CN107086894A - Markovian mimo channel modeling method is based under a kind of high-speed mobile - Google Patents

Markovian mimo channel modeling method is based under a kind of high-speed mobile Download PDF

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CN107086894A
CN107086894A CN201710334109.2A CN201710334109A CN107086894A CN 107086894 A CN107086894 A CN 107086894A CN 201710334109 A CN201710334109 A CN 201710334109A CN 107086894 A CN107086894 A CN 107086894A
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mrow
msubsup
msub
msup
scattering object
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廖勇
胡异
沈轩帆
张舒敏
陈玲
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Chongqing University
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Chongqing University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B17/00Monitoring; Testing
    • H04B17/30Monitoring; Testing of propagation channels
    • H04B17/391Modelling the propagation channel
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413MIMO systems

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Abstract

The present invention proposes to be based on markovian mimo channel modeling method under a kind of high-speed mobile.First, channel model is set up according to high ferro scene.Secondly, transmitting terminal and receiving terminal are obtained to the crucial channel parameter such as the azimuth of scattering object cluster according to the model set up.Furthermore, the time delay for propagating virtual link in scene is obtained by Markov chain model.Then, the shock response expression formula from i-th antenna of transmitting terminal to receiving terminal jth root antenna is obtained by the channel model set up.Then, obtained according to three-dimensional system of coordinate feature from transmitting terminal to scattering object cluster, the antenna vector of scattering object cluster to receiving terminal, and transmitting terminal is to the distance vector of receiving terminal.The mathematics for being derived by channel impulse response finally by mathematical formulae closes expression formula.This method specifically have studied the channel model under high ferro mobile context, employ Markov link model and obtain virtual link time delay in propagation scene, and consider antenna vector, leave angle and reach the angle of pitch of angular dimensions, so that set up model more closing to reality channel, solid theoretical foundation is provided to design high-quality ultrahigh speed mobile communication.

Description

Markovian mimo channel modeling method is based under a kind of high-speed mobile
Technical field
The present invention relates to the channel modeling method of high-speed mobile communications, particularly under high ferro system of broadband wireless communication Markovian mimo channel modeling method is based under a kind of high-speed mobile.
Background technology
With intelligent terminal and the high speed development of mobile Internet business, when user takes high ferro trip, there is more and more Mobile office and network entertainment requirements, such as videoconference, video request program, interactive game, online.Due to high-end business customer Converge, high ferro communication progressively turns into the displaying of each operator brand, obtains considerable economic profit and draw high high-end customer degree of adhesion New competitive field.And the target that existing communication standard is mainly applied is city low speed Movable cellular cell scene, and do not have Have and special design is carried out for high-speed mobile scene.Therefore, how in high-speed cruising, passenger flow concentration, volume of business height, deployment The high-quality network coverage, the significant challenge faced as operator and equipment vendor are provided in the complicated high ferro of scene.
Railway covering different from the past, high ferro covering will not only provide good speech business, and to data service It is required that very high.High ferro covers available business and is divided into 4 classes:Security monitoring class, media information class, voice class and mobile Internet Class.Security monitoring refers to security protection, passes monitoring high definition picture in real time back by communication network, it is ensured that high ferro safe operation.Media Information and mobile Internet type refer to provides the business such as Real-Time IP TV, video tour, mobile office and online in high ferro.But by It is lost greatly in high ferro car body and high-speed cruising can causes serious Doppler effect, causes the unstable of high ferro radio communication channel Property so that network quality rapid drawdown, significantly, speed of surfing the Internet is low, poor user experience for call drop.And existing cell mobile communication systems and The global mobile communication railway system (Global System for Mobile Communication-Railway, GSM-R) is Demand of the current and following high ferro user to high speed data transfer can not be met.
At present, studied for the existing researcher of channel modeling method under high-speed mobile.Have based on ray trace The geometry deterministic models (GeometryBasedDeterministicModel, GBDM) of method, deterministic models need substantial amounts of Measured data, computation complexity is high.There are the stochastic channel model based on geometry, such as monocyclic, bicyclic and model of ellipse, random letter The channel parameter of road model is also based on measured data to obtain, and computation complexity is higher.Also non-geometric stochastic model (Non- Geometrical StochasticModel, NGSM), such as finite state Markov based on high ferro radio communication NGSM, but this class model is only based on limited channel status, and the description for channel parameter is inaccurate.Therefore, based on existing Some modeling methods, modeling result and actual result error are larger.
Markov Chain is the discrete time stochastic process with Markov property in mathematics.During being somebody's turn to do, given In the case of current knowledge or information, the past (i.e. current before historic state) for prediction in the future (i.e. it is currently later not Carry out state) it is unrelated.Markov chain model can reveal that inherent law of the system in the transfer of different conditions interval, amendment system The fluctuation that system is produced by various chance mechanisms, therefore Markov chain model predicts effect for the larger data sequence of fluctuation Fruit is preferably.Therefore be used to Markov chain model obtain the channel parameter under high-speed mobile, calculating complexity can be reduced, raising is built The mould degree of accuracy.
To sum up, the method for having Channel Modeling now, their computational methods are complicated, modeling result and actual result Error is larger.This just needs those skilled in the art badly and solves corresponding technical problem.
The content of the invention
It is contemplated that at least solving technical problem present in prior art, a kind of shifting at a high speed is especially innovatively proposed It is dynamic lower based on markovian mimo channel modeling method.
It is markovian the invention provides being based under a kind of high-speed mobile in order to realize the above-mentioned purpose of the present invention Mimo channel modeling method, specific modeling process is as follows:
Set a high ferro scene, it is assumed that have multiple obstacles cluster in a wideband MIMO system, be modeled in one In individual three-dimensional system of coordinate, such as Fig. 1.Assuming that the antenna of transmitting terminal and receiving terminal is even linear array, transmitting terminal has MTRoot antenna, is received There is M at endRRoot antenna.The distance between transmitting terminal antenna is δT, the distance between receiving terminal antenna is δR.Assuming that emitter is three The origin of dimension coordinate system, it is D=(D, 0,0) that transmitting terminal is vectorial with the distance between receiving terminal.N-th of scattering object cluster is to transmitting terminal Distance vector beThe distance vector of n-th scattering object cluster to receiving terminal isI-th antenna of transmitting terminal is to connecing The horizon grange vector of receiving end jth root antenna isDistance vector of n-th of scattering object cluster to i-th antenna of transmitting terminal ForThe distance vector of n-th of scattering object cluster to receiving terminal jth root antenna isThe day of receiving terminal jth root antenna Line vector isThe antenna vector of i-th antenna of transmitting terminal isThe elevation angle and azimuth of receiving terminal antenna array are γR(t),ηR(t);The elevation angle and azimuth of transmitting terminal antenna array are γT(t),ηT(t);Receiving terminal is to n-th scattering object cluster The elevation angle and azimuth areThe elevation angle and azimuth of transmitting terminal to n-th of scattering object cluster areIt is false If transmitting terminal respectively has N number of scattering object cluster with receiving terminal, and matches one by one, each scattering object cluster Clustern(n= 1 ..., N) represent,The scattering object cluster around transmitting terminal is represented,Represent dissipating around receiving terminal Beam cluster.Communication environments between transmitting terminal and the scattering object cluster of receiving terminal regard virtual link as.Because train is in high-speed mobile In, it is not that scattering object cluster in each space is visible, i.e. partial dispersion body for array element in mimo antenna array Cluster only has scattering effect to the part that part array element is launched;Simultaneously with the quick movement of train, the scattering object cluster in space Distribution is also quickly changing relative to train and then is generating birth and death processes.Therefore, the time delay that virtual link is producedIt is also Fast-changing, we obtain the time delay of virtual link using Markov chain model
Therefore, the channel matrix of wideband MIMO channels can use a MR×MTComplex matrixRepresent, wherein j=1,2 ..., MR, i=1,2 ..., MT.In t delay, τ, from transmitting I-th antenna is held to channel impulse response (channel impulse response, CIR) h of receiving terminal jth root antennaji(t, It can τ) be expressed as:
Wherein, hn,ji(t) represent from i-th antenna of transmitting terminal to receiving terminal jth root antenna by n-th scattering object cluster CIR, τn(t) time delay of n-th of scattering object cluster is represented.
Wherein,For CIR line-of-sight component,For CIR non-line-of-sight component, and
Wherein, KjiFor this K factor of Lay;P1,ji(Pn,ji) for the power energy of first (n-th) scattering object cluster;fcIt is to carry Wave frequency rate;It is Doppler factor in line-of-sight component;Phase factor in line-of-sight component;fji,1It is first scattering object cluster In Doppler factor in non-line-of-sight component;Φji,1It is phase factor in non-line-of-sight component in first scattering object cluster;Equally, fji,n It is Doppler factor in n-th of scattering object cluster;Φji,nIt is phase factor in n-th of scattering object cluster.
Following formula can be obtained by mathematics geometrical relationship again:
Wherein,It is from t0The distance vector of moment to t n-th scattering object cluster to transmitting terminal is poor, It is from t0The distance vector of moment to t n-th scattering object cluster to receiving terminal is poor,It is from t0Moment is sent out to t I-th antenna in end is penetrated to the horizon grange vector difference of receiving terminal jth root antenna,It is n-th of scattering object cluster to transmitting terminal Distance vector,It is distance vector of n-th of scattering object cluster to receiving terminal;It is i-th antenna of transmitting terminal to reception Hold the horizon grange vector of jth root antenna;It is distance vector of n-th of scattering object cluster to i-th antenna of transmitting terminal,It is distance vector of n-th of scattering object cluster to receiving terminal jth root antenna;C is the light velocity;V is the motion-vector of receiving terminal; fmaxIt is maximum doppler frequency;Φ0It is the initial phase for launching end signal;λ is wavelength.
It is the time delay of virtual link between transmitting terminal and receiving terminal scattering cluster, is stochastic variable, passes through Ma Erke Husband's chain model can be obtained, and the virtual link time delay of t is only relevant with the time delay at t-1 moment, and expression is as follows:
Wherein, E is stochastic variable, obeys (D/c, τmax) be uniformly distributed;Δ t is time difference of the t to the t-1 moment; ε is the scene factor, related to the scene of setting;σ is delay spread.
By the three-dimensional coordinate of figure one, following formula can be obtained:
Wherein,It is the antenna vector of receiving terminal jth root antenna,The antenna vector of i-th antenna of transmitting terminal; γR(t),ηR(t) be receiving terminal antenna array the elevation angle and azimuth;γT(t),ηT(t) be transmitting terminal antenna array the elevation angle and side Parallactic angle;Be receiving terminal to the elevation angle and azimuth of n-th of scattering object cluster, be independent random variable, obey broad sense Gaussian Profile;Transmitting terminal, to the elevation angle and azimuth of n-th of scattering object cluster, is independent random variable, obeys wide Adopted Gaussian Profile;Be n-th scattering object cluster to the distance vector of transmitting terminal mould it is long,It is n-th of scattering object The mould of cluster to the distance vector of receiving terminal is long, is independent random variable, obeys exponential distribution.
Formula (17)-(23) are substituted into formula (7)-(16), then simultaneous formula (2)-(6) solution can be solved based on Markov Chain Mimo channel shock response hji(t,τ)。
Brief description of the drawings
Markovian mimo channel scattering model is based under Fig. 1 high-speed mobiles;
Flow chart based on markovian mimo channel modeling method under Fig. 2 high-speed mobiles.
Embodiment
Hereinafter, embodiments of the present invention are described, the example of the embodiment is shown in the drawings, wherein phase from beginning to end Same or similar label represents same or similar element or the element with same or like function.Below with reference to accompanying drawing The embodiment of description is exemplary, is only used for explaining the present invention, and is not considered as limiting the invention.
In the description of the invention, unless otherwise prescribed with limit, it is necessary to explanation, term " installation ", " connected ", " connection " should be interpreted broadly, for example, it may be mechanically connect or electrical connection or the connection of two element internals, can To be to be joined directly together, it can also be indirectly connected to by intermediary, for the ordinary skill in the art, can basis Concrete condition understands the concrete meaning of above-mentioned term.
Based on markovian mimo channel modeling process as shown in Fig. 2 specific as follows under high-speed mobile:
Step 1:Start;
Step 2:Set high ferro scene, it is assumed that have multiple obstacles cluster in a wideband MIMO system, be modeled in In one three-dimensional system of coordinate;Assuming that the antenna of transmitting terminal and receiving terminal is even linear array, transmitting terminal has MTRoot antenna, receiving terminal has MRRoot antenna;The distance between transmitting terminal antenna is δT, the distance between receiving terminal antenna is δR;Assuming that emitter is sat in three-dimensional The origin of system is marked, it is D=(D, 0,0) that transmitting terminal is vectorial with the distance between receiving terminal;Assuming that transmitting terminal respectively has N number of with receiving terminal Scattering object cluster, and match one by one, each scattering object cluster Clustern(n=1 ..., N) represent,Represent Scattering object cluster around transmitting terminal,Represent the scattering object cluster around receiving terminal;The scattering object of transmitting terminal and receiving terminal Communication environments between cluster regard virtual link as, and channel model is set up with this;
Step 3:The channel model set up according to step 2, obtains the antenna vector of receiving terminal jth root antennaTransmitting The antenna vector of i-th, end antennaThe elevation angle of receiving terminal antenna array and azimuth γR(t),ηR(t);Transmitting terminal antenna array The elevation angle and azimuth γT(t),ηT(t);Receiving terminal is to the elevation angle and azimuth of n-th of scattering object clusterIt is only Vertical stochastic variable, obeys generalized Gaussian distribution;Transmitting terminal is to the elevation angle and azimuth of n-th of scattering object clusterIt is Independent random variable, obeys generalized Gaussian distribution;The mould of n-th scattering object cluster to the distance vector of transmitting terminal is longN-th The mould of individual scattering object cluster to the distance vector of receiving terminal is longIt is independent random variable, obeys exponential distribution;
Step 4:With the quick movement of train, the scattering object cluster distribution in space is also quickly changing relative to train And then generate birth and death processes;Therefore, the time delay that virtual link is producedIt is also fast-changing, using Markov Chain mould Type obtains the time delay of virtual linkThe virtual link time delay of t is only relevant with the time delay at t-1 moment, embodies Formula is as follows:
Wherein, E is stochastic variable, obeys (D/c, τmax) be uniformly distributed;Δ t is time difference of the t to the t-1 moment; ε is the scene factor, related to the scene of setting;σ is delay spread;
Step 5:Obtain in t delay, τ, from i-th antenna of transmitting terminal to the Channel Impulse of receiving terminal jth root antenna Respond (channelimpulseresponse, CIR) hji(t,τ):
Wherein, hn,ji(t) represent from i-th antenna of transmitting terminal to receiving terminal jth root antenna by n-th scattering object cluster CIR, τn(t) time delay of n-th of scattering object cluster is represented, can be drawn by the 1st scattering object cluster according to the high ferro scene of setting CIR:
Wherein,For CIR line-of-sight component,For CIR non-line-of-sight component, and
Wherein, KjiFor this K factor of Lay;P1,jiFor the power energy of first scattering object cluster;fcIt is carrier frequency;It is Doppler factor in line-of-sight component;It is phase factor in line-of-sight component;fji,1It is non-direct-view point in first scattering object cluster Doppler factor in amount;Φji,1It is phase factor in non-line-of-sight component in first scattering object cluster;
Following formula can be obtained by mathematics geometrical relationship again:
Wherein,It is from t0The distance vector of moment to t n-th scattering object cluster to transmitting terminal is poor, It is from t0The distance vector of moment to t n-th scattering object cluster to receiving terminal is poor,It is from t0Moment is sent out to t I-th antenna in end is penetrated to the horizon grange vector difference of receiving terminal jth root antenna,It is n-th of scattering object cluster to transmitting terminal Distance vector,It is distance vector of n-th of scattering object cluster to receiving terminal;It is i-th antenna of transmitting terminal to reception Hold the horizon grange vector of jth root antenna;It is distance vector of the 1st scattering object cluster to i-th antenna of transmitting terminal,It is distance vector of the 1st scattering object cluster to receiving terminal jth root antenna;C is the light velocity;V is the motion-vector of receiving terminal; fmaxIt is maximum doppler frequency;Φ0It is the initial phase for launching end signal;λ is wavelength;
Likewise, can be drawn by n-th (n=2,3 ..., N) individual scattering object cluster according to set high ferro scene CIR:
Wherein, KjiFor this K factor of Lay;Pn,jiFor the power energy of n-th of scattering object cluster;fji,nIt is n-th of scattering object cluster Middle Doppler factor;Φji,nIt is phase factor in n-th of scattering object cluster;
Following formula can be obtained by mathematics geometrical relationship again:
Wherein,It is distance vector of n-th of scattering object cluster to i-th antenna of transmitting terminal,It is scattered n-th Distance vector of the beam cluster to receiving terminal jth root antenna;C is the light velocity;V is the motion-vector of receiving terminal;fmaxIt is maximum Doppler Frequency;Φ0It is the initial phase for launching end signal;λ is wavelength;
Step 6:The parameters such as antenna vector and distance vector are obtained according to three-dimensional system of coordinate, expression is as follows:
Wherein,It is the antenna vector of receiving terminal jth root antenna,The antenna vector of i-th antenna of transmitting terminal; γR(t),ηR(t) be receiving terminal antenna array the elevation angle and azimuth;γT(t),ηT(t) be transmitting terminal antenna array the elevation angle and side Parallactic angle;Be receiving terminal to the elevation angle and azimuth of n-th of scattering object cluster, be independent random variable, obey broad sense Gaussian Profile;Transmitting terminal, to the elevation angle and azimuth of n-th of scattering object cluster, is independent random variable, obeys wide Adopted Gaussian Profile;Be n-th scattering object cluster to the distance vector of transmitting terminal mould it is long,It is n-th of scattering object The mould of cluster to the distance vector of receiving terminal is long, is independent random variable, obeys exponential distribution;
Step 7:Obtain being based on markovian mimo channel shock response h under high-speed mobileji(t,τ);
Step 8:Terminate.
As described above, the present invention obtains the time delay for propagating scene virtual link using Markov Chain, in three-dimensional system of coordinate The parameters such as lower acquisition antenna vector, distance vector, by the CIR, angle spread, the Doppler that are derived from n-th of scattering object cluster The mathematic(al) representation of the parameters such as the factor, finally gives channel impulse response CIR.This method can specifically obtain high ferro mobile context Under there is markovian mimo channel model, provide solid theoretical base to study high-quality ultrahigh speed mobile communication Plinth.
The beneficial effects of the invention are as follows:
Traditional channel model based on the measurement of actual channel survey meter is time-consuming, effort, cost are high, computation complexity is high, And the high ferro channel model and motion that existing national and foreign standards tissue is put into effect can not meet growing customer demand, Solved for a long time using the present invention, the problem of channel model between high speed mobile terminal and road side base station.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show The description of example " or " some examples " etc. means to combine specific features, structure, material or the spy that the embodiment or example are described Point is contained at least one embodiment of the present invention or example.In this manual, to the schematic representation of above-mentioned term not Necessarily refer to identical embodiment or example.Moreover, specific features, structure, material or the feature of description can be any One or more embodiments or example in combine in an appropriate manner.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that:Not In the case of departing from the principle and objective of the present invention a variety of change, modification, replacement and modification can be carried out to these embodiments, this The scope of invention is limited by claim and its equivalent.

Claims (5)

1. markovian mimo channel modeling method is based under a kind of high-speed mobile, it is characterised in that comprise the following steps:
S1, starts;
S2, sets high ferro scene, it is assumed that have multiple obstacles cluster in a wideband MIMO system, be modeled in a three-dimensional In coordinate system;Assuming that the antenna of transmitting terminal and receiving terminal is even linear array, transmitting terminal has MTRoot antenna, receiving terminal has MRRoot antenna; The distance between transmitting terminal antenna is δT, the distance between receiving terminal antenna is δR;Assuming that original of the transmitting terminal in three-dimensional system of coordinate Point, it is D=(D, 0,0) that transmitting terminal is vectorial with the distance between receiving terminal;Assuming that transmitting terminal respectively has N number of scattering object with receiving terminal Cluster, and match one by one, each scattering object cluster Clustern(n=1 ..., N) represent,Represent in transmitting terminal The scattering object cluster of surrounding,Represent the scattering object cluster around receiving terminal;Between transmitting terminal and the scattering object cluster of receiving terminal Communication environments regard virtual link as, channel model is set up with this;
S3, transmitting terminal and receiving terminal are obtained to the crucial channel parameter such as the angle of pitch of scattering object cluster according to the model set up;
S4, as train is moved, obtains virtual link time delay in the propagation scene of t
S5, is obtained from i-th antenna of transmitting terminal by the channel model set up and passes through n-th (n=1,2,3 ..., N) individual scattering object cluster To the shock response expression formula of receiving terminal jth root antenna;
S6, obtains the antenna vector and scattering object cluster of transmitting terminal and receiving terminal to transmitting terminal and receiving terminal in three-dimensional system of coordinate Distance vector;
S7, is obtained by mathematical derivation and markovian mimo channel shock response h is based under high-speed mobileji(t,τ);
S8, terminates.
2. being based on markovian mimo channel modeling method under high-speed mobile according to claim 1, its feature exists In the S3 includes:
The channel model set up according to S2, obtains the antenna vector of receiving terminal jth root antennaI-th antenna of transmitting terminal Antenna vectorThe elevation angle of receiving terminal antenna array and azimuth γR(t),ηR(t);The elevation angle and orientation of transmitting terminal antenna array Angle γT(t),ηT(t);Receiving terminal is to the elevation angle and azimuth of n-th of scattering object clusterIt is independent random variable, Obey generalized Gaussian distribution;Transmitting terminal is to the elevation angle and azimuth of n-th of scattering object clusterIt is that independent random becomes Amount, obeys generalized Gaussian distribution;The mould of n-th scattering object cluster to the distance vector of transmitting terminal is longN-th of scattering object cluster Mould to the distance vector of receiving terminal is longIt is independent random variable, obeys exponential distribution.
3. being based on markovian mimo channel modeling method under high-speed mobile according to claim 1, its feature exists In the S4 includes:
With the quick movement of train, the scattering object cluster distribution in space is also quickly changing and then generated relative to train Birth and death processes;Therefore, the time delay that virtual link is producedIt is also fast-changing, void is obtained using Markov chain model Intend the time delay of linkThe virtual link time delay of t is only relevant with the time delay at t-1 moment, and expression is as follows:
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Wherein, E is stochastic variable, obeys (D/c, τmax) be uniformly distributed;Δ t is time difference of the t to the t-1 moment;ε is The scene factor is related to the scene of setting;σ is delay spread.
4. being based on markovian mimo channel modeling method under high-speed mobile according to claim 1, its feature exists In the S5 includes:
In t delay, τ, from i-th antenna of transmitting terminal to the channel impulse response (channel of receiving terminal jth root antenna Impulse response, CIR) hji(t,τ):
<mrow> <msub> <mi>h</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>h</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
Wherein, hn,ji(t) CIR from i-th antenna of transmitting terminal to receiving terminal jth root antenna by n-th of scattering object cluster is represented, τn(t) time delay of n-th of scattering object cluster is represented, the CIR by the 1st scattering object cluster can be drawn according to the high ferro scene of setting:
<mrow> <msub> <mi>h</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>h</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>N</mi> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
Wherein,For CIR line-of-sight component,For CIR non-line-of-sight component, and
<mrow> <msubsup> <mi>h</mi> <mrow> <mn>1.</mn> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mi>c</mi> </msub> <msub> <mi>&amp;tau;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <msubsup> <mi>&amp;pi;f</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msubsup> <mi>&amp;Phi;</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
<mrow> <msubsup> <mi>h</mi> <mrow> <mn>1.</mn> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>N</mi> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;Phi;</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
Wherein, KjiFor this K factor of Lay;P1,jiFor the power energy of first scattering object cluster;fcIt is carrier frequency;It is direct-view Doppler factor in component;It is phase factor in line-of-sight component;fji,1It is in first scattering object cluster in non-line-of-sight component Doppler factor;Φji,1It is phase factor in non-line-of-sight component in first scattering object cluster;
Following formula can be obtained by mathematics geometrical relationship again:
<mrow> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>&amp;Delta;D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>&amp;Delta;D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>c</mi> </mfrac> <mo>+</mo> <mover> <mi>&amp;tau;</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>&amp;Delta;D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>c</mi> </mfrac> </mrow>
<mrow> <msubsup> <mi>&amp;Delta;D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>&amp;Delta;D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>&amp;Delta;D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>f</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>f</mi> <mi>max</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mi>V</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mi>V</mi> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> </mrow>
<mrow> <msubsup> <mi>&amp;Phi;</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;Phi;</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow>
<mrow> <msub> <mi>f</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>f</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>R</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mi>V</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mi>V</mi> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> </mrow>
<mrow> <msub> <mi>&amp;Phi;</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;Phi;</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mo>&amp;lsqb;</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>+</mo> <mi>c</mi> <mover> <mi>&amp;tau;</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
Wherein,It is from t0The distance vector of moment to t n-th scattering object cluster to transmitting terminal is poor,Be from t0The distance vector of moment to t n-th scattering object cluster to receiving terminal is poor,It is from t0Moment is to t transmitting terminal I-th antenna to receiving terminal jth root antenna horizon grange vector difference,It is distance of n-th of scattering object cluster to transmitting terminal Vector,It is distance vector of n-th of scattering object cluster to receiving terminal;It is i-th antenna of transmitting terminal to receiving terminal The horizon grange vector of jth root antenna;It is distance vector of the 1st scattering object cluster to i-th antenna of transmitting terminal,It is distance vector of the 1st scattering object cluster to receiving terminal jth root antenna;C is the light velocity;V is the motion-vector of receiving terminal; fmaxIt is maximum doppler frequency;Φ0It is the initial phase for launching end signal;λ is wavelength;
Similarly, the CIR drawn by n-th (n=2,3 ..., N) individual scattering object cluster can be promoted according to set high ferro scene:
<mrow> <msub> <mi>h</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>N</mi> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> </mrow>
<mrow> <msubsup> <mi>h</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>N</mi> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;Phi;</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> </mrow>
Wherein, KjiFor this K factor of Lay;Pn,jiFor the power energy of n-th of scattering object cluster;fji,nIt is how general in n-th of scattering object cluster Strangle the factor;Φji,nIt is phase factor in n-th of scattering object cluster;
Following formula can be obtained by mathematics geometrical relationship again:
<mrow> <msub> <mi>f</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>f</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>R</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mi>V</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mi>V</mi> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;Phi;</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;Phi;</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mo>&amp;lsqb;</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>+</mo> <mi>c</mi> <mover> <mrow> <mi>&amp;tau;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mo>~</mo> </mover> <mo>&amp;rsqb;</mo> <mo>,</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow>
Wherein,It is distance vector of n-th of scattering object cluster to i-th antenna of transmitting terminal,It is n-th of scattering object Distance vector of the cluster to receiving terminal jth root antenna;C is the light velocity;V is the motion-vector of receiving terminal;fmaxIt is maximum Doppler frequency Rate;Φ0It is the initial phase for launching end signal;λ is wavelength.
5. being based on markovian mimo channel modeling method under high-speed mobile according to claim 1, its feature exists In the S6 includes:
The parameters such as antenna vector and distance vector are obtained according to three-dimensional system of coordinate, expression is as follows:
<mrow> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mi>j</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>T</mi> <mi>j</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>T</mi> <mi>j</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>M</mi> <mi>R</mi> </msub> <mo>-</mo> <mn>2</mn> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <msub> <mi>&amp;delta;</mi> <mi>R</mi> </msub> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>&amp;gamma;</mi> <mi>R</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>&amp;eta;</mi> <mi>R</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>&amp;gamma;</mi> <mi>R</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msup> <mi>&amp;eta;</mi> <mi>R</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <msup> <mi>&amp;gamma;</mi> <mi>R</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <mi>D</mi> </mrow>
<mrow> <msubsup> <mi>D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;xi;</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>cos&amp;theta;</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;xi;</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>sin&amp;theta;</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>sin&amp;xi;</mi> <mi>n</mi> <mi>R</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <mi>D</mi> </mrow> 3
<mrow> <msubsup> <mi>T</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>M</mi> <mi>T</mi> </msub> <mo>-</mo> <mn>2</mn> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <msub> <mi>&amp;delta;</mi> <mi>T</mi> </msub> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>&amp;gamma;</mi> <mi>T</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>&amp;eta;</mi> <mi>T</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>&amp;gamma;</mi> <mi>T</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msup> <mi>&amp;eta;</mi> <mi>T</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <msup> <mi>&amp;gamma;</mi> <mi>T</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>
<mrow> <msubsup> <mi>D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>D</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;xi;</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>cos&amp;theta;</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>cos&amp;xi;</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>sin&amp;theta;</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>sin&amp;xi;</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>
Wherein,It is the antenna vector of receiving terminal jth root antenna,The antenna vector of i-th antenna of transmitting terminal;γR (t),ηR(t) be receiving terminal antenna array the elevation angle and azimuth;γT(t),ηT(t) be transmitting terminal antenna array the elevation angle and orientation Angle;Be receiving terminal to the elevation angle and azimuth of n-th of scattering object cluster, be independent random variable, obey broad sense high This distribution;Transmitting terminal, to the elevation angle and azimuth of n-th of scattering object cluster, is independent random variable, obeys broad sense Gaussian Profile;Be n-th scattering object cluster to the distance vector of transmitting terminal mould it is long,It is n-th of scattering object cluster Mould to the distance vector of receiving terminal is long, is independent random variable, obeys exponential distribution.
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CN111263327B (en) * 2020-01-16 2022-06-03 合肥工业大学 Modeling method for multi-input multi-output single-ring model and simulation platform thereof
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CN114301558B (en) * 2021-12-10 2024-05-03 网络通信与安全紫金山实验室 Channel modeling method and device, electronic equipment and storage medium
CN114726464A (en) * 2022-03-07 2022-07-08 东南大学 Method for generating parameters of uplink and downlink asymmetric channel model
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