Exchange Economy in Two-User Multiple-Input Single-Output Interference Channels
Exchange Economy in Two-User Multiple-Input Single-Output Interference Channels
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DOI：
10.1109/jstsp.2011.2174962
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发表时间：
2012-04-01
影响因子：
7.5
通讯作者：
Jorswieck, Eduard A.
中科院分区：
文献类型：
--
作者：
Mochaourab, Rami;Jorswieck, Eduard A.
我们研究多输入单输出干扰信道中两个链路之间的冲突。这种设置是严格竞争的，可以与完全竞争的市场模型相关。在此类模型中，一般均衡理论用于确定帕累托最优的均衡措施。首先，我们认为链接是可以在自身内部交易商品的消费者。我们设置中的商品对应于波束成形向量。我们利用 Edgeworth 盒子（一种描述两个消费者的商品分配的图形工具）中消费者的冲突表示，为所有帕累托最优结果提供封闭式解决方案。然后，我们将链接之间的情况建模为竞争市场，该市场还定义了商品的价格。这种经济中的均衡称为瓦尔拉斯均衡，对应于使需求与供给相等的价格。我们计算了独特的瓦尔拉斯均衡，并提出了一个由仲裁员实现的协调过程，该仲裁员将瓦尔拉斯价格分配给消费者。然后，消费者以分散的方式计算与实现瓦尔拉斯均衡的波束成形向量相对应的最佳需求。这个结果是帕累托最优的，并且主导系统的非合作结果。因此，基于博弈论模型和求解概念，提供了一种用于多输入单输出干扰信道中波束形成问题的分布式实现的算法。
We study the conflict between two links in a multiple- input single-output interference channel. This setting is strictly competitive and can be related to perfectly competitive market models. In such models, general equilibrium theory is used to determine equilibrium measures that are Pareto optimal. First, we consider the links to be consumers that can trade goods within themselves. The goods in our setting correspond to beamforming vectors. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. Afterwards, we model the situation between the links as a competitive market which additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by an arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and dominates the noncooperative outcome of the systems. Thus, based on the game theoretic model and solution concept, an algorithm for a distributed implementation of the beamforming problem in multiple-input single-output interference channels is provided.