CN109639378B - Rectangular tunnel wireless propagation channel modeling method - Google Patents

Rectangular tunnel wireless propagation channel modeling method Download PDF

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CN109639378B
CN109639378B CN201910088590.0A CN201910088590A CN109639378B CN 109639378 B CN109639378 B CN 109639378B CN 201910088590 A CN201910088590 A CN 201910088590A CN 109639378 B CN109639378 B CN 109639378B
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周杰
陈珍
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Nanjing University of Information Science and Technology
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Abstract

The invention provides a modeling method of a rectangular tunnel wireless propagation channel, which is a statistical channel model for a tunnel V2V scattering environment, wherein a mobile transmitter and a receiver are both provided with uniform linear antenna arrays. It is assumed that the scatterers are freely distributed on the tunnel wall and that both the transmitter and the receiver are in motion. LOS and NLOS scattering conditions are considered in a rectangular tunnel scattering area. And analyzing the 3D tunnel geometric model to obtain a space-time-frequency cross-correlation function, a time self-correlation function and a frequency correlation function. In order to prove the reasonability and the feasibility of the model, the theoretical parameters of the invention are compared with the reference model, and the result shows that the time autocorrelation function and the frequency correlation function of the model are consistent with the reference channel model. Meanwhile, the influence of the model parameters on the Doppler power spectral density and the MIMO channel capacity is researched. The invention improves the performance of the tunnel V2V communication system by calculating the statistical characteristic parameters of the rectangular tunnel.

Description

Rectangular tunnel wireless propagation channel modeling method
Technical Field
The invention belongs to the field of statistical characteristic analysis of tunnels, and particularly relates to a rectangular tunnel wireless propagation channel modeling method.
Background
In recent years, the demand of vehicle-to-vehicle (V2V) communication systems in vehicle ad hoc networks (VANET) and Intelligent Transportation Systems (ITS) has been increasing, and thus has attracted extensive attention. In order to develop a more stable and efficient V2V communication system, the propagation channel needs to be accurately described. The antenna height of the communication node in the V2V link is typically lower than surrounding building and tree scatterers compared to conventional cellular systems. Due to this difference in propagation environments, extensive research into 2D and 3D models of the V2V communication channel is required. In the above model 2D V2V,
Figure BDA0001961234870000011
and Hogstad et al, assuming isotropic and non-isotropic scattering conditions, a geometric ellipse model consisting of several ellipses was introduced. Avazov and
Figure BDA0001961234870000012
etc. present street models under line-of-sight and non-line-of-sight propagation conditions. He and cheli et al propose a non-stationary T-junction model. Although 2D models are suitable for simulating certain environments, the V2V communication channel needs to be accurately described by elevation plane since scatterers higher than the antennas of V2V communication are subject to signal reflections from nearby buildings and other scatterers. Therefore, the 3D channel model is more accurate than the 2D channel model described above. Mohammed proposed a three-dimensional elliptical geometric scattering model for microcells. Nawaz and Qureshi et al propose to have at BSA three-dimensional model of a macrocell for a directional antenna. Yuan et al propose a novel three-dimensional double spherical geometric scattering model. Channel modeling of tunnel environments is equally important for many mountain cities where roads cross tunnels, and researchers have therefore extensively studied the characteristics of their mobile radio channels. By definition, the geometric channel model models the wireless propagation channel primarily by establishing probabilistic spatial relationships between the locations of the transmitter, receiver, and scatterers. The distribution of scatterers is an important aspect that affects the emission and arrival angles, and thus the above documents have made much research on the emission and arrival angles. In the three-dimensional scattering model, elevation and azimuth are also important, but are also easily ignored. When a real vehicle-mounted communication system is simulated, firstly statistical spatial channel parameters conforming to the actual wireless environment must be obtained, then a physical parameter statistical channel model is established according to the parameters, and the influence of the position of a vehicle, the size of a tunnel and the like on the channel is found.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a rectangular tunnel wireless propagation channel modeling method.
In order to achieve the purpose, the invention adopts the following technical scheme:
the rectangular tunnel wireless propagation channel modeling method is characterized by comprising the following steps:
step one, establishing a geometric model of a tunnel system according to the actual size of a rectangular tunnel, dividing the geometric model into a plurality of scatterers, wherein the scatterers are freely distributed, acquiring a propagation route by utilizing the positions of a transmitter, a receiver and the scatterers, configuring uniform linear antenna arrays on the transmitter and the receiver, acquiring a diffuse reflection component and a sight distance component of the tunnel model by utilizing the geometric relationship among the transmitter, the receiver and the scatterers in the rectangular tunnel, and adding the two components to obtain a time-varying transfer function of the model;
expressing the elevation angle and the azimuth angle of the antenna by using the position of the scatterer through a geometric relation and a trigonometric identity in a tunnel scattering scene;
step three, calculating the statistical characteristics of the tunnel model by combining the time-varying transfer function, the elevation angle and the azimuth angle;
and step four, obtaining the channel capacity of the tunnel model based on the transmission matrix of the diffuse reflection component and the line-of-sight component.
In order to optimize the technical scheme, the specific measures adopted further comprise:
in the first step, a transfer function H is obtained by using the transmission routes of any two antennas of the transmitting end and the receiving endkl(f', t), expressed as:
Figure BDA0001961234870000021
wherein
Figure BDA0001961234870000022
And
Figure BDA0001961234870000023
diffuse reflection component and line-of-sight component of the time-varying transfer function, respectively;
transmitting antenna element from the first uniform plane wave
Figure BDA0001961234870000024
Emitting a beam through the diffuser S(mno)To the k-th receiving antenna
Figure BDA0001961234870000025
Time-varying transfer function HklDiffuse reflection component in (f', t)
Figure BDA0001961234870000026
Expressed as:
Figure BDA0001961234870000027
wherein
Figure BDA0001961234870000028
Figure BDA0001961234870000029
Figure BDA00019612348700000210
Figure BDA00019612348700000211
Figure BDA00019612348700000212
Wherein M represents the total number of scatterers on the x-axis side, N represents the total number of scatterers on the y-axis side, O represents the total number of scatterers on the z-axis side, and cRDenotes a rice distribution factor, m denotes an m-th scatterer on the x-axis side, n denotes an n-th scatterer on the y-axis side, o denotes an o-th scatterer on the z-axis side, λ denotes a wavelength,
Figure BDA00019612348700000213
indicating that the first antenna of the transmitting end passes through the scatterer S(mno)The total distance to the kth antenna at the receiving end,
Figure BDA0001961234870000031
representing the transmitting end scatterer S(mno)The influence on the resulting doppler frequency is such that,
Figure BDA0001961234870000032
representing the receiver-side scatterer S(mno)Influence induced Doppler frequency, t represents time, θ(mno)Indicating the phase of the electromagnetic wave at a particular instant,
Figure BDA0001961234870000033
which is indicative of the propagation delay of the signal,
Figure BDA0001961234870000034
c0representing the speed of light, f' representing the frequency;
Figure BDA0001961234870000035
represents the arrival of the first antenna at the transmitting end at the scatterer S(mn0)The distance of (a) to (b),
Figure BDA0001961234870000036
represents a scatterer S(mno)The distance from the antenna to the kth antenna of the receiving end;
xmdenotes the abscissa, x, of the scattererTDenotes the abscissa, y, of the transmitter antenna arraynDenotes the ordinate, y, of the scattering bodyTRepresenting the ordinate, z, of the transmitter antenna arrayoRepresenting the vertical axis coordinate of the scatterer, zTRepresenting the vertical axis coordinate, M, of the transmitter antenna arrayTNumber of antennas, delta, representing the configuration of the transmitting endTIndicating the antenna element spacing, phi, at the transmitting endTRepresenting the elevation angle of the transmit side antenna array relative to the xy plane,
Figure BDA0001961234870000037
denotes the vertical emission angle EAOD, gamma of the emitting endTThe tilt angle of the transmitting-end antenna array is shown,
Figure BDA0001961234870000038
represents the horizontal emission angle AAOD of the transmitting end;
xRdenotes the abscissa, y, of the receiver antenna arrayRRepresenting the ordinate, z, of the receiver antenna arrayRRepresenting the vertical axis coordinate, M, of the receiver antenna arrayRIndicating the number of antennas, delta, allocated at the receiving endRIndicates the receiving end antenna unit spacing, phiRRepresenting the elevation angle of the receiving-end antenna array relative to the xy-plane,
Figure BDA0001961234870000039
indicating the vertical angle of arrival EAOA at the receiving end,γRthe tilt angle of the antenna array at the receiving end is shown,
Figure BDA00019612348700000310
representing the horizontal angle of arrival AAOA of the receiving end;
fTmaxrepresenting the maximum Doppler frequency, f, of the transmitting endTmax＝vT/λ，vTWhich is indicative of the speed at which the transmitter is traveling,
Figure BDA00019612348700000311
representing the included angle between the driving direction of the transmitter and the x axis;
fRmaxindicating the maximum Doppler frequency, f, of the receiving endRmax＝vR/λ，vRWhich is indicative of the speed at which the receiver is traveling,
Figure BDA00019612348700000312
representing the included angle between the driving direction of the receiver and the x axis;
time-varying transfer function HklLine-of-sight component in (f', t)
Figure BDA00019612348700000313
Expressed as:
Figure BDA00019612348700000314
wherein
Figure BDA0001961234870000041
Figure BDA0001961234870000042
Figure BDA0001961234870000043
In the formula (I), the compound is shown in the specification,
Figure BDA0001961234870000044
a rice distribution factor representing a line-of-sight component,
Figure BDA0001961234870000045
indicating the distance between the ith antenna at the transmitting end and the kth antenna at the receiving end,
Figure BDA0001961234870000046
representing the doppler frequency of the transmitting end in the line-of-sight path,
Figure BDA0001961234870000047
indicating the doppler frequency at the receiving end in the line-of-sight path,
Figure BDA0001961234870000048
representing propagation delay in a line-of-sight path;
Figure BDA0001961234870000049
the AAOD representing the line-of-sight component,
Figure BDA00019612348700000410
an EAOD representing a line-of-sight component,
Figure BDA00019612348700000411
the AAOA representing the line-of-sight component,
Figure BDA00019612348700000412
EAOA representing the line of sight component.
In the second step, the azimuth angle refers to a horizontal emission angle and a horizontal arrival angle, and the elevation angle refers to a vertical emission angle and a vertical arrival angle.
In the second step, the scattering body S is expressed by using Cartesian coordinates(mno)Wherein M is 1,2, …, M, N is 1,2, …, N, O is 1,2, …, O, (x) isT，yT，zT) And (x)R，yR，zR) Representing transmitter and receiver antenna arrays, respectivelyPosition, where 0. ltoreq. xT≤xR≤L，-W/2≤yR≤yTW/2 or less, L represents the length of the tunnel, W represents the width of the tunnel, scatterers S are used(mno)Position (x) ofm，yn，z0) Expressed as:
Figure BDA00019612348700000413
Figure BDA00019612348700000414
where T denotes a transmitter, R denotes a receiver, and α denotes a receiveri(xm，yn，z0) Representing AAOD of transmitter or AAOA, beta of receiveri(xm，yn，z0) EAOA, x representing EAOD of transmitter or EAOA, x of receiveriIndicating the abscissa, y, of the transmitter or receiveriIndicating the ordinate, z, of the transmitter or receiveriRepresenting the vertical axis coordinates of the transmitter or receiver.
In the third step, the statistical characteristics of the tunnel model include a space-time-frequency cross-correlation function, a space cross-correlation function, a time-frequency cross-correlation function, a time self-correlation function, a frequency correlation function and a doppler power spectral density.
In the third step, firstly, the property of uniform distribution of the free variables x and y is utilized to obtain probability density functions of x, y and z, and further obtain the joint probability density, and a space-time-frequency cross-correlation function, a time self-correlation function, a frequency correlation function and Doppler power spectral density between any two antennas are derived by combining a time-varying transfer function, an elevation angle and an azimuth angle as follows:
assuming that the number of scatterers tends to be infinite, a discrete random variable xm，ynAnd zoRepresented by the continuous variables x, y and z, respectively, x and y are uniformly distributed, and their probability density function is represented as:
Figure BDA0001961234870000051
Figure BDA0001961234870000052
wherein p isx(x) Probability density function, p, representing a continuous variable xy(y) a probability density function representing a continuous variable y;
the free variable z is represented as z ═ Wtan α/2, α is freely distributed in the interval [0, arctan (2H/W) ], H represents the tunnel height, and its probability density function is represented as:
Figure BDA0001961234870000053
wherein p isz(z) a probability density function representing a continuous variable z;
with the above probability density functions for the free variables x, y and z, the joint probability density function is expressed as:
Figure BDA0001961234870000054
wherein p isxyz(xyz) represents the joint probability density function of the continuous variables x, y, z; infinite energy and p of diffuse reflection component corresponding to differential equation dx, dy and dzxyz(x, y, z) dxdydz, and when M, N, O → ∞ 1/MNO ═ pxyz(x，y，z)dxdydz；
Time-varying transfer function Hkl(f', t) and Hk′l′The space-time-frequency cross-correlation function between (f', t) is:
Figure BDA0001961234870000061
wherein l 'represents the l' th antenna at the transmitting end, l '≠ l, k' represents the k 'th antenna at the receiving end, k'K, v' denotes frequency, τ denotes time, E {. cndot. } denotes the expectation operator, (. cndot.)*Which represents the complex conjugate of the light source,
Figure BDA0001961234870000062
a space-time-frequency cross-correlation function representing the diffuse reflection component,
Figure BDA0001961234870000063
a space-time-frequency cross-correlation function representing a line-of-sight component;
the space-time-frequency cross-correlation function of the diffuse reflection component is expressed as:
Figure BDA0001961234870000064
wherein
Figure BDA0001961234870000065
Figure BDA0001961234870000066
In the formula
Figure BDA0001961234870000067
And
Figure BDA0001961234870000068
representing intermediate variables taken for a simplified formula;
fT(x, y, z) denotes the transmit-side scatterer S(mno)Doppler frequency due to influence, influenced by the infinite scatterers, originally
Figure BDA0001961234870000069
Is converted into fT(x，y，z)；fR(x, y, z) denotes the transmit-side scatterer S(mno)Doppler frequency due to influence, influenced by the infinite scatterers, originally
Figure BDA00019612348700000610
Is converted into fR(X，y，z)；τ′kl(x, y, z) represents propagation delay, affected by the infinite scatterers, original
Figure BDA00019612348700000611
Is converted to τ'kl(x，y，z)；
Thus, the space-time-frequency cross-correlation function of the diffuse reflection component
Figure BDA00019612348700000612
Expressed as:
Figure BDA00019612348700000613
wherein
Figure BDA00019612348700000614
Figure BDA00019612348700000615
Figure BDA00019612348700000616
Figure BDA00019612348700000617
In the formula of alphaT(x, y, z) represents the AAOD of the transmitting end, affected by the infinite scatterer, the original
Figure BDA0001961234870000071
Conversion to alphaT(x，y，z)；βT(x, y, z) denotes EAOD at the emitting end, influenced by the infinite scatterer, originally
Figure BDA0001961234870000072
Conversion to betaT(x，y，z)；
αR(x, y, z) represents AAOA at the transmitting end, affected by the infinite scatterer, original
Figure BDA0001961234870000073
Conversion to alphaR(x，y，z)；βR(x, y, z) represents EAOA at the emitting end, affected by the infinite scatterer, original
Figure BDA0001961234870000074
Conversion to betaR(x，y，z)；
τ′klFor (x, y, z)
Figure BDA0001961234870000075
And
Figure BDA0001961234870000076
expressed as:
Figure BDA0001961234870000077
Figure BDA0001961234870000078
represents the arrival of the first antenna at the transmitting end at the scatterer S(mno)Is influenced by the infinite scattering body, originally
Figure BDA0001961234870000079
To be converted into
Figure BDA00019612348700000710
Figure BDA00019612348700000711
Represents a scatterer S(mno)The distance from the kth antenna to the receiving end is influenced by the infinite scatterer,originally
Figure BDA00019612348700000712
To be converted into
Figure BDA00019612348700000713
Then distance
Figure BDA00019612348700000714
And
Figure BDA00019612348700000715
expressed as:
Figure BDA00019612348700000716
Figure BDA00019612348700000717
similarly, the space-time-frequency cross-correlation function of the line-of-sight scattering component is:
Figure BDA00019612348700000718
wherein
Figure BDA00019612348700000719
Figure BDA00019612348700000720
The spatial cross-correlation function is defined as
Figure BDA00019612348700000721
I.e. equal to the space-time-frequency cross-correlation function pkl，k′l′(δT，δRV ', τ) is a value when v' is 0 and τ is 0, and thusThe spatial cross-correlation function is expressed as:
ρkl，k′l′(δT，δR)＝ρkl，k′l′(δT，δR，0，0)
the time-frequency cross-correlation function is defined as a time-varying transfer function of
Figure BDA0001961234870000081
And HklThe correlation of (f '+ v', t + τ) is expressed as
Figure BDA0001961234870000082
Spacing δ between antenna elementsTAnd deltaRWhen equal to 0, the time-frequency cross-correlation function is expressed as ρkl(v′，τ)＝ρkl，k′l′(0,0, v', τ), therefore, the time-frequency cross-correlation function is expressed as:
ρkl，k′l′(v′，τ)＝ρkl，k′l′(0，0，v′，τ)
link circuit
Figure BDA0001961234870000083
l＝1，2，...，MT，k＝1，2，...，MRThe time autocorrelation function of the time-varying transfer function is defined as
Figure BDA0001961234870000084
When the frequency variable v' is equal to 0, the time autocorrelation function is represented as rkl(τ)＝ρkl(0, τ), therefore, the expression thereof is obtained as:
rkl(τ)＝ρkl，k′l′(0，0，0，τ)
the frequency dependent function of the time-varying transfer function is defined as
Figure BDA0001961234870000085
When τ is 0, the time autocorrelation function is denoted as rkl(v′)＝ρkl(v',0), the frequency dependent function is expressed as:
rkl(v′)＝ρkl，k′l(0，0，v′，0)
the doppler power spectral density is a fourier transform of the temporal autocorrelation function with respect to τ, and is therefore expressed as:
Figure BDA0001961234870000086
wherein
Figure BDA0001961234870000087
Representing a fourier transform.
In the fourth step, for the compound with MTA transmitting antenna unit and MRIn a narrow-band MIMO system with multiple receiving antenna units, the maximum theoretical capacity with uniformly distributed transmit power and signal-to-noise ratio equal to SNR is expressed as:
Figure BDA0001961234870000088
where C represents the capacity of the channel and,
Figure BDA0001961234870000089
represents MR×MRDimension unit matrix, [. C]HIs a conjugate transpose of the matrix, H is the transmission matrix of the channel, and H ═ HDIF+HLOSIn which H isDIFAnd HLOSRespectively, the transmission matrices for the diffuse reflection and line-of-sight components.
The invention has the beneficial effects that: by calculating the statistical characteristic parameters of the rectangular tunnel, the performance of the tunnel V2V communication system is effectively improved.
Drawings
Fig. 1 is a transmission scenario of a rectangular tunnel.
Fig. 2 is a tunnel geometry scattering model.
Fig. 3 is the absolute value of the spatial cross-correlation function in the NLOS transmission scenario.
Fig. 4 is the absolute value of the spatial cross-correlation function in the LOS transmission scenario.
Fig. 5 is an absolute value of a time-frequency cross-correlation function in an NLOS transmission scenario.
Fig. 6 is an absolute value of a time-frequency cross-correlation function in an LOS transmission scenario.
Fig. 7a is a graph of the effect of the rice distribution factor on the time autocorrelation function (co-current driving).
Fig. 7b is a graph of the effect of the rice distribution factor on the time autocorrelation function (reverse run).
Fig. 8 is a graph of the effect of the leis distribution factor on the frequency dependent function.
Fig. 9 is a frequency dependent function for LOS and NLQS transmission scenarios.
Figure 10 is the doppler power spectral density.
Fig. 11 shows the channel capacity for different array element numbers and signal-to-noise ratios.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
The invention provides a modeling method of a rectangular tunnel wireless transmission channel, which is characterized in that a geometric model of the rectangular tunnel is constructed according to the size of the tunnel in reality, the geometric model is divided into a plurality of scatterers, the scatterers are freely distributed, and a transmission route is obtained by utilizing the positions of a transmitter, a receiver and the scatterers. The method comprises the steps of configuring uniform linear antenna arrays on a transmitter and a receiver, obtaining diffuse reflection and line-of-sight components of a tunnel model by utilizing the geometrical relation among the transmitter, the receiver and a scatterer in a rectangular tunnel, and adding the two components to obtain a time-varying transfer function of the model so as to research the time, space and frequency characteristics of a channel of the rectangular tunnel model. And obtaining an elevation angle and an azimuth angle by utilizing a geometric relation and a triangular identity in a tunnel scattering scene, further perfecting a time-varying transfer function of the model, and calculating a desired value of the transfer function of any two antenna propagation routes to obtain a space-time-frequency cross-correlation function of a line-of-sight and non-line-of-sight tunnel system.
The method comprises the following steps: establishing a geometric model of a tunnel system according to the actual size of a rectangular tunnel, as shown in fig. 1 and fig. 2, configuring uniform linear arrays for a transmitter and a receiver, and respectively obtaining time-varying transmission through the initial positions of a transmitting end and a receiving end and the geometric relation with a scattererThe diffuse reflection and the line-of-sight component of the function are added to obtain the first antenna of the transmitting end passing through the scatterer S(mno)Time-varying transfer function H to k antenna of transmitting terminalkl(f′，t)。
Obtaining a transfer function H by using the transmission routes of any two antennas of a transmitting end and a receiving endkl(f', t) can be expressed as:
Figure BDA0001961234870000101
wherein
Figure BDA0001961234870000102
And
Figure BDA0001961234870000103
respectively, the diffuse reflection and the line-of-sight components of the time-varying transfer function, wherein k represents the kth transmitting antenna of the transmitting end, l represents the lth transmitting antenna of the transmitting end, f' represents frequency, and t represents time.
Transmitting antenna element from the first uniform plane wave
Figure BDA0001961234870000104
Emitting a beam through the diffuser S(mno)To the k-th receiving antenna
Figure BDA0001961234870000105
Time-varying transfer function HklDiffuse reflection component in (f', t)
Figure BDA0001961234870000106
Can be expressed as:
Figure BDA0001961234870000107
wherein
Figure BDA0001961234870000108
Figure BDA0001961234870000109
Figure BDA00019612348700001010
Figure BDA00019612348700001011
Figure BDA00019612348700001012
In (3), the symbol cRRepresenting the Rice distribution factor, defined as the ratio of the average power of the line-of-sight component to the average power of the diffuse component, i.e. cR＝E{|HLOS(f′，t)|2}/E{|HDIF(f′，t)|2}. Phase theta(mno)Caused by the interaction of the emitted plane waves and the scatterers. Suppose phase θ(mno)Is independent and uniformly distributed random variable and follows uniform distribution in the interval [0, 2 pi ].
Figure BDA00019612348700001013
The propagation delay of the diffuse reflection component is represented by
Figure BDA00019612348700001014
Calculated as
Figure BDA00019612348700001015
Wherein c is0Is the speed of light. In (9) and (10), fTmaxAnd fRmaxRepresenting the maximum Doppler frequency associated with the transmitter and receiver, respectively, and defined as fTmax＝vTLambda and fRmax＝vRAnd/lambda, lambda is the wavelength.
Similarly, the time-varying transfer function Hkl(f', t) inComponent of apparent distance
Figure BDA00019612348700001016
Can be expressed as:
Figure BDA00019612348700001017
wherein
Figure BDA0001961234870000111
Figure BDA0001961234870000112
Figure BDA0001961234870000113
In the above-mentioned formula, the compound of formula,
Figure BDA0001961234870000114
and
Figure BDA0001961234870000115
aaod (eaod) and aaoa (eaod) representing the line of sight components, respectively.
Step two: the azimuth angle and the elevation angle can be expressed by the geometrical relation of the tunnel scattering scene and a trigonometric identity through the position of the scatterer.
Using cartesian coordinates (x, y, z) to represent the scatterer S(mno)(wherein M is 1,2, …, M, nn is 1,2, …, N, O is 1,2, …, O) and (x isT，yT，zT) And (x)R，yR，zR) (wherein 0. ltoreq. xT≤xRL is less than or equal to L and-W/2 is less than or equal to yR≤yT≦ W/2) indicates the position of the transmitter and receiver antenna arrays, respectively.
Figure BDA0001961234870000116
And
Figure BDA0001961234870000117
respectively, AAOD (MOA) and EAOD (EAOA). Using scatterers S(mno)Position (x) ofm，yn，z0) Expressed as:
Figure BDA0001961234870000118
Figure BDA0001961234870000119
where i ═ T (i ═ R) refers to the transmitter (receiver).
Step three: the method comprises the steps of firstly obtaining probability density functions of x, y and z by utilizing the property of uniform distribution of free variables x and y, further obtaining combined probability density, and deducing space-time-frequency cross-correlation functions, space cross-correlation functions, time-frequency cross-correlation functions, time self-correlation functions, frequency correlation functions and Doppler power spectral density between any two antennas by combining a time-varying transfer function, an elevation angle and an azimuth angle.
1. Space-time-frequency cross-correlation function
In the above model, the discrete random variable x is assumed to be infinite in the number of scatterersm，ynAnd zoCan be respectively expressed by continuous variables x, y and z, and when x expresses that the scatterer tends to be infinite, the abscissa of the scatterer is expressed by a discrete free variable xmConverting into a continuous variable x; y denotes that when the scatterer tends to infinity, the abscissa of the scatterer is represented by a discrete free variable ynConverting into a continuous variable y; z represents the abscissa of the scatterer as the scatterer approaches infinity by a discrete free variable z0Converted to a continuous variable z. Furthermore, assuming that x and y are uniformly distributed, the probability density function can be expressed as:
Figure BDA0001961234870000121
Figure BDA0001961234870000122
the free variable z may be expressed as z ═ Wtan α/2, where α is freely distributed in the interval [0, arctan (2H/W) ]. Thus, the probability density function can be expressed as:
Figure BDA0001961234870000123
with the above probability density functions for the free variables x, y, and z, the joint probability density function can be expressed as:
Figure BDA0001961234870000124
infinite energy and p of diffuse reflection component corresponding to differential equation dx, dy and dzxyz(x, y, z) dxdydz. When M, N, O → ∞ 1/MNO ═ pxyz(x，y，z)dxdydz。
Time-varying transfer function Hkl(f', t) and Hk′l′The space-time-frequency cross-correlation function between (f', t) is:
Figure BDA0001961234870000125
in the above equation, (. star) denotes the complex conjugate, and E {. cndot.) denotes the desired operator applicable to all the free variables.
Figure BDA0001961234870000126
The space-time-frequency cross-correlation function of the diffuse reflection component is expressed by equation (3):
Figure BDA0001961234870000127
wherein
Figure BDA0001961234870000128
Figure BDA0001961234870000131
The expression of the above formula is obtained by applying to the random phase theta(mno)The average of the results is carried out to obtain,
Figure BDA0001961234870000132
and
Figure BDA0001961234870000133
is the scatterer coordinate (x)m，yn，z0) As a function of (c).
Thus, the space-time-frequency cross-correlation function of the diffuse reflection component
Figure BDA0001961234870000134
Can be expressed as:
Figure BDA0001961234870000135
wherein
Figure BDA0001961234870000136
Figure BDA0001961234870000137
Figure BDA0001961234870000138
Figure BDA0001961234870000139
In the formula, AAOD (AAOA) alphaT(x，y，z)(αR(x, y, z)) and EAOD (EAOA) betaT(x，y，z)(βR(x, y, z)) are functions of the scatterer coordinates (x, y, z), respectively.
Thus, τ'kl(x, y, z) can be used
Figure BDA00019612348700001310
And
Figure BDA00019612348700001311
expressed as:
Figure BDA00019612348700001312
mentioned by using formulae (8) and (9)
Figure BDA00019612348700001313
And
Figure BDA00019612348700001314
then distance
Figure BDA00019612348700001315
And
Figure BDA00019612348700001316
can be expressed as:
Figure BDA00019612348700001317
Figure BDA00019612348700001318
similarly, the space-time-frequency cross-correlation function of the line-of-sight scattering component is:
Figure BDA0001961234870000141
wherein
Figure BDA0001961234870000142
Figure BDA0001961234870000143
2. Spatial cross-correlation function: representing the effect of line-of-sight and non-line-of-sight scenes, the spacing between the transmitting and receiving end antennas.
The spatial cross-correlation function is defined as
Figure BDA0001961234870000144
I.e. equal to the space-time-frequency cross-correlation function pkl，k′l′(δT，δRV ', τ) values when v' is 0 and τ is 0.
ρkl，k′l′(δT，δR)＝ρkl，k′l′(δT，δR，0，0) (33)
3. Time-frequency cross-correlation function: representing the impact of line-of-sight and non-line-of-sight scenes, time and frequency.
The time-frequency cross-correlation function is defined as a time-varying transfer function of
Figure BDA0001961234870000145
And HklThe correlation of (f '+ v', t + τ) can be expressed as
Figure BDA0001961234870000146
Spacing δ between antenna elementsTAnd deltaRWhen equal to 0, the time-frequency cross-correlation function can be expressed as ρkl(v′，τ)＝ρkl，k′l′(0,0, v', τ). Thus, the time-frequency cross-correlation function can be expressed as:
ρkl，k′l′(v′，τ)＝ρkl，k′l′(0，0，v′，τ) (34)
4. time autocorrelation function: representing the effects of line-of-sight and non-line-of-sight scenes, time, and direction of travel of the transmitter and receiver.
Link circuit
Figure BDA0001961234870000147
(l＝1，2，...，MT，k＝1，2，...，MR) The time autocorrelation function of the time-varying transfer function is defined as
Figure BDA0001961234870000148
When the frequency variable v' is equal to 0, the time autocorrelation function can be represented as rkl(τ)＝ρkl(0, τ), therefore, the expression thereof can be obtained as:
rkl(τ)＝ρkl，k′l′(0，0，0，τ) (35)
5. frequency-dependent function: line-of-sight and non-line-of-sight scenes, and frequency.
The frequency dependent function of the time-varying transfer function is defined as
Figure BDA0001961234870000149
When τ is 0, the time autocorrelation function may be represented as rkl(v′)＝ρkl(v', 0.) the frequency correlation function can be expressed as:
rkl(v′)＝ρkl，k′l′(0，0，v′，0) (36)
6. doppler power spectral density: tunnel width, transmitter and receiver travel direction, frequency.
The doppler Power Spectral Density (PSD) is the fourier transform of the temporal autocorrelation function with respect to τ, and can therefore be expressed as:
Figure BDA0001961234870000151
step four: and based on the obtained diffuse reflection and line-of-sight components and the antenna units set by the transmitting end and the receiving end, the channel capacity of the tunnel model can be obtained, and the influences of the number of antennas configured by the transmitting end and the receiving end and the signal-to-noise ratio are represented.
It is well known to have MTA transmitting antenna unit and MRFor a narrow-band MIMO system with multiple receive antenna elements, the maximum theoretical capacity for uniformly distributed transmit power and SNR equal to the SNR can be expressed as:
Figure BDA0001961234870000152
wherein
Figure BDA0001961234870000153
Is MR×MRDimension unit matrix, [. C]HIs a conjugate transpose of the matrix, H is the transmission matrix of the channel, and H ═ HDIF+HLOSIn which H isDIFAnd HLOSRespectively, the transmission matrices for the diffuse reflection and line-of-sight components.
For the modeling and statistical feature analysis of the studied rectangular tunnel wireless propagation channel, fig. 3 shows the effect of the antenna element spacing on the spatial cross-correlation function in the NLOS propagation scenario. As can be seen from the figure, the antenna element pitch δT＝δRWhen 0, the spatial cross-correlation function reaches a maximum of 1. As the element spacing increases, the spatial cross-correlation function gradually decays and fluctuates at steady state. Compared with fig. 4 in the LOS propagation scenario, the correlation between the two array elements is found to be large in the LOS transmission scenario.
Fig. 5 and 6 are graphs showing the effect of time and frequency on the time-frequency cross-correlation function in nlos (los) propagation scenarios, respectively. It can be seen from the figure that similar to fig. 3, 4, the antenna array element pitch δ isT＝δRWhen the value is 0, the time-frequency cross-correlation function reaches the maximum value 1; meanwhile, as time and frequency increase, the time-frequency cross-correlation function gradually attenuates and fluctuates in a stable state.
FIG. 7 shows the Rice distribution factor cREffect on time autocorrelation function (ACF)And (5) distribution diagram. Comparing fig. 7a and 7b, it can be found that: when the transmitter and receiver move in the same direction
Figure BDA0001961234870000154
ACF decays faster; when the directions are opposite
Figure BDA0001961234870000155
Higher ACF oscillation frequency than NLOS under LOS propagation condition and Rice distribution factor cRThe smaller the amplitude, the smaller the amplitude. Meanwhile, the reference model, the simulation model and the experimental data have good matching performance, and the accuracy of the geometric model is proved.
FIG. 8 shows the Rice distribution factor cRThe influence on the frequency dependent function (FCF) is plotted. As can be seen, the frequency correlation function increases with increasing frequency. When the frequency v' is larger than 60Hz, the smaller the Rice distribution factor is, the faster the frequency correlation function is attenuated, and the reference model, the simulation model and the experimental data are well fitted.
Fig. 9 shows the effect of tunnel cross-section width on the frequency dependent function in LOS and NLOS propagation scenarios. As can be seen, the coherence bandwidth decreases from 60MHz to 40MHz as the tunnel cross-sectional width increases from 3m to 5 m. As the width increases, the scattering paths interfere with each other, resulting in a gradual decrease in the coherence bandwidth of the channel model.
Fig. 10 shows the absolute values of the frequency dependent functions for different tunnel width values for LOS and NLOS cases. In LOS and NLOS propagation scenarios, the coherence bandwidth of the proposed channel model decreases as the tunnel width increases. Meanwhile, it can be seen that the FCF gradually decreases as the frequency increases. Interference between the scattering paths causes the FCF of the frequency to fluctuate faster, thereby reducing the coherence bandwidth.
Fig. 11 shows a distribution of the effect of the number of antennas and the signal-to-noise ratio on the channel capacity. As can be seen, the channel capacity gradually increases with the increase of the signal-to-noise ratio, and at the same time, the increase of the number of array elements also increases the channel capacity.
It should be noted that the terms "upper", "lower", "left", "right", "front", "back", etc. used in the present invention are for clarity of description only, and are not intended to limit the scope of the present invention, and the relative relationship between the terms and the terms is not limited by the technical contents of the essential changes.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (7)

1. The rectangular tunnel wireless propagation channel modeling method is characterized by comprising the following steps:
step one, establishing a geometric model of a tunnel system according to the actual size of a rectangular tunnel, dividing the geometric model into a plurality of scatterers, wherein the scatterers are freely distributed, acquiring a propagation route by utilizing the positions of a transmitter, a receiver and the scatterers, configuring uniform linear antenna arrays on the transmitter and the receiver, acquiring a diffuse reflection component and a sight distance component of the tunnel model by utilizing the geometric relationship among the transmitter, the receiver and the scatterers in the rectangular tunnel, and adding the two components to obtain a time-varying transfer function of the model;
expressing the elevation angle and the azimuth angle of the antenna by using the position of the scatterer through a geometric relation and a trigonometric identity in a tunnel scattering scene;
thirdly, calculating the statistical characteristics of the tunnel model by combining the time-varying transfer function, the elevation angle and the azimuth angle;
and step four, obtaining the channel capacity of the tunnel model based on the transmission matrix of the diffuse reflection component and the line-of-sight component.
2. The method of modeling a rectangular tunnel wireless propagation channel according to claim 1, characterized by: in the first step, the time-varying transfer function is obtained by using the propagation routes of any two antennas of the transmitter and the receiverHkl(f', t), expressed as:
Figure FDA0002990474840000011
wherein
Figure FDA0002990474840000012
And
Figure FDA0002990474840000013
diffuse reflection component and line-of-sight component of the time-varying transfer function, respectively;
transmitting uniform plane wave from the first antenna
Figure FDA0002990474840000014
Emitting a beam through the diffuser S(mno)To the k-th receiving antenna
Figure FDA0002990474840000015
Time-varying transfer function HklDiffuse reflection component in (f', t)
Figure FDA0002990474840000016
Expressed as:
Figure FDA0002990474840000017
wherein
Figure FDA0002990474840000018
Figure FDA0002990474840000019
Figure FDA00029904748400000110
Figure FDA00029904748400000111
Figure FDA0002990474840000021
Wherein M represents the total number of scatterers on the x-axis side, N represents the total number of scatterers on the y-axis side, O represents the total number of scatterers on the z-axis side, and cRDenotes a rice distribution factor, m denotes an m-th scatterer on the x-axis side, n denotes an n-th scatterer on the y-axis side, o denotes an o-th scatterer on the z-axis side, λ denotes a wavelength,
Figure FDA0002990474840000022
indicating that the first antenna of the transmitter passes through the scatterer S(mno)The total distance to the kth antenna of the receiver,
Figure FDA0002990474840000023
representing the transmitter scatterer S(mno)The influence on the resulting doppler frequency is such that,
Figure FDA0002990474840000024
representing receiver scatterers S(mno)Influence induced Doppler frequency, t represents time, θ(mno)Indicating the phase of the electromagnetic wave at a particular instant,
Figure FDA0002990474840000025
which is indicative of the propagation delay of the signal,
Figure FDA0002990474840000026
c0representing the speed of light, f' representing the frequency;
Figure FDA0002990474840000027
indicating the arrival of the first antenna of the transmitter at the scatterer S(mno)The distance of (a) to (b),
Figure FDA0002990474840000028
represents a scatterer S(mno)The distance to the kth antenna of the receiver;
xmdenotes the abscissa, x, of the scattererTDenotes the abscissa, y, of the transmitter antenna arraynDenotes the ordinate, y, of the scattering bodyTRepresenting the ordinate, z, of the transmitter antenna arrayoRepresenting the vertical axis coordinate of the scatterer, zTRepresenting the vertical axis coordinate, M, of the transmitter antenna arrayTNumber of antennas, delta, representing transmitter configurationTIndicating transmitter antenna spacing, phiTRepresenting the elevation angle of the transmitter antenna array relative to the xy plane,
Figure FDA0002990474840000029
indicating the vertical emission angle EAOD, gamma of the transmitterTIndicating the tilt angle of the transmitter antenna array,
Figure FDA00029904748400000210
represents the horizontal transmission angle AAOD of the transmitter;
xRdenotes the abscissa, y, of the receiver antenna arrayRRepresenting the ordinate, z, of the receiver antenna arrayRRepresenting the vertical axis coordinate, M, of the receiver antenna arrayRNumber of antennas, delta, representing receiver configurationRIndicating the receiver antenna spacing, phiRRepresenting the elevation angle of the receiver antenna array relative to the xy plane,
Figure FDA00029904748400000211
representing the vertical angle of arrival EAOA, gamma of the receiverRIndicating the tilt angle of the receiver antenna array,
Figure FDA00029904748400000212
represents the horizontal angle of arrival, AAOA, of the receiver;
fTmaxrepresenting the maximum Doppler frequency, f, of the transmitterTmax＝vT/λ，vTWhich is indicative of the speed at which the transmitter is traveling,
Figure FDA00029904748400000213
representing the included angle between the driving direction of the transmitter and the x axis;
fRmaxrepresenting the maximum Doppler frequency, f, of the receiverRmax＝vR/λ，vRWhich is indicative of the speed at which the receiver is traveling,
Figure FDA0002990474840000031
representing the included angle between the driving direction of the receiver and the x axis;
time-varying transfer function HklLine-of-sight component in (f', t)
Figure FDA0002990474840000032
Expressed as:
Figure FDA0002990474840000033
wherein
Figure FDA0002990474840000034
Figure FDA0002990474840000035
Figure FDA0002990474840000036
In the formula (I), the compound is shown in the specification,
Figure FDA0002990474840000037
a rice distribution factor representing a line-of-sight component,
Figure FDA0002990474840000038
indicating the distance of the ith antenna of the transmitter and the kth antenna of the receiver,
Figure FDA0002990474840000039
representing the doppler frequency of the transmitter in the line-of-sight path,
Figure FDA00029904748400000310
representing the doppler frequency of the receiver in the line-of-sight path,
Figure FDA00029904748400000311
representing propagation delay in a line-of-sight path;
Figure FDA00029904748400000312
the AAOD representing the line-of-sight component,
Figure FDA00029904748400000313
an EAOD representing a line-of-sight component,
Figure FDA00029904748400000314
the AAOA representing the line-of-sight component,
Figure FDA00029904748400000315
EAOA representing the line of sight component.
3. The method of modeling a rectangular tunnel wireless propagation channel according to claim 2, characterized in that: in the second step, the azimuth angle refers to a horizontal emission angle and a horizontal arrival angle, and the elevation angle refers to a vertical emission angle and a vertical arrival angle.
4. The rectangular tunnel wireless communication device of claim 3The road modeling method is characterized in that: in the second step, the scattering body S is expressed by using Cartesian coordinates(mno)Wherein M is 1,2, …, M, N is 1,2, …, N, O is 1,2, …, O, (x) isT,yT,zT) And (x)R,yR,zR) Respectively, the position of the transmitter and receiver antenna arrays, where 0 ≦ xT≤xR≤L，-W/2≤yR≤yTW/2 or less, L represents the length of the tunnel, W represents the width of the tunnel, scatterers S are used(mno)Position (x) ofm,yn,zo) The elevation and azimuth of the antenna are represented as:
Figure FDA0002990474840000041
Figure FDA0002990474840000042
where T denotes a transmitter, R denotes a receiver, and α denotes a receiveri(xm,yn,zo) Representing AAOD of transmitter or AAOA, beta of receiveri(xm,yn,z0) EAOA, x representing EAOD of transmitter or EAOA, x of receiveriIndicating the abscissa, y, of the transmitter or receiveriIndicating the ordinate, z, of the transmitter or receiveriRepresenting the vertical axis coordinates of the transmitter or receiver.
5. The method of modeling a rectangular tunnel wireless propagation channel according to claim 4, wherein: in the third step, the statistical characteristics of the tunnel model include a space-time-frequency cross-correlation function, a space cross-correlation function, a time-frequency cross-correlation function, a time self-correlation function, a frequency correlation function and a doppler power spectral density.
6. The method of modeling a rectangular tunnel wireless propagation channel according to claim 5, characterized in that: in the third step, firstly, the property of uniform distribution of the free variables x and y is utilized to obtain probability density functions of x, y and z, and further obtain the joint probability density, and a space-time-frequency cross-correlation function, a time self-correlation function, a frequency correlation function and Doppler power spectral density between any two antennas are derived by combining a time-varying transfer function, an elevation angle and an azimuth angle as follows:
assuming that the number of scatterers tends to be infinite, a discrete random variable xm，ynAnd zoRepresented by the continuous variables x, y and z, respectively, x and y are uniformly distributed, and their probability density function is represented as:
Figure FDA0002990474840000043
Figure FDA0002990474840000044
wherein p isx(x) Probability density function, p, representing a continuous variable xy(y) a probability density function representing a continuous variable y;
the free variable z is represented as z ═ Wtan α/2, α is freely distributed in the interval [0, arctan (2H/W) ], H represents the tunnel height, and its probability density function is represented as:
Figure FDA0002990474840000051
wherein p isz(z) a probability density function representing a continuous variable z;
with the above probability density functions for the free variables x, y and z, the joint probability density function is expressed as:
Figure FDA0002990474840000052
wherein p isxyz(xyz) represents the continuous variables x, y,z is a joint probability density function; infinite energy and p of diffuse reflection component corresponding to differential equation dx, dy and dzxyz(x, y, z) dxdydz, and when M, N, O → ∞ 1/MNO ═ pxyz(x,y,z)dxdydz；
Time-varying transfer function Hkl(f', t) and Hk'l'The space-time-frequency cross-correlation function between (f', t) is:
Figure FDA0002990474840000053
where l ' denotes the l ' th antenna of the transmitter, l ' ≠ l, k ' denotes the k ' th antenna of the receiver, k ' ≠ k, v ' denotes frequency, τ denotes time, E {. cndot.) denotes the expectation operator, (. cndot.)*Which represents the complex conjugate of the light source,
Figure FDA0002990474840000054
a space-time-frequency cross-correlation function representing the diffuse reflection component,
Figure FDA0002990474840000055
a space-time-frequency cross-correlation function representing a line-of-sight component;
the space-time-frequency cross-correlation function of the diffuse reflection component is expressed as:
Figure FDA0002990474840000056
wherein
Figure FDA0002990474840000057
Figure FDA0002990474840000058
In the formula
Figure FDA0002990474840000059
And
Figure FDA00029904748400000510
representing intermediate variables taken for a simplified formula;
fT(x, y, z) denotes the transmitter receiver S(mno)Doppler frequency due to influence, influenced by the infinite scatterers, originally
Figure FDA0002990474840000061
Is converted into fT(x,y,z)；fR(x, y, z) denotes the transmitter receiver S(mno)Doppler frequency due to influence, influenced by the infinite scatterers, originally
Figure FDA0002990474840000062
Is converted into fR(x,y,z)；τ'kl(x, y, z) represents propagation delay, affected by the infinite scatterers, original
Figure FDA0002990474840000063
Is converted to τ'kl(x,y,z)；
Thus, the space-time-frequency cross-correlation function of the diffuse reflection component
Figure FDA0002990474840000064
Expressed as:
Figure FDA0002990474840000065
wherein
Figure FDA0002990474840000066
Figure FDA0002990474840000067
Figure FDA0002990474840000068
Figure FDA0002990474840000069
In the formula of alphaT(x, y, z) denotes the AAOD of the transmitter, influenced by the infinite scatterers, originally
Figure FDA00029904748400000610
Conversion to alphaT(x,y,z)；βT(x, y, z) denotes EAOD of the transmitter, influenced by the infinite scatterer, originally
Figure FDA00029904748400000611
Conversion to betaT(x,y,z)；
αR(x, y, z) denotes the AAOA of the transmitter, influenced by the infinite scatterer, original
Figure FDA00029904748400000612
Conversion to alphaR(x,y,z)；βR(x, y, z) denotes EAOA of the transmitter, influenced by the infinite scatterer, original
Figure FDA00029904748400000613
Conversion to betaR(x,y,z)；
τ'klFor (x, y, z)
Figure FDA00029904748400000614
And
Figure FDA00029904748400000615
expressed as:
Figure FDA00029904748400000616
Figure FDA00029904748400000617
indicating the arrival of the first antenna of the transmitter at the scatterer S(mno)Is influenced by the infinite scattering body, originally
Figure FDA0002990474840000071
To be converted into
Figure FDA0002990474840000072
Figure FDA0002990474840000073
Represents a scatterer S(mno)The distance to the kth antenna of the receiver is influenced by infinite scatterers, the original distance
Figure FDA0002990474840000074
To be converted into
Figure FDA0002990474840000075
Then distance
Figure FDA0002990474840000076
And
Figure FDA0002990474840000077
expressed as:
Figure FDA0002990474840000078
Figure FDA0002990474840000079
similarly, the space-time-frequency cross-correlation function of the line-of-sight scattering component is:
Figure FDA00029904748400000710
wherein
Figure FDA00029904748400000711
Figure FDA00029904748400000712
The spatial cross-correlation function is defined as
Figure FDA00029904748400000713
I.e. equal to the space-time-frequency cross-correlation function pkl,k'l'(δT,δRV ', τ) when v' is 0 and τ is 0, the spatial cross-correlation function is therefore expressed as:
ρkl,k'l'(δT,δR)＝ρkl,k'l'(δT,δR,0,0)
the time-frequency cross-correlation function is defined as a time-varying transfer function of
Figure FDA00029904748400000714
And HklThe correlation of (f '+ v', t + τ) is expressed as
Figure FDA00029904748400000715
When the spacing between the antennas is deltaTAnd deltaRWhen equal to 0, the time-frequency cross-correlation function is expressed as ρkl(v',τ)＝ρkl,k'l'(0,0, v', τ), therefore, the time-frequency cross-correlation function is expressed as:
ρkl,k'l'(v',τ)＝ρkl,k'l'(0,0,v',τ)
link circuit
Figure FDA0002990474840000081
The time autocorrelation function of the time-varying transfer function is defined as
Figure FDA0002990474840000082
When the frequency variable v' is equal to 0, the time autocorrelation function is represented as rkl(τ)＝ρkl(0, τ), therefore, the expression thereof is obtained as:
rkl(τ)＝ρkl,k'l'(0,0,0,τ)
the frequency dependent function of the time-varying transfer function is defined as
Figure FDA0002990474840000083
When τ is 0, the time autocorrelation function is denoted as rkl(v')＝ρkl(v',0), the frequency dependent function is expressed as:
rkl(v′)＝ρkl,k'l'(0,0,v′,0)
the doppler power spectral density is a fourier transform of the temporal autocorrelation function with respect to τ, and is therefore expressed as:
Figure FDA0002990474840000084
wherein
Figure FDA0002990474840000085
Representing a fourier transform.
7. The method of modeling a rectangular tunnel wireless propagation channel according to claim 6, characterized in that: in the fourth step, for the compound with MTA transmitting antenna and MRFor a narrow-band MIMO system with multiple receive antennas, the maximum theoretical capacity for uniformly distributed transmit power and signal-to-noise ratio equal to SNR is given by:
Figure FDA0002990474840000086
where C represents the capacity of the channel and,
Figure FDA0002990474840000087
represents MR×MRDimension unit matrix, [. C]HIs a conjugate transpose of the matrix, H is the transmission matrix of the channel, and H ═ HDIF+HLOSIn which H isDIFAnd HLOSRespectively, the transmission matrices for the diffuse reflection and line-of-sight components.
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