Network management is a fundamental ingredient for efficient operation of wireless networks. With increasing bandwidth, number of antennas and number of users, the amount of information required for network management increases significantly. Therefore, distributed network management is a key to efficient operation of future networks. This paper focuses on the problem of distributed joint beamforming control and power allocation in ad-hoc mmWave networks. Over the shared spectrum, a number of multi-input-multi-output links attempt to minimize their supply power by simultaneously finding the locally optimal power allocation and beamformers in a self-organized manner. Our design considers a family of non-convex quality-of-service constraint and utility functions characterized by monotonicity in the strategies of the various users. We propose a two-stage, decentralized optimization scheme, where the adaptation of power levels and beamformer coefficients are iteratively performed by each link. We first prove that given a set of receive beamformers, the power allocation stage converges to an optimal generalized Nash equilibrium of the generalized power allocation game. Then we prove that iterative minimum-mean-square-error adaptation of the receive beamformer results in an overall converging scheme. Several transmit beamforming schemes requiring different levels of information exchange are also compared in the proposed allocation framework. Our simulation results show that allowing each link to optimize its transmit filters using the direct channel results in a near optimum performance with very low computational complexity, even though the problem is highly non-convex.

中文翻译：

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用于毫米波网络中节能功率分配和波束成形的非凸广义纳什博弈

网络管理是无线网络高效运行的基本要素。随着带宽、天线数量和用户数量的增加，网络管理所需的信息量显着增加。因此，分布式网络管理是未来网络高效运行的关键。本文重点研究自组织毫米波网络中的分布式联合波束成形控制和功率分配问题。在共享频谱上，许多多输入多输出链路试图通过同时以自组织方式找到局部最优功率分配和波束形成器来最小化它们的供电功率。我们的设计考虑了一系列非凸服务质量约束和效用函数，其特点是各种用户的策略具有单调性。我们提出了一个两阶段的分散优化方案，其中功率水平和波束形成器系数的适应由每个链路迭代地执行。我们首先证明给定一组接收波束形成器，功率分配阶段收敛到广义功率分配博弈的最优广义纳什均衡。然后我们证明了接收波束形成器的迭代最小均方误差自适应导致整体收敛方案。在建议的分配框架中，还比较了需要不同级别信息交换的几种发射波束成形方案。我们的仿真结果表明，允许每个链路使用直接信道优化其发送滤波器，即使问题是高度非凸的，也能以非常低的计算复杂度获得接近最优的性能。分散优化方案，其中功率水平和波束形成器系数的适应由每个链路迭代地执行。我们首先证明给定一组接收波束形成器，功率分配阶段收敛到广义功率分配博弈的最优广义纳什均衡。然后我们证明了接收波束形成器的迭代最小均方误差自适应导致整体收敛方案。在建议的分配框架中，还比较了需要不同级别信息交换的几种发射波束成形方案。我们的仿真结果表明，允许每个链路使用直接信道优化其发送滤波器，即使问题是高度非凸的，也能以非常低的计算复杂度获得接近最优的性能。分散优化方案，其中功率水平和波束形成器系数的适应由每个链路迭代地执行。我们首先证明给定一组接收波束形成器，功率分配阶段收敛到广义功率分配博弈的最优广义纳什均衡。然后我们证明了接收波束形成器的迭代最小均方误差自适应导致整体收敛方案。在建议的分配框架中，还比较了需要不同级别信息交换的几种发射波束成形方案。我们的仿真结果表明，允许每个链路使用直接信道优化其发送滤波器，即使问题是高度非凸的，也能以非常低的计算复杂度获得接近最优的性能。