Fast and accurate calculation method for transmission coefficient matrix between transmit and receive array antennas

Abstract

The invention discloses a method for quickly and accurately calculating a transmission coefficient matrix between transmitting and receiving array antennas, comprising the following steps: obtaining the port reflection coefficients, far-field component gains and electric field phases of all units of a transmitting array and a receiving array respectively in an independent environment; constructing the field gain vector of any transceiver unit channel through two-dimensional interpolation and vector field rotation transformation according to the spatial relative position relationship of any transceiver unit, and all channel results form a field gain vector matrix; using the equivalent circuit of a transmitting antenna and a receiving antenna, establishing a transmission model from a transmitting antenna feed source to a receiving antenna load end, and realizing accurate calculation of the amplitude and phase of the transmission coefficient between the transmitting and receiving antennas; and solving the transmission coefficient matrix using the field gain vector matrix between the transceiver arrays, the transceiver reflection coefficient matrix composed of the reflection coefficients of each unit of the transceiver array, and the distance correlation matrix composed of the distance between the transceiver arrays.

Description

[Technical field]

[0001] The present invention relates to the technical field of microwave wireless energy transmission, and in particular to a method for quickly and accurately calculating a transmission coefficient matrix between transceiver array antennas. [Background technology]

[0002] As a carrier of energy, whether electromagnetic waves can be transmitted through air is a topic that people have always wanted to study in depth. In this context, microwave wireless energy transmission technology of antennas came into being. In the field of microwave wireless energy transmission technology, the most critical issue is how to optimize the relevant parameters of array antennas to maximize the energy transmission efficiency between transceiver antennas. In existing research, the transceiver antenna system is usually regarded as a microwave network, and the maximum efficiency transmission analysis and optimization is performed through the scattering matrix in the network. The key challenge of this method is how to quickly obtain the scattering matrix. With the expansion of the scale of the transceiver array, the number of elements in the scattering matrix increases squarely, and it becomes very time-consuming to obtain these scattering parameters through electromagnetic simulation or experiments. The traditional Friis transmission formula can be used to calculate the transmission coefficient between antennas, especially when the polarization of the transceiver antennas is aligned, the calculation is relatively fast, but the transmission coefficient obtained only contains amplitude information and lacks phase information. In summary, the study of the fast and accurate calculation method of the transmission coefficient matrix between the transceiver array antennas has very strong practical significance and application value in the study of maximum efficiency wireless energy transmission.

[0003] In the prior art:

[0004] The Chinese invention patent (CN112531924A) formulated the scattering matrix in the engineering of designing antenna arrays for maximum wireless energy transmission efficiency. However, the formula does not take into account the phase of the transmitting antenna array and the receiving antenna array itself and the phase change in space, which will lead to incorrect excitation results in subsequent calculation optimization.

[0005] In 2018, Ondˇrej Franek proposed a phase alternative to Friis' Transmission Equation, in which the Friis transmission formula was modified so that the calculated transmission coefficient has phase information. However, it ignores the phase change caused by the mismatch between the transmission line and the antenna, and the result is not accurate enough. Moreover, it only discusses the transmission and reception of a single simple antenna, and does not consider the calculation of the transmission and reception transmission coefficient in a complex array environment.

[0006] JE HYEON PARK and others also conducted related research on transmission between multi-antenna arrays in 2021 (Analysis and Experiment on Multi-Antenna to Multi-Antenna RF Wireless Power Transfer), and proposed a corresponding method for calculating the transmission coefficient. However, the calculation needs to be performed in a spherical coordinate system, and the impedance matrix needs to be calculated and changed multiple times to obtain the result. The steps are complicated and the engineering application value is small. [Summary of the invention]

[0007] The purpose of the present invention is to overcome the above-mentioned shortcomings of the existing technology for calculating the transmission coefficient of the transceiver array in the maximum wireless energy transmission efficiency method, and propose a fast and accurate calculation method for the transmission coefficient matrix between the transceiver array antennas. Starting from the equivalent circuit model of the transceiver antenna, the method uses circuit theory and port network theory to matrix and analyze the transmission coefficient. The result is concise and accurate, and has a high theoretical value in the maximum wireless energy transmission efficiency method. Compared with the method of obtaining the transmission coefficient by full-wave simulation of the entire system, the calculation time of the array full-wave simulation alone and the result into the derived expression is greatly shortened, and it has a very high engineering application value.

[0008] The method for quickly and accurately calculating the transmission coefficient matrix between the transmitting and receiving array antennas of the present invention comprises the following steps:

[0009] Step 1: Obtain the port reflection coefficients, far-field component gains, and electric field phases of all components of the transmitting array and receiving array in an independent environment.

[0010] Step 2: According to the spatial relative position relationship of any transceiver unit, the field gain vector of any transceiver unit channel is constructed through two-dimensional interpolation and vector field rotation transformation, and all channel results form a field gain vector matrix.

[0011] In step 2, according to the spatial relative position relationship of any transceiver unit, the field gain vector of any transceiver unit channel is constructed through two-dimensional interpolation and vector field rotation transformation. All channel results form a field gain vector matrix. The specific operation is:

[0012] First, the far-field electric field phase and gain of each unit in the local coordinate system obtained in step 1 are two-dimensionally interpolated. After interpolation, for any unit, the far-field electric field phase and gain in any direction can be obtained by sampling the two-dimensional interpolation model.

[0013] Secondly, TX represents the transmitting antenna and RX represents the receiving antenna. Let θn,m, represents the elevation angle and azimuth angle of the nth receiving unit in the local spherical coordinate system of the mth transmitting unit. The unit vector of the rectangular coordinate system corresponding to the spherical coordinate system is The field gain vector of the mth transmitting unit at the position of the nth receiving unit can be expressed as:

[0014]

[0015] in

[0016]

[0017] Let θm,n, represents the elevation angle and azimuth angle of the mth transmitting unit in the local spherical coordinate system of the nth receiving unit. The unit vector of the rectangular coordinate system corresponding to the spherical coordinate system is The field gain vector of the nth receiving unit at the position of the mth transmitting unit can be expressed as:

[0018]

[0019] in

[0020]

[0021] It can be obtained by full-wave simulation, representative unit simulation or microwave darkroom testing.

[0022] Next, suppose is the unit vector of the global coordinate system. The unit vector of any local coordinate system can be obtained by multiplying the unit vector of the global coordinate system by the corresponding rotation matrix. In the global coordinate system, at the position of the nth receiving unit, the field gain vector of the mth transmitting unit can be expressed as:

[0023]

[0024] in

[0025]

[0026] In the global coordinate system, at the position of the mth transmitting unit, the field gain vector of the nth receiving unit can be expressed as:

[0027]

[0028] in

[0029]

[0030] Finally, at each unit position of the N-element receiving array, the field gain vector combination of the M-element transmitting array forms the field gain vector matrix g of the transmitting array G,TX

[0031]

[0032] At each unit position of the M-element transmitting array, the field gain vector combination of the N-element receiving array constitutes the field gain vector matrix g of the receiving array G,RX

[0033]

[0034] Step 3: Using the equivalent circuits of the transmitting antenna and the receiving antenna, a transmission model from the transmitting antenna feed to the receiving antenna load is established, which enables accurate calculation of the amplitude and phase of the transmission coefficient between the transmitting and receiving antennas.

[0035] In step 3, the equivalent circuits of the transmitting antenna and the receiving antenna are used to establish a transmission model from the transmitting antenna feed to the receiving antenna load end, which enables the accurate calculation of the amplitude and phase of the transmission coefficient between the transmitting and receiving antennas. The specific operations are as follows:

[0036] First, establish the transmission model from the transmitting antenna feed to the receiving antenna load end as follows: Figure 2 As shown. The voltage V induced by the receiving antenna RX loop OC for:

[0037]

[0038] in, and They represent the complex effective lengths of the transmitting antenna TX and the receiving antenna RX, respectively. TX is the current of the transmitting antenna loop, k = 2π / λ, λ is the working wavelength of the antenna, r is the distance between the receiving antenna and the transmitting antenna, η 0 represents the free space wave impedance.

[0039] Next, let the excitation source impedance be Z G , the load impedance is Z L , the equivalent impedance of the transmitting antenna TX is The equivalent impedance of the receiving antenna RX is The characteristic impedance of the transmission line is Z C . Assume the power supply impedance Z G And the load impedance Z L The characteristic impedance Z of the transmission line C When it matches exactly, there is Z G =Z L =Z C According to the circuit principle, the load voltage V L With the power supply voltage V G The ratio is:

[0040]

[0041] The reflection coefficients of the TX antenna and RX antenna are defined as:

[0042]

[0043] A two-port network is constructed with the connection between the transmission line and the transmitting antenna TX as port 1 and the connection between the receiving antenna RX and the transmission line as port 2. According to the port network theory and the circuit voltage division principle, the output voltage of port 2 is The input voltage of port 1 It can be expressed as:

[0044]

[0045] Antenna complex effective length The field gain vector of the antenna express:

[0046]

[0047] Finally, the transmission coefficient S from the transmitting antenna to the receiving antenna 21 It can be expressed by the field gain vector as:

[0048]

[0049] in

[0050]

[0051] Step 4: The transmission coefficient matrix is ​​obtained by using the field gain vector matrix between the transceiver arrays, the transceiver reflection coefficient matrix composed of the reflection coefficients of each unit of the transceiver array, and the distance correlation matrix composed of the distance between the transceiver arrays.

[0052] In step 4, the transmission coefficient matrix is ​​obtained by using the field gain vector matrix between the transceiver arrays, the transceiver reflection coefficient matrix composed of the reflection coefficients of each unit of the transceiver array, and the distance correlation matrix composed of the distance between the transceiver arrays. The specific operation is:

[0053] First, the reflection coefficient matrix of the M-element transmit array can be expressed as The reflection coefficient matrix of the N-element receiving array can be expressed as The corresponding parameter matrix is

[0054]

[0055] Let matrix R be the distance correlation matrix formed by the distance between the transmitting and receiving arrays

[0056]

[0057] Finally, the transmission coefficient matrix S is calculated tran :

[0058]

[0059] The advantages of the present invention are:

[0060] 1. The present invention mainly consists of two parts. The first is to derive the expression of the transmit and receive transmission coefficient of the unit through the transmit and receive antenna model. The second is to combine the array radiation pattern and gain information, use two-dimensional interpolation to construct the field gain vector matrix, and calculate the transmission coefficient matrix between the transmit and receive arrays.

[0061] 2. Based on the above two points, the transmission coefficient matrix between any two transceiver arrays can be calculated quickly and accurately, which greatly saves time compared to full-wave simulation of the entire system. It provides solid support for solving the transmission coefficient of ultra-large-scale transceiver arrays, and also provides theoretical support and engineering application value for the array's maximum efficiency transmission technology.

Brief Description of the Drawings

[0062] Figure 1 It is a flow chart of a method for quickly and accurately calculating a transmission coefficient matrix between transceiver array antennas of the present invention;

[0063] Figure 2 It is a schematic diagram of a transmission model from a transmitting antenna feed source to a receiving antenna load end of the present invention;

[0064] Figure 3 It is a structural schematic diagram of a simulation model of a transceiver array antenna of the present invention;

[0065] Figure 4 It is an amplitude comparison diagram of the transmission coefficient matrix calculated by the method of the present invention and the transmission coefficient matrix obtained by full-wave simulation of the transceiver system.

[0066] Figure 5 It is a phase comparison diagram of the transmission coefficient matrix calculated by the method of the present invention and the transmission coefficient matrix obtained by full-wave simulation of the transceiver system. [Specific implementation method]

[0067] The present invention will now be further described with reference to the accompanying drawings.

[0068] like Figure 1 As shown, the fast and accurate calculation method of the transmission coefficient matrix between the transmitting and receiving array antennas of the present invention comprises the following steps:

[0069] Step 1: Obtain the port reflection coefficients, far-field component gains, and electric field phases of all components of the transmitting array and receiving array in an independent environment.

[0070] Step 2: According to the spatial relative position relationship of any transceiver unit, the field gain vector of any transceiver unit channel is constructed through two-dimensional interpolation and vector field rotation transformation, and all channel results form a field gain vector matrix.

[0071] All channel results in step 2 constitute a field gain vector matrix. The specific operation is as follows: first, two-dimensional interpolation is performed on the far-field electric field phase and gain of each unit in the local coordinate system obtained in step 1. After interpolation, for any unit, the far-field electric field phase and gain in any direction can be obtained by sampling the two-dimensional interpolation model.

[0072] Secondly, TX represents the transmitting antenna and RX represents the receiving antenna. Let θn,m, represents the elevation angle and azimuth angle of the nth receiving unit in the local spherical coordinate system of the mth transmitting unit. The unit vector of the rectangular coordinate system corresponding to the spherical coordinate system is The field gain vector of the mth transmitting unit at the position of the nth receiving unit can be expressed as:

[0073]

[0074] in

[0075]

[0076] Let θm,n, represents the elevation angle and azimuth angle of the mth transmitting unit in the local spherical coordinate system of the nth receiving unit. The unit vector of the rectangular coordinate system corresponding to the spherical coordinate system is The field gain vector of the nth receiving unit at the position of the mth transmitting unit can be expressed as:

[0077]

[0078] in

[0079]

[0080] It can be obtained by full-wave simulation, representative unit simulation or microwave darkroom testing.

[0081] Next, suppose is the unit vector of the global coordinate system. The unit vector of any local coordinate system can be obtained by multiplying the unit vector of the global coordinate system by the corresponding rotation matrix. In the global coordinate system, at the position of the nth receiving unit, the field gain vector of the mth transmitting unit can be expressed as:

[0082]

[0083] in

[0084]

[0085] In the global coordinate system, at the position of the mth transmitting unit, the field gain vector of the nth receiving unit can be expressed as:

[0086]

[0087] in

[0088]

[0089] Finally, at each unit position of the N-element receiving array, the field gain vector combination of the M-element transmitting array forms the field gain vector matrix g of the transmitting array G,TX

[0090]

[0091] At each unit position of the M-element transmitting array, the field gain vector combination of the N-element receiving array constitutes the field gain vector matrix g of the receiving array G,RX

[0092]

[0093] Step 3: Using the equivalent circuits of the transmitting antenna and the receiving antenna, a transmission model from the transmitting antenna feed to the receiving antenna load is established, which enables accurate calculation of the amplitude and phase of the transmission coefficient between the transmitting and receiving antennas.

[0094] In step 3, the transmission coefficient amplitude and phase between the transmitting and receiving antennas are accurately calculated. The specific operation is as follows: First, a transmission model from the transmitting antenna feed to the receiving antenna load is established as follows: Figure 2 As shown. The voltage V induced by the receiving antenna RX loop OC for:

[0095]

[0096] in, and They represent the complex effective lengths of the transmitting antenna TX and the receiving antenna RX, respectively. TX is the current of the transmitting antenna loop, k = 2π / λ, λ is the working wavelength of the antenna, r is the distance between the receiving antenna and the transmitting antenna, η 0 represents the free space wave impedance.

[0097] Next, let the excitation source impedance be Z G , the load impedance is Z L , the equivalent impedance of the transmitting antenna TX is The equivalent impedance of the receiving antenna RX is The characteristic impedance of the transmission line is Z C. Assume the power supply impedance Z G And the load impedance Z L The characteristic impedance Z of the transmission line C When it matches exactly, there is Z G =Z L =Z C According to the circuit principle, the load voltage V L With the power supply voltage V G The ratio is:

[0098]

[0099] The reflection coefficient of the transmitting antenna TX and the receiving antenna RX is defined as:

[0100]

[0101] A two-port network is constructed with the connection between the transmission line and the transmitting antenna TX as port 1 and the connection between the receiving antenna RX and the transmission line as port 2. According to the port network theory and the circuit voltage division principle, the output voltage of port 2 is The input voltage V 1 + It can be expressed as:

[0102]

[0103] Antenna complex effective length The field gain vector of the antenna express:

[0104]

[0105] Finally, the transmission coefficient S from the transmitting antenna to the receiving antenna 21 It can be expressed by the field gain vector as:

[0106]

[0107] in

[0108]

[0109] Step 4: The transmission coefficient matrix is ​​obtained by using the field gain vector matrix between the transceiver arrays, the transceiver reflection coefficient matrix composed of the reflection coefficients of each unit of the transceiver array, and the distance correlation matrix composed of the distance between the transceiver arrays.

[0110] The transmission coefficient matrix is ​​obtained by solving in step 4. The specific operation is:

[0111] First, the reflection coefficient matrix of the M-element transmit array can be expressed as The reflection coefficient matrix of the N-element receiving array can be expressed as The corresponding parameter matrix is

[0112]

[0113] Let matrix R be the distance correlation matrix formed by the distance between the transmitting and receiving arrays

[0114]

[0115] Finally, the transmission coefficient matrix S is calculated tran :

[0116]

[0117] The fast and accurate calculation method of the transmission coefficient matrix between the transmitting and receiving array antennas proposed in the present invention can be further verified and explained through the following specific simulation examples.

[0118] Simulation example:

[0119] The simulation structure of the transceiver array in this example is as follows Figure 3 As shown in the figure, the transceiver system consists of a 4×4 uniform planar transmitting array and a 4×4 uniform planar receiving array, and the spacing between adjacent elements is 1 wavelength. Both arrays are composed of coaxially fed microstrip patch antennas, which are composed of a metal floor, a dielectric substrate, a rectangular patch, and a coaxial feed line. The dielectric substrate is Rogers 5880 (ε r =2.2), the operating frequency is 5GHz. Since the transmitting array is the same as the receiving array, it is only necessary to perform a full-wave simulation of the transmitting array in an independent environment to obtain the port reflection coefficient of each unit, the gain of each far-field component, and the electric field phase of each component. Then, two-dimensional interpolation is performed on the gain of each far-field component and the electric field phase of each component. The elevation angle between different transceiver units is determined according to the positional relationship between each transceiver antenna, and the corresponding field gain vector is obtained by sampling the unit radiation pattern after interpolation to form a field gain vector matrix. Finally, the transmission coefficient matrix expression obtained in step 4 is substituted to obtain the transmission coefficient matrix between the transceiver arrays.

[0120] like Figure 4 The figure shows the amplitude comparison diagram of the transmission coefficient matrix calculated by the method of the present invention and the transmission coefficient matrix obtained by full-wave simulation of the transceiver system. The amplitudes of all transmission coefficients are in good agreement, with the maximum error being 1.19 dB. Figure 5This is a phase comparison diagram of the transmission coefficient matrix calculated by the method of the present invention and the transmission coefficient matrix obtained by full-wave simulation of the transceiver system. The phases of all transmission coefficients are well matched, with the maximum error being 18.7°. In this simulation example, the method of obtaining the transmission coefficient matrix by full-wave simulation of the transceiver system takes 4h07min32s, while the method of the present invention takes only 5min46s to obtain the transmission coefficient by full-wave simulation of a single array and calculating it through four steps. (PC:Inter Core i7-12700 CPU@4.5GHz,RAM:64GB)

[0121] The simulation results show that the fast and accurate calculation method of the transmission coefficient matrix between the antennas of the transceiver array of the present invention is consistent with the result of the full-wave simulation of the transceiver system, which greatly saves time. It provides solid support for the solution of the transmission coefficient of the ultra-large-scale transceiver array, and also provides theoretical support and engineering application value for the array maximum efficiency transmission technology.

[0122] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the above embodiments, a person skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fast and accurate calculation method for the transmission coefficient matrix between the transmitting and receiving array antennas, characterized in that: The steps include: Step 1: Obtain the port reflection coefficients, far-field component gains, and electric field phases of all components of the transmitting array and receiving array in an independent environment; Step 2: According to the spatial relative position relationship of any transceiver unit, the field gain vector of any transceiver unit channel is constructed through two-dimensional interpolation and vector field rotation transformation, and all channel results form a field gain vector matrix; Step 3: Using the equivalent circuits of the transmitting antenna and the receiving antenna, a transmission model from the transmitting antenna feed to the receiving antenna load is established, which enables accurate calculation of the amplitude and phase of the transmission coefficient between the transmitting and receiving antennas. Step 4: The transmission coefficient matrix is ​​obtained by using the field gain vector matrix between the transceiver arrays, the transceiver reflection coefficient matrix composed of the reflection coefficients of each unit of the transceiver array, and the distance correlation matrix composed of the distance between the transceiver arrays; The step 3 can be specifically described as follows: (101) Establish a transmission model from the transmitting antenna feed to the receiving antenna load end, and the voltage V induced by the receiving antenna RX loop OC for: in, and They represent the complex effective lengths of the transmitting antenna TX and the receiving antenna RX, respectively. TX is the current of the transmitting antenna loop, k = 2π / λ, λ is the working wavelength of the antenna, r is the distance between the receiving antenna and the transmitting antenna, and η0 represents the free space wave impedance; (102) Let the excitation source impedance be Z G , the load impedance is Z L , the equivalent impedance of the transmitting antenna TX is The equivalent impedance of the receiving antenna RX is The characteristic impedance of the transmission line is Z C , assuming the power supply impedance Z G And the load impedance Z L The characteristic impedance Z of the transmission line C When it matches exactly, there is Z G =Z L =Z C According to the circuit principle, the load voltage V L With the power supply voltage V G The ratio is: The reflection coefficient of the transmitting antenna TX and the receiving antenna RX is defined as: A two-port network is constructed with the connection between the transmission line and the transmitting antenna TX as port 1 and the connection between the receiving antenna RX and the transmission line as port 2. According to the port network theory and the circuit voltage division principle, the output voltage of port 2 is The input voltage V1 of port 1 + It can be expressed as: V1 + =V G / 2 Antenna complex effective length The field gain vector of the antenna express: Transmission coefficient S from the transmitting antenna to the receiving antenna 21 It can be expressed by the field gain vector as: in The step 4 can be specifically described as follows: The reflection coefficient matrix of the M-element transmitting array can be expressed as The reflection coefficient matrix of the N-element receiving array can be expressed as The corresponding parameter matrix is Let matrix R be the distance correlation matrix formed by the distance between the transmitting and receiving arrays g G,TX represents the transmission coefficient matrix of the transmitting array, g G,RX Represents the transmission coefficient matrix of the receiving array, and the transmission coefficient matrix S is calculated tran :

2. The method for quickly and accurately calculating the transmission coefficient matrix between the transmitting and receiving array antennas according to claim 1, characterized in that: The step 2 can be specifically described as follows: (201) performing two-dimensional interpolation on the far-field electric field phase and gain in the local coordinate system of each unit obtained in step 1. After interpolation, for any unit, the far-field electric field phase and gain in any direction can be obtained by sampling the two-dimensional interpolation model; (202)TX represents the transmitting antenna, RX represents the receiving antenna; let θ n,m , represents the elevation angle and azimuth angle of the nth receiving unit in the local spherical coordinate system of the mth transmitting unit. The unit vector of the rectangular coordinate system corresponding to the spherical coordinate system is The field gain vector of the mth transmitting unit at the position of the nth receiving unit can be expressed as: in Let θ m,n , represents the elevation angle and azimuth angle of the mth transmitting unit in the local spherical coordinate system of the nth receiving unit. The unit vector of the rectangular coordinate system corresponding to the spherical coordinate system is The field gain vector of the nth receiving unit at the position of the mth transmitting unit can be expressed as: in All can be obtained by full-wave simulation, representative unit simulation or microwave darkroom testing; (203) is the unit vector of the global coordinate system. The unit vector of any local coordinate system can be obtained by multiplying the unit vector of the global coordinate system by the corresponding rotation matrix. In the global coordinate system, at the position of the nth receiving unit, the field gain vector of the mth transmitting unit can be expressed as: in In the global coordinate system, at the position of the mth transmitting unit, the field gain vector of the nth receiving unit can be expressed as: in (204) At each unit position of the N-element receiving array, the field gain vector combination of the M-element transmitting array forms the field gain vector matrix g of the transmitting array G,TX At each unit position of the M-element transmitting array, the field gain vector combination of the N-element receiving array constitutes the field gain vector matrix g of the receiving array G,RX 。

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