​​for l = -5, -4, -3, -2, -1, 1, 2, 3, 4, 5. l Value, each C l The value calculation method is the same, and parallel processing can also be performed here. Each C... l The value is calculated as follows:

[0049] Will Substitute into equation (9) and replace the part in equation (10) Calculate C l value

[0050]

[0051] 3.5 Based on formula (3), calculate the C corresponding to l = -M ~ M calculated in 3.4. l The values ​​are weighted using l to calculate the OAM value l1 with the keypoint (x1, y1) as the reference point:

[0052]

[0053] 4. Based on the OAM value calculated in step 3 and the corresponding keypoint (x,y) coordinates, use linear fitting to calculate the plane equation l(x,y)=P 00 +P 01 x+P 10 y. Typical fitting results in simulation are as follows: Figure 2 As shown on the right, when the noise of the original data is very small, the fitting degree is high, and there is no need to select a large number of key points. In this example, the 169 key points can be reduced to 3, and the angle measurement accuracy will not be significantly lost.

[0054] 5. Substitute the fitting parameters and electromagnetic wave wavelength λ into formula (6) to calculate and output the sine values ​​of the azimuth and elevation angles to be measured.

[0055] This invention is not limited to the specific embodiments described above, and various modifications and variations are possible. Any modifications, equivalent substitutions, or improvements made to the above embodiments based on the technical essence of this invention should be included within the scope of protection of this invention.

Claims

1. A non-plane wave single-pulse angle measurement method, characterized in that: Specifically, the following steps are included: 1) Preprocess the multi-channel digital array complex amplitude received signal, and obtain the electromagnetic field complex amplitude through analog-to-digital conversion. Represents the coordinates of each array element in a two-dimensional Cartesian coordinate system on the array surface; 2) Key points are selected on the plane of the digital array surface, with N coordinate points chosen. As a key point; 3) Numerical calculation of orbital angular momentum: The orbital angular momentum values ​​are calculated sequentially at N key points selected as reference centers. Let the m-th key point be... The formula for calculating its orbital angular momentum is as follows: (1) In the above formula, For the first The strength of the orbital angular momentum is calculated using the following formula: (2) In the formula To represent the full-plane integral, formula (2) uses the electromagnetic field complex amplitude coordinate transformation, from which... Complex amplitude in a rectangular coordinate system with the origin Turn to Complex amplitude in polar coordinates with origin , where r and These are the polar axis and polar angle, respectively; 4) Using the coordinates of N key points and their corresponding orbital angular momentum values ​​as the z-axis coordinates, a spatial plane is fitted to obtain: (3) The least squares method can be used for fitting, where... These are the fitting parameters; 5) Calculate the normal direction of the spatial plane to obtain the spatial incident angle to be measured. From the spatial plane fitting parameters obtained in step 4), the single-pulse angle measurement result can be obtained as follows: (4) In the formula, It is the azimuth angle. The pitch angle, The wavelength of the electromagnetic wave to be measured is denoted as .

2. The non-plane wave single-pulse angle measurement method according to claim 1, characterized in that: The number of key points satisfies .

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