CN112543498B - A Power Adaptive Allocation Method Based on Hierarchical Game Model - Google Patents

Abstract

Translated fromChinese

本发明公开了一种基于分层博弈模型的功率自适应分配方法，属于移动通信技术领域，解决无线资源中的功率自适应分配问题。将分层博弈的理论引入到5G异构融合网络中，建立由RNC、基站和基站用户构成的三层异构网络模型。RNC和基站之间采用斯坦克尔伯格博弈模型；基站用户根据各自对应的基站分配得到的功率采用非合作博弈的方式进一步博弈。该方法首先进行的是RNC向其下管理的各个基站分配功率，之后基站所包含的用户根据其所属基站分配到的功率作进一步的分配，从而实现功率的初次分配、再次分配、用户端功率分配的目标，进而能够减少干扰、提升系统容量。

The invention discloses a power self-adaptive allocation method based on a layered game model, which belongs to the technical field of mobile communication and solves the problem of power self-adaptive allocation in wireless resources. The theory of layered game is introduced into the 5G heterogeneous fusion network, and a three-layer heterogeneous network model consisting of RNC, base station and base station users is established. The Steinkelberg game model is used between the RNC and the base station; the users of the base station use a non-cooperative game to further play the game according to the power allocated by their corresponding base stations. In this method, the RNC first allocates power to each base station under its management, and then the users included in the base station further allocate the power according to the power allocated by the base station to which it belongs, so as to realize the initial power allocation, re-allocation, and power allocation of the user terminal. The goal is to reduce interference and increase system capacity.

Description

Translated fromChinese

一种基于分层博弈模型的功率自适应分配方法A Power Adaptive Allocation Method Based on Hierarchical Game Model

技术领域technical field

本发明属于移动通信技术领域，具体涉及一种基于分层博弈模型的功率自适应分配方法。The invention belongs to the technical field of mobile communication, and in particular relates to a power adaptive allocation method based on a layered game model.

背景技术Background technique

5G异构网络中网络密集化是5G发展的趋势，在基站大量部署的情况下研究5G异构融合网络中的资源分配等问题十分重要。Network densification in 5G heterogeneous networks is the trend of 5G development. It is very important to study issues such as resource allocation in 5G heterogeneous converged networks when base stations are deployed in large numbers.

一般在宏基站周围设置多个毫微微基站可以扩大覆盖面积，毫微微基站可以对宏基站覆盖不到的地方进行补充，毫微微基站与宏基站共用频谱资源，与此同时移动设备、数据流量的大幅增长会造成资源的紧缺。考虑到今后日益增长的数据流量及移动通信设备等情况，异构网络中会部署大量的毫微微基站，从而可以增强通信质量、提高通信速度等，但同时未来的网络资源将会变的非常珍贵，资源的分配问题不容忽视，需要解决好资源的供给和资源的需求之间的问题，将资源进行合理地分配可以维持整个通信系统的稳定性，同时也可以减少干扰从而提高用户的服务质量，并且能够提升系统容量、实现资源的高效利用，其中功率分配是资源管理中的研究任务之一，功率的合理分配可以有效的减少干扰、保障用户的通信质量。Generally, setting up multiple femto base stations around the macro base station can expand the coverage area. The femto base station can supplement the areas that cannot be covered by the macro base station. The femto base station and the macro base station share spectrum resources. Substantial growth will create a shortage of resources. Considering the increasing data traffic and mobile communication equipment in the future, a large number of femto base stations will be deployed in heterogeneous networks, which can enhance communication quality and speed, but at the same time, network resources will become very precious in the future. , the problem of resource allocation cannot be ignored. It is necessary to solve the problem between the supply of resources and the demand of resources. Reasonable allocation of resources can maintain the stability of the entire communication system, and at the same time, it can reduce interference and improve the quality of service for users. And it can improve the system capacity and realize the efficient use of resources. Among them, power allocation is one of the research tasks in resource management. Reasonable allocation of power can effectively reduce interference and ensure the communication quality of users.

发明内容SUMMARY OF THE INVENTION

本发明提出的一种基于分层博弈模型的功率自适应分配方法，从功率分配的角度出发，引入基于斯坦克尔伯格博弈与非合作博弈的功率控制方法和基于分层博弈的功率分配算法来解决5G异构融合网络中的功率分配问题。A power self-adaptive distribution method based on a layered game model proposed by the present invention, from the perspective of power distribution, introduces a power control method based on a Steinkelberg game and a non-cooperative game and a power distribution algorithm based on a layered game To solve the power allocation problem in the 5G heterogeneous converged network.

为了实现上述目的，本发明采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:

一种基于分层博弈模型的功率自适应分配方法，包括如下步骤：A power adaptive allocation method based on a hierarchical game model, comprising the following steps:

(1)在5G异构融合网络区域内，采用博弈论的理论基础构建由RNC、基站和基站用户组成的三层异构融合网络模型；(1) In the 5G heterogeneous fusion network area, the theoretical basis of game theory is used to build a three-layer heterogeneous fusion network model composed of RNC, base station and base station users;

(2)采用基于斯坦克尔伯格博弈与非合作博弈的功率控制方法得到最优发射功率；(2) Using the power control method based on the Steinkelberg game and the non-cooperative game to obtain the optimal transmit power;

(3)通过对分层博弈均衡解的分析得到斯坦克尔伯格博弈的均衡解；(3) The equilibrium solution of the Steinkelberg game is obtained by analyzing the equilibrium solution of the hierarchical game;

(4)采用基于分层博弈的功率分配算法得到收敛的功率值及各基站最优定价。(4) The power allocation algorithm based on hierarchical game is used to obtain the convergent power value and the optimal pricing of each base station.

优选地，所述步骤(2)中，RNC与基站之间采用斯坦克尔伯格博弈，RNC是博弈领导者，基站是跟随者；基站用户间采用非合作博弈得到各自的最优发射功率；Preferably, in the step (2), a Steinkelberg game is used between the RNC and the base station, where the RNC is the leader of the game and the base station is the follower; the users of the base station use a non-cooperative game to obtain their respective optimal transmit powers;

其中，斯坦克尔伯格博弈的具体过程为：Among them, the specific process of the Steinkelberg game is as follows:

在一给定时隙内，RNC对基站i单位功率的定价为λ_i，基站i的传输带宽为w_i，则基站i的链路传输速率如下：In a given time slot, the unit power of base station i is priced by RNC as λ_i , and the transmission bandwidth of base station i is_wi , then the link transmission rate of base station i is as follows:

其中，p_i表示基站i的发射功率，p_j表示基站j的发射功率，p₀表示RNC的传输功率，h_ii表示基站i与其用户的链路信道的功率增益，h_i0表示RNC与基站i之间的干扰链路增益，h_ij表示基站i与用户j的干扰链路增益，N为基站总数，i为任一基站且i∈{1,2,3…,N}；Among them, pi represents the transmit power of base station i, p_j represents the transmit power of base station_j , p₀ represents the transmission power of RNC, h_ii represents the power gain of the link channel between base station i and its users, and h_i0 represents the power gain between RNC and base station i The interference link gain between , h_ij represents the interference link gain between base station i and user j, N is the total number of base stations, i is any base station and i∈{1,2,3...,N};

基站i的效用函数U_i如下：The utility function U_i of base station i is as follows:

RNC的效用函数U_RNC如下：The utility function U_RNC of RNC is as follows:

其中，h_0i为基站i对基站用户的干扰链路增益；Among them, h_0i is the interference link gain of base station i to base station users;

综上所述，RNC的优化问题如下：In summary, the optimization problem of RNC is as follows:

其中，

分别为链路传输速率的上、下界；in,

are the upper and lower bounds of the link transmission rate, respectively;

基站的优化问题如下：The optimization problem of the base station is as follows:

式(5)和(6)共同构成了一次斯坦克尔伯格博弈过程，RNC在掌握了基站的最优策略的情况下对基站功率进行定价，基站通过观察RNC的定价后采取相应策略行动，调整自身发射功率；Equations (5) and (6) together constitute a Steinkelberg game process. The RNC price the base station power under the condition of mastering the optimal strategy of the base station, and the base station takes corresponding strategic actions after observing the pricing of the RNC, Adjust its own transmit power;

其中，基站用户间非合作博弈的过程是对式(6)进行求解，之后将其结果代入式(5)，求解RNC的优化问题，最后整个系统达到斯坦克尔伯格均衡；Among them, the process of non-cooperative game among base station users is to solve equation (6), and then substitute the result into equation (5) to solve the optimization problem of RNC, and finally the whole system reaches the Steinkelberg equilibrium;

其中，达到斯坦克尔伯格博弈均衡时的均衡解(λ^*，

)满足如下条件：Among them, the equilibrium solution (λ^* ,

) meets the following conditions:

U_RNC(λ^*,p^*)≥U_RNC(λ,p^*) (7)U_RNC (λ^* ,p^* )≥U_RNC (λ,p^* ) (7)

其中，λ^*为RNC的最优定价集合，p*为RNC的最优发射功率策略集合，λ为RNC对基站单位功率的定价，

为基站i的最优定价集合，

为基站i的最优发射功率策略集合。Among them, λ^* is the optimal pricing set of the RNC, p* is the optimal set of transmit power policies of the RNC, λ is the price of the unit power of the base station by the RNC,

is the optimal pricing set for base station i,

is the optimal transmit power strategy set of base station i.

优选地，所述步骤(3)的具体过程为：Preferably, the specific process of the step (3) is:

首先，利用倒推法求出基站用户非合作博弈达到纳什均衡时的最优发射功率，具体过程为：First, the optimal transmit power when the non-cooperative game of the base station users reaches the Nash equilibrium is obtained by using the backward method. The specific process is as follows:

对于给定的定价，式(6)有一最优解即基站的最优发射功率如下：For a given price, equation (6) has an optimal solution, that is, the optimal transmit power of the base station is as follows:

其中，(a)⁺为max{a,0}；Among them, (a)⁺ is max{a,0};

其次，将所求得的最优发射功率写成矩阵形式，代入到RNC的效用函数中进行化简；Secondly, write the obtained optimal transmit power in matrix form, and substitute it into the utility function of RNC for simplification;

最后，研究其效用函数与定价之间的关系，进而简化其优化问题，在系统模型达到斯坦克尔伯格均衡时求出RNC的最优定价，RNC的最优定价λ^*如下：Finally, the relationship between its utility function and pricing is studied, and its optimization problem is simplified. When the system model reaches the Steinkelberg equilibrium, the optimal pricing of RNC is obtained. The optimal pricing λ^* of RNC is as follows:

其中，

为λ_i的上界，n₀为RNC的噪声干扰；in,

is the upper bound of λ_i , and n₀ is the noise interference of RNC;

由式(10)和式(32)得到的最优发射功率和最优定价构成了斯坦克尔伯格博弈的均衡解(p_i(λ^*),λ^*)。The optimal transmit power and optimal pricing obtained by Equation (10) and Equation (32) constitute the equilibrium solution (_pi (λ^* ),λ^* ) of the Steinkelberg game.

优选地，所述步骤(4)的具体过程为：Preferably, the specific process of the step (4) is:

首先，RNC根据基站的初始发射功率计算各个基站的定价，并通过RNC将所得定价广播给对应的基站；First, the RNC calculates the pricing of each base station according to the initial transmit power of the base station, and broadcasts the obtained pricing to the corresponding base station through the RNC;

其次，基站收到定价后根据迭代函数对自身发射功率进行调整，Secondly, after receiving the pricing, the base station adjusts its own transmit power according to the iterative function.

迭代函数如下：The iteration function is as follows:

最后，设定迭代次数，得到各个基站的最优发射功率和RNC对各个基站的最优定价。Finally, the number of iterations is set to obtain the optimal transmit power of each base station and the optimal pricing of each base station by the RNC.

本发明所带来的有益技术效果：Beneficial technical effects brought by the present invention:

本发明提出的一种基于分层博弈模型的功率自适应分配方法，从功率分配的角度出发，引入基于斯坦克尔伯格博弈与非合作博弈的功率控制方法和基于分层博弈的功率分配算法来解决5G异构融合网络中的功率分配问题，从而能够有效的减少干扰、提高通信质量、提升通信系统的整体性能。A power self-adaptive distribution method based on a layered game model proposed by the present invention, from the perspective of power distribution, introduces a power control method based on a Steinkelberg game and a non-cooperative game and a power distribution algorithm based on a layered game To solve the power allocation problem in the 5G heterogeneous fusion network, it can effectively reduce interference, improve communication quality, and improve the overall performance of the communication system.

附图说明Description of drawings

图1为本发明的方法框图；Fig. 1 is the method block diagram of the present invention;

图2为本发明的三层异构网络模型示意图；2 is a schematic diagram of a three-layer heterogeneous network model of the present invention;

图3为本发明实施例的功率分配技术分类示意图；3 is a schematic diagram of classification of power distribution technologies according to an embodiment of the present invention;

图4为本发明的功率分配算法流程图。FIG. 4 is a flow chart of the power allocation algorithm of the present invention.

具体实施方式Detailed ways

下面结合附图以及具体实施方式对本发明作进一步详细说明：The present invention is described in further detail below in conjunction with the accompanying drawings and specific embodiments:

如图1所示为本发明的方法框图，包括如下四个过程：采用博弈论的理论基础来构建系统模型；采用基于斯坦克尔伯格博弈与非合作博弈的功率控制方法来得到最优发射功率；通过对分层博弈均衡解的分析得到博弈的均衡解；采用基于分层博弈的功率分配算法得到收敛的功率值及各基站最优定价。具体表现为：建立由无线网络控制器(RNC，RadioNetwork Controller)、基站和基站用户构成的三层异构网络模型，在异构融合网络中干扰问题不容忽视，为提高自身吞吐量基站应提高发射功率，但这会产生更多的干扰，从而影响系统性能，采用分层博弈的方法并考虑干扰问题，系统整体基于斯坦克尔伯格博弈模型进行分析，在基站的效用函数中设置代价函数，以非合作博弈的方式达到稳定状态，RNC根据基站均衡状态时的发射功率得到对其所收取的定价，整个系统达到斯坦克尔伯格均衡。同时，设计了一种功率分配算法，证明了其收敛性并实现了功率分配处理，得到了RNC对基站的定价及基站效用函数等。Figure 1 is a block diagram of the method of the present invention, which includes the following four processes: using the theoretical basis of game theory to build a system model; using a power control method based on the Steinkelberg game and non-cooperative game to obtain the optimal transmission Power; the equilibrium solution of the game is obtained by analyzing the equilibrium solution of the hierarchical game; the power distribution algorithm based on the hierarchical game is used to obtain the convergent power value and the optimal pricing of each base station. The specific performance is as follows: establish a three-layer heterogeneous network model composed of Radio Network Controller (RNC, Radio Network Controller), base stations and base station users. power, but this will generate more interference, which will affect the system performance. The layered game method is adopted and the interference problem is considered. The whole system is analyzed based on the Steinkelberg game model, and the cost function is set in the utility function of the base station. In a non-cooperative game, the stable state is reached, and the RNC obtains the price charged by the base station according to the transmission power in the equilibrium state, and the whole system reaches the Steinkelberg equilibrium. At the same time, a power allocation algorithm is designed, which proves its convergence and realizes the power allocation processing, and obtains the RNC's pricing of the base station and the base station utility function.

下面对每一过程作进一步的具体描述。Each process is further described in detail below.

(1)基于博弈论构建三层异构融合网络模型(1) Build a three-layer heterogeneous fusion network model based on game theory

博弈可分为合作博弈和非合作博弈，即根据博弈过程中局中人是否能够达成一个共识即达成一个具有约束力的协议进行分类。若可以达成这一共识则为合作博弈，反之为非合作博弈。合作博弈重点研究局中人的相互合作过程，强调的是整体利益，通过合作使每个局中人都能够得到自身的利益从而提高整体利益；非合作博弈过程中局中人之间未能达成共识，局中人以自己的利益为出发点采取相应的策略方案，重点在于追求个人利益的最大化。Games can be divided into cooperative games and non-cooperative games, that is, they are classified according to whether the players in the game can reach a consensus, that is, reach a binding agreement. If this consensus can be reached, it is a cooperative game, otherwise it is a non-cooperative game. The cooperative game focuses on the process of mutual cooperation among the players, emphasizing the overall interests. Through cooperation, each player can obtain their own interests to improve the overall interests; in the process of non-cooperative games, the players cannot reach an agreement Consensus, players take their own interests as the starting point to adopt corresponding strategic plans, focusing on the pursuit of maximizing personal interests.

斯坦克尔伯格博弈是非合作博弈的一个分支，博弈过程中的局中人根据博弈的等级顺序可分为领导者(Leader)和跟随者(Follower)，斯坦克尔伯格博弈的稳定状态为斯坦克尔伯格博弈均衡(SE,Stackelberg Equilibrium)，在博弈时，领导者先行动，之后跟随者做出行动，可以将其看成是双层博弈过程，博弈高层即领导者掌握跟随者的博弈信息选择自身策略行为，博弈的低层即跟随者看到领导者采取的策略后，选择适合自己的策略。The Steinkelberg game is a branch of the non-cooperative game. The players in the game can be divided into leaders and followers according to the hierarchical order of the game. The stable state of the Steinkelberg game is Stackelberg Equilibrium (SE, Stackelberg Equilibrium), in the game, the leader acts first, and then the follower acts, which can be regarded as a two-layer game process. The game information chooses its own strategic behavior. The lower level of the game, that is, the follower sees the strategy adopted by the leader and chooses the strategy that suits him.

图2为本发明的三层异构网络模型示意图，建立一个由无线网络控制器RNC、基站和基站用户构成的三层异构融合网络模型，无线网络控制器给基站分配功率，之后再将功率作进一步的分配，实现用户端的功率分配。Fig. 2 is a schematic diagram of a three-layer heterogeneous network model of the present invention. A three-layer heterogeneous converged network model consisting of a radio network controller RNC, a base station and a base station user is established. The radio network controller allocates power to the base station, and then transfers the power to the base station. Make further allocation to realize the power allocation of the user end.

通信网络中采用正交频分多址接入(OFDMA，Orthogonal Frequency DivisionMultiplexing Access)技术，基站用户共用一个频段进行数据传输，假设系统内已完成子信道的分配工作，同属于一个基站的多位用户不能同时占用一个信道资源，因此在某一特定时隙内基站只有一个活跃用户，在这一时隙内该活跃用户向所属基站传输数据信息。Orthogonal Frequency Division Multiple Access (OFDMA) technology is used in the communication network. Base station users share a frequency band for data transmission. Assuming that the allocation of sub-channels has been completed in the system, multiple users belonging to the same base station One channel resource cannot be occupied at the same time, so the base station has only one active user in a certain time slot, and the active user transmits data information to the affiliated base station in this time slot.

设有N个基站，i为任一基站且i∈{1,2,3…,N}，i＝0表示RNC。i基站所服务的用户的接收信干噪比(SINR，Signal To Interference plus Noise Ratio)为：There are N base stations, i is any base station and i∈{1,2,3...,N}, i=0 means RNC. The received Signal to Interference and Noise Ratio (SINR, Signal To Interference plus Noise Ratio) of the user served by the i base station is:

其中，p_i表示基站i的发射功率，p_j表示基站j的发射功率，p₀表示RNC的传输功率，h_ii表示基站i与其用户的链路信道的功率增益，h_i0表示RNC与基站i之间的干扰链路增益，h_ij表示基站i与用户j的干扰链路增益，n₀表示RNC的噪声干扰。Among them, pi represents the transmit power of base station i, p_j represents the transmit power of base station_j , p₀ represents the transmission power of RNC, h_ii represents the power gain of the link channel between base station i and its users, and h_i0 represents the power gain between RNC and base station i The interference link gain between , h_ij represents the interference link gain between base station i and user j, and n₀ represents the noise interference of the RNC.

(2)基于斯坦克尔伯格博弈与非合作博弈的功率控制方法(2) Power control method based on Steinkelberg game and non-cooperative game

针对在5G异构融合网络中的资源分配问题中的功率分配问题，其分配技术主要有以下三种：For the power allocation problem in the resource allocation problem in the 5G heterogeneous converged network, there are three main allocation techniques:

①集中式功率分配：在集中式分配技术中会设置一个集中控制中心，用于搜索和存储信道、功率、信噪比等方面的相关信息，并通过集中控制中心分配通信系统的资源，如频谱资源、功率资源等，合理分析并负责整体网络的资源利用与分配问题，在集中控制中心与用户终端设备相互合作的基础上实现系统的利益最大化。①Centralized power distribution: In the centralized distribution technology, a centralized control center will be set up to search and store relevant information such as channels, power, signal-to-noise ratio, etc., and allocate the resources of the communication system, such as frequency spectrum, through the centralized control center. resources, power resources, etc., reasonably analyze and be responsible for the resource utilization and allocation of the overall network, and maximize the benefits of the system on the basis of the cooperation between the centralized control center and the user terminal equipment.

集中式功率分配过程需要集中控制中心对用户提供的信息进行统一保存和管理，之后根据所得到的信息对系统的功率资源进行统一的分配，在上述过程中需要大量的信息，并且用户端需要与集中控制中心不断地进行信息的交互，这就需要保证一定数量的基础设备从而实现集中控制中心的功能，但在实际应用场景中很难实现，加之集中控制处理的过程十分复杂、繁琐，因此在实际通信系统中很少用到集中式功率分配方法。The centralized power allocation process requires the centralized control center to uniformly store and manage the information provided by the user, and then uniformly allocate the power resources of the system according to the obtained information. A large amount of information is required in the above process, and the user end needs to communicate with the user. The centralized control center continuously exchanges information, which requires a certain number of basic equipment to realize the function of the centralized control center, but it is difficult to achieve in practical application scenarios. In addition, the process of centralized control processing is very complicated and cumbersome. The centralized power distribution method is rarely used in practical communication systems.

②分布式功率分配：在分布式功率分配过程中没有集中控制中心，与集中式功率分配技术相比，不需要用户向集中控制中心提供和传输自己的数据信息，网络系统中的用户终端不需要与其他用户交互信息，只需要考虑自身的传输速率，为提高传输速率则需要提高自身发射功率，通常会运用博弈论的相关理论进行研究，构造一个用户间相互博弈的模型，以传输速率最大化为博弈目标进行博弈，从而达到整个系统的稳定状态，用户终端均能实现最优性能。因分布式功率分配技术较集中式技术简单，且花费较少，在实际中应用较为广泛。②Distributed power distribution: There is no centralized control center in the process of distributed power distribution. Compared with the centralized power distribution technology, users do not need to provide and transmit their own data information to the centralized control center, and user terminals in the network system do not need to To exchange information with other users, you only need to consider your own transmission rate. In order to increase the transmission rate, you need to increase your own transmission power. Usually, related theories of game theory are used to conduct research to construct a game model between users to maximize the transmission rate. The game is played for the game target, so as to achieve the stable state of the whole system, and the user terminal can achieve the optimal performance. Because the distributed power distribution technology is simpler and less expensive than the centralized technology, it is widely used in practice.

③半分布式功率分配：将集中式功率分配与分布式功率分配结合起来即为半分布式功率分配，集中控制中心与基站之间进行统一的集中分配处理，之后基站对各自管理的区域实现进一步的功率分配。③Semi-distributed power distribution: The combination of centralized power distribution and distributed power distribution is called semi-distributed power distribution. Unified centralized distribution processing is performed between the centralized control center and the base station. power distribution.

基于图3功率分配技术所构建的5G异构融合网络模型进行功率分配问题的研究，在斯坦克尔伯格博弈中RNC作为博弈领导者，基站作为跟随者根据RNC的行动做出相应的策略，用户之间通过非合作博弈的方法得到各自的最优策略，即最优发射功率。Based on the 5G heterogeneous fusion network model constructed by the power allocation technology in Figure 3, the power allocation problem is studied. In the Steinkelberg game, the RNC acts as the game leader, and the base station acts as a follower to make corresponding strategies according to the actions of the RNC. The users obtain their own optimal strategies through non-cooperative game methods, that is, the optimal transmit power.

为减少对用户的干扰，RNC对基站进行定价，若定价过低，基站所得功率过多，则会对RNC产生干扰，RNC为了自身的效用及利益，会提高其定价，基站所得功率会相应减少，RNC定价与基站功率相互影响，共同构成了斯坦克尔伯格博弈，基站会根据RNC的定价选择自身最优发射功率，用户间通过非合作博弈达到纳什均衡，即求出其最佳发射功率，之后利用求得的最优发射功率进行RNC最优定价的研究，此时整个系统达到斯坦克尔伯格均衡，最优定价与最优发射功率的集合即为斯坦克尔伯格博弈的均衡解，此时博弈双方通过改变自身的策略不能继续增加自己的利益，博弈达到了稳定状态。In order to reduce the interference to users, the RNC sets the price for the base station. If the price is too low and the power obtained by the base station is too much, it will cause interference to the RNC. For its own utility and interests, the RNC will increase its price, and the power obtained by the base station will be reduced accordingly. , RNC pricing and base station power interact with each other, which together constitute the Steinkelberg game. The base station will choose its own optimal transmit power according to the RNC pricing, and users will reach Nash equilibrium through non-cooperative game, that is, find their optimal transmit power. , and then use the obtained optimal transmit power to study the optimal pricing of RNC. At this time, the whole system reaches the Steinkelberg equilibrium, and the set of optimal pricing and optimal transmit power is the equilibrium of the Steinkelberg game. At this time, both sides of the game cannot continue to increase their own interests by changing their own strategies, and the game has reached a stable state.

①RNC与基站之间的斯坦克尔伯格博弈①Stankelberg game between RNC and base station

在一给定时隙内，设RNC对基站i单位功率的定价为λ_i，基站i的传输带宽为w_i，则基站i的链路传输速率可表示为：In a given time slot, let RNC price the unit power of base station i as λ_i , and the transmission bandwidth of base station i as_wi , then the link transmission rate of base station i can be expressed as:

设基站i的效用函数为U_i，可表示为：Let the utility function of base station i be U_i , it can be expressed as:

基站的效用函数由两部分组成，第一部分为用户以信噪比为基础的对数形式的收益函数，第二部分为RNC对基站功率设定的代价函数，效用函数为两部分之差。The utility function of the base station consists of two parts. The first part is the user's logarithmic gain function based on the signal-to-noise ratio. The second part is the cost function set by the RNC for the base station power. The utility function is the difference between the two parts.

与此同时，RNC要设置合理的定价来减少对用户的干扰，设RNC的效用函数为U_RNC,可表示为：At the same time, RNC should set a reasonable price to reduce the interference to users. Let the utility function of RNC be U_RNC , which can be expressed as:

其中，h_0i为基站i对用户的干扰链路增益。Among them, h_0i is the interference link gain of base station i to the user.

综上所述，RNC的优化问题可表示为：To sum up, the optimization problem of RNC can be expressed as:

其中，

分别为链路传输速率的上、下界，为保证基站i和用户进行数据传输时的服务质量(QoS，Quality of Service)。in,

are the upper and lower bounds of the link transmission rate, respectively, in order to ensure the quality of service (QoS, Quality of Service) when the base station i and the user perform data transmission.

基站的优化问题可表示为：The optimization problem of the base station can be expressed as:

式(5)和(6)共同构成了一次斯坦克尔伯格博弈过程，RNC在掌握了基站的最优策略的情况下对基站功率进行定价，基站通过观察RNC的行为即其定价后采取相应策略行动，调整自身发射功率以使自身利益最大化，对该过程的斯坦克尔伯格均衡定义如下：Equations (5) and (6) together constitute a Steinkelberg game process. The RNC prices the power of the base station under the condition of mastering the optimal strategy of the base station. A strategic action that adjusts its own transmit power to maximize its own benefit, the Steinkelberg equilibrium for this process is defined as follows:

λ^*为RNC的最优定价集合，

为基站i的最优发射功率策略集合，若满足：λ^* is the optimal pricing set of RNC,

is the optimal transmit power policy set of base station i, if it satisfies:

U_RNC(λ^*,p^*)≥U_RNC(λ,p^*) (7)U_RNC (λ^* ,p^* )≥U_RNC (λ,p^* ) (7)

(λ^*，

)为上述斯坦克尔伯格博弈过程的均衡解。(λ^* ,

) is the equilibrium solution of the above-mentioned Steinkelberg game process.

②用户间的非合作博弈②Non-cooperative game between users

对于斯坦克尔伯格博弈的均衡点的求解，可以采用倒推的方法，对给定的定价，用户间通过非合作博弈的方式达到NE，求得用户的最优发射功率，即对式(6)进行求解，之后将其结果代入式(5)，求解RNC的优化问题，最后整个系统达到SE。For the solution of the equilibrium point of the Steinkelberg game, the backward method can be used. For a given price, the users can reach NE through a non-cooperative game, and the optimal transmit power of the user can be obtained, that is, the formula ( 6) Solve, and then substitute the result into equation (5) to solve the optimization problem of RNC, and finally the whole system reaches SE.

(3)分层博弈均衡解的分析得到斯坦克尔伯格博弈的均衡解(3) Analysis of the equilibrium solution of the hierarchical game to obtain the equilibrium solution of the Steinkelberg game

在求解上述优化问题时，利用倒推法首先求出用户非合作博弈达到纳什均衡时的均衡解，即求出其最优发射功率，并证明所求均衡解存在且唯一，下一步将所求得的最优发射功率写成矩阵形式，代入到RNC的效用函数中进行化简，进一步研究其效用函数与定价之间的关系，进而简化其优化问题，在系统模型达到斯坦克尔伯格均衡时求出RNC的最优定价，所求得的最优发射功率和最优定价构成了斯坦克尔伯格博弈的均衡解。When solving the above optimization problem, firstly, the equilibrium solution when the user's non-cooperative game reaches the Nash equilibrium is obtained by using the backward method, that is, the optimal transmit power is obtained, and the equilibrium solution is proved to exist and is unique. The obtained optimal transmit power is written in the form of a matrix, which is substituted into the utility function of the RNC for simplification, and the relationship between its utility function and pricing is further studied, and its optimization problem is simplified. When the system model reaches the Steinkelberg equilibrium The optimal price of RNC is obtained, and the obtained optimal transmit power and optimal price constitute the equilibrium solution of the Steinkelberg game.

①对非合作博弈中纳什均衡解的分析①Analysis of Nash equilibrium solutions in non-cooperative games

对于给定的定价，式(6)有一最优解即基站的最优发射功率为：For a given price, equation (6) has an optimal solution, that is, the optimal transmit power of the base station is:

因功率值非负，当不传输数据时，功率值为0，所以可写成如下形式：Because the power value is non-negative, when no data is transmitted, the power value is 0, so it can be written in the following form:

其中，(a)⁺表示max{a,0}。where (a)⁺ represents max{a,0}.

证明如下：The proof is as follows:

对式(3)求一阶导数得：Taking the first derivative of equation (3), we get:

对式(3)求二阶导数得：Taking the second derivative of equation (3), we get:

令一阶导数为0，得：Let the first derivative be 0, we get:

由式(13)可解得基站的最优发射功率为：From equation (13), the optimal transmit power of the base station can be obtained as:

对于某一给定的时隙，当

时，将其代入式(3)可求得λ_i的上界为：For a given time slot, when

When , substituting it into formula (3) can obtain the upper bound of λ_i as:

定理1为：当

时，用户间非合作博弈达到的纳什均衡存在，并且纳什均衡解可表示为：Theorem 1 is: when

When , the Nash equilibrium achieved by the non-cooperative game among users exists, and the Nash equilibrium solution can be expressed as:

p^*＝H^-1m (16)p^* = H^-1 m (16)

其中，in,

证明如下：The proof is as follows:

对于非合作博弈的纳什均衡，其均衡解的存在需满足p为非空凸集合以及U_i相对于p为连续凸函数。For the Nash equilibrium of non-cooperative game, the existence of the equilibrium solution must satisfy that p is a non-empty convex set and U_i is a continuous convex function relative to p.

针对第一个条件，p应满足p∈{p^min，p^max}，且p^min≥0，每一个基站均会得到分配的功率，所以可知p为非空集合，满足第一个条件。For the first condition, p should satisfy p∈{p^min , p^max }, and if p^min ≥ 0, each base station will get the allocated power, so it can be known that p is a non-empty set and satisfies the first condition.

针对第二个条件，根据基站i的效用函数U_i所列公式可知其相对于p_i为连续函数，由式(12)可知U_i相对于p_i的二阶导数小于0，U_i相对于p_i为连续凸函数，满足第二个条件。For the second condition, according to the formula of the utility function U_i of base station i, it can be known that it is a continuous function relative to p_i , and it can be seen from equation (12) that the second derivative of U_i relative to p_i is less than 0, and U_i relative to p i is less than 0. p_i is a continuous convex function that satisfies the second condition.

综上，证明该纳什均衡点存在。To sum up, it is proved that the Nash equilibrium exists.

对于在条件范围内的λ_i，式(10)可化成：For λ_i within the conditional range, equation (10) can be transformed into:

将其写成矩阵形式：Write it in matrix form:

Hp^*＝m (20)Hp^* =m(20)

式(20)进一步可得到式(16)。Formula (20) can further lead to formula (16).

②对斯坦克尔伯格均衡解的分析②Analysis of Steinkelberg Equilibrium Solution

将求得的最优发射功率代入到RNC的优化问题中，可得：Substituting the obtained optimal transmit power into the optimization problem of RNC, we can get:

由于在5G异构融合网络中基站分布非常密集，任意一个基站到其他基站用户的干扰链路增益相同，并且基站i到基站用户j的干扰衰落远小于基站j到基站用户j的衰落，所以可将h_ij看做一个常数h，则RNC的效用函数式(21)可表示成：Since the base stations are very densely distributed in the 5G heterogeneous fusion network, the gain of the interference link from any base station to other base station users is the same, and the interference fading from base station i to base station user j is much smaller than the fading from base station j to base station user j, so it is possible to Considering h_ij as a constant h, the utility function formula (21) of RNC can be expressed as:

定理2为U_RNC(λ_i)是关于λ_i的单调递增函数，是关于λ_i的凸函数。Theorem 2 is that U_RNC (λ_i ) is a monotonically increasing function about λ_i and a convex function about λ_i .

证明如下：The proof is as follows:

将h_ij看做常数h，且h_ii>>h，链路增益矩阵H可写成如下形式：Considering h_ij as a constant h, and h_ii >>h, the link gain matrix H can be written in the following form:

其中，因h_ii>>h_ij＝h，令：Among them, because h_ii >> h_ij =h, let:

根据已有方法求H的逆矩阵得：According to the existing method to find the inverse matrix of H, we get:

其中，in,

因

所以α_iα_j≈0，则H^-1可继续写成如下形式：because

So α_i α_j ≈0, then H^-1 can continue to be written in the following form:

将所求得的H^-1代入式(21)得：Substitute the obtained H^-1 into formula (21) to get:

对式(28)求一阶导数得：Taking the first derivative of equation (28), we get:

由式(29)可知U_RNC(λ_i)是关于λ_i的单调递增函数。It can be known from equation (29) that U_RNC (λ_i ) is a monotonically increasing function of λ_i .

对式(28)求二阶导数得：Taking the second derivative of equation (28), we get:

由式(30)可知U_RNC(λ_i)是关于λ_i的凸函数。It can be known from equation (30) that U_RNC (λ_i ) is a convex function with respect to λ_i .

RNC的优化问题根据定理2可简化为：According to Theorem 2, the optimization problem of RNC can be simplified as:

即求解RNC的优化问题可简化为求解式(31)，则RNC的最优定价λ^*为：That is, the optimization problem of solving RNC can be simplified to solve equation (31), then the optimal pricing λ^* of RNC is:

由式(10)和式(32)可知，(p_i(λ^*),λ^*)为斯坦克尔伯格博弈的均衡解。It can be known from equations (10) and (32) that (_pi (λ^* ),λ^* ) is the equilibrium solution of the Steinkelberg game.

(4)采用基于分层博弈的功率分配算法得到收敛的功率值及各基站最优定价。(4) The power allocation algorithm based on hierarchical game is used to obtain the convergent power value and the optimal pricing of each base station.

设置一迭代函数，基于迭代函数功率可以逐渐收敛到均衡点，系统达到稳定状态，迭代函数为：An iterative function is set. Based on the power of the iterative function, the power can gradually converge to the equilibrium point, and the system reaches a stable state. The iterative function is:

定理3为标准函数，满足正定性、单调性和可测量性。Theorem 3 is a standard function that satisfies positive definiteness, monotonicity and measurability.

证明如下：The proof is as follows:

①正定性：功率值非负，I(p)>0。①Positive determinism: the power value is non-negative, and I(p)>0.

②单调性：② Monotonicity:

根据式(16)可得：According to formula (16), we can get:

对式(34)求一阶导数得：Taking the first derivative of equation (34), we get:

由式(35)可知I(p)即

是关于λ_i的单调递减函数。From equation (35), it can be known that I(p) is

is a monotonically decreasing function with respect to_λi .

③可测量性：③Measurability:

根据式(14)变形可得：According to the deformation of formula (14), it can be obtained:

对任意β≥1，有For any β≥1, we have

对于任意的β≥1，都有βI(p)-I(βp)>0，I(p)即具有可测量性。For any β≥1, there is βI(p)-I(βp)>0, and I(p) is measurable.

通过定理3能够证明该功率分配算法的收敛性，表1为算法伪代码表。The convergence of the power allocation algorithm can be proved by Theorem 3, and Table 1 is the pseudo-code table of the algorithm.

表1算法伪代码表Table 1 Algorithm pseudocode table

该算法中采用了斯坦克尔伯格博弈模型，RNC作为博弈的领导者，基站作为跟随者，主要分为以下几个步骤:The Steinkelberg game model is used in the algorithm. RNC acts as the leader of the game and base station acts as the follower. It is mainly divided into the following steps:

①RNC根据基站的初始发射功率计算各个基站的定价，并通过RNC将所得定价广播给对应的基站；①RNC calculates the pricing of each base station according to the initial transmit power of the base station, and broadcasts the obtained pricing to the corresponding base station through the RNC;

②基站收到定价后根据迭代公式对自身发射功率进行调整；② After the base station receives the pricing, it adjusts its own transmit power according to the iterative formula;

③设定迭代次数，得到各个基站的最优发射功率和RNC对各个基站的最优定价。③ Set the number of iterations to obtain the optimal transmit power of each base station and the optimal pricing of each base station by the RNC.

根据图4算法流程图所示的功率分配算法，基站接收到RNC的定价λ_i后进行功率的迭代，收敛到最优发射功率

之后RNC根据收敛的功率值进行自身定价的更新并得到最优定价，得到的RNC最优定价和基站的最优发射功率共同构成了博弈的均衡解。According to the power allocation algorithm shown in the algorithm flow chart in Figure 4, the base station performs power iteration after receiving the RNC's pricing λ_i , and converges to the optimal transmit power

Afterwards, the RNC updates its own pricing according to the converged power value and obtains the optimal price. The obtained optimal price of the RNC and the optimal transmit power of the base station together constitute the equilibrium solution of the game.

当然，上述说明并非是对本发明的限制，本发明也并不仅限于上述举例，本技术领域的技术人员在本发明的实质范围内所做出的变化、改型、添加或替换，也应属于本发明的保护范围。Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the essential scope of the present invention should also belong to the present invention. the scope of protection of the invention.

Claims (1)

Translated fromChinese

1.一种基于分层博弈模型的功率自适应分配方法，其特征在于，包括如下步骤：1. a power adaptive allocation method based on a hierarchical game model, is characterized in that, comprises the steps:(1)在5G异构融合网络区域内，采用博弈论的理论基础构建由RNC、基站和基站用户组成的三层异构融合网络模型；(1) In the 5G heterogeneous fusion network area, the theoretical basis of game theory is used to build a three-layer heterogeneous fusion network model composed of RNC, base station and base station users;(2)采用基于斯坦克尔伯格博弈与非合作博弈的功率控制方法得到最优发射功率；(2) Using the power control method based on the Steinkelberg game and the non-cooperative game to obtain the optimal transmit power;(3)通过对分层博弈均衡解的分析得到斯坦克尔伯格博弈的均衡解；(3) The equilibrium solution of the Steinkelberg game is obtained by analyzing the equilibrium solution of the hierarchical game;(4)采用基于分层博弈的功率分配算法得到收敛的功率值及各基站最优定价；(4) The power allocation algorithm based on hierarchical game is used to obtain the converged power value and the optimal pricing of each base station;所述步骤(2)中，RNC与基站之间采用斯坦克尔伯格博弈，RNC是博弈领导者，基站是跟随者；基站用户间采用非合作博弈得到各自的最优发射功率；In the step (2), a Steinkelberg game is used between the RNC and the base station, the RNC is the game leader, and the base station is the follower; the users of the base station use a non-cooperative game to obtain their respective optimal transmit powers;其中，斯坦克尔伯格博弈的具体过程为：Among them, the specific process of the Steinkelberg game is as follows:在一给定时隙内，RNC对基站i单位功率的定价为λ_i，基站i的传输带宽为w_i，则基站i的链路传输速率如下：In a given time slot, the unit power of base station i is priced by RNC as λ_i , and the transmission bandwidth of base station i is_wi , then the link transmission rate of base station i is as follows:

其中，p_i表示基站i的发射功率，p_j表示基站j的发射功率，p₀表示RNC的传输功率，h_ii表示基站i与其用户的链路信道的功率增益，h_i0表示RNC与基站i之间的干扰链路增益，h_ij表示基站i与用户j的干扰链路增益，N为基站总数，i为任一基站且i∈{1,2,3…,N}；Among them, pi represents the transmit power of base station i, p_j represents the transmit power of base station_j , p₀ represents the transmission power of RNC, h_ii represents the power gain of the link channel between base station i and its users, and h_i0 represents the power gain between RNC and base station i The interference link gain between , h_ij represents the interference link gain between base station i and user j, N is the total number of base stations, i is any base station and i∈{1,2,3...,N};基站i的效用函数U_i如下：The utility function U_i of base station i is as follows:

RNC的效用函数U_RNC如下：The utility function U_RNC of RNC is as follows:

其中，h_0i为基站i对基站用户的干扰链路增益；Among them, h_0i is the interference link gain of base station i to base station users;综上所述，RNC的优化问题如下：In summary, the optimization problem of RNC is as follows:

其中，

分别为链路传输速率的上、下界；in,

are the upper and lower bounds of the link transmission rate, respectively;基站的优化问题如下：The optimization problem of the base station is as follows:

式(5)和(6)共同构成了一次斯坦克尔伯格博弈过程，RNC在掌握了基站的最优策略的情况下对基站功率进行定价，基站通过观察RNC的定价后采取相应策略行动，调整自身发射功率；Equations (5) and (6) together constitute a Steinkelberg game process. The RNC price the base station power under the condition of mastering the optimal strategy of the base station, and the base station takes corresponding strategic actions after observing the pricing of the RNC, Adjust its own transmit power;其中，基站用户间非合作博弈的过程是对式(6)进行求解，之后将其结果代入式(5)，求解RNC的优化问题，最后整个系统达到斯坦克尔伯格均衡；Among them, the process of non-cooperative game among base station users is to solve equation (6), and then substitute the result into equation (5) to solve the optimization problem of RNC, and finally the whole system reaches the Steinkelberg equilibrium;其中，达到斯坦克尔伯格博弈均衡时的均衡解

满足如下条件：Among them, the equilibrium solution when the Steinkelberg game equilibrium is reached

The following conditions are met:U_RNC(λ^*,p^*)≥U_RNC(λ,p^*) (7)U_RNC (λ^* ,p^* )≥U_RNC (λ,p^* ) (7)

其中，λ^*为RNC的最优定价集合，p*为RNC的最优发射功率策略集合，λ为RNC对基站单位功率的定价，

为基站i的最优定价集合，

为基站i的最优发射功率策略集合；Among them, λ^* is the optimal pricing set of the RNC, p* is the optimal set of transmit power policies of the RNC, λ is the price of the unit power of the base station by the RNC,

is the optimal pricing set for base station i,

is the optimal transmit power strategy set of base station i;所述步骤(3)的具体过程为：The concrete process of described step (3) is:首先，利用倒推法求出基站用户非合作博弈达到纳什均衡时的最优发射功率，具体过程为：First, the optimal transmit power when the non-cooperative game of the base station users reaches the Nash equilibrium is obtained by using the backward method. The specific process is as follows:对于给定的定价，式(6)有一最优解即基站的最优发射功率如下：For a given price, equation (6) has an optimal solution, that is, the optimal transmit power of the base station is as follows:

其中，(a)⁺为max{a,0}；Among them, (a)⁺ is max{a,0};其次，将所求得的最优发射功率写成矩阵形式，代入到RNC的效用函数中进行化简；Secondly, write the obtained optimal transmit power in matrix form, and substitute it into the utility function of RNC for simplification;最后，研究其效用函数与定价之间的关系，进而简化其优化问题，在系统模型达到斯坦克尔伯格均衡时求出RNC的最优定价，RNC的最优定价λ^*如下：Finally, the relationship between its utility function and pricing is studied, and its optimization problem is simplified. When the system model reaches the Steinkelberg equilibrium, the optimal pricing of RNC is obtained. The optimal pricing λ^* of RNC is as follows:

其中，

为λ_i的上界，n₀为RNC的噪声干扰；in,

is the upper bound of λ_i , and n₀ is the noise interference of RNC;由式(10)和式(32)得到的最优发射功率和最优定价构成了斯坦克尔伯格博弈的均衡解(p_i(λ^*),λ^*)；The optimal transmit power and optimal pricing obtained from equations (10) and (32) constitute the equilibrium solution of the Steinkelberg game (p_i (λ^* ),λ^* );所述步骤(4)的具体过程为：The concrete process of described step (4) is:首先，RNC根据基站的初始发射功率计算各个基站的定价，并通过RNC将所得定价广播给对应的基站；First, the RNC calculates the pricing of each base station according to the initial transmit power of the base station, and broadcasts the obtained pricing to the corresponding base station through the RNC;其次，基站收到定价后根据迭代函数对自身发射功率进行调整，Secondly, after receiving the pricing, the base station adjusts its own transmit power according to the iterative function.迭代函数如下：The iteration function is as follows:

最后，设定迭代次数，得到各个基站的最优发射功率和RNC对各个基站的最优定价。Finally, the number of iterations is set to obtain the optimal transmit power of each base station and the optimal pricing of each base station by the RNC.

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