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arXiv 1202.6348cs.ITcond-mat.stat-mechcs.SImath.IT
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随机无线网络中的功率优化

Power Optimization in Random Wireless Networks

Aris L. Moustakas, Panayotis Mertikopoulos, Nicholas Bambos

摘要:

考虑发射机-接收机对的无线网络,其中发射机调整其功率以在存在干扰的情况下维持目标SINR水平。在本文中,我们分析了最佳的功率矢量,实现这一目标,在大型,随机网络中获得的“擦除”有限部分的节点从一个规则的发射机-接收机对格。我们表明,这个问题是相当于所谓的安德森模型的电子运动在肮脏的金属已被广泛用于在随机环境中的扩散分析。一个标准的近似这个模型是所谓的相干势近似(CPA)的方法,我们适用于评估的第一和第二阶样本内统计的最佳功率矢量在一维和二维系统。这种方法等同于随机矩阵理论和自由概率的传统技术,但虽然一般准确(并与数值模拟一致),但它无法完全描述系统:特别是,以这种方式获得的结果无法预测功率控制何时变得不可行。在这方面,我们发现,无限系统总是不稳定的目标SINR超过一定的值,但任何有限的系统只有一个小的概率变得不稳定。这种不稳定的概率是成比例的尾巴的系统的本征值分布的计算指数精度使用的安德森模型及其与随机介质中的随机行走的关系内开发的方法。最后,使用这些技术,我们还计算了系统的功率分布下的功率控制和Foschini-Miljanic功率控制算法在随机擦除的存在下的收敛速度的尾部。总的来说,在本文中,我们试图在直觉论证和形式证明之间取得平衡。

英文摘要:

Consider a wireless network of transmitter-receiver pairs where the transmitters adjust their powers to maintain a target SINR level in the presence of interference. In this paper, we analyze the optimal power vector that achieves this target in large, random networks obtained by "erasing" a finite fraction of nodes from a regular lattice of transmitter-receiver pairs. We show that this problem is equivalent to the so-called Anderson model of electron motion in dirty metals which has been used extensively in the analysis of diffusion in random environments. A standard approximation to this model is the so-called coherent potential approximation (CPA) method which we apply to evaluate the first and second order intra-sample statistics of the optimal power vector in one- and two-dimensional systems. This approach is equivalent to traditional techniques from random matrix theory and free probability, but while generally accurate (and in agreement with numerical simulations), it fails to fully describe the system: in particular, results obtained in this way fail to predict when power control becomes infeasible. In this regard, we find that the infinite system is always unstable beyond a certain value of the target SINR, but any finite system only has a small probability of becoming unstable. This instability probability is proportional to the tails of the eigenvalue distribution of the system which are calculated to exponential accuracy using methodologies developed within the Anderson model and its ties with random walks in random media. Finally, using these techniques, we also calculate the tails of the system's power distribution under power control and the rate of convergence of the Foschini-Miljanic power control algorithm in the presence of random erasures. Overall, in the paper we try to strike a balance between intuitive arguments and formal proofs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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