CN107371213A - Based on the joint Power control under double-deck game framework and the control method of source node selection - Google Patents

Based on the joint Power control under double-deck game framework and the control method of source node selection Download PDF

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CN107371213A
CN107371213A CN201710359000.4A CN201710359000A CN107371213A CN 107371213 A CN107371213 A CN 107371213A CN 201710359000 A CN201710359000 A CN 201710359000A CN 107371213 A CN107371213 A CN 107371213A
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node
source node
selection
via node
subgame
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周彦果
张海林
周韬
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Xidian University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W40/00—Communication routing or communication path finding
    • H04W40/02—Communication route or path selection, e.g. power-based or shortest path routing
    • H04W40/04—Communication route or path selection, e.g. power-based or shortest path routing based on wireless node resources
    • H04W40/08—Communication route or path selection, e.g. power-based or shortest path routing based on wireless node resources based on transmission power
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H04L5/0032—Distributed allocation, i.e. involving a plurality of allocating devices, each making partial allocation
    • H04L5/0035—Resource allocation in a cooperative multipoint environment
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/06—Testing, supervising or monitoring using simulated traffic
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W40/00—Communication routing or communication path finding
    • H04W40/02—Communication route or path selection, e.g. power-based or shortest path routing
    • H04W40/22—Communication route or path selection, e.g. power-based or shortest path routing using selective relaying for reaching a BTS [Base Transceiver Station] or an access point
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

In Multi-source multi-relay collaborative network, to avoid assisting excessive interference between the via node of same source node and realizing the maximization of utility of via node, it is proposed that a kind of control method of joint Power control and source node selection based under double-deck game framework.The evolution subgame alternating iteration that this method is selected by the non-cooperation subgame of via node Power Control and source node, reasonable selection of the via node to source node is realized while being disturbed between suppressing via node, and demonstrates the unique existence of double-deck game Nash Equilibrium.The double-deck game distributed method that simulation result shows to be proposed can make system convergence to Nash Equilibrium.

Description

Based on the joint Power control and the control of source node selection under double-deck game framework Method
Technical field
The invention belongs to wireless network communication technical field, and in particular to a kind of joint work(based under double-deck game framework Rate controls and the control method of source node selection.
Background technology
Wireless cooperative relay technology because its can strengthening system anti-fading ability, improve transmission rate and simultaneously expand covering model Enclose, and be widely used in wireless network.Rational relay selection and Power Control can be while service quality be ensured Minimize transmit power.Therefore, relay selection and Power Control are always the hot issue in wireless cooperative network research.Example Such as：Document [Maric I and Yates R, " Bandwidth and power allocation for cooperative Strategies in Gaussian relay networks, " in IEEE Transactions on Information Theory, 2010, vol.56, no.4, pp.1880-1889] in propose a kind of joint applied to amplification forward collaboration network Relay selection and power allocation scheme.The program determines optimal relaying subset and realizes the optimal of relaying using water-filling algorithm Power distribution.Document [Wu Di, Zhu Gang, Zhao Dong-mei, et al, " Cross-layer design of joint Relay selection and power control scheme in relay-based multi-cell networks, " In IEEE Wireless Communications and Networking Conference, Quintana Roo, 2011, Pp. 251-256] relay selection and Power Control have been considered in relay auxiliary cellular network, it is proposed that and a kind of cross-layer is set Meter scheme is to increase average network capacity and suppress to disturb.Effective tool of the game theory as research network resource allocation problem, Have been used for solving the problems such as trunk node selection and Power Control of wireless cooperative network.In Multi-source multi-relay collaborative network In, document [Xiao Hai-lin and Ouyang Shan. " Power control game in multisource multirelay cooperative communication systems with a quality-of-service Constraint, " in IEEE Transactions on Intelligent Transportation Systems, 2015, Vol.16, no.l, pp.41-50] propose based on the power control algorithm of game theory to minimize general power.The algorithm is subtracting Systematic function is improved while few energy expenditure.Document [Baidas M W and MacKenzie A B, " An auction mechanism for power allocation in multi-source multi-relay cooperative Wireless networks, " in IEEE Transactions on Wireless Communications, 2012, Vol.11, no.9, pp.3250-3260] propose it is a kind of upwards asked price clock auction algorithm effectively to control multi-source more in After the via node transmit power of collaborative network.A branch of the evolutionary Game as game theory, can be used for network dynamic and wins Play chess the modeling of problem.In amplification forward collaboration network, document [Liu Ling-ya, Hua Cun-qing, Chen Cai- Lian, et al, " Semidistributed relay selection and power allocation for outage Minimization in cooperative relaying networks, " in IEEE Transactions on Vehicular Technology, 2017, vol.66, no.l, pp.295-305] using evolutionary game theory carry out relay selection With power distribution to reduce the outage probability of receiving terminal.In relay auxiliary cellular network, evolutionary Game is made to solve endless Dynamic trunking select permeability under the conditions of full information.Optimal transmit power will not only be selected by possessing the via node of cooperation resource, Also source node is reasonably selected with maximum utility.In cooperative cognitive junction network, document [Zhang Zhao-wei and Zhang Hai-lin, " A variable-population evolutionary game model for resource Allocation in cooperative cognitive relay networks, " in IEEE Communications Letters, 2013, vol.17, no.2, pp.361-364] using evolutionary game theory solve via node source node selection Problem.
Currently with the resource allocation problem multi-focus in game theory solution cordless communication network in Static Game, it is impossible to very The state issues of network during good prediction node long-term evolution.In above-mentioned document, entered using traditional non-cooperative game theory The scheme of row power injection control, it is impossible to realize dynamic trunk node selection.And carry out relaying choosing using evolutionary game theory The scheme selected can not realize the optimal power dynamic control problem of node.Describe to manage herein by dynamic modeling is carried out to system Property network node state change with time process, traditional non-cooperative game and evolutionary game theory are combined applied to more It is determined that also achieving the reasonable selection of source node while via node optimal transmit power in the multi-relay collaborative network of source.
The content of the invention
In view of the foregoing defects the prior art has, it is an object of the invention to provide one kind to be based under double-deck game framework Joint Power control and source node selection control method.The control method is combined using double-deck game framework to via node Power Control and source node select permeability are modeled, by the distributed algorithm of double-deck game, it is determined that via node most The reasonable selection of source node is also achieved while excellent transmit power.
To achieve the above object, the technical solution adopted by the present invention：This is based on the joint Power control under double-deck game framework System and the control method of source node selection, it is characterised in that：The control method is two layers：First layer is entered using non-cooperation subgame The control of row via node transmit power, the second layer carry out the selection of source node using evolution subgame, and double-deck game is distributed Algorithm is finally made system reach double-deck game and received by the alternately control of via node transmit power and the selection of source node Assorted equilibrium, realize the reasonable distribution of Multi-source multi-relay collaborative network resource.
The first layer subgame is the non-cooperation subgame of via node Power Control, is assisting same source node The non-cooperation subgame of Power Control is formd in set of relay nodes, between via node, via node Power Control is most Optimization problem represents as follows：
In formula,For via node R maximum transmit power, uRFor the net utility function of via node；For same Each via node of assistance source node in signal slot, the vector that Nash Equilibrium is made up of their optimal transmit power, With representing, wherein in when being equilibrium state in addition to via node, the vector of other optimal transmit powers compositions of via node；Pass through Successive ignition, this non-cooperation subgame are finally reached Nash Equilibrium, i.e., under the limitation of maximum transmit power, each via node can To obtain unique optimal transmit power.
The second layer subgame uses evolution subgame, and via node can be modeled as developing to the select permeability of source node Subgame, in moment t, it is n that the via node number scale of source node S is assisted in selectionS(t), the sum of System relays node isSelection assists the via node proportion of source node S to be represented by xS(t)=nS(t)/K, vector x (t)=[x1 (t), L, xM(t)] it is used for representing the state that t trunk node selection assists source node；
In the evolution subgame of trunk node selection source node, replica locating represents as follows：
In formula, δ is evolution step-length, can be used for controlling the evolution speed of trunk node selection source node；
Define uS(t) it is set of relay nodes ΓSAverage net utility function,Represent all relaying sections in whole system The average net utility function of point, then uS(t) andIt is expressed as：
In formula, S, l ∈ Ф, by the iteration that develops several times, evolution subgame eventually converges to true by following equations group Fixed Evolutionarily Stable Strategy：
The double-deck game distributed algorithm is the iteration of alternately two kinds of subgames of via node, finally reaches system To Nash Equilibrium, it is expressed as follows：
(1) during t=0, each via node random selection transmit power and the source node assisted；
(2) selection assists all via nodes of same source node S to proceed by the non-cooperation subgame of Power Control；
(3) in t, via node R optimal transmit power is obtained by formula (16)
IfMake t=t+1, repeat step (3)；
Otherwise, Power Control subgame terminates to go to step (4)；
(4) determined to assist all via nodes of source node S according to step (3), optimal transmit power vector nowVia node proceeds by the evolution subgame of source node selection；
(5) for set of relay nodes ΓSAverage net utility function uS(t)：
IfIt is dominating stragegy that then source node S is assisted in selection, and via node keeps the selection of this source node constant；
IfIt is inferior position strategy that then source node S is assisted in selection, and via node is abandoned assisting the source node, and with general RateSelect another source node Q so that
(6) judge whether to reach Evolutionary Equilibrium of the via node to source node select permeability：
IfSub-carrier selection evolution subgame terminates；
Otherwise, t=t+1, return to step (5) are made；
(7) judge whether system reaches the Nash Equilibrium of whole double-deck game：
IfGo to step (2)；
Otherwise, step (8) is gone to；
(8) Nash Equilibrium of double-deck game is reached, double-deck game terminates.
Using the beneficial effect of above-mentioned technical proposal：The present invention is based on the joint Power control under double-deck game framework and source The control method of node selection, it is for two kinds of game behaviors present in Multi-source multi-relay collaborative network：Between via node Power Control game and source node selection evolutionary Game, non-cooperation subgame and evolution subgame is respectively adopted come in carrying out After the control of node transmit power and the selection of source node, and propose under double-deck game framework a kind of joint Power control and The distributed algorithm of source node selection.
The non-cooperation subgame of via node Power Control
Non-cooperative game emphasizes personal financing and personal optimizing decision, and the Nash Equilibrium as non-cooperative game solution can guarantee that In the case where other participant's effectiveness are not lowered, the effectiveness of participant oneself is maximized.Assisting same source node The non-cooperation subgame of Power Control is formd in set of relay nodes, between via node.Therefore, via node Power Control Optimization problem can represent as follows：
In formula,For via node R maximum transmit power.Receiving for the non-cooperation subgame of Power Control is proved in theorem 1 Assorted balanced be present and unique.
Theorem 1. non-cooperative game G=[Ψ, { PR, { uR, Ψ be participate in game via node set, { PRIt is ginseng With the policy space of the via node transmit power of game, uRFor the net utility function of via node.If to all R ∈ Ψ, Have
1.{PRIt is that a non-NULL on Euclidean space compacts convex subset.
2.uRIn PROn be continuous and recessed.
So there is Nash Equilibrium and unique in the game.
Prove：Appointing takes R ∈ Ψ, via node R a policy space to be presentThe policy space includes relaying and saved Point R forwards all transmit powers that may be chosen during source node identification.Appoint and take PR∈{PR, it can be seen that via node R transmission Power space { PRIt is non-NULL compact subset.
Defined according to convex set, give q1, q2∈{PR, then forHave：
Two formulas are added, can be obtained
Therefore, { P can be obtainedRIt is convex set.
To uRFirst derivative and second dervative is asked to obtain respectively：
In formula,
Due toVia node R net utility function uRIt is on PRConcave function.Therefore the subgame is assorted equal in the presence of receiving Weighing apparatus and only
One, theorem 1 must be demonstrate,proved.
By formula (8), further obtain
Formula (9) is made to be equal to 0, gained equation is represented by transmit power P selected by via node RRQuadratic equation：
In formula,
It is ρ that we, which define via node R and assist the income cost ratio of source node S,S, R, the threshold value of selection assistance source node S For
According to the property of quadratic equation, the necessary condition that formula (10) has solution is B2-4AC≥0.Therefore income cost ratio ρS, RIt should meet：
It can be obtained by formula (12), work as ρS, RMore than threshold valueWhen, via node R can select to assist source node S.Full Under conditions of sufficient formula (12), the quadratic equation of solution formula (10), normal solution is taken, is obtained：
Limited in view of the transmit power of via node, via node R transmit power when can obtain equilibrium state
Each via node for assisting source node S in same signal slot, Nash Equilibrium is by the optimal of them The vector of transmit power composition, is usedRepresent, whereinΓ when being equilibrium stateSIn in addition to via node R, other relayings The vector of the optimal transmit power composition of node.By successive ignition, this non-cooperation subgame is finally reached Nash Equilibrium, i.e., most Under big transmit power limitation, each via node can obtain unique optimal transmit power.At that point, ΓSIn set All via nodes all can not in the case where other via node transmit powers are constant, by unilaterally lifted transmit power come Increase the net utility of itself.
The evolution subgame of trunk node selection source node
In the timing of via node transmit power one, different source nodes is assisted to bring different incomes to via node. Therefore, via node can select the source node of maximum return can be brought to be assisted to it.Via node is by reasonably selecting Source node maximises itself effectiveness, it is achieved thereby that effective utilization of Internet resources.
Via node can be modeled as evolution subgame to the select permeability of source node.In moment t, source node S is assisted in selection Via node number scale be nS(t), the sum of System relays node isThe via node institute of source node S is assisted in selection Accounting example is represented by xS(t)=nS(t)/K.Vector x (t)=[x1(t), L, xM(t)] it is used for representing that t via node selects Select the state for assisting source node.
In the evolution subgame of trunk node selection source node, replica locating represents as follows：
In formula, δ is evolution step-length, can be used for controlling the evolution speed of trunk node selection source node.
Define uS(t) it is set of relay nodes ΓSAverage net utility function,Represent all relaying sections in whole system The average net utility function of point.Then uS(t) andIt is expressed as：
In formula, S, l ∈ Φ.By the iteration that develops several times, evolution subgame eventually converges to true by following equations group Fixed Evolutionarily Stable Strategy：
This dynamical system existence anduniquess Evolutionary Equilibrium solution x is proved in theorem 2*(t)=[x1 *(t), L, xM *(t)]。
2. 1 dynamical system f (x of theoremS(t)), for arbitrary S ∈ Φ,If T at any time, xS(t) be [0,..) in the range of measurable function, and function f (xS(t)) to xS(t) first derivative is to connect It is continuous, then this dynamical system existence and unique solution.
Prove：Formula (16) is substituted into f (xS(t)), can obtain：
Any time t, function f (xS(t)) to xS(t) first derivative is continuous.Due to xS(t) be [0, ∞) scope Interior measurable function, then f (xS(t) it is also) measurable function in this section.For convenience of description, order：
Formula (19) is substituted into formula (18), had
For arbitraryAssuming thatThen have：
We are constructed fuction g (xS(t))：
g(xS(t))=F1(xS(t))-KH0xS(t) (22)
In formula, H0=max (ui).WillSubstitute into g (xS(t)), then have：
To function g (xS(t)) derivation, can obtain：
Therefore, function g (xS(t)) with variable xS(t) increase and monotone decreasing, therefore can obtainWith reference to Formula (23) can obtain：
To arbitrary l ∈ Φ, can obtain：
In formula,
By formula (25) and formula (26), can obtain：
Therefore, function f (xS(t) Lipschitz conditions) are met, this dynamical system existence and unique solution, theorem 2 must be demonstrate,proved.
In the case where via node primarily determines that transmit power by Power Control subgame, based on evolutionary game theory, Selection source node is assisted again.When trunk node selection assists the u of source node SS(t) it is more thanWhen, this selection can be recognized To be dominating stragegy, next moment selection assists the via node quantity of source node S to increase；Conversely, this selection is considered as It is inferior position strategy, next moment selection assists the via node quantity of source node S to reduce.Evolution subgame is by repeatedly changing In generation, may finally reach evolutionarily stable state, i.e., the net utility function of each via node can obtain unique optimal solution.Source The Evolutionarily Stable Strategy of node selection assists the state vector x of source node with trunk node selection*(t)=[x1 *(t), L, xM * (t)] represent.Now, the via node for assisting the average net utility of via node of same source node to be equal to whole system is averagely net Effectiveness, all via nodes no longer change the source node of assistance.
Double-deck game distributed algorithm
Above two subgame is put into double-deck game framework, it is proposed that a kind of double-deck game distributed algorithm.The algorithm The alternately iteration of two kinds of subgames of via node, finally makes system reach Nash Equilibrium.
Brief description of the drawings
The specific embodiment of the present invention is described in further detail below in conjunction with the accompanying drawings.
Fig. 1 is Multi-source multi-relay collaborating network system model；
Fig. 2 is via node transmit power state；
Fig. 3 is that the source node of via node selects state；
Fig. 4 contrasts for via node net utility.
Embodiment
As shown in figure 1, there is M source node in Multi-source multi-relay collaborative network, S ∈ Φ@{ 1, L, M }, K relaying are denoted as Node, R ∈ Γ@{ 1, L, K } and N number of destination node are denoted as, are denoted as D ∈ Ω@{ 1, L, N }.It is right therewith that each source node has The destination node answered.Channel gain G between node i and node jI, jRepresent.Information transfer each time, via node can only select Select and assist a source node, and the transmit power of via node is no more than maximum transmit power.
In the present invention, via node uses amplification forwarding agreement.Destination node D, which is received, comes from the direct of source node S Link signal to noise ratio is designated as γS, D, the repeated link signal to noise ratio of the repeated node R of source node S to destination node D is designated as γS, R, D：
In formula, PSRepresent the transmit power of source node S, PRRepresent via node R transmit power, σ2Represent additive Gaussian The variance of white noise.The transmission rate that destination node D is obtained using maximum-ratio combing is represented by：
In formula, W represents transmission bandwidth, rSRepresent the set of relay nodes of assistance source node S.Destination node D saves except relaying The speed R that point R is obtained outside assistingD-RRepresent：
To ensure the fairness between via node, the contribution and reference lifted according to via node to source node speed Sharply methods, construct via node R utility function rR：
rR=αS(RD-RD-R) (31)
In formula, αSRepresent the income for assisting the via node R per unit speed of source node S to be obtained.By formula (29) and (30) formula (31) is substituted into, is had：
Aggregative formula (28) and (32) are as can be seen that via node R utility function rRThe not only transmit power P with itselfR It is relevant, also with set of relay nodes ΓSIn other via nodes transmit power it is relevant.The utility function of via node is with hair Send the increase of power and monotonic increase, each via node have the motivation for selecting maximum transmit power.This will necessarily be to other Via node interferes, so as to reduce network performance.To solve this problem, a kind of pricing mechanism is introduced, in via node The cost paid required for it is formulated while benefit, to realize fair allocat of the resource between via node.Via node is imitated Difference with function and cost function is exactly net utility function uR：
uR=rR-cRPR (33)
In formula, cRThe cost paid by via node R per unit of powers.
This is based on the joint Power control under double-deck game framework and the control method of source node selection, it is characterised in that： The control method is two layers：First layer carries out the control of via node transmit power using non-cooperation subgame, and the second layer uses Evolution subgame carries out the selection of source node, the control that double-deck game distributed AC servo system passes through alternately via node transmit power The selection of system and source node, finally makes system reach double-deck game Nash Equilibrium, realizes Multi-source multi-relay collaborative network resource Reasonable distribution.
The non-cooperation subgame of the via node Power Control of the first layer, assisting the relaying section of same source node The non-cooperation subgame of Power Control is formd in point set, between via node, the optimization of via node Power Control is asked Topic represents as follows：
In formula,For via node R maximum transmit power, uRFor the net utility function of via node；For same Each via node of assistance source node in signal slot, the vector that Nash Equilibrium is made up of their optimal transmit power, With representing, wherein in when being equilibrium state in addition to via node, the vector of other optimal transmit powers compositions of via node；Pass through Successive ignition, this non-cooperation subgame are finally reached Nash Equilibrium, i.e., under the limitation of maximum transmit power, each via node can To obtain unique optimal transmit power.
The second layer uses evolution subgame, and via node can be modeled as sub win of developing to the select permeability of source node Play chess, in moment t, it is n that the via node number scale of source node S is assisted in selectionS(t), the sum of System relays node is Selection assists the via node proportion of source node S to be represented by xS(t)=nS(t)/K, vector x (t)=[x1(t), L, xM (t)] it is used for representing the state that t moment trunk node selection assists source node；
In the evolution subgame of trunk node selection source node, replica locating represents as follows：
In formula, δ is the step K that develops, and can be used for controlling the evolution speed of trunk node selection source node；
Define uS(t) it is set of relay nodes ΓSAverage net utility function,Represent all relaying sections in whole system The average net utility function of point, then uS(t) andIt is expressed as：
In formula, S, l ∈ Φ, by the iteration that develops several times, evolution subgame eventually converges to true by following equations group Fixed Evolutionarily Stable Strategy：
The double-deck game distributed AC servo system is the iteration of alternately two kinds of subgames of via node, finally reaches system To Nash Equilibrium, it is expressed as follows：
(1) during t=0, each via node random selection transmit power and the source node assisted；
(2) selection assists all via nodes of same source node S to proceed by the non-cooperation subgame of Power Control；
(3) in t, via node R optimal transmit power is obtained by formula (14)
IfMake t=t+1, repeat step (3)；
Otherwise, Power Control subgame terminates to go to step (4)；
(4) determined to assist all via nodes of source node S according to step (3), optimal transmit power vector nowVia node proceeds by the evolution subgame of source node selection；
(5) for set of relay nodes ΓSAverage net utility function uS(t)：
IfIt is dominating stragegy that then source node S is assisted in selection, and via node keeps the selection of this source node constant；
IfIt is inferior position strategy that then source node S is assisted in selection, and via node is abandoned assisting the source node, and with general RateSelect another source node Q so that
(6) judge whether to reach Evolutionary Equilibrium of the via node to source node select permeability：
IfSub-carrier selection evolution subgame terminates；
Otherwise, t=t+1, return to step (5) are made；
(7) judge whether system reaches the Nash Equilibrium of whole double-deck game：
IfGo to step (2)；
Otherwise, step (8) is gone to；
(8) Nash Equilibrium of double-deck game is reached, double-deck game terminates.
By the validity of the double-deck game distributed algorithm proposed to above method simulating, verifying.Simulation parameter is set Put as follows：Source node number M=2, via node number K=100, destination node number N=2, transmission bandwidth W=1, assist source node S The income α that is obtained of via node per unit speedS=20, the cost c that via node R per unit of powers are paidR=0.1, The transmit power P of source node SS=1, source node S to destination node D direct link channel gains GS, D=1, source node S is in After the channel gain G of node RS, RThe channel gain G of=1, via node R to destination node DR, D=1, additive white Gaussian noise Variances sigma2=1.Randomly select via node 1 and via node 51 has carried out the analysis of transmit power and net utility.
When Fig. 2 is described using double-deck game playing algorithm, the transmit power of via node 1 and via node 51 is with non-cooperation The change of game iterations.In the case where via node randomly chooses initial transmission power, by iteration several times, relaying The transmit power of node finally converges to Nash Equilibrium, no longer changes, so as to demonstrate the receipts of the non-cooperation subgame of Power Control Holding back property.
When Fig. 3 is given using double-deck game playing algorithm, selection assists the via node quantity of each source node with iteration time Several change, it is shown that the source node selection state of via node after each iteration.Under original state, there are 10 via node choosings Select and assist source node 1, there are 90 trunk node selections to assist source node 2.Due to assisting the relaying section of source node 1 and source node 2 The income that point per unit speed is obtained is identical, by 4 random evolution iteration, respectively has 50 trunk node selections to assist source section Point 1 and source node 2, i.e. the evolution subgame of trunk node selection source node reach Evolutionary Equilibrium state.
It can be seen that the net utility of via node 1 and via node 51 with the change of iterations from Fig. 4 simulation curve Trend.The change of via node net utility can be divided into four parts, the trunk node selection source node of each section corresponding diagram 3 An iteration.In via node random selection initial transmission power and in the case of assisting source node, by iteration several times, in Net utility after node finally converges to Nash Equilibrium, no longer changes.It is as can be seen that rich by non-cooperation subgame and the son that develops The alternating iteration played chess, finally makes whole system converge to Nash Equilibrium.
The present invention is by the resource allocation in Multi-source multi-relay collaborative network, using double-deck game framework to via node Joint Power is controlled and source node select permeability is modeled.It the model describe the non-conjunction of transmit power between via node Make the evolutionary Game of game and source node selection.Demonstrate double-deck game equilibrium state to exist and unique, and give bilayer The distributed algorithm of game.Simulation result shows the algorithm it is determined that also achieving source while via node optimal transmit power The reasonable selection of node.

Claims (4)

  1. A kind of 1. control method of joint Power control and source node selection based under double-deck game framework, it is characterised in that： The control method is two layers：First layer carries out the control of via node transmit power using non-cooperation subgame, and the second layer uses Evolution subgame carries out the selection of source node, the control that double-deck game distributed algorithm passes through alternately via node transmit power The selection of system and source node, finally makes system reach double-deck game Nash Equilibrium, realizes Multi-source multi-relay collaborative network resource Reasonable distribution.
  2. 2. as claimed in claim 1 based on the joint Power control under double-deck game framework and the controlling party of source node selection Method, it is characterised in that：The non-cooperation subgame of the first layer, in the set of relay nodes for assisting same source node, in After the non-cooperation subgame that Power Control is formd between node, the optimization problem of via node Power Control represents as follows：
    In formula,For via node R maximum transmit power, uRFor the net utility function of via node；For in same signal Each via node of source node is assisted in time slot, the vector that Nash Equilibrium is made up of their optimal transmit power, uses table Show, wherein in when being equilibrium state in addition to via node, the vector of other optimal transmit power compositions of via node；By multiple Iteration, this non-cooperation subgame are finally reached Nash Equilibrium, i.e., under the limitation of maximum transmit power, each via node can obtain To unique optimal transmit power.
  3. 3. as claimed in claim 1 based on the joint Power control under double-deck game framework and the controlling party of source node selection Method, tool are characterised by：The second layer subgame uses evolution subgame, and via node can model to the select permeability of source node For evolution subgame, in moment t, it is n that the via node number scale of source node S is assisted in selections(t), the sum of System relays node ForSelection assists the via node proportion of source node S to be represented by xs(t)=ns(t)/K, vector x (t)= [x1(t), L, xM(t)] it is used for representing the state that t trunk node selection assists source node；
    In the evolution subgame of trunk node selection source node, replica locating represents as follows：
    In formula, δ is evolution step-length, can be used for controlling the evolution speed of trunk node selection source node；
    Define us(t) it is set of relay nodes ΓsAverage net utility function,Represent all via nodes in whole system Average net utility function, then us(t) andIt is expressed as：
    In formula, S, l ∈ Φ, by the iteration that develops several times, evolution subgame eventually converges to what is determined by following equations group Evolutionarily Stable Strategy：
  4. 4. as claimed in claim 1 based on the joint Power control under double-deck game framework and the controlling party of source node selection Method, it is characterised in that：The double-deck game distributed algorithm is the iteration of alternately two kinds of subgames of via node, is finally made System reaches Nash Equilibrium, is expressed as follows：
    (1) during .t=0, each via node random selection transmit power and the source node assisted；
    (2) selections assist all via nodes of same source node S to proceed by the non-cooperation subgame of Power Control；
    (3) obtains via node R optimal transmit power in t by formula (14)
    IfMake t=t+1, repeat step (3)；
    Otherwise, Power Control subgame terminates to go to step (4)；
    (4) determines to assist all via nodes of source node S according to step (3), optimal transmit power vector nowVia node proceeds by the evolution subgame of source node selection；
    (5) is for set of relay nodes ΓsAverage net utility function us(t)：
    IfIt is dominating stragegy that then source node S is assisted in selection, and via node keeps the selection of this source node constant；
    IfIt is inferior position strategy that then source node S is assisted in selection, and via node is abandoned assisting the source node, and with probabilitySelect another source node Q so that
    (6) judges whether to reach Evolutionary Equilibrium of the via node to source node select permeability：
    IfSub-carrier selection evolution subgame terminates；
    Otherwise, t=t+1, return to step (5) are made；
    (7) judges whether system reaches the Nash Equilibrium of whole double-deck game：
    IfGo to step (2)；
    Otherwise, step (8) is gone to；
    (8) Nash Equilibrium of double-deck game is reached, double-deck game terminates.
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