Robust game-theoretic algorithms for distributed resource allocation in wireless communications
Robust game-theoretic algorithms for distributed resource allocation in wireless communications
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发表时间：
2011
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通讯作者：
Amod J. G. Anandkumar
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作者：
Amod J. G. Anandkumar
通过最优功率控制在高斯干扰信道中实现分布式速率最大化算法的主要博弈论解决方案需要完美的信道知识，但由于各种原因（例如估计误差、反馈量化以及信道估计和信号传输之间的延迟），这在实践中是不可能的。因此，本论文旨在通过设计和分析鲁棒博弈论算法来解决这个问题，该算法用于在有界信道不确定性的情况下实现高斯干扰信道的速率最大化。针对有界信道不确定性下的单天线频率选择性高斯干扰信道，制定了鲁棒速率最大化博弈。该博弈的鲁棒优化均衡解与信道不确定性的概率分布无关。研究了均衡的存在性和唯一性，并给出了均衡唯一性的充分条件。提出了计算均衡解的分布式算法，并证明当博弈具有唯一均衡时，可以保证渐近收敛。针对两个用户场景分析了该博弈均衡时的总速率和无政府状态价格，并表明在某些条件下随着通道不确定性的增加而改善。这些结果表明，当不确定性增加时，鲁棒解决方案会更接近频分多址 (FDMA) 解决方案。对于 FDMA 全局最优的系统，这会带来更高的总速率和更低的无政府状态成本。还根据类似原理开发了在存在信道不确定性的情况下针对多天线高斯干扰信道的鲁棒速率最大化博弈。结果表明，这种鲁棒博弈与修改通道矩阵的名义博弈是等价的。提出并描述了该博弈的鲁棒优化平衡及其计算的分布式算法。给出了算法平衡唯一性和渐近收敛性的充分条件。数值模拟用于确认这些算法的行为。本文的分析和数值结果表明，信道不确定性不一定是有害的，但确实可以在特定情况下提高网络性能，在这种情况下，纳什均衡解效率相当低，信道不确定性会导致用户贪婪性降低。
The predominant game-theoretic solutions for distributed rate-maximization algorithms in Gaussian interference channels through optimal power control require perfect channel knowledge, which is not possible in practice due to various reasons, such as estimation errors, feedback quantization and latency between channel estimation and signal transmission. This thesis therefore aims at addressing this issue through the design and analysis of robust gametheoretic algorithms for rate-maximization in Gaussian interference channels in the presence of bounded channel uncertainty. A robust rate-maximization game is formulated for the single-antenna frequency-selective Gaussian interference channel under bounded channel uncertainty. The robust-optimization equilibrium solution for this game is independent of the probability distribution of the channel uncertainty. The existence and uniqueness of the equilibrium are studied and sufficient conditions for the uniqueness of the equilibrium are provided. Distributed algorithms to compute the equilibrium solution are presented and shown to have guaranteed asymptotic convergence when the game has a unique equilibrium. The sum-rate and the price of anarchy at the equilibrium of this game are analyzed for the two-user scenario and shown to improve with increase in channel uncertainty under certain conditions. These results indicate that the robust solution moves closer to a frequency division multiple access (FDMA) solution when uncertainty increases. This leads to a higher sum-rate and a lower price of anarchy for systems where FDMA is globally optimal. A robust rate-maximization game for multi-antenna Gaussian interference channels in the presence of channel uncertainty is also developed along similar principles. It is shown that this robust game is equivalent to the nominal game with modified channel matrices. The robust-optimization equilibrium for this game and a distributed algorithm for its computation are presented and characterized. Sufficient conditions for the uniqueness of the equilibrium and asymptotic convergence of the algorithm are presented. Numerical simulations are used to confirm the behaviour of these algorithms. The analytical and numerical results of this thesis indicate that channel uncertainty is not necessarily detrimental, but can indeed result in improvement of performance of networks in particular situations, where the Nash equilibrium solution is quite inefficient and channel uncertainty leads to reduced greediness of users.