CN107911860A - Power distribution method in NOMA systems based on price and with rate fairness ratio - Google Patents

Power distribution method in NOMA systems based on price and with rate fairness ratio Download PDF

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Publication number
CN107911860A
CN107911860A CN201711059490.2A CN201711059490A CN107911860A CN 107911860 A CN107911860 A CN 107911860A CN 201711059490 A CN201711059490 A CN 201711059490A CN 107911860 A CN107911860 A CN 107911860A
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mrow
msub
base station
power
mtd
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王正强
文陈陈
成蕖
孟宪辉
樊自甫
万晓榆
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Chongqing University of Post and Telecommunications
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/241—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account channel quality metrics, e.g. SIR, SNR, CIR, Eb/lo
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/243—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account interferences
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/267—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the information rate
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/30—TPC using constraints in the total amount of available transmission power
    • H04W52/34—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • H04W52/346—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading distributing total power among users or channels

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Quality & Reliability (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The power distribution method based on price and with rate fairness ratio in a kind of NOMA systems is claimed in the present invention, including：Initialize systematic parameter；According to the Game Relationship between base station income and user's income, the equilibrium relationships between base station price and user emission power are drawn, and the payoff maximization problem of base station is converted into the Power Control Problem of base station using the equation relation；Base station income optimization problem is converted into rate allocation again, rate allocation equivalence is converted into the optimization problem of single argument t by the method for variable replacement；Optimal single argument t is solved based on dichotomy*；According to optimal t*Value, obtains the speed and power p of each useri, and using the relation between power and power price and base station income, obtain optimal power price λ*With base station income UBS.On the premise of the communication quality between ensureing base station user and user fairness, optimal base station income can be obtained.The optimal power allocation method of the present invention not only can increase base station income and summation speed in certain area, and have obvious advantage in terms of user fairness.

Description

Power distribution method in NOMA systems based on price and with rate fairness ratio
Technical field
The invention belongs to power control techniques field in NOMA systems, is specifically based on price and with speed in NOMA systems The power distribution method of rate unfair portion.
Background technology
In NOMA systems, delivering power and pay base station price come into line number that user can be distributed base station by obtaining According to transmission.First, the interaction in NOMA systems between base station and multiple users is simulated using Stackelberg games.Base station As the leader of game, the transimission power for being preferably each user selects price；Follower of the user as game, based on base The price formulated of standing selects the price of itself by non-cooperative game.The price of base station can directly affect the transmission work(of user Rate, in order to ensure that number one maximizes, base station needs to control the power of user using rational pricing strategy.Wherein, base The income stood is the transimission power of all users and the product of its power price；The income of user is the achievable speed of the user With paying the difference between base station power distribution.If base station price is too low, number one is smaller；And base station price is too high, User can be because of extravagent price without selecting the transimission power.Therefore, it is necessary to a kind of preferable pricing strategy, ensure user and Communication quality between base station, while maximize the income of base station.
In recent years, the power distribution research in NOMA systems is just receiving more and more attention.Existing literature is retrieved It was found that pertinent literature is as follows：
Chongyang Li et al. people exist《2016 IEEE Wireless Communications Letters, Dec.2016,vol.5,no.6,pp.664-667.》On delivered entitled " Price-Based Power Allocation for The article of Non-Orthogonal Multiple Access Systems ".This article have studied base in downlink NOMA systems The power between multiple users of standing distributes, and the interactive relation between base station and multiple users is designed as Stackelberg games. The revenue function of base station is ultimately expressed as the non-convex optimization problem of power distribution between multiple users.By former problem be decoupled into three it is excellent Beggar's problem, and propose the power alternate optimization method based on price and solved, but this method do not account for user it Between fairness.
Chinliang Wang et al. exist《2016 IEEE Wireless Communications Letters, Oct.2016, vol.5, no.5, pp.532-535.》On delivered entitled " Power Allocation for a Downlink The article of Non-Orthogonal Multiple Access System ".This article have studied comprising a base station and two use The NOMA power distribution at family.The optimal closed solutions of power distribution can be obtained by Karush-Kuhn-Tucker (KKT) condition, But this method is suitable only for the situation of the access of two users, method has certain limitation.
From correlative study, in order to meet the communication quality between user and base station and maximize the income of base station, need Base station is wanted to formulate a rational power price for user so as to control the transimission power of user.The present invention is based on power and speed Between relation, the income problem of base station is first converted into rate allocation；Then each user is obtained using variable replacement Iptimum speed.A kind of therefore, it is proposed to NOMA power distribution methods with the constraint of rate fairness ratio.
The content of the invention
Present invention seek to address that above problem of the prior art.Propose a kind of communication matter between base station-user is ensured On the premise of amount and user fairness, the power distribution method of optimal base station income can be obtained.Technical scheme It is as follows：
A kind of power distribution method in NOMA systems based on price and with rate fairness ratio, it includes following step Suddenly：
1), initialize and NOMA systematic parameters are set, including the ambient noise of user's number, channel gain, base station end, speed The rate unfair portion factor, the maximum transmission power of base station；
2), according to the Game Relationship between base station income and user's income, using lower floor's problem of game of user, base is drawn The equilibrium relationships stood firm between valency and user emission power, and converted the payoff maximization problem of base station using the equation relation For the Power Control Problem of base station；
3), using the relation between power and speed, the Power Control Problem of base station is converted into rate allocation, is led to Rate allocation equivalence is converted into the optimization problem of single argument t by the method for crossing variable replacement；
4) optimization problem of single argument t, is solved based on dichotomy, and obtains optimal t*；
5), according to the optimal t of acquisition*It is worth to the speed and power p of each useri, and using power and power price and Relation between the income of base station obtains optimal power price λ*With base station income UBS。
Further, step 1) the initialization NOMA systematic parameters include：M,hi(i=1 ..., M), σ2,wi(wi= σ2/|hi|2,wM+1=0), αi,Ptol, wherein, M is user's number, hiIt is channel gain of the base station to i-th of user, and according to The mode of descending sorts | h1|2＜ | h2|2＜ ... ＜ | hM|2, σ2It is the ambient noise of base station end, wi(wi=σ2/|hi|2,wM+1= 0) be noise and channel gain business, αiIt is rate fairness scale factor, for ensureing the fairness of user, PtolIt is base station Maximum transmission power.
Further, in the step 2), closed using Stackelberg games come the interaction between anolog base station and user System, leader of the base station as game, to distribute to the power setting price of each user, therefore the income of base station is defined as：
R1:R2:...:RM=α1:α2:...:αM
And follower of the user as game, selection is so that the maximized work(of self benefits after price is made in base station Rate.User's income includes two parts, and a part is the speed realized, a part is the cost for paying base station, is expressed as
maxUi=Ri-λipi
s.t pi>=0, i=1,2 ..., M }
The speed realized wherein at i-th of user can be subject to disturbing for the user of channel gain bigger
According to the Game Relationship between above base station and user, the equation between base station price and user emission power is obtained Relation
If the power price formulated is more than λiWhen, user understands selling at exorbitant prices without buying the power, and base station is not given at this time The user distributes any power；Therefore only consider to be less than or equal to λiPower price.Using the equation relation by the receipts of base station Beneficial maximization problems is converted into the income U of the Power Control Problem of base station, i.e. base stationBSIt is expressed as：
R1:R2:...:RM=α1:α2:...:αM
4th, further, in step 3), according to the relation between power and speed, power when speed is as variable is write For
Using the relation between power and speed, the Power Control Problem of base station is converted into rate allocation
R1:R2:...:RM=α1:α2:...:αM
Rate allocation equivalence is converted into the optimization problem of single argument t by the method for variable replacement
t≥0
Further, in step 4), the object function of the optimization problem of single argument t is a monotonic decreasing function, whenWhen, optimum value t can be obtained*.Obtained using dichotomy optimal t*Value：A solution section t ∈ [a, b] on t values is obtained using scaling method first,Meet H (a) * h (b) ＜ 0.Section is once solved per computing to halve, until obtaining optimal t*Value, meets h (t*)=0.
5th, it is further, in step 5), according to the optimal t of acquisition*Value, obtains the speed R of each useri=αit*, i ∈ 1 ..., M } and powerAnd according to the pass between power and power price and base station income System, respectively obtains optimal power price λ*,With base station income UBS,
Advantages of the present invention and have the beneficial effect that：
The present invention is directed to downlink NOMA systems, there is provided a kind of power based on price and with rate fairness ratio distributes Method, it is intended to maximize the income of base station.Stackelberg games be used in simulation NOMA systems base station and multiple users it Between interaction.The income optimization of base station is realized by fixing a price, and the optimization of the income of user is distributed by power and realized.Rate fairness The introducing of ratio can well ensure user fairness, especially edge customer so that each user can realize speed. And the power distribution method can obtain most on the premise of the communication quality between ensureing base station-user and user fairness Excellent base station income.
The step of specific innovation of the invention：First, using the relation between power and speed, derive using speed as variable Power expression, the income optimization problem of base station is converted to rate allocation by equivalence；Secondly, association rate unfair portion The factor simultaneously introduces variable t, and optimal t is obtained using dichotomy*；Then, rate-allocation is obtained by variable replacement, calculates use therewith The power distribution at family, optimal power are fixed a price and the optimal income of base station；Finally, the property of the simulating, verifying NOMA power distribution methods Energy.
Brief description of the drawings
Fig. 1 is to be based on price in the NOMA systems for the offer that the present invention provides preferred embodiment and carry rate fairness ratio Power distribution method flow chart；
Fig. 2 is base station yield curve figure of the present invention when the maximum transmission power of base station increases to 20dbm from 0；
Fig. 3 is system summation rate profile of the present invention when the maximum transmission power of base station increases to 20dbm from 0；
Fig. 4 is fairness index curve diagram of the present invention when the maximum transmission power of base station increases to 20dbm from 0.
Fig. 5 is that minimum normalization user rate of the present invention when the maximum transmission power of base station increases to 20dbm from 0 is bent Line chart.
Embodiment
Below in conjunction with the attached drawing in the embodiment of the present invention, the technical solution in the embodiment of the present invention is carried out clear, detailed Carefully describe.Described embodiment is only the part of the embodiment of the present invention.
The present invention solve above-mentioned technical problem technical solution be：
The present embodiment is the power allocation scheme based on price and with rate fairness ratio, the letter between base station and user Road is modeled as hi Value M=3, it is assumed thatAnd set Put αi=1, i=1,2 ..., M.As base stations total transmission power is from 0dB-20dB changes, assessment base is carried out respectively using emulation The performance stood in terms of income, system summation speed, fairness index and minimum normalizing rate.Wherein Fig. 2 and Fig. 3 is that base station is received The performance curve variation diagram of benefit and system summation speed；Fig. 4 and Fig. 5 is fairness index and the property of minimum normalization user rate Energy curvilinear motion figure, for detecting user fairness performance.
The first step, initializes and sets each systematic parameter：M,hi(i=1 ..., M), σ2,wi(wi=σ2/|hi|2,wM+1 =0), αi,Ptol
Wherein, M is user's number, hiIt is channel gain of the base station to i-th of user, and sorts in the way of descending |h1|2＜ | h2|2＜ ... ＜ | hM|2, σ2It is the ambient noise of base station end, wi(wi=σ2/|hi|2,wM+1=0) it is noise and channel The business of gain, αiIt is rate fairness scale factor, for ensureing the fairness of user's (especially edge customer), PtolIt is base station Maximum transmission power.
Second step, using Stackelberg games come the interactive relation between anolog base station and user, base station is as game Leader, to distribute to the power setting price of each user, therefore the income of base station is defined as：
R1:R2:...:RM=α1:α2:...:αM
And follower of the user as game, selection is so that the maximized work(of self benefits after price is made in base station Rate.User's income includes two parts, and a part is the speed realized, a part is the cost for paying base station, is expressed as
maxUi=Ri-λipi
s.t pi>=0, i=1,2 ..., M }
The speed realized wherein at i-th of user can be subject to disturbing for the user of channel gain bigger
According to the Game Relationship between above base station and user, the equation between base station price and user emission power is obtained Relation
If the power price formulated is more than λiWhen, user understands selling at exorbitant prices without buying the power, and base station is not given at this time The user distributes any power；Therefore only consider to be less than or equal to λiPower price.Using the equation relation by the receipts of base station Beneficial maximization problems is converted into the income U of the Power Control Problem of base station, i.e. base stationBSIt is expressed as：
R1:R2:...:RM=α1:α2:...:αM
3rd step：According to the relation between power and speed, power when speed is as variable is written as
Using the relation between power and speed, the Power Control Problem of base station is converted into rate allocation
R1:R2:...:RM=α1:α2:...:αM
Rate allocation equivalence is converted into the optimization problem of single argument t by the method for variable replacement
t≥0
Power expression using speed as variable derives as follows：
It can be obtained according to the relation between speed and power：So：
Obtain:
Obtain:
…
Derived, can be obtained according to recursion method：
4th step：The object function of the optimization problem of single argument t is a monotonic decreasing function, whenWhen, optimal value t can be obtained*.Obtained first using scaling method One solution section t ∈ [a, b] on t values,Meet h (a) * h (b) ＜ 0.Per computing once Solution section halves, until obtaining optimal t*Value, meets h (t*)=0.
5th step：According to the optimal t of acquisition*Value, obtains the speed R of each useri=αit*, i ∈ { 1 ..., M } and work( RateAnd according to the relation between power and power price and base station income, respectively obtain power Price λ*,With base station income UBS,
In the present embodiment, power distribution algorithm and tradition based on NOMA are constrained with rate fairness ratio by what is carried The power alternative optimization algorithm based on price contrasted in terms of base station income and the total speed two of system.Fig. 2 gives The base station yield curve figure changed with base stations total transmission power 0dB-20dB；Fig. 3 is become with base stations total transmission power 0dB-20dB The system summation rate profile of change.According to Fig. 2 and Fig. 3, the base station yield curve and system of two kinds of power distribution methods Summation rate curve is all with P/ σ2Increase and rise.As P/ σ2When smaller, the base of the power alternate optimization method based on price Income of standing and summation speed bigger；And when large, base station income and the summation speed higher of power distribution method of the present invention.This It is because the power alternate optimization method based on price is the method for a suboptimum and each user selfishly maximizes itself Income, causes performance to be lost and in the inequitable resource allocation of user's generation in high s/n ratio region；And the power of the present invention Distribution method is all optimal method in whole signal-to-noise ratio region.
Fig. 4 is the fairness index curve map changed with base stations total transmission power 0dB-20dB.Fairness index is defined ForAs seen from the figure, optimal power allocation method of the invention has obvious excellent in terms of user fairness Gesture.Fig. 5 is the minimum normalization user rate curve map with base stations total transmission power 0dB-20dB changes.Minimum normalization user Speed is defined asWherein { α1,α2,...,αMIt is one group of value being predefined.As seen from the figure, originally The performance of the minimum normalization user rate of invention is substantially better than the power alternate optimization method based on price.
Optimal power allocation method is put forward according to Fig. 2, Fig. 3, Fig. 4, Fig. 5 base station receipts are improved in high s/n ratio region Benefit and system summation speed, and there is obvious advantage in terms of fairness index and minimum normalization.This method obtains The optimal power price and power distribution strategies, institute's extracting method of base station can efficiently solve the money based on price in NOMA systems The relevant issues such as source distribution.
The above embodiment is interpreted as being merely to illustrate the present invention rather than limits the scope of the invention. After the content for having read the record of the present invention, technical staff can make various changes or modifications the present invention, these equivalent changes Change and modification equally falls into the scope of the claims in the present invention.

Claims (6)

  1. A kind of 1. power distribution method in NOMA systems based on price and with rate fairness ratio, it is characterised in that including Following steps：
    1), initialize and NOMA systematic parameters are set, including the ambient noise of user's number, channel gain, base station end, speed are public Flat scale factor, the maximum transmission power of base station；
    2), according to the Game Relationship between base station income and user's income, using lower floor's problem of game of user, show that base station is determined Equilibrium relationships between valency and user emission power, and the payoff maximization problem of base station is converted into base using the equation relation The Power Control Problem stood；
    3), using the relation between power and speed, the Power Control Problem of base station is converted into rate allocation, passes through change Rate allocation equivalence is converted into the optimization problem of single argument t by the method that amount is replaced；
    4) optimization problem of single argument t is solved based on dichotomy, and obtains optimal t*；
    5) according to the optimal t of acquisition*It is worth to the speed and power p of each useri, and utilize power and power price and base station Relation between income obtains optimal power price λ*With base station income UBS。
  2. 2. the power distribution method in NOMA systems according to claim 1 based on price and with rate fairness ratio, It is characterized in that, step 1) the initialization NOMA systematic parameters include：M,hi(i=1 ..., M), σ2,wi(wi=σ2/|hi |2,wM+1=0), αi,Ptol, wherein, M is user's number, hiIt is channel gain of the base station to i-th of user, and according to descending Mode sort | h1|2＜ | h2|2＜ ... ＜ | hM|2, σ2It is the ambient noise of base station end, wi(wi=σ2/|hi|2,wM+1=0) it is The business of noise and channel gain, αiIt is rate fairness scale factor, for ensureing the fairness of user, PtolIt is the maximum of base station Transimission power.
  3. 3. the power distribution method in NOMA systems according to claim 2 based on price and with rate fairness ratio, It is characterized in that, in the step 2), using Stackelberg games come the interactive relation between anolog base station and user, base The leader to stand as game, to distribute to the power setting price of each user, therefore the income of base station is defined as：
    <mrow> <msub> <mi>U</mi> <mrow> <mi>B</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>&amp;GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
    R1:R2:...:RM=α1:α2:...:αM
    And follower of the user as game, selection is so that the maximized power of self benefits after price is made in base station. User's income includes two parts, and a part is the speed realized, a part is the cost for paying base station, is expressed as
    maxUi=Ri-λipi
    s.t pi>=0, i=1,2 ..., M }
    The speed realized wherein at i-th of user can be subject to disturbing for the user of channel gain bigger
    <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow> <mrow> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> <mo>}</mo> </mrow>
    According to the Game Relationship between above base station and user, the equilibrium relationships between base station price and user emission power are obtained
    <mrow> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>+</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    If the power price formulated is more than λiWhen, user understands selling at exorbitant prices without buying the power, and the user is not given in base station at this time Distribute any power；Therefore only consider to be less than or equal to λiPower price, using the equation relation by the Income Maximum of base station Change problem is converted into the income U of the Power Control Problem of base station, i.e. base stationBSIt is expressed as：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mrow> <mi>B</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mfrac> <mrow> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow> <mrow> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>M</mi> </msubsup> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>:</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>:</mo> <mn>...</mn> <mo>:</mo> <msub> <mi>R</mi> <mi>M</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <mo>:</mo> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>:</mo> <mn>...</mn> <mo>:</mo> <msub> <mi>&amp;alpha;</mi> <mi>M</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>
  4. 4. the power distribution method in NOMA systems according to claim 3 based on price and with rate fairness ratio, It is characterized in that, in step 3), according to the relation between power and speed, power when speed is as variable is written as
    <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>M</mi> </munderover> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>M</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>w</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mi>e</mi> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>j</mi> </munderover> <msub> <mi>R</mi> <mi>k</mi> </msub> </mrow> </msup> <mo>-</mo> <msub> <mi>w</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> <mo>}</mo> </mrow>
    Using the relation between power and speed, the Power Control Problem of base station is converted into rate allocation
    <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mfrac> <mn>1</mn> <msup> <mi>e</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> </msup> </mfrac> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>w</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mi>e</mi> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>j</mi> </munderover> <msub> <mi>R</mi> <mi>k</mi> </msub> </mrow> </msup> <mo>-</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
    R1:R2:...:RM=α1:α2:...:αM
    Rate allocation equivalence is converted into the optimization problem of single argument t by the method for variable replacement
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>min</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mfrac> <mn>1</mn> <msup> <mi>e</mi> <mrow> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> <mi>t</mi> </mrow> </msup> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>w</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mi>e</mi> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>j</mi> </munderover> <msub> <mi>&amp;alpha;</mi> <mi>k</mi> </msub> <mi>t</mi> </mrow> </msup> <mo>-</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&amp;GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>
  5. 5. the power distribution method in NOMA systems according to claim 4 based on price and with rate fairness ratio, It is characterized in that, in step 4), the object function of the optimization problem of single argument t is a monotonic decreasing function, whenWhen, optimum value t can be obtained*.Obtained using dichotomy optimal Value：A solution section t ∈ [a, b] on t values is obtained using scaling method first,Meet h (a) * h (b) ＜ 0.Section is once solved per computing to halve, until obtaining optimal t*Value, meets h (t*)=0.
  6. 6. the power distribution method in NOMA systems according to claim 5 based on price and with rate fairness ratio, It is characterized in that, in step 5), according to the optimal t of acquisition*Value, obtains the speed R of each useri=αit*, i ∈ 1 ..., M } and powerAnd according to the relation between power and power price and base station income, obtain respectively To optimal power price λ*,With base station income UBS,
CN201711059490.2A 2017-11-01 2017-11-01 Power distribution method in NOMA systems based on price and with rate fairness ratio Pending CN107911860A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109636190A (en) * 2018-12-13 2019-04-16 中国联合网络通信集团有限公司 The acquisition methods and device of base station operation information
CN111315020A (en) * 2020-02-12 2020-06-19 电子科技大学 Power distribution method based on fairness and optimal spectrum efficiency
CN112533275A (en) * 2020-11-13 2021-03-19 北京科技大学 Power control and interference pricing method and device for renewable energy heterogeneous network

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109636190A (en) * 2018-12-13 2019-04-16 中国联合网络通信集团有限公司 The acquisition methods and device of base station operation information
CN109636190B (en) * 2018-12-13 2020-11-17 中国联合网络通信集团有限公司 Method and device for acquiring base station operation information
CN111315020A (en) * 2020-02-12 2020-06-19 电子科技大学 Power distribution method based on fairness and optimal spectrum efficiency
CN111315020B (en) * 2020-02-12 2022-04-19 电子科技大学 Power distribution method based on fairness and optimal spectrum efficiency
CN112533275A (en) * 2020-11-13 2021-03-19 北京科技大学 Power control and interference pricing method and device for renewable energy heterogeneous network

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