CN106656612B - A kind of approximation method for super-intensive network system traversal and rate - Google Patents

A kind of approximation method for super-intensive network system traversal and rate Download PDF

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CN106656612B
CN106656612B CN201611238107.5A CN201611238107A CN106656612B CN 106656612 B CN106656612 B CN 106656612B CN 201611238107 A CN201611238107 A CN 201611238107A CN 106656612 B CN106656612 B CN 106656612B
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base station
user
rate
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intensive network
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CN106656612A (en
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李国兵
祝志奇
吕刚明
张国梅
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Xian Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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Abstract

The invention discloses a kind of approximation methods for super-intensive network system traversal and rate, comprising the following steps: 1) obtains the traversal and rate expression formula of super-intensive network according to super-intensive network system model；2) approximate expression of super-intensive network and rate is obtained according to mathematical knowledges such as random geometries.It is different from other technologies scheme, the influence of noise is considered in approximation method of the invention, this allows for the present invention while good approximation precision under guaranteeing high s/n ratio, has approximation quality more better than other schemes in the environment of low signal-to-noise ratio.

Description

A kind of approximation method for super-intensive network system traversal and rate
Technical field:
The invention belongs to super-intensive network fields in wireless communication field, and in particular to one kind is used for super-intensive network system The approximation method of traversal and rate.
Background technique:
With the fast development of mobile Internet and Internet of Things, current cellular network has been insufficient for people increasingly The data traffic demand of growth.In order to meet the growing flow demand of people, the 5th Generation Mobile Communication System (5G's) is ground Hair has been put on schedule.The target of 5G first is that thousand times of power system capacity growths are realized, to realize this target, super-intensive network Concept be proposed out.Super-intensive network considerably increases system appearance by largely disposing low power nodes in given area Amount, it is considered to be realize the key technology that thousand times of capacity increase.
Different from traditional network, there is a large amount of base stations in super-intensive network, and wherein the density of base station reaches even super The density of user is crossed.Although the dense deployment of low power base station can be with lifting region handling capacity, it will also be brought Challenge.Such as: due to the expansion of network size, the irregular deployment of base station and base station user ratio in super-intensive network environment Change, the network optimization will become complex.This allows for the traditional scheme based on instantaneous channel state information and is no longer applicable in. Therefore, the solution based on statistical channel status information arouses great concern.In this case, rate of traversal Just become an important indicator of super-intensive network.Unfortunately, the expression formula of super-intensive network traverser and rate is also very multiple Miscellaneous, which limits its applications.Existing approximation method some has ignored noise, and some has obtained approximate bound, but It is them is carried out in the environment of super-intensive network.
In super-intensive network, the expansion of network size and the irregular deployment of base station are so that the network optimization becomes abnormal tired It is difficult.This allows for attracting attention based on the rate of traversal of statistical channel status information, but its complicated expression formula Its application of limitation.In addition, also no one is for the detailed research of this problem progress in the research of super-intensive network.
In conclusion it is necessary that traversal and rate, which are approximately studied, in super-intensive network.
Summary of the invention:
It is an object of the invention in view of the foregoing drawbacks and insufficient, propose it is a kind of for super-intensive network system traversal and The approximation method of rate, the approximation method can effectively reduce the complexity of rate of traversal calculating.
In order to achieve the above objectives, the present invention adopts the following technical scheme that realize:
A kind of approximation method for super-intensive network system traversal and rate, comprising the following steps:
1) traversal and rate expression formula of super-intensive network are obtained according to super-intensive network system model；
2) approximate expression of super-intensive network and rate is obtained according to mathematical knowledges such as random geometries.
A further improvement of the present invention lies in that step 1) includes following realization step:
101) system model is established
Consider the super-intensive network an of downlink, including N number of base station and K user, wherein full frequency multiplex between base station, respectively WithWithIndicate base station and user set, indicate base station and user with k and n, and assume in network exist include base station with User is one-to-one, and one-to-many and many-one is to a variety of connection types, it is assumed that channel path loss factor-alpha > 2, multipath fading clothes The rayleigh distributed for being 1 from mean value；
102) user terminal Signal to Interference plus Noise Ratio is calculated
Signal to Interference plus Noise Ratio when user k connection base station n are as follows:
Wherein, PknAnd dknIt is the transmission power and distance when base station n services for user k, h respectivelyknIt is base station n and user k Between channel coefficients, similarly, PijIt is transmission power when base station j services for user i, hkjAnd dkjBe base station j and user k it Between channel coefficients and distance, α be path-loss factor,It is the variance of receiving end white Gaussian noise；
103) user terminal rate is calculated
Rate when user k connection base station n are as follows:
Rkn=log2(1+SINRkn) (2)
104) computing system and rate are as follows:
105) computing system traversal and rate are as follows:
A further improvement of the present invention lies in that step 2) includes following realization step:
201) equation converts
Wherein,
202) utilize Lyapunov central-limit theorem by XknAnd YknIt is approximately normal distribution
Wherein,Represent normal distribution；
203) relationship being distributed using normal distribution and Gamma, will be approximately Gamma distribution
Wherein
Wherein, Γ represents Gamma distribution, kx, kyAnd θx, θyIt is EY respectivelyknAnd DYknForm parameter and scale parameter, EXknAnd DXknRespectively XknMean value and variance, EYknAnd DYknRespectively YknMean value and variance, and
204) the characteristic E of Gamma is utilizedXLnX=ψ (k)+ln (θ), obtains:
Wherein ψ () is digamma function；
205) according to the approximate expression of digammaIt obtains
Wherein [0,1] a ∈.
The present invention has the advantage that:
Compared with prior art, present invention utilizes number of base stations in super-intensive network is numerous, the characteristic of serious interference, because Distracter can be approximately normal distribution according to Lyapunov central-limit theorem by this, this allows for the present invention and is more suitable for surpassing The environment of dense network.Secondly, the relationship that the present invention is distributed according to normal distribution and Gamma, has obtained system traversal and rate Approximate expression, this greatly reduces the complexity of emulation.Finally, the approximation side different, of the invention from other technologies scheme The influence of noise is considered in method, this allows for the present invention while good approximation precision under guaranteeing high s/n ratio, in low letter Make an uproar has approximation quality more better than other schemes than in the environment of.
Detailed description of the invention:
Fig. 1 is the system time of the present invention and Monte Carlo simulation when user density is respectively 200,400,600UE/km3 Go through the performance comparison figure of rate.
When Fig. 2 gives user density 600UE/km3, the property of the single user rate of traversal of the present invention and Monte Carlo simulation It can comparison diagram.
Specific embodiment:
Present invention is further described in detail with reference to the accompanying drawing:
Approximation method proposed by the present invention for super-intensive network system traversal and rate, comprising the following steps:
The first step obtains the traversal and rate expression formula of super-intensive network according to system model.
Consider the super-intensive network an of downlink, including N number of base station and K user, wherein full frequency multiplex between base station.In order to Facilitate and uses respectivelyWithThe set for indicating base station and user, indicates base station and user with k and n.Assuming that in network exist include Base station is one-to-one with user, a variety of connection types such as one-to-many and many-one.
Assuming that channel path loss factor-alpha > 2, multipath fading obeys the rayleigh distributed that mean value is 1, then user k connection The Signal to Interference plus Noise Ratio when n of base station are as follows:
Wherein, PknAnd dknIt is the transmission power and distance when base station n services for user k, h respectivelyknIt is base station n and user k Between channel coefficients.Similarly, PijIt is transmission power when base station j services for user i, hkjAnd dkjBe base station j and user k it Between channel coefficients and distance, α be path-loss factor,It is the variance of receiving end white Gaussian noise；It can be with from formula (1) Obtain rate when user k connection base station n are as follows:
Rkn=log2(1+SINRkn) (2)
From formula (2) it is recognised that system and rate are as follows:
Therefore, system traversal and rate are as follows:
Second step obtains the approximate expression of super-intensive network and rate according to mathematical knowledges such as random geometries.
For simplicity, first by 1+SINRknIt is expressed as
Wherein,
After base station and the position of user determineIt is a constant, if it is assumed that PijIf being also constant, then Ykn It can be counted as the form for the Gamma stochastic variable sum that mean value and variance are different from.Although its variance and mean value are difficult It obtains, it is contemplated that the number of base station and user huge in super-intensive network, can be limited using Lyapunov center pole Reason is to handle this problem.
Lemma 1 (Lyapunov central-limit theorem): assuming that being X1,X2... it is a column mean and variance is respectively μiWith Independent random variable.Definition
If there is a certain δ > 0 Lyapunov condition is set up, that is, meets
So, when d tends to infinity, (Xi-ui)/snAnd will converge to standardized normal distribution.
According to lemma 1, so that it may by XknAnd YknIt is approximately normal distribution, it was demonstrated that as follows.
It proves:
As δ=1, formula (7) can be write as
Therefore, if formula (7) is set up at this time, so that it may by XknAnd YknIt is approximately normal distribution.Firstly,
According to the relationship of Gamma distribution variance and mean value, formula (7) can become:
Wherein, xi=| Xi-ui|。
In order to calculateFirstly the need of calculated xiProbability density function
Then it can calculate
(13), which are inserted into formula (11), to be had
To sum up, problem must be demonstrate,proved.
It therefore, can be with YknIt is approximately
Wherein,Represent normal distribution.
It is available according to the characteristic of normal distribution
Similarly, XknAlso it can be approximated to be normal distribution, i.e.,
At this point it is possible to which traversal and rate are written as
Wherein, XknAnd YknIt is all normally distributed random variable.
In random geometry, only Gamma distribution can smoothly solve logarithm expectation, therefore consider normal distribution approximation Continue to solve for Gamma distribution.
Lemma 2: when k is sufficiently large, Gamma distribution will converge to mean value and variance is respectively μ=k θ and σ2=k θ2Just State distribution, wherein k and θ is the form parameter and scale parameter of Gamma distribution respectively.
According to lemma 2, it is known that when meeting condition:
Wherein, k is sufficiently large, XknWithIt can be approximately Gamma distribution, i.e.,
Wherein
Wherein, Γ represents Gamma distribution, kx, kyAnd θx, θyIt is EY respectivelyknAnd DYknForm parameter and scale parameter, EXknAnd DXknRespectively XknMean value and variance, EYknAnd DYknRespectively YknMean value and variance, and
It proves as follows.
It proves:
In view of the network size of super-intensive network, can be calculated with the limitForm parameter, it may be assumed that
Wherein,AmidAnd AmaxIt is A respectivelyijAverage value and maximum value.
Therefore,It can be approximated to be Gamma distribution, similarlyAlso it can be approximated to be Gamma distribution.
The property E being distributed according to GammaXLnX=ψ (k)+ln (θ), available:
Wherein ψ () is digamma function.
Due to being the form of function, in order to which simplification needs to do it further approximation, i.e.,
Wherein [0,1] a ∈.
To sum up, traversal and rate can be approximately:
Consider path-loss factor α=4, base station height is 20 meters.It declines assuming that fading channel obeys the Rayleigh that mean value is 1 It falls.Every curve emulates the realization of 10000 secondary channels and is averaged.Base station and user's random placement, their density are respectively 1000SBS/km3 and 600UE/km3.Finally, taking a is 0.5.It is respectively 200,400,600UE/km3 that Fig. 1, which gives user density, When, the performance comparison of the system rate of traversal of the present invention and Monte Carlo simulation.As can be seen that for whole system, the present invention It is proposed method no matter in the case where low signal-to-noise ratio or high s/n ratio performance is all very close to standard curve.
When Fig. 2 gives user density 600UE/km3, the property of the single user rate of traversal of the present invention and Monte Carlo simulation It can comparison.Three users select at random.As can be seen that for single user, the present invention propose method no matter in low signal-to-noise ratio or Performance is all very close to standard curve in the case where high s/n ratio.
On total, it can be seen that the rate of traversal approximation method proposed in the present invention is under the premise of guaranteeing accuracy, significantly Reduce the complexity of rate of traversal calculating.

Claims (1)

1. a kind of approximation method for super-intensive network system traversal and rate, which comprises the following steps:
1) traversal and rate expression formula of super-intensive network are obtained according to super-intensive network system model；It is following to realize step:
101) system model is established
Consider the super-intensive network an of downlink, including N number of base station and K user, wherein full frequency multiplex between base station, is used respectively WithThe set for indicating base station and user, indicates base station and user with k and n, and assumes that existing in network includes base station and user It is one-to-one, the one-to-many and a variety of connection types of many-one, it is assumed that channel path loss factor-alpha > 2, multipath fading obey mean value For 1 rayleigh distributed；
102) user terminal Signal to Interference plus Noise Ratio is calculated
Signal to Interference plus Noise Ratio when user k connection base station n are as follows:
Wherein, PknAnd dknIt is the transmission power and distance when base station n services for user k, h respectivelyknIt is between base station n and user k Channel coefficients, similarly, PijIt is transmission power when base station j services for user i, hkjAnd dkjIt is between base station j and user k Channel coefficients and distance, α are path-loss factors,It is the variance of receiving end white Gaussian noise；
103) user terminal rate is calculated
Rate when user k connection base station n are as follows:
Rkn=log2(1+SINRkn) (2)
104) computing system and rate are as follows:
105) computing system traversal and rate are as follows:
Wherein, EhDesired operation is sought in expression；
2) approximate expression of super-intensive network and rate is obtained according to random geometry mathematical knowledge；Including realizing step as follows:
201) equation converts
Wherein,
202) utilize Lyapunov central-limit theorem by XknAnd YknIt is approximately normal distribution
Wherein,Represent normal distribution；
203) relationship being distributed using normal distribution and Gamma, will be approximately Gamma distribution
Wherein
Wherein, Γ represents Gamma distribution, kx, kyAnd θx, θyIt is EY respectivelyknAnd DYknForm parameter and scale parameter, EXknWith DXknRespectively XknMean value and variance, EYknAnd DYknRespectively YknMean value and variance, and
204) the characteristic E of Gamma is utilizedXLnX=ψ (k)+ln (θ), obtains:
Wherein ψ () is digamma function；
205) according to the approximate expression of digammaIt obtains
Wherein [0,1] a ∈.
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