CN108900258B - Method for analyzing influence of vibration on wireless signal propagation - Google Patents

Method for analyzing influence of vibration on wireless signal propagation Download PDF

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CN108900258B
CN108900258B CN201810152449.8A CN201810152449A CN108900258B CN 108900258 B CN108900258 B CN 108900258B CN 201810152449 A CN201810152449 A CN 201810152449A CN 108900258 B CN108900258 B CN 108900258B
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vibration
multipath
distribution
amplitude
pitch angle
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CN108900258A (en
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周峰
牟丹
韩明超
孙国良
汲书强
陈晓贝
张颖艳
周开波
孟艾立
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China Academy of Information and Communications Technology CAICT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B15/00—Suppression or limitation of noise or interference
    • H04B15/02—Reducing interference from electric apparatus by means located at or near the interfering apparatus
    • H04B15/04—Reducing interference from electric apparatus by means located at or near the interfering apparatus the interference being caused by substantially sinusoidal oscillations, e.g. in a receiver or in a tape-recorder
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/707—Spread spectrum techniques using direct sequence modulation
    • H04B1/7097—Interference-related aspects
    • H04B1/711—Interference-related aspects the interference being multi-path interference

Abstract

The invention relates to a method for analyzing the influence of vibration on wireless signal propagation, which utilizes a multi-mirror image analysis method to set a transmitting and receiving deviceThe antennas form a system with a transmitting and receiving frequency off c The wave length of the electric wave is lambda, multipath is generated by reflection, the physical mechanism of the reflection is induced current, the induced current is used as a secondary source to excite an electromagnetic field generated, namely, a reflected wave according to the boundary condition of the electromagnetic wave on the surface of a conductor, and for the secondary source causing the multipath, each multipath corresponds to a mirror image emission source, and the horizontal angle power and the pitch angle power between the body of the transmitting antenna and a mirror image are analyzed; determining a time domain expression function of wireless signal transmission fading along with mechanical vibration, and further determining fading margin W L (dB) and maximum allowable amplitude peak-to-peak value of mechanical vibration of systemr dmax. The method can more reasonably and accurately predict the change of the transmission loss of the wireless communication signal, and has important roles in the analysis, design, planning and optimization of a wireless communication system.

Description

Method for analyzing influence of vibration on wireless signal propagation
Technical Field
The invention belongs to the field of radio signal transmission, and particularly relates to a method for analyzing influence of vibration on radio signal propagation.
Background
The vibration is ubiquitous in daily environment, the vibration caused by natural phenomena such as wind, rain, waves and the like, and the vibration caused by human factors such as vehicles, machines, sound waves and the like, in the reliability analysis of wireless communication, the vibration can cause the vibration of the transmitting and receiving antenna, and further cause the relative displacement of the antenna and the installation position, and the displacement can affect the multipath phase of the wireless signal propagation, which in turn leads to fluctuations in the transmission loss of signals, especially in wireless systems with shorter wavelengths, such as the fifth generation mobile communication systems using millimeter waves, which are more sensitive to vibration shifts, and, in particular, when the antenna is installed in an environment with vibration caused by natural phenomena such as mechanical vibration, vehicle vibration, wind, rain, waves and the like, the conventional wave propagation analysis method does not consider the variation of the reception intensity with the vibration caused by the vibration, which is incomplete.
Disclosure of Invention
In order to solve the problems, the invention provides a method which is simple and reduces the influence of the analysis vibration on the wireless signal propagation caused by the fluctuation of the transmission loss of the signal due to the vibration.
The technical scheme of the invention is as follows: a method of analyzing the effects of vibration on the propagation of a wireless signal, the method;
a system is formed by the transmitting and receiving antennas, and the transmitting and receiving frequency of the system is fcThe wave length is lambda, and multipath is generated by reflection, and the physical mechanism of reflection is induced current, and according to the boundary condition of the electromagnetic wave on the surface of a conductor, the electromagnetic field generated by the induced current as a 'secondary source' excitation is the reflected wave. For the 'secondary source' causing the multipath, the invention provides a multi-mirror image analysis method, each multipath is considered to correspond to a mirror image emission source, and a 'transmitting antenna mirror image 0' can be considered to correspond to a transmitting antenna body, as shown in fig. 1.
Under the condition of line of sight (LoS), a proper spherical coordinate system is established by taking the receiving antenna as an origin, and the X axis of an equivalent rectangular coordinate system can be taken by taking the main radial direction of the LoS as the origin. Assuming that the body and mirror of the transmitting antenna are in the horizontal angular interval
Figure GDA0001806993600000021
Inner uniform distribution, and the horizontal angle power distribution spectrum of each multipath satisfies the distribution function
Figure GDA0001806993600000022
Typically, a gaussian distribution can be taken, i.e., formula (1):
Figure GDA0001806993600000023
setting the body and mirror image of transmitting antenna in pitch angle interval [ -k ]θσθ,kθσθ]Inner uniform distribution, the pitch angle power distribution spectrum distribution of each multipath can be expressed as a function fθ[P(θ)]More typically, laplace distributions P (θ) to La (μ) are obtainedθ,σθ) I.e. satisfying formula (2):
Figure GDA0001806993600000024
to facilitate the calculation can be
Figure GDA0001806993600000028
And muθAre all 0. Generating two sets of NpathAre respectively arranged at
Figure GDA0001806993600000025
And [ -k ]θσθ,kθσθ]Random number sequence with uniformly distributed intervals to set multi-path horizontal angle and pitch angle, then supposing that the angle coordinate corresponding to a certain multi-path is
Figure GDA0001806993600000026
Then based on
Figure GDA0001806993600000027
And fθ[P(θ)]The normalized calculation reference value is the received power under the condition that the antenna gain and the transmitted power are normalized, and a transmission model can be selected according to specific conditions. Typically, the transmit-receive distance d may be used0Received power PW obtained by calculation of upper free space model0As shown in formula (3).
PW0[dB]＝-{32.45+20lgfc[GHz]+20lgd0[m]} (3)，
Assume the initial phase Ph0 of a certain multipathiSatisfying random distribution in (0,2 pi) interval, receiving normalized relative power as the product of corresponding horizontal angle normalized relative power ratio and pitch angle normalized relative power ratio, squaring the product to obtain the normalized amplitude coefficient M of the multipathiThen the distance of the equivalent mirror source of the multipath is calculated using equation (4):
Figure GDA0001806993600000031
the spherical coordinates of the equivalent mirror source of the multipath are
Figure GDA0001806993600000032
Then its corresponding rectangular coordinates are:
Figure GDA0001806993600000033
the acceleration function of the vibration of the transmitting antenna body is analyzed, and from the measurement result of the mass in the early period, the response acceleration of the antenna is the main frequency f under the excitation of wind loadvIn some cases, there may be second harmonics. The acceleration in the direction of X, Y, Z can be expressed as:
Figure GDA0001806993600000034
in the formula: t is time, ax1Is the amplitude of the fundamental wave of vibration in the X direction, ax2Is the amplitude of the second harmonic of the vibration in the X direction, px1Is the amplitude of the fundamental wave of vibration in the X direction, px2Is the initial phase of the second harmonic of the vibration in the X direction. a isy1Is the amplitude of the fundamental wave of vibration in the Y direction, ay2Is the amplitude of the second harmonic of the vibration in the Y direction, py1Is the amplitude of the fundamental wave of vibration in the Y direction, py2Is the initial phase of the second harmonic of the vibration in the Y direction. a isz1Is the amplitude of the fundamental wave of vibration in the Z direction, az2Is the amplitude of the second harmonic of the vibration in the Z direction, pz1Is in the Z directionThe amplitude of the fundamental wave of the vibration,
pz2is the initial phase of the second harmonic of vibration in the Z direction;
since the initial velocity and displacement are both 0, the displacement amount is calculated by integration:
Figure GDA0001806993600000041
due to the effect of the mirror reflection, the displacement of the ith mirror of the transmitting antenna can be expressed as:
Figure GDA0001806993600000042
in the formula: sxi，Syi，SziAre all { -1,1} binary random sequences,
Sxi，Syi，Sziare { -1,1} binary random sequences, and the physical mechanism of the random sequences is considered as follows: the equivalent reflecting surfaces are horizontal, flat and vertical, and the number of the reflecting surfaces is an odd number or an even number, which is random. Considering only the influence of vibration and not the change of other factors of propagation environment, Sx is used in simulationi，Syi，SziAfter random generation, it will not change with time. For the ith multipath component, the vibration generates micro displacement, so the influence on the alignment angle and amplitude of the transmitting and receiving antenna can be ignored, and the key is to influence the signal phase. The amount of variation in the propagation distance due to vibration is:
the phase of the ith multipath varies with time due to vibration △ di(t) is:
Figure GDA0001806993600000044
wherein λ is the wavelength of the radio wave, Ph0iInitial phase of multipath, △ di(t)Variation in propagation distance due to vibration;
the normalized received vector magnitude M at the receiving end after multipath superpositionr(t) is:
Figure GDA0001806993600000051
if a direct path exists, to ensure that the term i ═ 0 participates in the summation, the change in transmission loss with time can be calculated by the following equation:
Loss(t)[dB]＝-{PW0[dB]+20lg|Mr(t)|} (12)
loss (T) is a periodic function whose period is the period T of the vibrationv＝1/fv. The displacement range of the mechanical vibration is denoted as rdThe wavelength of the wireless signal is denoted as λ, WIDTHloss(dB) represents loss (t) [ dB ]]I.e. the maximum minus the minimum within a period, STDloss(dB) represents loss (t) [ dB ]]Standard deviation of the sequence over one period. WIDTH due to the randomness of multipath itselfloss(dB) and STDloss(dB) also presents randomness, but the median of multiple repeated simulation meets a certain statistical rule.
Is provided with (a)x-base,ay-base,az-base) Is the basic form of acceleration, determined by equation (6), with acceleration set according to equation (13), where kaIs the coefficient of the change in amplitude of the signal,
repeating for multiple times (such as N) under the condition that the power angular domain distribution parameters of the multipath are the samecaseSub) simulation, WIDTHloss(dB) and STDlossThe median of (dB) exhibits a relatively stable state, denoted as WIDTHloss-M(dB) and STDloss-M(dB), and the simulation result is fitted, which shows WIDTHloss-M(dB) and STDloss-M(dB) and r in the corresponding vibration regimedλ is related and can be expressed as:
Figure GDA0001806993600000061
Figure GDA0001806993600000062
the result of arctan operation in equations (14) and (15) is expressed in radians, and W is represented under different multipath angular distribution conditionsmax、kw、SmaxAnd kSThe parameters have different values, and the typical values are as follows: coefficient of distribution width W max30, distribution width of displacement coefficient k W2, coefficient of standard deviation SmaxDisplacement coefficient k of standard deviation 6S＝3。
It is obvious that the vibration causes spatial modulation of electromagnetic waves, i.e. fluctuation of the reception intensity of radio signals, which means that: the electromagnetic wave transceiving system needs to prepare a certain fading margin to avoid the adverse effect. Assume that it is desired that the fading margin to be prepared due to vibration is WL(dB), the maximum system amplitude peak-to-peak value (i.e., displacement range) rdmaxSatisfies the following conditions:
Figure GDA0001806993600000064
the invention has the beneficial effects that: by adopting the technical scheme, the method can more reasonably and accurately predict the change of the transmission loss of the wireless communication signal under the condition of physical vibration, and has important roles in analysis, design, planning and optimization of a wireless communication system. Particularly in the analysis and design of millimeter wave wireless communication systems, wireless vehicle networking communication systems and Internet of things/industrial Internet wireless communication systems in mechanical vibration environments.
Drawings
FIG. 1 is a diagram of a plurality of mirror sources corresponding to multipath.
FIG. 2 is a schematic diagram of a fading time domain curve caused by antenna vibration at a transceiving distance of 15m in an embodiment of 30 GHz.
FIG. 3 is a plot of simulated discrete points and median statistics for calculation example two.
FIG. 4 is a plot of simulated discrete points and median statistics values for calculation example two.
FIG. 5 is a plot of simulated discrete points and median statistics for calculation example three.
FIG. 6 is a plot of simulated discrete points and median statistics for calculation example four.
FIG. 7 is a graph of the median statistic curve of the fourth calculation example and the fitted curves of equations (14) and (15).
Detailed Description
The technical solution of the present invention is further described with reference to the following specific embodiments.
Referring to fig. 1-7, a method for analyzing the effect of vibration on wireless signal propagation according to the present invention is disclosed, wherein the method 1. a method for analyzing the effect of vibration on wireless signal propagation is characterized in that the method uses a multi-mirror analysis method, and the transmitting and receiving antennas form a system, and the transmitting and receiving frequency of the system is fcThe wave length of the electric wave is lambda, multipath is generated by reflection, the physical mechanism of the reflection is induced current, the induced current is used as a secondary source to excite an electromagnetic field generated, namely, a reflected wave according to the boundary condition of the electromagnetic wave on the surface of a conductor, and for the secondary source causing the multipath, each multipath corresponds to a mirror image emission source, and the horizontal angle power and the pitch angle power between the body of the transmitting antenna and a mirror image are analyzed; finally determining a fading margin WL(dB) and system amplitude peak-to-peak value rdmax。
The method comprises the following specific steps: firstly, establishing a proper spherical coordinate system by taking a receiving antenna as an origin, taking the receiving antenna as the origin, and taking the LoS major diameter direction as the X axis of an equivalent rectangular coordinate system, if the body and the mirror image of the transmitting antenna are in a horizontal angle intervalInner uniform distribution, and the horizontal angle power distribution spectrum of each multipath satisfies the distribution function
Figure GDA0001806993600000072
If the body and mirror of the transmitting antenna are in the pitch angle range [ -k ]θσθ,kθσθ]Inner uniform distribution, and the power distribution spectrum distribution of pitch angle of each multipath is expressed as a function fθ[P(θ)]，
Make mu for easy calculationφAnd muθAre all 0, produce two sets of NpathAre respectively arranged at
Figure GDA0001806993600000083
And [ -k ]θσθ,kθσθ]Random number sequence with uniformly distributed intervals to set multi-path horizontal angle and pitch angle, then supposing that the angle coordinate corresponding to a certain multi-path is
Figure GDA0001806993600000084
Then based on
Figure GDA0001806993600000085
And fθ[P(θ)]The normalized calculation reference value is the receiving power under the condition that the antenna gain and the transmitting power are normalized;
assume the initial phase Ph0 of a certain multipathiSatisfying random distribution in (0,2 pi) interval, receiving normalized relative power as the product of corresponding horizontal angle normalized relative power ratio and pitch angle normalized relative power ratio, squaring the product to obtain the normalized amplitude coefficient M of the multipathiThen, the distance d of the equivalent mirror source of the multipath is calculated using equation (4)i：
Figure GDA0001806993600000086
In the formula: miNormalized amplitude coefficient for multipath, d0The distance of a direct path between the transmitting and receiving antennas;
based on the obtained spherical coordinates of the multipath equivalent mirror image source is
Figure GDA0001806993600000087
Determination of the coordinates x of the body of the transmitting antennai、yi、zi：
Figure GDA0001806993600000091
Secondly, the acceleration is the main frequency f according to the response of the antennavThen the acceleration in the direction of X, Y, Z can be expressed as:
Figure GDA0001806993600000092
in the formula: t is time, ax1Is the amplitude of the fundamental wave of vibration in the X direction, ax2Is the amplitude of the second harmonic of the vibration in the X direction, px1Is the amplitude of the fundamental wave of vibration in the X direction, px2Is the initial phase of the second harmonic of the vibration in the X direction. a isy1Is the amplitude of the fundamental wave of vibration in the Y direction, ay2Is the amplitude of the second harmonic of the vibration in the Y direction, py1Is the amplitude of the fundamental wave of vibration in the Y direction, py2Is the initial phase of the second harmonic of the vibration in the Y direction. a isz1Is the amplitude of the fundamental wave of vibration in the Z direction, az2Is the amplitude of the second harmonic of the vibration in the Z direction, pz1Is the amplitude of the fundamental wave of vibration in the Z direction, pz2Is the initial phase of the second harmonic of vibration in the Z direction;
since the initial velocity and displacement are both 0, the displacement amount is calculated by integration:
Figure GDA0001806993600000093
due to the effect of mirror reflection, the displacement of the ith mirror of the transmitting antenna is expressed as:
Figure GDA0001806993600000094
in the formula: sxi，Syi，SziAre all { -1,1} binary random sequences,
the amount of variation in the propagation distance due to vibration is:
Figure GDA0001806993600000101
the phase of the ith multipath as a function of time due to vibration is then:
Figure GDA0001806993600000102
then after multipath superposition, the normalized received vector magnitude at the receiving end is:
Figure GDA0001806993600000103
in the formula: n is a radical ofpathIs the number of random numbers in the sequence,
if a direct path exists, to ensure that the term i ═ 0 participates in the summation, the change in transmission loss with time can be calculated by the following equation:
Loss(t)[dB]＝-{PW0[dB]+20lg|Mr(t)|} (12)
is provided with (a)x-base,ay-base,az-base) Is the basic form of acceleration, determined by equation (6), the acceleration being set according to equation (13),
Figure GDA0001806993600000104
wherein k isaIs amplitudeCoefficient of variation
Repeating N under the condition that the power angular domain distribution parameters of the multipath are the samecaseSub-simulation, WIDTHloss(dB) and STDlossThe median of (dB) exhibits a relatively stable state, denoted as WIDTHloss-M(dB) and STDloss-M(dB), and the simulation result is fitted, which shows WIDTHloss-M(dB) and STDloss-M(dB) and r in the corresponding vibration regimedλ is related, then expressed as:
Figure GDA0001806993600000111
Figure GDA0001806993600000112
the result of arctan operation in equations (14) and (15) is expressed in radians, and the distribution width coefficient W is given under different multipath angular distribution conditionsmaxDistribution width displacement coefficient kwCoefficient of standard deviation Smax；
Assume that it is desired that the fading margin to be prepared due to vibration is WL(dB), the maximum system amplitude peak-to-peak value (i.e., displacement range) rdmaxSatisfies the following conditions:
Figure GDA0001806993600000113
Figure GDA0001806993600000114
example 1:
TABLE 1 example Condition parameters
Figure GDA0001806993600000115
Figure GDA0001806993600000121
Table 2 example a simulation result
Figure GDA0001806993600000122
Figure GDA0001806993600000141
Example 2:
table 3 example two Condition parameters
Figure GDA0001806993600000151
Table 4 example two simulation results
Figure GDA0001806993600000152
Figure GDA0001806993600000171
Figure GDA0001806993600000181
Example 3:
table 5 examples three condition parameters
Figure GDA0001806993600000182
Table 6 example three simulation results
Figure GDA0001806993600000211
Example 4:
table 7 examples four condition parameters
Figure GDA0001806993600000221
Table 8 example three simulation results
Figure GDA0001806993600000222
Figure GDA0001806993600000231
Figure GDA0001806993600000241
Figure GDA0001806993600000251

Claims (3)

1. A method for analyzing the influence of vibration on radio signal transmission features that a multi-mirror image analysis method is used, and the transmitting-receiving antennas are arranged to form a system with the frequency fcThe wave wavelength is lambda, the reflection generates multiple paths, and the physical mechanism of the reflection is induced current according to the boundary condition of the electromagnetic wave on the surface of the conductorThe current is used as a secondary source to excite an electromagnetic field generated, namely a reflected wave, for the secondary source causing multipath, each multipath corresponds to a mirror image emission source, and the horizontal angle power and the pitch angle power between the body of the transmitting antenna and a mirror image are analyzed; determining a time domain expression function of wireless signal transmission fading along with mechanical vibration, and further determining fading margin WL(dB) and maximum allowable amplitude peak-to-peak value r of mechanical vibration of systemdmax。
2. The method according to claim 1, characterized by the specific steps of: firstly, establishing a proper spherical coordinate system by taking a receiving antenna as an origin, taking the receiving antenna as the origin, and taking the LoS major diameter direction as the X axis of an equivalent rectangular coordinate system, if the body and the mirror image of the transmitting antenna are in a horizontal angle interval
Figure FDA0002181461540000011
Inner uniform distribution, and the horizontal angle power distribution spectrum of each multipath satisfies the distribution function
Figure FDA0002181461540000012
Figure FDA0002181461540000013
In the formula (I), the compound is shown in the specification,is the pitch angle distribution of the multi-path,
Figure FDA0002181461540000015
is the standard deviation of the multi-path pitch angle distribution,
Figure FDA0002181461540000016
is a mathematical expectation of the pitch angle distribution of the multipath,
Figure FDA0002181461540000017
is a multi-path pitch angle power distributionA spectral function;
if the body and mirror image of the transmitting antenna are in the pitch angle interval
Figure FDA0002181461540000018
Inner uniform distribution, kφAnd kθSpreading factors of horizontal angle and pitch angle distribution respectively, and the power distribution spectrum distribution of pitch angle of each multipath is expressed as a function fθ[P(θ)]，
Figure FDA0002181461540000019
Figure FDA00021814615400000110
Where θ is the pitch angle distribution of the multipath, σθIs the standard deviation, mu, of the multi-path pitch angle distributionθIs the mathematical expectation of the multipath pitch angle distribution, fθ[P(θ)]Is a multipath pitch angle power distribution spectrum function;
make mu for easy calculationφAnd muθAre all 0, produce two sets of NpathAre respectively arranged at
Figure FDA0002181461540000021
And [ -k ]θσθ,kθσθ]Random number sequence with uniformly distributed intervals to set multi-path horizontal angle and pitch angle, then supposing that the angle coordinate corresponding to a certain multi-path is
Figure FDA0002181461540000022
Then based on
Figure FDA0002181461540000023
And fθ[P(θ)]The normalized calculation reference value is the receiving power under the condition that the antenna gain and the transmitting power are normalized;
assume the initial phase Ph0 of a certain multipathiWithin the range of (0,2 pi)Receiving the normalized relative power which is the product of the corresponding horizontal angle normalized relative power ratio and the pitch angle normalized relative power ratio, squaring the product to obtain the normalized amplitude coefficient M of the multipathiThen, the distance d of the equivalent mirror source of the multipath is calculated using equation (4)i：
Figure FDA0002181461540000024
In the formula: miNormalized amplitude coefficient for multipath, d0The distance of a direct path between the transmitting and receiving antennas;
based on the obtained spherical coordinates of the multipath equivalent mirror image source is
Figure FDA0002181461540000025
Determination of the coordinates x of the body of the transmitting antennai、yi、zi：
Figure FDA0002181461540000026
Secondly, the acceleration is the main frequency f according to the response of the antennavThen the acceleration in the direction of X, Y, Z can be expressed as:
Figure FDA0002181461540000031
in the formula: t is time, ax1Is the amplitude of the fundamental wave of vibration in the X direction, ax2Is the amplitude of the second harmonic of the vibration in the X direction, px1Is the amplitude of the fundamental wave of vibration in the X direction, px2Is the initial phase of the second harmonic of the vibration in the X direction; a isy1Is the amplitude of the fundamental wave of vibration in the Y direction, ay2Is the amplitude of the second harmonic of the vibration in the Y direction, py1Is the amplitude of the fundamental wave of vibration in the Y direction, py2Is the initial phase of the second harmonic of the vibration in the Y direction; a isz1Is the amplitude of the fundamental wave of vibration in the Z direction, az2Is a Z squareAmplitude of the second harmonic of upward vibration, pz1Is the amplitude of the fundamental wave of vibration in the Z direction, pz2Is the initial phase of the second harmonic of vibration in the Z direction;
since the initial velocity and displacement are both 0, the displacement amount is calculated by integration:
Figure FDA0002181461540000032
due to the effect of mirror reflection, the displacement of the ith mirror of the transmitting antenna is expressed as:
Figure FDA0002181461540000033
in the formula: sxi，Syi，SziAre all { -1,1} binary random sequences,
the amount of variation in the propagation distance due to vibration is:
Figure FDA0002181461540000034
the phase of the ith multipath as a function of time due to vibration is then:
Figure FDA0002181461540000035
then after multipath superposition, the normalized received vector magnitude at the receiving end is:
in the formula: n is a radical ofpathIs the number of multipath, j is the unit of imaginary number,
if a direct path exists, to ensure that the term i ═ 0 participates in the summation, the change in transmission loss with time can be calculated by the following equation:
Loss(t)[dB]＝-{PW0[dB]+20lg|Mr(t)|} (12)。
3. the method of claim 2, further comprising the steps of: is provided with (a)x-base,ay-base,az-base) Is the basic form of acceleration, the expression of acceleration at X, Y, Z has the expression of fundamental wave plus second harmonic, the acceleration is set according to the expression (13),
Figure FDA0002181461540000042
in the formula (I), the compound is shown in the specification,
Figure FDA0002181461540000043
in the form of a three-dimensional vector of acceleration, kaIs the coefficient of amplitude variation;
repeating N under the condition that the power angular domain distribution parameters of the multipath are the samecaseSub-simulation, WIDTHloss(dB) and STDlossThe median of (dB) exhibits a relatively stable state, denoted as WIDTHloss-M(dB) and STDloss-M(dB), and the simulation result is fitted, which shows WIDTHloss-M(dB) and STDloss-M(dB) and r in the corresponding vibration regimedλ is related, then expressed as:
Figure FDA0002181461540000044
the result of arctan operation in equations (14) and (15) is expressed in radians, and the distribution width coefficient W is given under different multipath angular distribution conditionsmaxDistribution width displacement coefficient kwCoefficient of standard deviation Smax, loss of(ii) a Standard deviation displacement coefficient ks,WIDTHloss(dB) represents the distribution interval width of the transmission loss time-varying sequence, namely the maximum value and the minimum value in one period, and represents that the transmission loss time-varying sequence is in oneStandard deviation in cycles, rdRefers to the amplitude of the mechanical vibration of the transmitting and receiving antenna;
assume that the fading margin to be prepared due to vibration is WL(dB), the maximum system amplitude peak-to-peak value, i.e., the displacement range rdmaxSatisfies the following conditions:
Figure FDA0002181461540000051
Figure FDA0002181461540000052
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