CN108882247A - A kind of cognitive radio networks resource allocation methods based on Contract Theory - Google Patents
A kind of cognitive radio networks resource allocation methods based on Contract Theory Download PDFInfo
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Abstract
The invention discloses a kind of cognitive radio networks resource allocation methods based on Contract Theory, introduce Contract Theory solve to combine under the conditions of strong imperfect information backscattering radio frequency time resource assignment problem：In contract, draft side and signing side of the primary user PU and time user SU respectively as contract；Under the conditions of strong imperfect information, the probability that PU occurs according to different type SU is that each SU drafts Optimal Contract；If the contract drafted can meet the excitation versatility IC and individual rationality IR condition of SU simultaneously, SU can be using the contract as most having contract and sign the contract；The maximum value that contract problem reduction is PU utility function under the conditions of meeting IC and IR at the same time is optimized to solve.Solves the performance optimization problem in existing model RFPB-CRN in the case where strong imperfect information.
Description
【Technical field】
The invention belongs to wireless communication technology fields, and in particular to a kind of cognitive radio networks money based on Contract Theory
Source distribution method.
【Background technique】
Cognitive radio networks (CRN) be generation information technology important component and one of efficient communication
Important development stage is intended to intelligently utilize usable spectrum resource.Recently, it with the development of RF energy collection technique, mentions
A kind of new communication plan, i.e. radio frequency powered cognitive radio networks are gone out.However, since primary user accounts in most of time
With channel, so the throughput performance of secondary user is severely limited.
Recently, in " the Ambient backscatter of document 1:wireless communication out ofthin
Draw in air [Acm Sigcomm Computer Communication Review, vol.43, no.4, pp.39-50,2013] "
Environment backscatter technique is entered.By combining radio frequency powered cognitive radio networks with environment backscatter technique, draw
Enter a kind of novel wireless network, that is, combines the radio frequency powered cognition wireless network (RFPB-CRN) of backscattering.However, being
The network performance being optimal, the backscattering of data and RF energy collect between time distribution become one and compel to be essential
The serious problems to be solved.
Recently, RFPB-CRN performance optimization problem also results in extensive concern.2 " Ambient of document
backscatter:a new approach to improve network performance for RF-powered
cognitive radio networks[IEEE Transactions on Communications,vol.65,no.9,
Pp.3659-3674, Sept.2017] " optimal time assignment problem in RFPB-CRN is had studied, the distribution is by a pair of of PU and SU
Composition.The document considers the scene of two kinds of cognitive radios, that is, formula (underlay) and cover type (overlay) coexists.?
" the Optimal time sharing in RF-powered backscatter cognitive radio networks of document 3
[2017IEEE International Conference on Communications(ICC),Paris,France,
May.2017] " in, the author investigation network optimization problem of RFPB-CRN, wherein ST passes through balanced backscattering time and energy
Acquisition time is measured to optimize to realize maximization overall network throughput.It is different from document 2 and document 3,4 " Overlay of document
RF-poweredbackscatter cognitive radio networks:A game theoretic approach[IEEE
International Conference on Communications (ICC), Paris, France, May.2017] " it proposes
The reciprocation in RFPB-CRN between a pair of ST and PU is analyzed using Lothar Staber Er Baige (Stackelberg) game, this
It is a kind of effective solution scheme, overall network performance can be improved, but is not particularly suited for the scene of multiple ST.
In general, the feelings of SU information and channel status known to PU are concentrated mainly on about the research of RFPB-CRN at present
Condition.But compared to for Complete Information state, consider that the scene of imperfect information is more meaningful.In addition, with the increasing of SU quantity
Add, the time centralised allocation method of distribution will bring very big complexity to PU.Recently, Contract Theory has been applied to object
In networking (IoT) and cognitive radio networks.It is closed since each ST can decide whether to sign by considering the ability of oneself
About, therefore Contract Theory is suitable under information asymmetry scene.
【Summary of the invention】
The object of the present invention is to provide a kind of cognitive radio networks resource allocation methods based on Contract Theory, to solve
Performance optimization problem in existing model RFPB-CRN in the case where strong imperfect information.
The present invention uses following technical scheme：A kind of cognitive radio networks resource allocation methods based on Contract Theory,
Introduce Contract Theory solve to combine under the conditions of strong imperfect information backscattering radio frequency time resource assignment problem：It is closing
In about, draft side and signing side of the primary user PU and time user SU respectively as contract；Under the conditions of strong imperfect information, PU according to
It is that each SU drafts Optimal Contract according to the different type SU probability occurred；If the excitation that the contract drafted can meet SU simultaneously is logical
With property IC and individual rationality IR condition, then SU can be using the contract as most having contract and sign the contract；Optimize contract
Problem reduction is that the maximum value of PU utility function under the conditions of meeting IC and IR at the same time solves.
Further, the following contents is specifically included：
Step 1, building use the RFPB-CRN model of contract incentive mechanism, including PU and n time users of a primary user
SU；
Step 2 solves reverse choice problem：Under the conditions of strong imperfect information, it is assumed that PU only knows the type sum n of SU
With the probability of each type SU, PU can provide a series of contracts for different types of SU；
Step 3 solves moral hazard problem：PU designs backscattering and the time directly transmitted in contract, reaches SU's
Transimission power is maximum, to realize the remuneration highest of PU；
Step 4, the utility function for solving PU；
Step 5 solves optimization contract problem：Solve while meeting the maximum of PU utility function under the conditions of IC and IR
Value.
Further, the particular content of step 1 is that Contract Theory is made of a PU and n different types of SU and adopts
With the RFPB-CRN model of contract incentive mechanism, PU provides a contract (b, t) for motivating SU backscattering or transmitting for SU
Information, wherein what b was indicated is the time of SU backscattering, and what t was indicated is the time of the direct transmitting information of SU, and i-th of SU is signed
Contract be denoted as (bi,ti), by total backscattering timeIt is normalized to 1, STiThe time for collecting RF energy is 1-bi。
Further, the particular content of step 2 is, under the conditions of strong imperfect information, it is assumed that PU only knows the type of SU
The probability β of total n and each type SUi∈ [0,1], and have
The ability of n SU corresponds to n different type, is labeled as θ ∈ { θ1,...,θi,...,θn}；
And assume θ1< ... < θi< ... < θn, i ∈ { 1 ..., n } (2),
Wherein, the type of SU represents all personal information of ST, and θ represents the ST transmission successful degree of difficulty of information,
In order to solve reverse choice problem, PU can provide a series of contract (b for different types of SUi,ti), i ∈ { 1 ..., n }.
Further, the particular content of step 3 is that the transimission power of ST is labeled as p, the corresponding cost function table of power
It is shown as：
ψ (p)=α p2(3),
Wherein α indicates cost coefficient；PU designs contract (bi,ti) in backscattering and the time directly transmitted, reach SU's
Transimission power is maximum, to realize the remuneration highest of PU.
Further, the particular content of step 4 is to remember xiAs STiTransmission rate, the probability of success for transmitting information can
To be expressed as：
ρ(xi)=θixi∈ (0,1) (4),
Fixed backscattering rate representation is Rb, CbAnd CtIt respectively indicates ST backscattering and is transferred directly to the report of PU
Reward coefficient；
STiTransimission power can be expressed asWherein η is energy conversion factor；Assuming that each ST collects the function of energy
Rate be it is identical, be denoted as Ph；Therefore contract (b is signedi,ti) after, SUiUtility function can be expressed as：
SU signs contract (bi,ti) after, the utility function of PU is：
The total utility function representation of PU is：
Further, the particular content of step 5 is to optimize contract problem to be converted into maximization PU cost letter
Number,
It is expressed as：
Wherein x 'iIndicate STiSign contract (bj,tj) when information emission rate be respectively among these there are two condition
Excitation versatility (IC) and individual rationality (IR), the two conditions can guarantee STiTend to select contract (bi,ti) without
It is (bj,tj), and a non-negative utility function can be obtained；
Signing contract (bi,ti) after, STiNeed to obtain the optimal transmission rate x under a direct transmission modei *, this
It can be by maximizing SUiUtility function achieve the goal；
Pass through taylor series expansion
Formula (9) is brought into formula (5), available approximate optimal rate, expression is：
Equally, STiIt is (b in contractj,tj) when optimal rate be：
By xi *WithSubstitute the x in formula (8)iWith x ', φ=R is definedb-Cb, then the utility function maximization problems of PU
It can be converted into：
IR condition is only to θ1It is restricted, IC condition can abbreviation be only θiAnd θi-1Between restriction condition；The abbreviation claims
For local I C condition (LDIC)；
Therefore, the utility function maximization problems of PU can be with abbreviation：
Maximization problems about formula (13) can be solved by method of Lagrange multipliers.
Further, formula (13) maximization solve the specific steps are：
Assuming that λiIt is the Lagrange multiplier of IC and IR condition with μ, ν is that the backscattering time Lagrange of distribution multiplies
Son；Therefore, formula (13) can be rewritten into：
3n+2 partial differential equations can be formed altogether in formula (14), respectively：
By solving 3n+2 partial differential equations, it will be able to obtain optimal contract (bi,ti),i∈{1,...,n}。
Compared with prior art, the present invention at least has the advantages that：The present invention is the strong imperfect information the case where
Under can optimize RFPB-CRN performance.The optimization of network performance side that simultaneously there is the contract of Low market efficiency and moral hazard to be realized
Case has lesser performance loss compared with the optimal distributing scheme under the conditions of Complete Information, but considers strong imperfect information
Condition has a more preferably applicability, lesser performance loss this be acceptable.
【Detailed description of the invention】
Fig. 1 is the RFPB-CRN illustraton of model that the present invention uses contract incentive mechanism；
Fig. 2 is the time frame structure figure of RFPB-CRN model of the present invention；
Fig. 3 is the Optimal Contract of different type SU of the present invention；
Fig. 4 is that type of the present invention is θ5SU in backscattering remuneration CbContract when variation；
Fig. 5 is the backscattering remuneration C of PU of the present inventionbPU utility function trend chart when variation；
Fig. 6 is the backscattering remuneration C of PU of the present inventionbSU utility function trend chart when variation；
Fig. 7 is the backscattering remuneration C of PU of the present inventionbTotal utility function trend chart when variation.
【Specific embodiment】
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
One, the cognitive radio networks resource allocation methods based on Contract Theory：
Optimal Contract algorithm specially under Low market efficiency and moral hazard problem, including the following contents：
1. Contract Theory：
About the RFPB-CRN model using contract incentive mechanism as shown in Figure 1, different types of by a PU and n
SU composition.In the model, PU provides a contract (b, t) for SU and is used to motivate SU backscattering or transmitting information, wherein b table
What is shown is the time of SU backscattering, and what t was indicated is the time of the direct transmitting information of SU.(b, t) in contract is although contain only
Time used in SU, but also imply the remuneration that PU is paid required for the corresponding time.SU uses backscattering or transmitting information
Time it is more, to more in requisition for the remuneration for paying PU.
It is as shown in Figure 2 for the time frame structure of RFPB-CRN model.The contract that i-th of SU is signed is denoted as (bi,ti).For
Without loss of generality, the present invention is by total backscattering timeIt is normalized to 1, therefore STiCollect RF energy time be
1-bi。
The information rate of backscattering is fixed value, but it is different that SU, which directly transmits the rate of information,.Assuming that directly
Transmitting information pattern, only there are two types of results：(power that SR is received reaches minimum threshold, P to transmission successi> PT) or transmission failure
(Pi≤PT).Due to information imperfection, power threshold can not be known, but what was certain was that the transmission power of ST is higher, transmission
Successful probability is bigger.
2 reverse choice problems：
Under the conditions of strong imperfect information, it is assumed that PU only knows the probability β of the type sum n and each type SU of SUi∈
[0,1], and have
The ability of n SU corresponds to n different type, is labeled as θ ∈ { θ1,...,θi,...,θn}.And assume
θ1< ... < θi< ... < θn, i ∈ { 1 ..., n } (2),
Wherein, the type of SU represents all personal information of ST, such as channel gain and the distance between ST and SR.Letter
For list, θ represents the ST transmission successful degree of difficulty of information.
In order to solve reverse choice problem, PU can provide a series of contract (b for different types of SUi,ti), i ∈
{1,...,n}。
3. moral hazard problem：
For Successful transmissions information, increase is reached the general of threshold value in the case where not knowing numerical value by higher transimission power
Rate.The transimission power of ST is labeled as p, and the corresponding cost function of power is expressed as：
ψ (p)=α p2(3),
Wherein α indicates cost coefficient.
Due to the asymmetry of information, PU is the transimission power p for not knowing ST, and this phenomenon is claimed in Contract Theory
For moral hazard problem.In order to solve this problem, PU should design contract (bi,ti) in backscattering and directly transmit when
Between, the transimission power for reaching SU is maximum, to realize the remuneration highest of PU.
4. utility function：
Remember xiAs STiTransmission rate, due to receive power substantially by xiAnd θiIt determines, therefore transmits information
The probability of success can be expressed as：
ρ(xi)=θixi∈ (0,1) (4),
Fixed backscattering rate representation is Rb, CbAnd CtIt respectively indicates ST backscattering and is transferred directly to the report of PU
Reward coefficient.
By Shannon's theorems it is found that STiTransimission power can be expressed asWherein η is energy conversion factor.Assuming that every
A ST collect energy power be it is identical, be denoted as Ph.Therefore contract (b is signedi,ti) after, SUiUtility function can indicate
For：
SU signs contract (bi,ti) after, the utility function of PU is：
Due to reverse choice problem, PU only knows the probability that the type of different SU occurs, therefore, the total utility function table of PU
It is shown as：
5. optimal problem solves：
Maximization PU cost function can be converted by optimizing contract problem, be expressed as：
Wherein x 'iIndicate STiSign contract (bj,tj) when information emission rate.There are two conditions among these, are respectively
Excitation versatility (IC) and individual rationality (IR), the two conditions can guarantee STiTend to select contract (bi,ti) without
It is (bj,tj), and a non-negative utility function can be obtained.
Signing contract (bi,ti) after, STiNeed to obtain the optimal transmission rate x under a direct transmission modei *, this
It can be by maximizing SUiUtility function achieve the goal.Pass through taylor series expansion
Formula (9) is brought into formula (5), available approximate optimal rate, expression is：
Equally, STiIt is (b in contractj,tj) when optimal rate be：
By xi *WithSubstitute the x in formula (8)iWith x ', φ=R is definedb-Cb, then the utility function maximization problems of PU
It can be converted into：
Solution about formula (12) can be with bibliography 5 " Contract Theory [Cambridge, MA, USA:
MIT Press,2004]".Precisely, by analysis it is found that IR condition is only to θ1It is restricted, IC condition can abbreviation be only
There is θiAnd θi-1Between restriction condition.The abbreviation is known as local I C condition (LDIC).
Therefore, the utility function maximization problems of PU can be with abbreviation：
Maximization problems about formula (13) can be solved by method of Lagrange multipliers.Assuming that λiIt is IC with μ
With the Lagrange multiplier of IR condition, ν is the Lagrange multiplier of backscattering time distribution.Therefore, formula (13) can change
It is write as：
3n+2 partial differential equations can be formed altogether in formula (14), respectively：
By solving 3n+2 partial differential equations, it will be able to obtain optimal contract (bi,ti),i∈{1,...,n}。
Two, the Optimal Contract under Low market efficiency：
Assuming that the transmission rate under each direct transmission mode of ST is fixed asTherefore, moral hazard problem is just not present
, only remaining reverse choice problem.Maximization problems is just rewritten as
Solution about formula (16), which can directly be found out, to be come, and is
Three, the Optimal Contract under moral hazard：
Assuming that PU knows the type information of each SU, then reverse choice problem is just not present, only remaining moral hazard
Problem.Optimization problem at this time is consistent with the optimization problem of centralization distribution under the conditions of Complete Information, and PU can be found
The optimal value of each SU.The optimization problem of PU is converted into the optimization problem of each SU at this time, is expressed as
The optimization problem (18) can be solved using formula (13) identical method.
Four, analysis of simulation result
In the simulation, different types of SU number is 10, i.e. n=10.Each type θ is seti=0.1i, and assume
Different types of SU submits to similarly be distributed, i.e. βi=1/n.For convenience in emulation, the rate of backscattering is set as Rb=
2, the power of collection of energy is Ph=2, the unit of medium-rate is kbps, power unit mW.In addition, directly under transmission mode
The remuneration C to PUt=1, energy conversion factor η=0.1.
Fig. 3 illustrates the Optimal Contract allocation plan of different type SU.By simulation result it can be seen that with SU energy
The promotion of power, i.e. θiBecome larger, time for directly transmitting can increasingly be grown in the contract that SU is signed, and be used for backscatter transmission
Time it is shorter and shorter.Even when the type of SU is θ10When, the time directly transmitted, backscatter transmission are only remained in contract
Time be 0, i.e., when PU be in " busy ", SU always all in collection energy state；And when SU is θ1When, on the contrary,
The time of backscatter transmission is only remained in contract, the time directly transmitted is 0, i.e., when PU is in " free time ", SU is always
All without backscattering.
Type is θ5SU in backscattering remuneration CbContract variation tendency when variation is as shown in Figure 4.It can from figure
Out, work as CbWhen increase, the remuneration for paying PU required for backscattering at this time increases, and the cost of ST backscattering increases.Therefore
SU is more likely to selection and carries out information transmission using direct mode.In addition, working as CbWhen increase, total transmission time is opposite
The reduction answered.
Fig. 5 illustrates the backscattering remuneration C of PUbSystem performance performance when variation.Wherein Fig. 5 is PU utility function
Variation, works as CbWhen increase, Low market efficiency becomes smaller with moral hazard problem and the PU utility function only under moral hazard problem,
And the PU utility function only under reverse choice problem is held essentially constant.Fig. 6 is the utility function variation tendency of SU, due to only
Under conditions of having a kind of problem to occur, the utility function of SU always remains as 0, and Low market efficiency is deposited simultaneously with moral hazard problem
Under the conditions, the utility function of SU can be with CbIncrease and declines.Fig. 7 illustrates the variation tendency of total utility function, total to imitate
With the sum of the utility function of utility function and SU that function representation is PU, by figure as can be seen that the variation of total utility function
Trend and the utility function of PU are essentially identical.It is otherwise noted that Low market efficiency is simultaneous with moral hazard problem
Under the conditions of with the total utility functional value difference very little under the conditions of only moral hazard, illustrate that there is Low market efficiency and morals wind simultaneously
The contract of danger has lesser performance loss compared with Complete Information condition, but in view of strong imperfect information condition has more
Excellent applicability, lesser performance loss this be acceptable.
The invention belongs to wireless communication technology fields, are related to a kind of radio frequency of combination backscattering based on Contract Theory
(RF) power supply cognition wireless network (CRN) time resource distribution method.The radio frequency powered of combining environmental backscatter technique recognizes
Radio net is a kind of newborn communication mode.However, the assignment problem of time still seriously limits the system performance.With
Centralized time resource distribution method in previous paper under Complete Information is different, and present invention introduces Contract Theories to solve by force not
Time assignment problem under the conditions of Complete Information.Wherein, strong imperfect information condition refers to that primary user (PU) only knows every type
The probability distribution of the secondary user transmitting terminal (ST) of type.In this contract, primary user and time user (SU) respectively as the seller and
Buyer.Mutuality of interest between primary user and secondary user can be with the contract about information transmission time and payment amount of signing
It is associated.Then, we discuss that three kinds lead to the case where there are Low market efficiency and moral hazards due to information asymmetry.This
Outside, it is further formulated by using method of Lagrange multipliers and solves contract problem optimal under three kinds of scenes.Finally, emulation
The result shows that while there is Low market efficiency and the contract of moral hazard to have lesser performance damage compared with Complete Information condition
Lose, it is contemplated that strong imperfect information condition has a more preferably applicability, lesser performance loss this be acceptable.
Present invention introduces Contract Theories, and to solve to combine under the conditions of strong imperfect information the radio frequency of backscattering, (RF power supply is recognized
Know the time resource assignment problem of wireless network (RFPB-CRN).In contract, primary user (PU) and time user (SU) make respectively
For the side of drafting and signing side of contract；Under the conditions of strong imperfect information, PU is each according to the probability that different type SU occurs
SU drafts Optimal Contract；If the contract drafted can meet the excitation versatility (IC) and individual rationality (IR) item of SU simultaneously
Part, then SU can be using the contract as most having contract and sign the contract；I.e. optimization problem abbreviation is to meet IC and IR at the same time
Under the conditions of PU utility function maximum value solve.Analyzed by IC the and IR condition to the optimization problem, can abbreviation be
Local I C condition (LDIC).Then partial differential equation are converted to the optimization problem after the abbreviation using method of Lagrange multipliers
The Solve problems of group are simultaneously solved.
The above content is merely illustrative of the invention's technical idea, and this does not limit the scope of protection of the present invention, all to press
According to technical idea proposed by the present invention, any changes made on the basis of the technical scheme each falls within claims of the present invention
Protection scope within.
Claims (8)
1. a kind of cognitive radio networks resource allocation methods based on Contract Theory, which is characterized in that introduce Contract Theory and come
Solve the time resource assignment problem that the radio frequency of backscattering is combined under the conditions of strong imperfect information：In contract, primary user PU
With secondary user SU respectively as the side of drafting and signing side of contract；Under the conditions of strong imperfect information, PU is according to different type SU
The probability of appearance is that each SU drafts Optimal Contract；If the contract drafted can meet the excitation versatility IC and individual of SU simultaneously
Reasonability IR condition, then SU can be using the contract as most having contract and sign the contract；I.e. optimize contract problem reduction be
While meeting the maximum value solution of PU utility function under the conditions of IC and IR.
2. a kind of cognitive radio networks resource allocation methods based on Contract Theory as described in claim 1, feature exist
In specifically including the following contents：
Step 1, building use the RFPB-CRN model of contract incentive mechanism, including PU and n user SU of a primary user；
Step 2 solves reverse choice problem：Under the conditions of strong imperfect information, it is assumed that PU only knows the type sum n of SU and every
The probability of a type SU, PU can provide a series of contracts for different types of SU；
Step 3 solves moral hazard problem：PU designs backscattering and the time directly transmitted in contract, reaches the transmission of SU
Power is maximum, to realize the remuneration highest of PU；
Step 4, the utility function for solving PU；
Step 5 solves optimization contract problem：Solve while meeting the maximum value of PU utility function under the conditions of IC and IR.
3. a kind of cognitive radio networks resource allocation methods based on Contract Theory as claimed in claim 2, feature exist
In the particular content of the step 1 is that Contract Theory is made of a PU and n different types of SU and is motivated using contract
The RFPB-CRN model of mechanism, PU provide a contract (b, t) for SU and are used to motivate SU backscattering or transmitting information, wherein b
What is indicated is the time of SU backscattering, and what t was indicated is the time of the direct transmitting information of SU, and the contract that i-th of SU is signed is denoted as
(bi,ti), by total backscattering timeIt is normalized to 1, STiThe time for collecting RF energy is 1-bi。
4. a kind of cognitive radio networks resource allocation methods based on Contract Theory as claimed in claim 2, feature exist
In the particular content of the step 2 is, under the conditions of strong imperfect information, it is assumed that PU only knows the type sum n of SU and each
The probability β of type SUi∈ [0,1], and have
The ability of n SU corresponds to n different type, is labeled as θ ∈ { θ1,...,θi,...,θn}；
And assume θ1< ... < θi< ... < θn, i ∈ { 1 ..., n } (2),
Wherein, the type of SU represents all personal information of ST, and θ represents the ST transmission successful degree of difficulty of information, in order to
Reverse choice problem is solved, PU can provide a series of contract (b for different types of SUi,ti), i ∈ { 1 ..., n }.
5. a kind of cognitive radio networks resource allocation methods based on Contract Theory as claimed in claim 2, feature exist
In the particular content of the step 3 is the transimission power of ST to be labeled as p, the corresponding cost function of power is expressed as：
ψ (p)=α p2(3),
Wherein α indicates cost coefficient；PU designs contract (bi,ti) in backscattering and the time directly transmitted, reach the transmission of SU
Power is maximum, to realize the remuneration highest of PU.
6. a kind of cognitive radio networks resource allocation methods based on Contract Theory as claimed in claim 2, feature exist
In the particular content of the step 4 is to remember xiAs STiTransmission rate, the probability of success for transmitting information can be expressed as：
ρ(xi)=θixi∈ (0,1) (4),
Fixed backscattering rate representation is Rb, CbAnd CtIt respectively indicates ST backscattering and is transferred directly to the remuneration system of PU
Number；
STiTransimission power can be expressed asWherein η is energy conversion factor；Assuming that the power that each ST collects energy is
It is identical, it is denoted as Ph；Therefore contract (b is signedi,ti) after, SUiUtility function can be expressed as：
SU signs contract (bi,ti) after, the utility function of PU is：
The total utility function representation of PU is：
7. a kind of cognitive radio networks resource allocation methods based on Contract Theory as claimed in claim 2, feature exist
In the particular content of the step 5 is to optimize contract problem to be converted into maximization PU cost function, is expressed as：
Wherein xi' indicate STiSign contract (bj,tj) when information emission rate among these there are two condition be that excitation is logical respectively
With property (IC) and individual rationality (IR), the two conditions can guarantee STiTend to select contract (bi,ti) rather than (bj,
tj), and a non-negative utility function can be obtained；
Signing contract (bi,ti) after, STiNeed to obtain the optimal transmission rate x under a direct transmission modei *, this can be with
By maximizing SUiUtility function achieve the goal；
Pass through taylor series expansion
Formula (9) is brought into formula (5), available approximate optimal rate, expression is：
Equally, STiIt is (b in contractj,tj) when optimal rate be：
By xi *WithSubstitute the x in formula (8)iWith x ', φ=R is definedb-Cb, then the utility function maximization problems of PU can turn
It turns to：
IR condition is only to θ1It is restricted, IC condition can abbreviation be only θiAnd θi_1Between restriction condition；The abbreviation is known as office
Portion's IC condition (LDIC)；
Therefore, the utility function maximization problems of PU can be with abbreviation：
Maximization problems about formula (13) can be solved by method of Lagrange multipliers.
8. a kind of cognitive radio networks resource allocation methods based on Contract Theory as claimed in claim 7, feature exist
In the maximization of, the formula (13) solve the specific steps are：
Assuming that λiIt is the Lagrange multiplier of IC and IR condition with μ, ν is the Lagrange multiplier of backscattering time distribution；Cause
This, formula (13) can be rewritten into：
3n+2 partial differential equations can be formed altogether in formula (14), respectively：
By solving 3n+2 partial differential equations, it will be able to obtain optimal contract (bi,ti),i∈{1,...,n}。
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