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首页> 外文期刊>IEEE Transactions on Cognitive Communications and Networking >Normalized Nash Equilibrium for Power Allocation in Cognitive Radio Networks
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Normalized Nash Equilibrium for Power Allocation in Cognitive Radio Networks

机译：认知无线电网络中用于功率分配的归一化Nash均衡

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摘要

We consider a cognitive radio system consisting of several secondary networks and primary user-terminals (primary-UTs). In a secondary network, a secondary-base station (secondary-BS) transmits to a secondary-user terminal (secondary-UT) with certain power. Secondary-BSs are constrained to allocate transmitting powers such that the total interference at each primary-UT is below a given threshold. We formulate the power allocation problem as a concave noncooperative game with secondary-BSs as players and multiple primary-UTs enforcing coupled constraints. The equilibrium selection is based on the concept of normalized Nash equilibrium (NNE). When the interference at a secondary-UT from adjacent secondary-BSs is negligible, the NNE is shown to be unique for any strictly concave utility. The NNE is also shown to be the solution of a concave potential game. We propose a distributed algorithm, which converges to the unique NNE. When the interference at a secondary-UT from adjacent secondary-BSs is not negligible, an NNE may not be unique and the computation of the NNE has exponential complexity. To avoid these drawbacks, we introduce the concept of weakly normalized Nash equilibrium (WNNE), which keeps the most of NNEs' interesting properties but, in contrast to the latter, the WNNE can be determined with low complexity. We show the usefulness of the WNNE when the utility function is the Shannon capacity.
机译：我们考虑由几个辅助网络和主要用户终端（主要UT）组成的认知无线电系统。在辅助网络中，辅助基站（secondary-BS）以一定的功率发送到辅助用户终端（secondary-UT）。辅BS被约束以分配发射功率，使得每个主UT处的总干扰低于给定阈值。我们将功率分配问题表述为一个凹的非合作博弈，其中次要BS作为参与者，而多个主要UT则执行耦合约束。均衡选择基于归一化纳什均衡（NNE）的概念。当相邻子BS在子UT处的干扰可忽略不计时，对于任何严格凹入的效用，NNE都是唯一的。 NNE也显示为凹势博弈的解决方案。我们提出了一种分布式算法，该算法可以收敛到唯一的NNE。当来自相邻辅BS的辅UT处的干扰不可忽略时，NNE可能不是唯一的，并且NNE的计算具有指数复杂性。为避免这些缺点，我们引入了弱归一化的Nash平衡（WNNE）概念，该概念保留了NNE的大部分有趣特性，但与后者相反，可以以低复杂度确定WNNE。当效用函数是香农容量时，我们展示了WNNE的有用性。

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