CN103117824A - Authorized user frequency spectrum pricing method based on Bertrand static game - Google Patents

Abstract

The invention relates to an authorized user frequency spectrum pricing method, particularly relates to an authorized user frequency spectrum pricing method the Bertrand static game and is to solve the problem that existing frequency spectrum pricing methods are high in algorithm complexity, and excessively ideal in design of benefit functions of authorized users. The method includes the following steps of obtaining a requirement matrix of secondary users; establishing a benefit function of the secondary users by using a theory of surplus values according to the requirement matrix; obtaining a frequency spectrum demand function of the secondary users to authorized users according to the benefit function of the secondary users; obtaining a benefit function of the authorized users on the basis of the prior three steps; using the Bertrand game theory to obtain nash equilibrium of a payoff function which is the benefit function of the authorized users; and establishing a simultaneous system of equations to obtain stable frequency spectrum prices of each authorized user so as to achieve frequency spectrum pricing. The authorized user frequency spectrum pricing method can be applied to cognitive radio communication systems.

Description

A kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game

Technical field

The present invention relates to the authorized user frequency spectrum pricing method based on the Bertrand Static Game.

Background technology

In cognitive radio communication systems, cognitive user is obtained the mandate spectrum information by frequency spectrum detection, thereby uses the channel that is in idle condition.But inevitably there is error probability in frequency spectrum detection, and this can impact authorized user.So cognitive user is carried out certain economic compensation to authorized user in the use authority frequency range, this is the very valuable thinking that promotes the cognitive radio development, therefore, formulates a practical authorized user frequency spectrum pricing strategy very important.The relation in cognitive radio communication systems according to authorized user and cognitive user is quoted differentiation oligopoly market economic theory, can solve well authorized user frequency spectrum pricing problem.In present method, mainly have two problems: algorithm complex is too high and the design of authorized user benefit function is too idealized.Utilize the theoretical authorized user frequency spectrum pricing problem that solves of dynamic game theory and genetic evolution, can dynamically adjust in real time the authorized user price of spectrum, but algorithm complex is too high, is difficult to actual conditions.For the authorized user benefit function, at present algorithm only considers that bandwidth reduces the impact on authorized user, and ignores the interference that the new spectrum requirement of authorized user itself and cognitive user use frequency spectrum cause authorized user.

Summary of the invention

The present invention will solve that the algorithm complex of existing frequency spectrum pricing method is high, the too Utopian problem of authorized user benefit function design, thereby a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game is provided.

A kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game, carry out according to the following steps:

Step 1, according to the spectrum requirement function of cognitive user to authorized user, obtain the requirement matrix of cognitive user;

Step 2, according to the requirement matrix that obtains in step 1, utilize theory of surplus value to set up the cognitive user benefit function;

Step 3, according to the cognitive user benefit function described in step 2, obtain cognitive user for the spectrum requirement function of authorized user;

Step 4, on the basis in first three step, the authorized user benefit function is designed, at first consider authorized user frequency spectrum income, secondly, consider to authorize because frequency spectrum is sold the loss that causes, thus authorized user's benefit function;

Step 5, utilize the Bertrand game theory to obtain Nash Equilibrium take the benefit function of authorized user as pay off function;

Step 6, according to balance policy in step 5, Simultaneous Equations can obtain the stable price of spectrum of each authorized user, thereby has realized the frequency spectrum price.

Beneficial effect of the present invention: the present invention has designed an algorithm simple considering the loss of authorized user demand and disturbing on the basis of loss, can apply to actual authorized user benefit function.Then, utilize Bertrand Static Game theory to obtain the stable equilibrium pricing strategy of authorized user, thereby realize the efficient utilization of frequency spectrum.The present invention has overcome present method and has existed the method complexity large, be difficult to apply to reality, and the too Utopian shortcoming of authorized user benefit function design, the frequency spectrum pricing method that the present invention proposes, significantly reduced the complexity of computing, approach authorized user actual gain situation, the availability of frequency spectrum of system improves greatly.

Description of drawings

Fig. 1 is structured flowchart of the present invention, and wherein cognitive user contacts by cognitive base station pre-authorized subscriber frequency spectrum.

Embodiment

Embodiment one: in conjunction with Fig. 1, this embodiment is described, in cognitive radio system, based on the authorized user frequency spectrum pricing method of Bertrand Static Game, it is realized by following steps:

Step 1, according to the spectrum requirement function of cognitive user to authorized user, obtain the requirement matrix of cognitive user;

Step 2, according to the requirement matrix that obtains in step 1, utilize theory of surplus value to set up the cognitive user benefit function;

Step 3, according to the cognitive user benefit function described in step 2, obtain cognitive user for the spectrum requirement function of authorized user;

Step 4, on the basis in first three step, the authorized user benefit function is designed, at first consider authorized user frequency spectrum income, secondly, consider to authorize because frequency spectrum is sold the loss that causes, thus authorized user's benefit function;

Step 5, utilize the Bertrand game theory to obtain Nash Equilibrium take the benefit function of authorized user as pay off function;

Step 6, according to balance policy in step 5, Simultaneous Equations can obtain the stable price of spectrum of each authorized user, thereby has realized the frequency spectrum price.

Beneficial effect of the present invention: the present invention has designed an algorithm simple considering the loss of authorized user demand and disturbing on the basis of loss, can apply to actual authorized user benefit function.Then, utilize Bertrand Static Game theory to obtain the stable equilibrium pricing strategy of authorized user, thereby realize the efficient utilization of frequency spectrum.The present invention has overcome present method and has existed the method complexity large, be difficult to apply to reality, and the too Utopian shortcoming of authorized user benefit function design, the frequency spectrum pricing method that the present invention proposes, significantly reduced the complexity of computing, approach authorized user actual gain situation, the availability of frequency spectrum of system improves greatly.

Embodiment two: present embodiment is that the detailed process of step 1 is as follows to the further illustrating of embodiment one:

In cognitive radio system, whole system is considered to differentiation number morning market field model, and having an IV oligarch is authorized user, and M consumer is cognitive user, p _iBe the price of spectrum of formulating of authorized user j, q _iBe the frequency spectrum quantity of selling.The cognitive user demand function can be expressed as linear function, and cognitive user is to authorized user, spectrum requirement can be expressed as:

p _j＝α _j-γ _j，1q ₁-γ _j,2q ₂…-γ _j,iq _i-γ _j,Nq _N；

In formula, α _j=log ₂(1+KSNR _j); K is spectrum gap; SNR _jBe signal to noise ratio; γ _j,iFor frequency spectrum between authorized user substitutes, its span is :-1≤γ _j,i≤ 1, work as γ _j,iCan replace fully between=1 expression authorized user frequency spectrum, work as γ _j,iUncorrelated mutually between=0 expression frequency spectrum, be independent of each other, work as γ _j,i=-1 expression authorized user frequency spectrum interdepends, and complements one another;

The requirement matrix that can be got cognitive user by following formula is: P=α-γ Q;

In formula:

P=(p ₁p ₂P _jP _N) ^TBe authorized user price of spectrum vector; α=(α ₁α ₂α _jα _N) ^ΤBe the spectrum efficiency vector; Q=(q ₁q ₂Q _jQ _N) ^ΤFor authorized user is sold the band fat vector; Alternative factor matrix between different authorized user frequency spectrums can be expressed as:

$\mathrm{\γ}=\left(\begin{array}{cccccc}{\mathrm{\γ}}_{\mathrm{1,1}}& {\mathrm{\γ}}_{\mathrm{1,2}}& \·\·\·& {\mathrm{\γ}}_{1,i}& \·\·\·& {\mathrm{\γ}}_{1,N}\\ {\mathrm{\γ}}_{\mathrm{2,1}}& {\mathrm{\γ}}_{\mathrm{2,2}}& \·\·\·& {\mathrm{\γ}}_{2,i}& \·\·\·& {\mathrm{\γ}}_{2,N}\\ & \·& & & \·& \\ & \·& & & \·& \\ & \·& & & \·& \\ {\mathrm{\γ}}_{j,1}& {\mathrm{\γ}}_{j,2}& \·\·\·& {\mathrm{\γ}}_{j,i}& \·\·\·& {\mathrm{\γ}}_{j,N}\\ & \·& & & \·& \\ & \·& & & \·& \\ & \·& & & \·& \\ {\mathrm{\γ}}_{N,1}& {\mathrm{\γ}}_{N,2}& \·\·\·& {\mathrm{\γ}}_{N,i}& \·\·\·& {\mathrm{\γ}}_{N,N}\end{array}\right);$

Embodiment three: present embodiment is that the detailed process of step 2 is as follows to the further illustrating of embodiment one or two:

According to the requirement matrix that obtains in step 1, utilize theory of surplus value to set up the cognitive user benefit function, it can be expressed as:

U _SU=∫(α-γ·Q)dQ-P·Q ^Τ；

By further derivation, cognitive user benefit function expression is as follows:

$U_{\mathrm{SU}}\left(P\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{q}_j-\frac{1}{2}(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{q}_i^2+2\mathrm{\υ}\underset{j\≠i}{\overset{N}{\mathrm{\Σ}}}{q}_i{q}_j)-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{q}_i;$

In formula:

For authorized user self, its frequency spectrum substitutes the factor and satisfies γ _i,i=1; The authorized user alternative factor of frequency spectrum each other satisfies γ _j,i=γ _i,j=υ;

Embodiment four: present embodiment is that the detailed process of step 3 is as follows to the further illustrating of one of embodiment one to three:

According to the cognitive user benefit function described in step 2, obtain cognitive user for the spectrum requirement D of authorized user i _i(P), be expressed as follows:

$D_i\left(P\right)=\frac{({\mathrm{\α}}_i-p_i)(\mathrm{\υ}(N-2)+2)\mathrm{\υ}{\mathrm{\Σ}}_{j\≠i}({\mathrm{\α}}_j-p_j)}{(\mathrm{\υ}(N-1)+1)(1-\mathrm{\υ})};$

Embodiment five: present embodiment is that the detailed process of step 4 is as follows to the further illustrating of one of embodiment one to four:

On the basis in first three step, the authorized user benefit function is designed: at first consider authorized user frequency spectrum income, for authorized user i, it sells frequency spectrum acquisition income is p _iD _i(p); Secondly, consider to authorize because frequency spectrum is sold the loss that causes, this loss mainly is comprised of two parts, be respectively the demand loss and disturb loss, so-called demand loss, be that authorized user is owing to selling frequency spectrum, and make self new spectrum requirement to satisfy and the loss that causes, in order to quantize the loss of authorized user, authorized user is being sold frequency spectrum during this period of time in Δ t, demand number for frequency satisfies Poisson process, that is to say, this random process is stationary random process, and is irrelevant with zero-time, therefore, authorized user i is k to frequency demand number _iProbability be:

$P_{k_i}\left(\mathrm{\Δt}\right)=\frac{{\left({\mathrm{\λ}}^{\left(i\right)}\mathrm{\Δt}\right)}^{k_i}}{k_i!}{e}^{{\mathrm{\λ}}^{\left(i\right)}\mathrm{\Δt}},k_i=\mathrm{0,1,2,3},...;$

In formula: λ ⁽ⁱ⁾Be authorized user i average arrival rate;

The interference that the so-called cognitive user of disturbing loss namely using causes authorized user, the bandwidth of selling to authorized user is directly proportional, from the user's that can obtain the authorization loss function:

In formula:

Be respectively the demand loss factor and disturb loss factor, being constant;

So the benefit function of authorized user can be expressed as follows:

Embodiment six: present embodiment is that the detailed process of step 5 is as follows to the further illustrating of one of embodiment one to five:

Utilize the Bertrand game theory to obtain Nash Equilibrium take the benefit function of authorized user as pay off function, use p _-i={ p ₁, p ₂..., p _NRepresent except authorized user i the strategy set of other authorized users, p _iBe the bid strategy of authorized user i, therefore, p=p _-i∪ { p _i, use p _N ^*Expression Nash Equilibrium strategy:

${p_i}^{*}=\arg \underset{p_i}{\max }E\left[U_i^{\mathrm{payoff}}(p_{-i}^{*}\∪\{p_i\left\}\right)\right];$

Thereby can obtain:

$p_i^{*}=\frac{1}{2}(\frac{{\mathrm{\α}}_i(\mathrm{\υ}(N-2)+2)-\mathrm{\υ}{\mathrm{\Σ}}_{j\≠i}({\mathrm{\α}}_j-p_j)}{(\mathrm{\υ}(N-1)+1)(1-\mathrm{\υ})}+{\mathrm{\τ}}_1^{\left(i\right)}\frac{(\mathrm{\υ}(N-2)+2)}{(\mathrm{\υ}(N-1)+1)(1-\mathrm{\υ})});$

Embodiment seven: present embodiment is that the detailed process of step 6 is as follows to the further illustrating of one of embodiment one to six:

According to balance policy in step 5, with p ₁ ^*To p _N ^*Simultaneous Equations can obtain the stable price of spectrum of each authorized user, thereby has realized the frequency spectrum price.

The present invention has designed an algorithm simple considering the loss of authorized user demand and disturbing on the basis of loss, can apply to actual authorized user benefit function.Then, utilize Bertrand Static Game theory to obtain the stable equilibrium pricing strategy of authorized user, thereby realize the efficient utilization of frequency spectrum.The present invention has overcome present method and has existed the method complexity large, be difficult to apply to reality, and the too Utopian shortcoming of authorized user benefit function design, the frequency spectrum pricing method that the present invention proposes, significantly reduced the complexity of computing, approach authorized user actual gain situation, the availability of frequency spectrum of system improves greatly.

The differentiation oligopoly market model that the present invention adopts is described cognitive system, and utilizes Principles of Economics and static Bertrand theory of games to realize authorized user frequency spectrum price.

Claims (7)

1. authorized user frequency spectrum pricing method based on the Bertrand Static Game is characterized in that it carries out according to the following steps:

Step 1, according to the spectrum requirement function of cognitive user to authorized user, obtain the requirement matrix of cognitive user;

Step 2, according to the requirement matrix that obtains in step 1, utilize theory of surplus value to set up the cognitive user benefit function;

Step 3, according to the cognitive user benefit function described in step 2, obtain cognitive user for the spectrum requirement function of authorized user;

Step 4, on the basis in first three step, the authorized user benefit function is designed, at first consider authorized user frequency spectrum income, secondly, consider to authorize because frequency spectrum is sold the loss that causes, thus authorized user's benefit function;

Step 5, utilize the Bertrand game theory to obtain Nash Equilibrium take the benefit function of authorized user as pay off function;

Step 6, according to balance policy in step 5, Simultaneous Equations can obtain the stable price of spectrum of each authorized user, thereby has realized the frequency spectrum price.

2. a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game as claimed in claim 1 is characterized in that the detailed process of step 1 is as follows:

In cognitive radio system, whole system is considered to differentiation number morning market field model, and having N oligarch is authorized user, and M consumer is cognitive user, p _iBe the price of spectrum of formulating of authorized user i, q _iBe the frequency spectrum quantity of selling.The cognitive user demand function can be expressed as linear function, and cognitive user can be expressed as the spectrum requirement of authorized user j:

p _j=α _j-γ _j,1q ₁-γ _j,2q ₂…-γ _j,iq _i-γ _j,Nq _N；

In formula, α _j=log ₂(1+KSNR _j); K is spectrum gap; SNR _jBe signal to noise ratio; γ _j,iFor frequency spectrum between authorized user substitutes, its span is :-1≤γ _j,i≤ 1, work as γ _j,iCan replace fully between=1 expression authorized user frequency spectrum, work as γ _j,iUncorrelated mutually between=0 expression frequency spectrum, be independent of each other, work as γ _j,i=-1 expression authorized user frequency spectrum interdepends, and complements one another;

The requirement matrix that can be got cognitive user by following formula is: P=α-γ Q;

In formula:

P=(p ₁p ₂P _jP _N) ^TBe authorized user price of spectrum vector; α=(α ₁α ₂α _jα _N) ^ΤBe the spectrum efficiency vector; Q=(q ₁q ₂Q _jQ _N) ^ΤFor authorized user is sold the band fat vector; Alternative factor matrix between different authorized user frequency spectrums can be expressed as:

$\mathrm{\γ}=\left(\begin{array}{cccccc}{\mathrm{\γ}}_{\mathrm{1,1}}& {\mathrm{\γ}}_{\mathrm{1,2}}& \·\·\·& {\mathrm{\γ}}_{1,i}& \·\·\·& {\mathrm{\γ}}_{1,N}\\ {\mathrm{\γ}}_{\mathrm{2,1}}& {\mathrm{\γ}}_{\mathrm{2,2}}& \·\·\·& {\mathrm{\γ}}_{2,i}& \·\·\·& {\mathrm{\γ}}_{2,N}\\ & \·& & & \·& \\ & \·& & & \·& \\ & \·& & & \·& \\ {\mathrm{\γ}}_{j,1}& {\mathrm{\γ}}_{j,2}& \·\·\·& {\mathrm{\γ}}_{j,i}& \·\·\·& {\mathrm{\γ}}_{j,N}\\ & \·& & & \·& \\ & \·& & & \·& \\ & \·& & & \·& \\ {\mathrm{\γ}}_{N,1}& {\mathrm{\γ}}_{N,2}& \·\·\·& {\mathrm{\γ}}_{N,i}& \·\·\·& {\mathrm{\γ}}_{N,N}\end{array}\right).$

3. a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game as claimed in claim 2 is characterized in that the detailed process of step 2 is as follows:

According to the requirement matrix that obtains in step 1, utilize theory of surplus value to set up the cognitive user benefit function, it can be expressed as:

U _SU=∫(α-γ·Q)dQ-P·Q ^Τ；

By further derivation, cognitive user benefit function expression is as follows:

$U_{\mathrm{SU}}\left(P\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{q}_j-\frac{1}{2}(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{q}_i^2+2\mathrm{\υ}\underset{j\≠i}{\overset{N}{\mathrm{\Σ}}}{q}_i{q}_j)-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{q}_i;$

In formula:

For authorized user self, its frequency spectrum substitutes the factor and satisfies γ _i,i=1; The authorized user alternative factor of frequency spectrum each other satisfies γ _j,i=γ _i,j=υ.

4. a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game as claimed in claim 3 is characterized in that the detailed process of step 3 is as follows:

According to the cognitive user benefit function described in step 2, obtain cognitive user for the spectrum requirement D of authorized user i _i(P), be expressed as follows:

$D_i\left(P\right)=\frac{({\mathrm{\α}}_i-p_i)(\mathrm{\υ}(N-2)+2)\mathrm{\υ}{\mathrm{\Σ}}_{j\≠i}({\mathrm{\α}}_j-p_j)}{(\mathrm{\υ}(N-1)+1)(1-\mathrm{\υ})}.$

5. a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game as claimed in claim 4 is characterized in that the detailed process of step 4 is as follows:

On the basis in first three step, the authorized user benefit function is designed: at first consider authorized user frequency spectrum income, for authorized user i, it sells frequency spectrum acquisition income is p _iD _i(p); Secondly, consider to authorize because frequency spectrum is sold the loss that causes, this loss mainly is comprised of two parts, be respectively the demand loss and disturb loss, so-called demand loss, be that authorized user is owing to selling frequency spectrum, and make self new spectrum requirement to satisfy and the loss that causes, in order to quantize the loss of authorized user, authorized user is being sold frequency spectrum during this period of time in Δ t, demand number for frequency satisfies Poisson process, that is to say, this random process is stationary random process, and is irrelevant with zero-time, therefore, authorized user i is k to frequency demand number _iProbability be:

$P_{k_i}\left(\mathrm{\Δt}\right)=\frac{{\left({\mathrm{\λ}}^{\left(i\right)}\mathrm{\Δt}\right)}^{k_i}}{k_i!}{e}^{{\mathrm{\λ}}^{\left(i\right)}\mathrm{\Δt}},k_i=\mathrm{0,1,2,3},...;$

In formula: λ ⁽ⁱ⁾Be authorized user i average arrival rate;

The interference that the so-called cognitive user of disturbing loss namely using causes authorized user, the bandwidth of selling to authorized user is directly proportional, from the user's that can obtain the authorization loss function:

In formula:

Be respectively the demand loss factor and disturb loss factor, being constant;

So the benefit function of authorized user can be expressed as follows:

6. a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game as claimed in claim 5 is characterized in that the detailed process of step 5 is as follows:

Utilize the Bertrand game theory to obtain Nash Equilibrium take the benefit function of authorized user as pay off function, use p _-i={ p ₁, p ₂..., p _NRepresent except authorized user i the strategy set of other authorized users, p _iBe the bid strategy of authorized user i, therefore, p=p _-i∪ { p _i, use p _i ^*Expression Nash Equilibrium strategy:

${p_i}^{*}=\arg \underset{p_i}{\max }E\left[U_i^{\mathrm{payoff}}(p_{-i}^{*}\∪\{p_i\left\}\right)\right];$

Thereby can obtain:

$p_i^{*}=\frac{1}{2}(\frac{{\mathrm{\α}}_i(\mathrm{\υ}(N-2)+2)-\mathrm{\υ}{\mathrm{\Σ}}_{j\≠i}({\mathrm{\α}}_j-p_j)}{(\mathrm{\υ}(N-1)+1)(1-\mathrm{\υ})}+{\mathrm{\τ}}_1^{\left(i\right)}\frac{(\mathrm{\υ}(N-2)+2)}{(\mathrm{\υ}(N-1)+1)(1-\mathrm{\υ})}).$

7. a kind of authorized user frequency spectrum pricing method based on the Bertrand Static Game as claimed in claim 6 is characterized in that the detailed process of step 6 is as follows:

According to balance policy in step 5, with p ₁ ^*To p _N ^*Simultaneous Equations can obtain the stable price of spectrum of each authorized user, thereby has realized the frequency spectrum price.

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