CN102448159B - Interference management-based power and speed combined control gaming method - Google Patents

Abstract

The purpose of the present invention is to provide a power-rate joint control game method based on interference management in a cognitive radio system. Aiming at the shortcomings of the existing interference temperature model in reducing the interference received by the primary user, this method strengthens the subjective initiative of the primary user in interference control. While the secondary users play games with each other, adjust the transmission power and transmission rate, and reduce the interference between the secondary users, the primary user monitors the interference received from the secondary users, and while ensuring that the interference threshold is not exceeded, an interference penalty factor is designed. Secondary users with greater interference will be punished more, and the transmission power of secondary users will be allocated further reasonably to reduce interference to primary users.

Description

Interference Management Based Power Rate Joint Control Game Method

technical field

The invention relates to a resource allocation scheme in a cognitive radio system, in particular to a power-rate joint control game method based on interference management, and belongs to the field of information technology.

Background technique

It is well known that the radio frequency spectrum is a valuable natural resource and is generally authorized for use by governments. The spectrum resource allocation method defined earlier is static, and different communication systems can only work in authorized dedicated frequency bands. With the rapid development of wireless communication technology, more and more wireless devices are widely used, spectrum resources are gradually becoming scarce, and become the most valued non-renewable resources in modern society. Especially in recent years, as many users have begun to access the Internet through technologies such as wireless local area network (WLAN) and wireless personal area network (WPAN) working in unlicensed frequency bands, spectrum resources have become increasingly tight. Coupled with the fact that the current wireless services are beginning to develop towards multimedia integrated services, higher download rates and wider spectrum are required, and the lack of spectrum becomes a serious obstacle to high-performance data services. The Federal Communications Commission (FCC) of the United States has conducted a large number of investigations and studies on the use of various frequency bands, and found that the utilization rate of spectrum in the authorized frequency bands is very low. Mainly manifested in: in the hundreds of MHz-3GHz wireless frequency bands with very tight frequency requirements, some frequency bands are idle most of the time, others are occasionally occupied, and others are used for industry, science, medical treatment and land mobile In the frequency band of the communication part, the competition is quite fierce. Obviously, the static spectrum allocation strategy implemented in the past has become a bottleneck with the rapid development of communication technology.

Therefore, it is necessary to introduce a dynamic spectrum access technology to utilize those underused spectrum resources to realize dynamic spectrum allocation, thereby greatly improving spectrum utilization. In order to effectively utilize idle frequency bands in various regions and time periods, people have proposed cognitive radio technology. Wireless communication devices with this cognitive function can be accessed in a certain "opportunistic way" To the licensed frequency bands with few communication services. Therefore, it creates a new situation for solving the problems of insufficient spectrum resources, realizing dynamic spectrum management, and improving spectrum utilization.

The concept of cognitive radio (CR: cognitive radio) was proposed by Joseph Mitola in 1999. Cognitive radio refers to a new intelligent wireless communication technology based on software radio as an extended platform. It can perceive the characteristics of the surrounding wireless environment, use the method of constructing understanding to learn, intelligently communicate with the communication network through the radio knowledge description language, adjust the transmission parameters in real time, and make the wireless transmission of the system adapt to the change of the input radio excitation. In order to achieve high reliability and efficient spectrum utilization of the communication system no matter when and where.

The cognitive process in cognitive radio technology begins with the induction of radio stimuli and ends with the act of reacting. A basic cognitive radio working cycle will go through three basic processes: wireless transmission scene analysis, channel state estimation and its capacity prediction, power control and spectrum management, which are executed sequentially to realize the cognitive function of the CR system.

The game theory analysis of cognitive radio describes the development prospect of the combination of cognitive radio technology and game theory for us. In several key technologies of cognitive radio, the research on decision-making and selection issues can all use the idea of game theory, as long as we find Appropriate utility functions can use game theory to make the algorithm converge to an equilibrium state, and find an adaptive optimal algorithm for solving these problems. The combination of game theory and cognitive radio will surely lay a deeper theoretical foundation for the development of cognitive radio, and play a positive role in promoting its further research. The game theory analysis plan of cognitive radio, has carried out a detailed demonstration on how to use game theory to analyze cognitive radio, so that the combination of game theory and cognitive radio research system will provide future generations with the use of game theory to study cognitive radio Related technologies provide the basis.

Contents of the invention

Technical problem: The purpose of the present invention is to provide a game method based on interference management for joint control of power and rate, aiming at the shortcomings of the existing interference temperature model in reducing the interference received by the primary user, and strengthening the subjectivity of the primary user in interference control. initiative. While the secondary users play games with each other, adjust the transmission power and transmission rate, and reduce the interference between the secondary users, the primary user monitors the interference received from the secondary users, and while ensuring that the interference threshold is not exceeded, an interference penalty factor is designed. Secondary users with greater interference will be punished more, and the transmission power of secondary users will be allocated further reasonably to reduce interference to primary users.

Technical solution: The present invention provides a power-rate joint control game method based on interference management. Each user plays with each other, adjusts the transmission power and transmission rate, and realizes the maximum benefit of each user. The primary user monitors the interference from secondary users. While ensuring that the interference threshold is not exceeded, an interference penalty factor is designed. The secondary users with greater interference will be punished more severely, and the transmission power of secondary users will be allocated further reasonably. Reduce interference to primary users.

The concrete steps of this method are:

是主用户效用部分的收益，表示主用户对所有次用户干扰的惩罚之和，N是次用户的个数，λ为主用户对次用户的干扰惩罚因子，g_i是次用户i到主用户基站BS_p的路径损耗因子，p_i是相应的次用户i的发射功率；第二项

表示次用户的干扰给主用户带来的性能损失，

为次用户对主用户的总干扰，I^tar为干扰的目标值，I_th是主用户定义的干扰门限，也是主用户可承受的干扰的最大值；i=1,2，……N；a. The main user utility function is defined as $u_p=\mathrm{\λ}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{g}_i-\frac{{(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{g}_i-I^{\mathrm{tar}})}^2}{I_{\mathrm{the\; th}}},$ It consists of two parts: the first

is the income of the utility part of the primary user, which means the sum of the punishment of the primary user to all secondary users, N is the number of secondary users, λ is the interference penalty factor of the primary user to the secondary user, g _i is the secondary user i to the primary user The path loss factor of the base station BS _p , p _i is the transmit power of the corresponding secondary user i; the second term

Indicates the performance loss caused by the interference of the secondary user to the primary user,

For the total interference of the secondary user to the primary user, I ^tar is the target value of interference, I _th is the interference threshold defined by the primary user, and is also the maximum value of the interference that the primary user can bear; i=1,2,...N;

是次用户的净收益，定义为吞吐量R_iln(kγ_i)与发射功率p_i的比值，R_i是次用户i的传输速率，ln(kγ_i)是次用户i的帧成功接收概率,k是常数，γ_i是次用户的接收信干比，因此R_iln(kγ_i)是次用户经过一定误码之后的传输速率，设帧成功接收概率为p_c(0≤p_c≤1)，则

是次用户的目标接收信干比，信干比 ${\mathrm{\γ}}_i(R_i,p_i)=\frac{W}{R_i}\frac{h_i{p}_i}{\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}{h}_j{p}_j+{\mathrm{\σ}}^2},\∀i=\mathrm{1,2},...,N,$ 其中W是共享的频谱带宽，h_i是次用户i至次用户基站BS_s的路径损耗因子，σ²是次用户网络功率分配的背景噪声；第二项为次用户系统针对次用户发射功率的增加进行相应的惩罚，由cp_i表示，其中c为常数；第三项bλp_ig_i是主用户对次用户i的干扰惩罚，其中b是常数，λ是干扰惩罚因子；b. The utility of the secondary user is defined as $u_i^{\mathrm{the\; s}}=\frac{R_i\ln \left({\mathrm{k\γ}}_i\right)}{p_i}-{\mathrm{cp}}_i-{\mathrm{b\λp}}_i{g}_i,$ It consists of three items: the first

The net income of the secondary user is defined as the ratio of the throughput R _i ln(kγ _i ) to the transmission power p _i , R _i is the transmission rate of the secondary user i, ln(kγ _i ) is the frame success probability of the secondary user i , k is a constant, γ _i is the receiving signal-to-interference ratio of the secondary user, so R _i ln(kγ _i ) is the transmission rate of the secondary user after a certain bit error, and the probability of successful frame reception is p _c (0≤p _c ≤ 1), then

The user's target receiving signal-to-interference ratio, signal-to-interference ratio ${\mathrm{\γ}}_i(R_i,p_i)=\frac{W}{R_i}\frac{h_i{p}_i}{\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}{h}_j{p}_j+{\mathrm{\σ}}^2},\∀i=\mathrm{1,2},...,N,$ where W is the shared spectrum bandwidth, h _i is the path loss factor from secondary user i to secondary user base station BS _s , σ ² is the background noise of secondary user network power allocation; the second item is the secondary user system’s transmit power for secondary user Increase the corresponding penalty, represented by cp _i , where c is a constant; the third item bλp _i g _i is the interference penalty of the primary user to the secondary user i, where b is a constant, and λ is the interference penalty factor;

时，主用户的效用达到最大，即 $\frac{\∂U_p}{{\∂p}_i}={\mathrm{\λg}}_i-2\frac{g_i(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{g}_i-I^{\mathrm{tar}})}{I_{\mathrm{th}}}=0,$ 求解得到干扰惩罚因子 $\mathrm{\λ}=2\frac{(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{g}_i-I^{\mathrm{tar}})}{I_{\mathrm{th}}}.$ c. Determine the interference penalty factor: when

When , the utility of the primary user reaches the maximum, that is, $\frac{\∂u_p}{{\∂p}_i}={\mathrm{\λg}}_i-2\frac{g_i(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{g}_i-I^{\mathrm{tar}})}{I_{\mathrm{the\; th}}}=0,$ Solve to get the interference penalty factor $\mathrm{\λ}=2\frac{(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{p}_i{g}_i-I^{\mathrm{tar}})}{I_{\mathrm{the\; th}}}.$

Beneficial effects: the purpose of the present invention is to provide a power-rate joint control game method based on interference management in a cognitive radio system. Aiming at the shortcomings of the existing interference temperature model in reducing the interference received by the primary user, the subjective initiative of the primary user in interference control is strengthened. While the secondary users play games with each other, adjust the transmission power and transmission rate, and reduce the interference between the secondary users, the primary user monitors the interference received from the secondary users, and while ensuring that the interference threshold is not exceeded, an interference penalty factor is designed. Secondary users with greater interference will be punished more, and the transmission power of secondary users will be allocated further reasonably to reduce interference to primary users. At the same time, in the secondary user network, due to the reduction of the transmission power, the interference between the secondary users is reduced, and the receiving signal-to-interference ratio has been improved to a certain extent.

Description of drawings

FIG. 1 is a diagram of an interference model of a cognitive radio system.

Detailed ways

The interference model involved in the present invention is shown in FIG. 1 . Analyze the cognitive radio network that shares the spectrum in the underlay mode. The primary user PU _s and the secondary user SU _s coexist and share the same spectrum (the bandwidth is W (MHz)), and the authorized primary user communicates with the primary user base station BS _p , non-authorized secondary users use code division multiple access (CDMA) to communicate with the secondary user base station BS _s (Figure 1). The transmit power of the secondary user will cause certain interference to the primary user and affect the communication quality of the primary user. In order to prevent communication performance from deteriorating due to interference, the primary user defines an interference threshold to limit the maximum interference of secondary users to primary users. In addition, the primary user will impose a certain penalty on the secondary user, and further limit the interference of the secondary user on the basis of the interference threshold.

Regarding the interference to the primary user, the existing method is to use an interference threshold mechanism to limit the transmission power of the secondary user, which alleviates the unfavorable situation of interference to the primary user to a certain extent. However, the interference threshold is the maximum interference that the primary user can bear. It is always a constant during the process of power adjustment of the secondary user. For the interference of the primary user, the present invention provides a new interference-based power-rate joint control game method. While the secondary users play games with each other, adjust the transmission power and transmission rate, and reduce the interference between secondary users, the primary user monitors the interference from the secondary user network (a network composed of all secondary users) in real time. On the basis of not exceeding the interference threshold, Correspondingly punish the secondary users who interfere with their communication, further reduce the transmission power of the secondary users, and reduce the interference to themselves.

The key to game analysis is to establish a reasonable game model, and the key to building a model is to choose an appropriate utility function, and on this basis, give the proof of the existence and uniqueness of Nash equilibrium, and finally seek the first-order optimization of the utility function to find the Nash equilibrium. balance point.

1. Define the utility function

Define the master user utility as follows:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; tar</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

的发射功率，g_i是次用户

到主用户基站BS_p的路径损耗因子（g_i＝a/(D_i)⁴，a是常数，D_i是次用户

至主用户基站BS_p的距离（米）），干扰的目标值I^tar，I_th是主用户定义的干扰门限，也是主用户可承受的干扰的最大值。In the above formula, λ represents the interference penalty of the primary user to the secondary user, and p _i is the corresponding secondary user

The transmit power of , g _i is the secondary user

The path loss factor to the primary user base station BS _p (g _i =a/(D _i ) ⁴ , where a is a constant and D _i is the secondary user

The distance to the primary user base station BS _p (meters)), the interference target value I ^tar , I _th is the interference threshold defined by the primary user, and is also the maximum value of interference that the primary user can bear.

表示主用户对所有次用户干扰的惩罚之和（N是次用户的个数）；

表示次用户的干扰给主用户带来的性能损失。It can be seen from formula (1) that the main user’s income consists of two parts:

Indicates the sum of penalties for the primary user to interfere with all secondary users (N is the number of secondary users);

Indicates the performance loss caused by the interference of the secondary user to the primary user.

Considering the price paid by the secondary user due to the interference caused by the primary user, the utility function of the secondary user is established:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k\&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; cp</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b\&lambda;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

的传输速率，ln(kγ_i)是次用户

的帧成功接收概率（k是常数，γ_i是次用户的接收信干比），b,c是常数。where R _i is the secondary user

The transmission rate of , ln(kγ _i ) is the secondary user

The probability of successful reception of the frame (k is a constant, γ _i is the receiving signal-to-interference ratio of the secondary user), b, c are constants.

The first item in Equation (2) is the net income of the secondary user; in the secondary user network, each secondary user wants to increase its transmit power to increase the receiving SIR, but it will bring unavoidable interference to other users. Therefore, the transmit power of the secondary user is limited to a certain extent, and the secondary user system will have a corresponding penalty for the increase of the transmit power of the secondary user, which is represented by the second item; the third item is the interference penalty of the primary user to the secondary user i.

2. The interference penalty factor defined by the main user

According to the idea of game theory, when the transmission power of the secondary user converges, the utility of the primary user reaches the maximum value. have

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Derivation of formula (1) with respect to p _i , combined with formula (3):

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&lambda;g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\frac{{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; tar</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Right now

$\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\frac{<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; tar</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

越大时，主用户对次用户的惩罚因子也越大。The above formula is the penalty factor for the primary user to the secondary user. It can be seen from this formula that the total interference of the current user

The larger the value, the greater the penalty factor for the primary user to the secondary user.

3. Proof of the existence and uniqueness of Nash equilibrium

Let s=(s ₁ ,s ₂ ,...,s _n ) be a game with n individuals G={S ₁ ,S ₂ ,...,S _n ;U ₁ ,U ₂ ,...,U _n } A strategy portfolio for each player i if:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

For all s _i ∈ S _i holds true, then we call the strategy combination s=(s ₁ ,s ₂ ,...,s _n ) a Nash equilibrium of the game. Among them, s _-i represents the combination of strategies selected by all participants except i in n.

Theorem 1 (Existence) In n-person game G={S ₁ ,S ₂ ,...,S _n ;U ₁ ,U ₂ ,...,U _n }, if for all i=1,2 ,...,N all have the following conditions:

(1) S _i is a non-empty, convex compact set in Euclidean space;

(2) U _i is a continuous quasi-concave function.

Then G={S ₁ , S ₂ ,...,S _n ; U ₁ , U ₂ ,...,U _n } has a Nash equilibrium solution.

有p_min≤p_i≤p_max和R_min≤R_i≤R_max，条件（1）满足。Game for the present invention

There are p _min ≤ p _i ≤ p _max and R _min ≤ _{R i} ≤ R _max , condition (1) is satisfied.

Derivation of formula (2):

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k\&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; bg</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Derivative again:

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k\&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; \&rsqb;</span>}{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; bg</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

是p_i的凹函数。ln(kγ _i )≤1, so the above formula $\frac{{\&PartialD;}^2{u}_i^{\mathrm{the\; s}}}{{{\&PartialD;p}_i}^2}\&le;0,\&ForAll;i=\mathrm{1,2},...,N,$ therefore

is a concave function of p _i .

In the same way,

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

是R_i的凹函数。条件（2）满足。therefore

is a concave function of R _i . Condition (2) is satisfied.

In summary,

存在纳什均衡解 $\left\{\right\{p_1^{*},R_1^{*}\},\{p_2^{*},R_2^{*}\},...,\{p_N^{*},R_N^{*}\left\}\right\}.$

There is a Nash equilibrium solution $\left\{\right\{p_1^{*},R_1^{*}\},\{p_2^{*},R_2^{*}\},...,\{p_N^{*},R_N^{*}\left\}\right\}.$

R⁺表示正实数）。Theorem 2 (uniqueness) For n-person game G={S ₁ ,S ₂ ,...,S _n ;U ₁ ,U ₂ ,...,U _n }, if the optimal response function υ(S)= {υ ₁ (S),υ ₂ (S),...,υ _n (S)} is a standard function, then the existence of the Nash equilibrium solution {S ₁ ^* , S ₂ ^* , . .., _Sn ^* } is unique. (υ _i (S)={S _i ∈ R ⁺ : U _i (S _i ,S _-i )≥U _i (S _i ',S _-i ),

R ⁺ means a positive real number).

A function is a standard function if it meets the following criteria:

——Constantly positive: υ(S)≥0;

——Monotonicity: If S≥S', then υ(S)≥υ(S');

——Extensibility: For any real number α≥1, αυ(S)>υ(αS).

定义最佳响应函数如下：Game for the present invention

The best response function is defined as follows:

Power optimal response function:

φ _i (p _-i )＝{u _i ^s (p _i ,p _-i )≥u _i ^s (p _i ',p _-i )} (10)

Rate optimal response function:

Since the best response function is a standard function. Therefore, the Nash equilibrium solution only one.

具有唯一存在的纳什均衡解

In summary, the game

has a unique Nash equilibrium solution

For the power-rate joint control game method, the specific implementation process of the update algorithm of the transmit power and transmission rate is as follows:

(1) Set the initial values p _i (0) and R _i (0) of the transmission power and transmission rate of secondary user i.

(2) Define the penalty factor for the interference of the primary user to the secondary user according to the maximum utility U _p of the primary user.

以实现次用户效用

的最优。(3) Use game theory to find the best transmission power and transmission rate for each secondary user i

sub-user utility

the best.

(4) If the transmission power meets the accuracy requirements, and the interference of the secondary user to the primary user does not exceed the interference threshold, the game is stable.

Claims (1)

1. A power rate joint control game method based on interference management, characterized in that the specific steps of the method are: a. The main user utility function is defined as $u_p=\mathrm{\&lambda;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_i{g}_i-\frac{{(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_i{g}_i-I^{\mathrm{tar}})}^2}{I_{\mathrm{the\; th}}},$ It consists of two parts: the first

is the income of the utility part of the primary user, which means the sum of the punishment of the primary user to all secondary users, N is the number of secondary users, λ is the interference penalty factor of the primary user to the secondary user, g _i is the secondary user i to the primary user The path loss factor of the base station BS _p , p _i is the transmit power of the corresponding secondary user i; the second term

Indicates the performance loss caused by the interference of the secondary user to the primary user,

For the total interference of the secondary user to the primary user, I ^tar is the target value of interference, I _th is the interference threshold defined by the primary user, and is also the maximum value of the interference that the primary user can bear; i=1,2,...N; b. The utility of the secondary user is defined as $u_i^{\mathrm{the\; s}}=\frac{R_i\ln \left({\mathrm{k\&gamma;}}_i\right)}{p_i}-{\mathrm{cp}}_i-{\mathrm{b\&lambda;p}}_i{g}_i,$ It consists of three items: the first The net income of the secondary user is defined as the ratio of the throughput R _i ln(kγ _i ) to the transmission power p _i , R _i is the transmission rate of the secondary user i, ln(kγ _i ) is the frame success probability of the secondary user i , k is a constant, γ _i is the receiving signal-to-interference ratio of the secondary user, so R _i ln(kγ _i ) is the transmission rate of the secondary user after a certain bit error, and the probability of successful frame reception is p _c (0≤p _c ≤ 1), then

The user's target receiving signal-to-interference ratio, signal-to-interference ratio ${\mathrm{\&gamma;}}_i(R_i,p_i)=\frac{W}{R_i}\frac{h_i{p}_i}{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Sigma;}}}{h}_j{p}_j+{\mathrm{\&sigma;}}^2},\&ForAll;i=\mathrm{1,2},...,N,$ where W is the shared spectrum bandwidth, h _i is the path loss factor from secondary user i to secondary user base station BS _s , σ ² is the background noise of secondary user network power allocation; the second item is the transmission power of secondary user system for secondary user Increase the corresponding penalty, represented by cp _i , where c is a constant; the third item bλp _i g _i is the interference penalty of the primary user to the secondary user i, where b is a constant, and λ is the interference penalty factor; c. Determine the interference penalty factor: when

When , the utility of the primary user reaches the maximum, that is, $\frac{{\&PartialD;u}_p}{\&PartialD;p_i}={\mathrm{\&lambda;g}}_i-2\frac{g_i(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_i{g}_i-I^{\mathrm{tar}})}{I_{\mathrm{the\; th}}}=0,$ Solve to get the interference penalty factor $\mathrm{\&lambda;}=2\frac{(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_i{g}_i-I^{\mathrm{tar}})}{I_{\mathrm{the\; th}}};$ For the power-rate joint control game method, the specific implementation process of the update algorithm of the transmit power and transmission rate is as follows: (1) Set the initial values p _i (0) and R _i (0) of the transmission power and transmission rate of secondary user i; (2) Define the penalty factor for the interference of the primary user to the secondary user according to the maximum utility U _p of the primary user; (3) Using game theory, for each secondary user i, find the optimal transmission power and transmission rate {p _i ^* , R _i ^* } to achieve secondary user utility the best; (4) If the transmission power meets the accuracy requirements, and the interference of the secondary user to the primary user does not exceed the interference threshold, the game is stable.

Images