CN110532631B - 6G communication antenna array element position tolerance determination method based on channel capacity sensitivity - Google Patents

6G communication antenna array element position tolerance determination method based on channel capacity sensitivity Download PDF

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CN110532631B
CN110532631B CN201910707319.0A CN201910707319A CN110532631B CN 110532631 B CN110532631 B CN 110532631B CN 201910707319 A CN201910707319 A CN 201910707319A CN 110532631 B CN110532631 B CN 110532631B
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antenna
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array element
tolerance
sensitivity
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CN110532631A (en
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王从思
王艳
严粤飞
薛松
连培园
周澄
刘菁
郑元鹏
杜彪
李海华
黎昞
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Xidian University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q3/00—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system
    • H01Q3/26—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture
    • H01Q3/30—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture varying the relative phase between the radiating elements of an array
    • H01Q3/34—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture varying the relative phase between the radiating elements of an array by electrical means

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Abstract

The invention discloses a method for determining the position tolerance of an array element of a 6G communication antenna based on channel capacity sensitivity, which comprises the steps of determining the design index of the position tolerance of the array element to be the electric field intensity of the array antenna, and calculating the electrical property of the array antenna under an ideal condition; calculating the sensitivity of position error of the array element and describing the increase speed of array element tolerance in iteration; generating array element random normal error samples; calculating the electrical property change conditions of the antennas corresponding to all the samples; judging the number of error samples meeting the performance requirement; calculating the tolerance of the iteration of the last step and outputting the array element position tolerance aiming at the electric field intensity and the channel capacity of the array antenna; and comparing the position tolerance, taking the smaller one as the position tolerance of the final array element of the 6G communication antenna, and carrying out performance test by using the structure-electromagnetic coupling model again. The method can effectively judge the influence degree of the position tolerance of each antenna array element in the whole array surface structure of the antenna on the electrical property and the channel quality of the antenna, thereby guiding the tolerance design of the phased array antenna of the 6G communication base station.

Description

6G communication antenna array element position tolerance determination method based on channel capacity sensitivity
Technical Field
The invention belongs to the technical field of communication antennas, and particularly relates to a method for determining position tolerance of a 6G communication antenna array element based on channel capacity sensitivity.
Background
Unlike conventional base station antennas, 6G antennas will "customize" the signal for the end user using Beam Forming (Beam Forming) and Beam Tracking (Beam Tracking) techniques. The beam forming technology expands the high-frequency wireless coverage range and reduces wireless interference; the beam tracking technology enables the 6G beams to flexibly adjust the direction, realizes quick and frequent switching between the beams in a high-speed scene, and provides consistent high-speed connection for a designated terminal. The realization of the functions is attributed to the normal work of each antenna unit in the 6G base station phased array antenna, and all array elements can obtain ideal high-gain and high-directivity wave beams only by being arranged according to the designed positions strictly. However, since the manufacturing, processing and installation processes of the array antenna always have errors, the actual position of the antenna unit inevitably deviates from the ideal position, and the communication performance of the system is deteriorated. For the traditional low-frequency band antenna, due to the fact that the working wavelength of the traditional low-frequency band antenna is large, machining and mounting errors are not enough to cause large influence on the electrical performance of the antenna. However, because the 6G base station phased-array antenna works in a millimeter-wave frequency band, and the working wavelength is in a millimeter-scale range, although the sizes of the antenna unit and the components in the array are smaller, the whole communication system is easier to realize, higher requirements are provided for the installation accuracy of the position of the array element, and because the tiny installation errors are likely to be in the same order of magnitude as the working wavelength, the antenna electrical performance and the channel quality are affected non-negligibly. Therefore, it is necessary to quantitatively investigate the effect of position tolerances (including x and y directional mounting accuracy, and z directional flatness) of a 6G base station phased array antenna unit on the performance of a communication system.
Further, engineering experience has shown that antenna elements in different positions have different degrees of influence on the electrical performance of the array antenna, for example, the elements in the center of the front surface are usually affected to a greater degree than the elements in the edge positions. In view of the fact that the 6G base station works in a high frequency band, the requirement on the accuracy of the antenna unit in the installation process is higher, the cost is higher, and after all, the deployment cost of the 6G base station is increased by the increase of the scale of the array antenna, the upgrading of the radio frequency device process and the like; but the precision requirement cannot be set too low, otherwise, the communication performance requirement is not ensured, and the preset technical index cannot be reached.
At present, a great deal of research is carried out at home and abroad, the influence of random errors in excitation current on the radiation pattern of the array antenna is researched and analyzed by Ruze from the aspect of probability statistics, and the influence of random errors in a geometric structure and the excitation current on gain and side lobe levels is researched by Gilbert and Elliot. In the aspect of tolerance design, Hsiao researches the relationship between the maximum sidelobe level of the phased array antenna and random errors through a statistical method, which has important significance in a radar system. The statistical method is a theoretical method for determining array element tolerance by carrying out modeling on the maximum side lobe horizontal distribution in a radiation directional diagram considering random errors and deriving a relational expression between the random errors and the array radiation directional diagram so as to carry out reverse deduction according to design requirements. Similar to the former, Tantan discusses the average statistical property and probability density function of the error lobe of the array antenna, and derives the influence relation between the random error and the side lobe and the directivity, and finally, the critical value of the random error is reversely deduced according to the design requirement of the antenna and is used as the tolerance.
Therefore, it is more necessary to quantitatively clear the influence degree of the position tolerance of each antenna unit in the whole array surface structure of the 6G base station antenna on the electrical performance and the channel quality of the antenna one by one, that is, the sensitivity of the two technical indexes of the electric field strength and the channel capacity of the 6G base station antenna on the position of the array element is respectively analyzed, so that the requirement of the tolerance is conveniently and reasonably determined, and the cost performance of the 6G base station array antenna is excellent. If the sensitivity is higher, the influence degree of the position error of the array element on the technical index is higher, and the installation precision and the flatness of the array element need to be strictly controlled in the engineering; otherwise, the corresponding relaxation requirement can be met, the index requirement is met, the cost is saved, and the efficiency is improved.
Disclosure of Invention
In order to solve the above-mentioned defects in the prior art, an object of the present invention is to provide a method for determining a position tolerance of an array element of a 6G communication antenna based on channel capacity sensitivity, which can effectively solve the problem of the degree of influence of the position tolerance of each antenna element in the whole array structure of the 6G base station antenna on the electrical performance and the channel quality of the antenna, thereby guiding the tolerance design of the 6G base station phased array antenna.
The invention is realized by the following technical scheme.
A method for determining position tolerance of an antenna element of a 6G communication based on channel capacity sensitivity comprises the following steps:
(1) firstly, determining the design index of array element position tolerance as the electric field intensity of the array antenna, and calculating the electrical property of the array antenna under an ideal condition;
(2) determining the increasing speed of the array element tolerance in the x, y and z directions in the iteration by selecting proper array element position error sensitivity matrixes in the x, y and z directions respectively
Figure BDA0002152557300000031
The rate of increase being described by the inverse of the sensitivity, i.e.
Figure BDA0002152557300000032
And appropriate adjustments can be made by changing the constant α;
(3) the position tolerance of the initial array element is 0, and the increasing speed is utilized
Figure BDA0002152557300000033
Increasing the tolerance step by step and respectively
Figure BDA0002152557300000034
The standard deviation is used as a random normal error sample of the array element in a corresponding interval
Figure BDA0002152557300000035
(4) Calculating the electrical property variation of the antenna corresponding to all samples by using a structure-electromagnetic coupling model of the 6G base station phased array antenna, and counting the number of error samples meeting the electrical property requirement;
(5) judging whether the number of the error samples meets the performance requirement, if so, entering the step (6), otherwise, repeating the steps (3) to (5) until the requirement is met;
(6) tolerance of the last iteration
Figure BDA0002152557300000036
I.e. the position tolerance of the array element for the electric field strength of the array antenna
Figure BDA0002152557300000041
(7) Repeating the steps (1) to (6) aiming at the array element position tolerance of which the design index is the channel capacity, and outputting the array element position tolerance sigma aiming at the channel capacityx C,σy C,σz C；
(8) Comparison of
Figure BDA0002152557300000042
And σx C,σy C,σz CTaking the smaller as the position tolerance sigma of the final 6G communication antenna array elementx,σy,σzAnd performing performance test by using the structure-electromagnetic coupling model again.
Further, calculating the corresponding increasing speed of the position tolerance of the array element in the step (2)
Figure BDA0002152557300000043
The method comprises the following steps:
(2a) adding array element position error (delta x) according to a formulamn,Δymn,Δzmn) A structure-electromagnetic coupling model can be obtained;
(2b) according to the directional diagram function f of the array antennaa(theta, phi) actual position (x ') of array element'mn,y'mn,z'mn) The sensitivity matrix of the directional diagram function of the array antenna to the position error of the (m, n) th array element can be obtained;
(2c) the rate of increase can be described by the inverse of the sensitivity.
Further, in the step (5), it is determined whether the number of error samples satisfying the performance requirement is just less than 95% of the total number of samples.
Further, in the step (7), the array element position tolerance sigma for the channel capacity is outputx C,σy C,σz CAnd sensitivity matrix
Figure BDA0002152557300000044
In the process (3), a calculation formula corresponding to the step (2) is adopted for calculation.
Compared with the prior art, the invention has the following characteristics:
1. the position error sample number meeting the electrical performance requirement is judged by utilizing a channel capacity sensitivity model and a structure-electromagnetic coupling model of the 6G base station phased array antenna, the position tolerance of the array element of the communication antenna is determined, the rapid calculation of the position tolerance of the array element of the 6G base station phased array antenna can be realized, guidance suggestions are given to antenna installation, and theoretical guarantee is provided for the design of the 6G phased array antenna.
2. The method for determining the position tolerance of the communication antenna array element based on the channel capacity sensitivity is established, the tolerance of each array element can be adjusted in a reference mode instead of adjusting all the array elements by using a uniform tolerance, so that the suggestion of the tolerance value of each array element in the 6G phased array antenna is quickly given, guidance is provided for engineering designers in the process of installing the antenna, the working efficiency is improved, the product development cost is reduced, and the service performance of the product is guaranteed.
Drawings
FIG. 1 is a flow chart of a method for determining position tolerance of an antenna element of a 6G communication based on channel capacity sensitivity according to the present invention;
FIG. 2 is a schematic diagram of a rectangular grid arrangement of a 6G base station phased array antenna;
fig. 3(a) - (c) are graphs of sensitivity distribution of random position error of array elements with θ equal to 30 ° on the plane with Φ equal to 0 °, respectively;
fig. 4(a) - (c) are graphs of sensitivity distribution of random position error of array elements with θ being 30 ° on the plane with Φ being 90 ° respectively;
fig. 5(a) and (b) are position tolerances of array elements corresponding to different scanning angles in the x direction with respect to the electric field intensity of the array antenna, respectively;
fig. 6(a) and (b) are position tolerances of array elements corresponding to different scanning angles with respect to the electric field intensity of the array antenna, respectively;
FIGS. 7(a) and (b) are position tolerances of array elements corresponding to different scanning angles in the z direction with respect to the electric field intensity of the array antenna, respectively;
fig. 8(a) and (b) are position tolerances of array elements corresponding to different scan angles in the x direction for channel capacity, respectively;
FIGS. 9(a) and (b) are position tolerances of array elements at different scan angles in the y-direction for channel capacity, respectively;
FIGS. 10(a) and (b) are the position tolerances of the array elements in the z-direction at different scan angles for the channel capacity, respectively;
fig. 11(a) - (c) are the ideal case and the 3D gain pattern after adding the tolerance, respectively, at different scan angles.
Detailed Description
The invention is further described in detail below with reference to the drawings and examples, but the invention is not limited thereto.
As shown in fig. 1, the method for determining the position tolerance of the antenna element of the 6G communication based on the channel capacity sensitivity specifically includes the following steps:
step 1, determining the design index of array element position tolerance as the electric field intensity of the array antenna, and calculating the electrical property of the array antenna under an ideal condition.
Firstly, determining the design index of array element position tolerance to be the electric field intensity of an array antenna, taking a rectangular grid array antenna as an example for a 6G base station phased array antenna, and calculating the electrical property of the array antenna under an ideal condition by using the following formula as shown in figure 2;
Figure BDA0002152557300000061
in the formula (I), the compound is shown in the specification,
Figure BDA0002152557300000062
the electrical performance of the array antenna is represented in a rational condition, M and N respectively represent the number of rows and columns of the array antenna, M is more than or equal to 0 and less than or equal to M, N is more than or equal to 0 and less than or equal to N, and dx,dyThe spacing between array elements, I, of rows and columns of the array antenna, respectivelymnDenotes the amplitude of the excitation current, k 2 pi/lambda denotes the wave constant, lambda is the wavelength of the antenna, betamnDenotes an intra-array phase difference between an (m, n) -th array element provided by the phase shifter and a (0,0) -th reference array element, u ═ sin θ sin φ, v ═ sin θ cos φ denotes a direction cosine of an angle of a direction (θ, φ) in which a far-field observation point is located with respect to x and y coordinate axes, respectively, u ═ sin θ sin φ0＝sinθ0sinφ0,v0＝sinθ0cosφ0Respectively, the maximum beam direction (theta) of the antenna0,φ0) The direction cosine of the included angle between the coordinate axes x and y, j represents an imaginary number.
Step 2, determining the increasing speed of array element tolerance in iteration by selecting proper array element position error sensitivity matrixes in the directions of x, y and z respectively
Figure BDA0002152557300000071
For sensitivity the larger the value the more stringent the tolerance is, and the opposite is true for increasing speed, the more stringent the tolerance the unit increases speed. Thus, the increase speed can be described by the inverse of the sensitivity, i.e.
Figure BDA0002152557300000072
And appropriate adjustments can be made by changing the constant alpha.
(2a) Adding array element position error (delta x) according to formula (1)mn,Δymn,Δzmn) A structure-electromagnetic coupling model as shown in formula (2) can be obtained;
Figure BDA0002152557300000073
in the formula (f)a(theta, phi) represents the electrical performance of the array antenna in the presence of array element position error, (deltax)mn,Δymn,Δzmn) Indicates the position offset of the (m, n) th array element, (Deltax)0,0,Δy0,0,Δz0,0) The position offset of the (0,0) -th array element is shown, w is the direction cosine of an included angle of the direction (theta, phi) of the far-field observation point relative to the coordinate axis of z, and w is cos theta.
(2b) Obtaining an array antenna directional pattern function f according to the formula (2)a(theta, phi) actual position (x ') of array element'mn,y'mn,z'mn)＝(mdx+Δxmn,ndy+Δym，nΔzm)nPartial derivative of the array antenna directional diagram function to the (m, n) th array element position error can be obtained
Figure BDA0002152557300000074
Figure BDA0002152557300000075
Figure BDA0002152557300000076
Figure BDA0002152557300000081
Wherein (x'mn,y'mn,z'mn) Indicating the actual position of the (m, n) -th array element in the presence of a position error,
Figure BDA0002152557300000082
a sensitivity matrix of an array antenna directional pattern function to an (m, n) th array element position error,
Figure BDA0002152557300000083
the sensitivity matrixes of the directional diagram function of the array antenna to the (m, n) th array element in the x direction, the y direction and the z direction are respectively.
(2c) The rate of increase can be described by the inverse of the sensitivity, i.e.
Figure BDA0002152557300000084
In the formula (I), the compound is shown in the specification,
Figure BDA0002152557300000085
in order to increase the speed of the mounting accuracy of the array elements in the directions of the x and y coordinate axes,
Figure BDA0002152557300000086
α is a constant for controlling an increasing speed for increasing the flatness of the array element mounting in the z-coordinate axis direction.
Step 3, utilizing the increased speed
Figure BDA0002152557300000087
The tolerance is gradually increased and respectively
Figure BDA0002152557300000088
This is used as the standard deviation to generate array element random normal error samples in the corresponding interval.
The position tolerance of the initial array element is 0, and the random normal error sample of the array element is
Figure BDA0002152557300000089
And 4, calculating the electrical property variation of the antenna corresponding to all samples by using the structure-electromagnetic coupling model of the 6G base station phased array antenna, and counting the number of error samples meeting the electrical property requirement.
And (3) calculating the electrical property variation of the antenna corresponding to all samples by using the structure-electromagnetic coupling model of the 6G base station phased array antenna shown in the formula (2).
Step 5, judging the number of error samples meeting the performance requirement
And (5) if the error sample number is just less than 95% of the total sample number, entering the step (7), otherwise, repeating the steps (3) to (5) until the requirement is met.
Step 6, countingCalculating the tolerance of the last iteration
Figure BDA00021525573000000810
Outputting array element position tolerance for array antenna electric field strength
Figure BDA00021525573000000811
And 7, repeating the steps (1) to (6) aiming at the array element position tolerance of which the design index is the channel capacity, and outputting the array element position tolerance sigma aiming at the channel capacityx C,σy C,σz C。
Array element position tolerance sigma at output for channel capacityx C,σy C,σz CAnd sensitivity matrix
Figure BDA0002152557300000091
The corresponding calculation formula in the process of (2) is as follows:
Figure BDA0002152557300000092
Figure BDA0002152557300000093
Figure BDA0002152557300000094
Figure BDA0002152557300000095
Figure BDA0002152557300000096
wherein C denotes a channel capacity (bps), B denotes a channel operating bandwidth (Hz), d denotes a distance between transmitting and receiving antennas, and N denotes0Is the power spectral density (W/Hz), P, of additive white Gaussian noiseTRepresenting the transmission power of the transmitting antenna, FR(theta, phi) represents the normalized field strength directional pattern function of the receiving antenna, GRRepresenting the maximum radiation directional gain, F, of the receiving antennaT,BS(theta, phi) denotes the normalized field strength directional pattern function of the transmitting antenna at the base station end, GT,BSRepresents the maximum radiation direction gain, gamma, of the transmitting antenna at the base station endRRepresents the matching coefficient of the receiving end, characterizes the matching degree of the receiving antenna and the load and gamma when the conjugate matchesR1, γ in the same wayTRepresenting a transmitting end matching coefficient; cos (ξ) represents the polarization matching factor,
Figure BDA0002152557300000097
a sensitivity matrix representing the channel capacity versus the (m, n) -th array element position error,
Figure BDA0002152557300000098
respectively representing the sensitivity matrixes of the channel capacity to the position errors of the (m, n) th array elements in the x direction, the y direction and the z direction.
Step 8, comparison
Figure BDA0002152557300000099
And σx C,σy C,σz CTaking the smaller as the position tolerance sigma of the final 6G communication antenna array elementx,σy,σzAnd performing performance test by using the structure-electromagnetic coupling model again.
The advantages of the present invention can be further illustrated by the following simulation experiments:
first, simulation condition
In this example 6G, the operating frequency of the large-scale array antenna model of the communication base station is 28GHz, the antenna model includes 256 array elements, the array element spacing is λ/2, and the base station is a 6-sector antenna structure, where an 8 × 8 sub-array corresponding to a certain beam is selected as a research object, that is, the scanning range of the radiation pattern is θ e (-0.1419,0.1477), and Φ e (0,2 pi). And selecting gain loss less than 0.5dB, sidelobe level lifting amount less than 5dB and channel capacity loss amount less than 5Mbps as communication performance indexes of the 6G base station phased-array antenna.
Second, output array element position tolerance sigmax,σy,σz
1. Calculating array element position tolerance for array antenna electric field strength
Figure BDA0002152557300000101
The excitation current amplitude of the 6G base station phased array antenna model is subject to Taylor weighting, and sensitivity distribution conditions of theta 30 degrees, phi 0 degrees or 90 degrees are selected because sensitivity values in three directions all show gradually increasing change trends as the scanning angle theta increases. The sensitivity value distribution of the electric field intensity of the array antenna to the random position error of the array element is calculated by the formulas (3) to (6) as shown in fig. 3(a), (b), (c), 4(a), (b) and (c), and the mounting accuracy (x and y direction position tolerance) and the mounting flatness (z direction position tolerance) of the array element obtained by the calculation are shown in fig. 5(a), (b), fig. 6(a), (b) and fig. 7(a) and (b) and have the unit of mm. Comparing fig. 5(a) and 5(b), it is possible to select the array element mounting accuracy in the x direction more strictly, and similarly, to select the array element mounting accuracy in the y and z directions, fig. 6(b) and 7 (b).
2. Computing array element position tolerance sigma for channel capacityx C,σy C,σz C
Similarly, the array element mounting accuracy (x and y direction position tolerances) and the array element mounting flatness (z direction position tolerance) calculated by the equations (8) to (11) are expressed in mm in fig. 8(a) and (b), fig. 9(a) and (b), and fig. 10(a) and (b), and fig. 8(a) in which the x direction array element mounting accuracy is more strict is obtained by comparing fig. 8(a) and (b), and fig. 9(b) and fig. 10(b) in which the y direction and the z direction array element mounting accuracy are similarly selected.
3. Comprehensive comparison
Figure BDA0002152557300000111
And σx C,σy C,σz C
Comprehensive pairDetermining the final mounting position tolerance sigma of each array element according to the tolerance results in the directions of x, y and z corresponding to the two indexesx,σy,σzFIGS. 8(a), 9(b), and 10(b) are views.
Third, simulation result and analysis
It can be seen from all tolerance profiles that the tolerance value for the central region is minimal for each direction, requiring more stringent control. The above tolerance calculation result also corresponds to the sensitivity distribution result, that is, the larger the sensitivity, the stricter the tolerance is, and for example, the z-direction position tolerance distribution shows a tendency of gradually increasing from the inside to the outside.
Will depend on the final tolerance σx,σy,σzThe generated random position error of the array element is applied to the displacement field of the antenna array structure, and the structure-electromagnetic coupling model is used to perform the performance verification again, and the results are shown in fig. 11(a), (b), (c) and table 1.
Table 1 base station antenna electrical property variation before and after tolerance is added
Figure BDA0002152557300000112
According to the result, after the position tolerance of the array element is adjusted, the maximum gain loss of the base station array antenna directional diagram is 0.2029dB, the maximum side lobe level is increased by 2.6253dB, and the maximum loss of the channel capacity is 2.2164 Mbps. According to the method, the position tolerance of the array element determined by the method can meet the requirement of a communication performance index, the feasibility and the effectiveness of the method are proved, the difficulty of manufacturing an antenna array surface and installing the array element is reduced to a certain extent, the contribution to the development, deployment and operation cost of a 6G base station is made, and the method has a certain reference value for engineering application.

Claims (4)

1. The method for determining the position tolerance of the 6G communication antenna element based on the channel capacity sensitivity is characterized by comprising the following steps of:
(1) firstly, determining the design index of array element position tolerance as the electric field intensity of the array antenna, and calculating the electrical property of the array antenna under an ideal condition;
(2) determining the increasing speed of the array element tolerance in the x, y and z directions in the iteration by selecting proper array element position error sensitivity matrixes in the x, y and z directions respectively
Figure FDA0002722081620000011
The inverse of the sensitivity is used to determine the rate of increase, and appropriate adjustments can be made to the rate of increase by varying the constant α;
(3) the position tolerance of the initial array element is 0, and the increasing speed is utilized
Figure FDA0002722081620000012
Increasing the tolerance step by step and respectively
Figure FDA0002722081620000013
Generating array element random normal error samples in corresponding intervals as standard deviation
Figure FDA0002722081620000014
(4) Calculating the electrical property variation of the antenna corresponding to all samples by using a structure-electromagnetic coupling model of the 6G base station phased array antenna, and counting the number of error samples meeting the electrical property requirement;
(5) judging whether the number of the error samples meets the performance requirement, if so, entering the step (6), otherwise, repeating the steps (3) to (5) until the requirement is met;
(6) tolerance of the last iteration
Figure FDA0002722081620000015
I.e. the position tolerance of the array element for the electric field strength of the array antenna
Figure FDA0002722081620000016
(7) To is directed atThe design index is the array element position tolerance of the channel capacity, the steps (1) to (6) are repeated, and the array element position tolerance sigma aiming at the channel capacity is outputx C,σy C,σz C；
(8) Comparison of
Figure FDA0002722081620000017
And σx C,σy C,σz CTaking the smaller as the position tolerance sigma of the final 6G communication antenna array elementx,σy,σzAnd the structure-electromagnetic coupling model is used again for performance test;
the step (1) is carried out according to the following process:
firstly, determining the design index of array element position tolerance as the electric field intensity of the array antenna, and calculating the electrical property of the array antenna under an ideal condition by using the following formula;
Figure FDA0002722081620000021
wherein M and N respectively represent the number of rows and columns of the array antenna, M is more than or equal to 0 and less than or equal to M, N is more than or equal to 0 and less than or equal to N, and dx,dyThe spacing between array elements, I, of rows and columns of the array antenna, respectivelymnDenotes the amplitude of the excitation current, k 2 pi/lambda denotes the wave constant, lambda is the wavelength of the antenna, betamnDenotes an intra-array phase difference between an (m, n) -th array element provided by the phase shifter and a (0,0) -th reference array element, u ═ sin θ sin φ, v ═ sin θ cos φ denotes a direction cosine of an angle of a direction (θ, φ) in which a far-field observation point is located with respect to x and y coordinate axes, respectively, u ═ sin θ sin φ0＝sinθ0sinφ0,v0＝sinθ0cosφ0Respectively, the maximum beam direction (theta) of the antenna0,φ0) The direction cosine of the included angle between the coordinate axes x and y, j represents an imaginary number.
2. The method for determining the position tolerance of the antenna element of the 6G communication based on the channel capacity sensitivity according to the claim 1, wherein the step (2) is carried out according to the following procedures:
(2a) adding array element position error (delta x) according to formula (1)mn,Δymn,Δzmn) A structure-electromagnetic coupling model as shown in formula (2) can be obtained;
Figure FDA0002722081620000022
in the formula (f)a(theta, phi) represents the electrical performance of the array antenna in the presence of array element position error, (deltax)mn,Δymn,Δzmn) Indicates the position offset of the (m, n) th array element, (Deltax)0,0,Δy0,0,Δz0,0) The position offset of the (0,0) th array element is shown, w represents the direction cosine of an included angle of the direction (theta, phi) of the far-field observation point relative to the coordinate axis of z, and w is cos theta;
(2b) obtaining an array antenna directional pattern function f according to the formula (2)a(theta, phi) actual position (x ') of array element'mn,y'mn,z'mn)＝(mdx+Δxmn,ndy+Δymn，Δzmn) The sensitivity matrix of the directional diagram function of the array antenna to the position error of the (m, n) th array element can be obtained;
Figure FDA0002722081620000031
Figure FDA0002722081620000032
Figure FDA0002722081620000033
Figure FDA0002722081620000034
wherein (x'mn,y'mn,z'mn) Indicating the actual position of the (m, n) -th array element in the presence of a position error,
Figure FDA0002722081620000035
a sensitivity matrix of an array antenna directional pattern function to an (m, n) th array element position error,
Figure FDA0002722081620000036
sensitivity matrixes of an array antenna directional diagram function to the (m, n) th array element in the x direction, the y direction and the z direction are respectively;
(2c) the rate of increase can be described by the inverse of the sensitivity, i.e.
Figure FDA0002722081620000037
In the formula (I), the compound is shown in the specification,
Figure FDA0002722081620000038
in order to increase the speed of the mounting accuracy of the array elements in the directions of the x and y coordinate axes,
Figure FDA0002722081620000039
α is a constant for controlling an increasing speed for increasing the flatness of the array element mounting in the z-coordinate axis direction.
3. The method for determining the position tolerance of the antenna element of the 6G communication based on the channel capacity sensitivity according to the claim 1, wherein the step (5) judges whether the number of error samples meeting the performance requirement is just less than 95% of the total number of samples.
4. The method for determining the position tolerance of the antenna element of the 6G communication based on the channel capacity sensitivity according to the claim 1, wherein the step (7) is carried out as follows:
array element position tolerance sigma at output for channel capacityx C,σy C,σz CAnd sensitivity matrix
Figure FDA00027220816200000310
The corresponding calculation formula in the process of (2) is as follows:
Figure FDA0002722081620000041
Figure FDA0002722081620000042
Figure FDA0002722081620000043
Figure FDA0002722081620000044
Figure FDA0002722081620000045
wherein C represents channel capacity, B represents channel operating bandwidth, λ is wavelength of antenna, α is constant for controlling increasing speed, d represents distance between transmitting and receiving antennas, and N is0Is the power spectral density, P, of additive white Gaussian noiseTRepresenting the transmission power of the transmitting antenna, FR(theta, phi) represents the normalized field strength directional pattern function of the receiving antenna, GRRepresenting the maximum radiation directional gain, F, of the receiving antennaT,BS(theta, phi) denotes the normalized field strength directional pattern function of the transmitting antenna at the base station end, GT,BSRepresents the maximum radiation direction gain, gamma, of the transmitting antenna at the base station endRRepresenting the receiver-side matching coefficient, gammaTRepresenting a transmitting end matching coefficient; cos (ξ) represents the polarization matching factor,
Figure FDA0002722081620000046
a sensitivity matrix (x ') representing the channel capacity versus the position error of the (m, n) th array element'mn,y'mn,z'mn) Indicating the actual position of the array element, fa(theta, phi) represents the array antenna pattern function,
Figure FDA0002722081620000047
respectively representing the sensitivity matrixes of the channel capacity to the position errors of the (m, n) th array elements in the x direction, the y direction and the z direction.
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