基于博弈论的合作中继网络竞争资源共享.doc

基于博弈论的合作中继网络竞争资源共享摘要这篇文章考虑了合作传输网络中一个中继和多个用户节点间的资源共享问题。我们把这个问题作为一个卖方的市场竞争问题来阐述，并使用博弈论来联合考虑中继和用户的受益。同时提出一种分布式的算法来寻求纳什均衡，即，博弈的解决方法，而且对所提算法的收敛性进行了分析。仿真结果证明提出的博弈能够激励自私的用户节点间的合作分集并有效地协调用户节点间的资源分配。关键词资源分配，合作中继，博弈论，纳什均衡。.引言合作传输的基本思想是允许网络中的节点互相帮助中继信息来固有的空间分集，这在中继信道是可实现的。由于中继代表着资源（能量或带宽）的消耗，在商业网络中，必须解决下面两个基本问题：一是，什么时候中继，也就是什么时候使用中继有益；二是，如何中继，也就是中继如何在用户节点间分配它的资源。大多数先前在合作传输资源分配上的研究都是基于集中控制的。为了以一种分布的方式解决上面提到的两个问题，博弈论是研究自私节点间相互作用和彼此合作的一种自然的和强有力的工具。在这个领域，文献1基于合作博弈论研究了一种对称的中继模型，这个模型中每个节点既作为源节点也作为中继。文献2提出了一个Stackelberg博弈来进行资源分配。这个博弈是作为买方的市场竞争来阐述的，其中多个中继在价格方面互相竞争以从给单个用户提供功率中获得最高利润。不同于1和2，我们研究一个非对称模型，考虑一个中继如何在多个竞争的用户间协调资源分配这个问题。通过把它作为一个卖方的市场竞争问题来阐述和使用基于价格的非合作博弈来联合考虑中继和用户的利益。.系统模型和问题阐述一个非对称中继模型如图1所示。一个源节点 和一个中继节点 组成的发送-接收对被当作一个用户 。设计靠近目的节点的节点 作为潜在的中继。不失一般性，我们在系统中使用放大-转发（AF）合作协议，并基于频分多址（FDMA）来考虑系统。给每个节点分配 用于传输。中继 愿意和用户分享部分带宽用于合作传输。在2和3中，中继一个数据包所要求的能量是恒定的。让 表示系统中现存的用户集。如果中继 给用户 分带宽 ，它将中继源 产生数据的 。这就意味着源 的数据的 部分将以合作的方式来发送，剩下的 部分只能没有任何中继地直接发送到目的节点 。合作是对资源的真正消耗，中级可以通过把它的带宽卖给用户来补偿。用带宽量 ，也就是用户 想从中继买的，定义用户 的策略。中继向用户要价的价格方程同5中定义为： （2-1）上式中 和 是非负常数， 表示所有用户采用的策略集。给定现在的价格 ，每个自私的用户倾向于通过调整它的策略最大化它的利益/效用。由于价格 取决于所有用户的策略用户间的资源竞争确实是一个策略博弈。我们称它为合作传输博弈（CTG）。一种量化在高的吞吐量和低的能量消耗间折中的效用方程定义为 （比特每焦耳），如4中，式中 和 分别是用户的吞吐量和传输功率。考虑到用户用带宽 传输打包入 比特的帧中的 比特数据，用户的吞吐量可以表示为 ，式中 是接近于一帧正确接收率 的效率函数。用户的效用可以理解为每消耗一焦耳能量成功接收到的数据比特数。 让 ， 和 分别表示从源 到目的 ，从源 到中继 和从中继 到目的 的无线信道的SNR。那么，用户 AF合作信道的有效SNR可用式 : 给出。这儿，我们定义用户 的效用函数如下: (2-2)上式中 是源 的传输功率，式 是用带宽 直接传输得到的吞吐量，式 是中继 用带宽 帮助合作传输得到的吞吐量，最后一项， ，表示用户 为中继 的资源消耗所支付的报酬。.解决博弈纳什均衡（NE）是非合作博弈的解决方法。在NE，假设其他用户都是最佳策略，没有用户可以通过采取另一种策略来提高自己的效用。由于价格 是由所有用户的要求决定的，把（2-1）式代入（2-2）式中，可得， (3-1)上式中， .除了用户 之外所有用户的最佳策略集是 。用户 的最佳策略由下式给出 （3-2）所有用户的最佳策略集 , 就是CTG的NE。为了解决CTG，我们对（3-1）式取 的微分，并且让所有的微分都等于 。那么，可得下面的 个等式： （3-3）等式集合的解就是CTG的NE。然而，由于每个用户采用 的策略对于其他用户都是可用的，只能以集中的方式解决这个问题。我们提出一种效用更新函数来以一种分布的方式寻求CTG 的NE： （3-4）上式中， 是用户 的速度调整参数， 是在时刻 分配给用户 的带宽量， 是在时刻 时用户 采取的策略。这个效用更新函数是基于从微经济学中借用的边缘利润函数。这个算法的基本思想是用户 的NE策略必须保证在任何时候 。除此之外，如果在时刻 分配给用户 的带宽量少于最佳值， 将会从零变为正。根据（3-4）式，在时刻 ，用户 将增加他的要求来最大化他的效用。如果在时刻 分配给用户 的带宽量多于最佳值，情况就相反。当达到NE时，条件 就会满足。之就意味着用户 不能通过采取一种不同的策略来单方面提高自己的效用。这种分析证明如果式（3-4）以一种分布和反复的方式执行，用户的策略就会收敛到NE。一个用户的合作激发策略基于合作博弈理论在合作传递网络1,2已经表明合作分集被广泛应用到无线网络，在无线网络主要包括节点，每个节点仅有一个天线，合作分集协助扩展系统和增加系统连接的可靠性。合作分集通过网络节点工作在数据传输方面再而实现虚拟天线技术。这个发生主要通过许多节点传输冗余信号以不同的路径，这就允许目的终端区接收平均信号通道的变化。合作分集的好处是非常可取的，对于那些无线应用的主要问题是带宽和能量。然而，当它是切实可行的在一些情况下,假设合作在精制于是应用,没有理由假设网络节点将无私配合。事实上，考虑到是独立的实体,节点随机合作徒将不断扩大他们的资源,节点一定是自私的。换句话说，节点是专为灭他们的资源最大限度地发挥各自的利益。并没有明显的效益其他节点转发数据用户。与此同时,然而,也希望节点其他节点提出了自己的数据。在这种情况下，博弈论方法可以用来模型网络，引导互动理性的决策者之间。在3，基于纳什均衡问题的合作策略被提出，去解决两个问题：尤其是什么时候合作和如何合作的问题。作者首先提出了一个对成的系统模型，由两个用户和一个基站（AP）。关于合作博弈理论,和基于纳什均衡，一个合作带宽分配策略被提出。在4，价格算法被提出了多次无线网络去鼓励自主的节点通过补偿。在5，发射功率被指定ad hoc网络和去帮助其他节点决定合作意向。依据结果6， 7提出价格补偿促进合作分集在自私的节点用于商业网络ad hoc网络。在8中这个研究,提供了依据评价理论方法各种理论中为了促进合作。本质上,这种阐述了理论方法的敏感性的选择效用函数。上文中的合作中继网络,一个用户选择其最佳传递可能个别用户和形式请求合作。不过,考虑到随机位置和移动自然到来的每一户,移动终端引发合作传输可能不是最优传输的中继。为此,利用定价的概念来培育用户之间的合作可能更合适让用户传送数据合作对方在3中被描述。获得合作,中继既可以选择其他适当的网络节点合作或可以选择直接传送。然而,当谈到价格补偿方案、一个非合作条件博弈论通常作为一个起始点。这些研究的不足就是他们集中个人利益，而不是对整个集体利益。然而基于合作博弈论这个策略在3中被提及。关于最优解对于博弈论来说。这使得整个系统效益达到最大，能做到公平。.仿真结果一个两用户的仿真系统如图2-1所示。路径增益定为 ，噪声水平是 。假定所有的节点都有相同的 的传输功率，带宽为 ，速度调整参数 ，最初的策略是 ，对于价格方程（2-1）， 。仿真中用到的其它参数包括 ， ，对于不相关频移键控， 。定位两个源节点和两个目的节点分别在（0，-50），（0，50），（200，-50）和（200，50）中继 的 坐标固定在80，它的 坐标从-200到200变化。用 表示 的 坐标。图2表示两用户才中继 买的最佳带宽量，而图3描述了在NE时中继的相关要价。当 时，用户1购买的带宽量逐渐增到最大，而用户2购买的几乎为0。这是因为，在这个区域，中继 更靠近 而不是 。当 时，来自两个源节点到中继的信道条件都变好了。尽管服务价格继续增加，用户2愿意从中继购买更多的带宽用于合作传输。当中继移到（80，0）时，因为两个用户到中继的信道条件相同，资源在两个用户间公平分配。而且，由于在这一点上用户的需求是最高的，中继的收入也达到最大。当 时，情况相反。由于中继的 坐标代表节点的信道，第一部分中提到的两个基本问题就得到了解决。注意在这儿不考虑时变的衰落。否则，中继 的 坐标将代替 坐标代表信道条件。.结论这篇文章在基于FDMA的合作中继网络中提出了一种非合作博弈来进行资源分配，同时提出一种分布式算法来寻求用于解决何时和如何合作这两个基本问题的博弈的Nash均衡。附录5 英文资料Competitive resource sharing based on game theory in cooperative relay networksABSTRACT:This letter considers the problem of resource sharing among a relay and multiple user nodes in cooperative transmission networks. We formulate this problem as a sellers market competition and use a non-cooperative game to jointly consider the benefits of the relay and the users. We also develop a distributed algorithm to search the Nash equilibrium, the solution of the game. The convergence of the proposed algorithm is analyzed. Simulation results demonstrate that the proposed game can stimulate cooperative diversity among the selfish user nodes and coordinate resource allocation among the user nodes effectively. KEYWORDS:Resource allocation, Cooperative relay, Game theory, Nash equilibrium.I. IntroductionThe basic idea of cooperative transmission is to allow nodes in a network to help relay information for each other so as to exploit the inherent spatial diversity which is available in the relay channels. Since relaying represents a cost of resource (energy or bandwidth), in commercial networks, the following two basic issues must be dealt with: when to relay, that is, when it is beneficial to use the relay, and how to relay, that is, how the relay should allocate its resource among the user nodes.Most previous work on resource allocation for cooperation transmission is based on centralized control. To tackle the two problems just mentioned in a distributed way, game theory is a natural and powerful tool which studies how selfish nodes interact and cooperate with each other. In this area, Zhaoyang 1 studied a symmetric relay model in which each node can act as both a source and a relay based on the cooperative game theory. Beibei 2 proposes a Stackelberg game to perform the resource allocation. The game is formulated as a buyers market competition where multiple relays compete with each other in terms of price to gain the highest profit from offering power to a single user. Unlike 1 and 2, we study an asymmetric relay model by considering the problem of how a relay should coordinate resource allocation among multiple competing users. We formulate this problem as a sellers market competition and use a pricing-based non-cooperative game to jointly consider the benefits of the relay and the users. II. System Model and Problem FormulationAn asymmetric relay model is illustrated in Fig. 1. A transmitterreceiver pair including a source node and destination node is referred to as a user . A node closer to the destination nodes is designated as the potential relay. Without the loss of generality, we employ the amplify-and-forward (AF) cooperation protocol in the system and consider basing the system on frequency-division multiple access (FDMA). Each node is allocated Hz bandwidth for transmission. The relay is willing to share portions of its bandwidth with the users for cooperative transmission. The energy required to relay a packet is assumed to be constant as in 2 and 3. Fig.1. Cooperative communication system modelLet denote the set of users currently in the system. If decides to share bandwidth with user , it will relay of the data originating from source . That means of source s data will be transmitted in a cooperative manner, and the remaining - parts can only be directly transmitted to destination without any relaying.Cooperation refers to a real cost of resource expenditure, and the relay could cover this cost by selling its bandwidth to the users. Define user s strategy as the bandwidth size, , that he wants to buy from the relay. The pricing function used by the relay to charge the users is defined as in 5 as （2-1） where and are non-negative constants, and denotes the set of strategies adopted by all users. Given the current relaying price , each selfish user prefers to maximize his benefit/utility by adjusting his strategy. Since price depends on the strategies of all users, the resource competition between the users is actually a strategic game. We call it a cooperative transmission game (CTG). A kind of utility function which can qualify the tradeoff between achieving high throughput and low energy consumption is defined as (bits per Joule) as in 4, where and are users throughput and transmission power, respectively. Considering that the user transmits bits of data packed into a frame of bits with bandwidth , the throughput of the user can be expressed as , where is the efficiency function to approximate the probability of correct reception of a frame, . The utility of a user is then interpreted as the number of data bits successfully received per joule of energy consumed. Let , , and denote the SNRS of the wireless channels from source to destination , source to relay , and relay to destination , respectively. Then, the effective SNR of the AF cooperative channel of user is given by . Here, we define user s utility function as ， ， （2-2） Where is the transmit power of source , is the through put derived from the direct transmission with bandwidth , is the throughput derived from the cooperative transmission helped by relay with bandwidth , and the last term, , represents the payment paid by user to relay for resource consumption.III. Solving the GameThe Nash equilibrium (NE) is the solution to a non-cooperative game. At the NE, no user can increase his utility by choosing a different strategy, given the other users best strategies.Since the relaying price c is determined by the demand of all users, by substituting (2-1) into (2-2), we obtain all users, by substituting (2-1) into (2-2), we obtain , (3-1)Where . Denote the set of best strategies of all users except user as . The best strategy of user is given by , . (3-2)The best strategy profile of all the users, is then the NE of the CTG.To solve the CTG, we take the derivative of (3) with respect to and set each derivative to 0. Then, we can have the following set of N equations: . (3-3)The solution of this equation set is the NE of the CTG. However, it can only be solved in a centralized manner since the strategies adopted by other users should be available to each user.We developed a strategy update function to help users search the NE of the CTG in a distributed manner: (3-4)Where is the speed adjustment parameter of user , is the amount of bandwidth allocated to user at time t, and is the strategy that will be adopted by user at time .a user cooperation stimulating strategy based on cooperative game theory in cooperative relay networksCooperative diversity 1, 2 has been widely proposed for applications in wireless networks. In a wireless network consists of a collection of nodes, each having a single antenna, cooperative diversity assists to enlarge system coverageand increase link reliability. Cooperative diversity works by having the network nodes assist in data transmission, thus achieving a virtual antenna array. This occurs through having a number of nodes to transmit redundant signals over different paths, which allows the destination terminal to receive average channel variations.The benefits of cooperative diversity are highly desirable for those wireless applications in which the chief concerns are bandwidth and energy. However, while it is realistic to assume cooperation under some circumstances, in commercial applications, there is no reason for assuming that the network nodes will cooperate unselfishly. In fact, given that nodes are independent entities and that random cooperative acts will expend their resources, nodes are necessarily selfish.In other words, nodes consume their resources solely to maximize their benefits. There is no apparent benefit in a user forwarding data for other nodes. At the same time, however, the node would also prefer to have other nodes forward its own data. In such a situation, a game theoretic approach can be used to model the network and to guide the interactions between rational decision-makers. In 3, NBS was proposed to solve two basic problems, specifically when to cooperate and how to cooperate. The authors first present a symmetric system model comprising of two users and an access point (AP). With reference to cooperative game theory, and based on the Nash bargaining solution, a cooperation bandwidth allocation strategy is then proposed. In 4, a pricing algorithm was presented for multi-hop wireless networks that encourage forwarding among autonomous nodes via reimbursement. In 5, a power-aware reputation system to stimulate cooperation on power-aware routing was formulated for ad hoc networks and to help each node determine its cooperation willingness from its own reputation. Based on the results given in 3, presented a pricing game for stimulating cooperative diversity among selfish nodes in a commercial wireless ad hoc network. The work in then reviewed this research and offered an evaluation of the various game theoretic approaches for stimulating cooperation. Essentially, this illustrated the sensitivity of the game theoretic approach to the choice of utility functions.In the context of cooperative relay network, one user might individually select its best relay user and form a request for cooperation. Nevertheless, considering the random arrival position and the mobile nature of each user, the mobile terminal which initiates cooperative transmission in turn may not be the optimal forwarding candidate for the relay. To this end, the concept of using pricing to foster cooperation among users is arguably more appropriate than to having users cooperatively relaying data for each other as described in 3. With gains obtained from cooperation, the relay can either select other appropriate nodes for cooperation or can choose to transmit directly. However, when it comes to pricing-based schemes, a non-cooperative game theory is often used as a starting point. This is shown by researchers contributing to4. The main disadvantage of these works is that they concentrate on individual user utility, rather than utility of the entire system. By contrast, based on cooperative game theory, the scheme proposed in 3 can achieve general Pareto optimal performance for cooperative games. This will help in maximizing an entire system payoff, while also ensuring fairness on cooperative game theory, the scheme proposed in 3 can achieve general Pareto optimal performance for cooperative games. This will help in maximizing an entire system payoff, while also ensuring fairness.This strategy update function is based on the marginal profit function borrowed from microeconomics, which only depends on the pricing information from the relay. The basic idea of the algorithm is that each user s NE strategy should ensure at any time. Otherwise, if the bandwidth size allocated to user is less than the optimal one at time , will change from zero to positive. According to (6), user will increase his/her demand at time to maximize his/her utility. If the bandwidth size allocated to user is more than the optimal one at time t, the situation reverses. When the NE is reached, the condition is satisfied. This means user cannot unilaterally improve his/her utility by choosing a different strategy. This analysis demonstrates that the users strategies could converge to the NE if (6) is performed in a distributed and iterative manner.IV. Simulation ResultsA two-user simulated system is shown in Fig. 1. The path gain is set to , and the noise level is W. We assume all the nodes have the same transmit power of 0.1W, bandwidth size of 1 MHz, speed adjustment parameter with =0.01, and initial strategy with . For the pricing function (1), we use a=0 and . The other parameters used in the simulations include L=64, M=80, and for non-coherent frequency shift