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首页> 外文期刊>IEEE Transactions on Information Theory >Wireless Max–Min Utility Fairness With General Monotonic Constraints by Perron–Frobenius Theory
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Wireless Max–Min Utility Fairness With General Monotonic Constraints by Perron–Frobenius Theory

机译：Perron–Frobenius理论的具有一般单调约束的无线最大-最小效用公平性

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摘要

This paper presents a systematic approach for solving wireless max–min utility fairness optimization problems in multiuser wireless networks with general monotonic constraints. These problems are often challenging to solve due to their nonconvexity. By establishing a connection between this class of optimization problems and the class of conditional eigenvalue problems that can be addressed by a generalized nonlinear Perron–Frobenius theory, we show how these problems can be solved optimally using an iterative algorithm that converges geometrically fast. The mathematical development in this paper unifies previous work and allows us to handle a broader class of competitive utility functions with general nonlinear monotonic constraints. Several representative applications illustrate the effectiveness of the proposed framework, including the max–min quality-of-service subject to robust interference temperature constraints in cognitive radio networks, the min–max weighted mean-square error subject to signal-to-interference-and-noise ratio constraints in multiuser downlink systems, the max–min throughput subject to nonlinear power constraints in energyefficient wireless networks, the max–min sigmoid utility in multimedia wireless networks, and the min–max outage probability subject to outage constraints in heterogeneous wireless networks. Numerical results are presented to demonstrate the fast-convergence behavior of the algorithms to the optimal fixed-point solution characterized by our generalized nonlinear Perron–Frobenius theoretic framework.
机译：本文提出了一种系统的方法来解决具有一般单调约束的多用户无线网络中的无线最大-最小效用公平性优化问题。这些问题由于其不凸性，通常很难解决。通过在这类优化问题和可以用广义非线性Perron-Frobenius理论解决的条件特征值问题之间建立联系，我们展示了如何使用几何上快速收敛的迭代算法来最佳地解决这些问题。本文中的数学发展统一了以前的工作，使我们能够处理具有一般非线性单调约束的更广泛的竞争效用函数。几个有代表性的应用说明了所提出框架的有效性，包括认知无线电网络中受到鲁棒干扰温度约束的最大-最小服务质量，受到信号干扰和干扰的最小-最大加权均方误差多用户下行链路系统中的噪声比约束，高能效无线网络中的最大-最小吞吐量受非线性功率约束，多媒体无线网络中的最大-最小乙状结肠效用以及异构无线网络中受中断约束的最小-最大中断概率。数值结果表明了算法的快速收敛性能，以我们的广义非线性Perron-Frobenius理论框架为特征的最优定点解。

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