无线缓存网络的能量优化问题

论文总字数：22814字

摘 要

本文的研究对象为小型基站网络SCNs中的小型基站与中型基站链接构成的无线传感网络的能量优化问题，对该问题进行了数学建模与推导，并对结果进行了仿真，并研究了凸优化问题中内点惩罚函数法的相关算法。

本文的研究表明，小型基站可以将内容缓存至本地缓存中，并通过主动缓存策略实现两种下载增益：预下载增益和本地缓存增益。结合两个增益构建的模型为可解的凸优化数学模型。通过求解该数学模型，可以得到传输时间段内，任意时刻本地缓存的文件以及任意时刻中型基站与小型基站的传输速率。研究表明，随着文件分布偏度的提高，所获得的增益越大。

本文研究的内点惩罚函数法研究的对象分别是惩罚函数的构成和无约束优化算法的选择。分别研究了对数内点惩罚函数和倒数内点惩罚函数，梯度下降方法和牛顿法对内点惩罚函数求解的影响。研究表明，在初始点选择合适的情况下，牛顿法在求解速度上优于梯度下降法。

关键词：无线缓存网络、能量优化、凸优化、惩罚函数

Energy optimization problems in wireless cache networks

Abstract

The object of this paper is energy optimization problem of the wireless backhaul link of SCNs small base with medium base station. This paper builds the mathematical model,makes deduction of the problem and the results of the simulation and do some research about the correlation algorithm of interior point penalty function method of convex optimization problems.

In this paper, the research shows that the small base station can cache the content to the local cache, and achieve two kinds of download gain: pre download gain and local cache gain. By introducing the active cache policy, the model can be built as a convex optimization model with two gain. By solving the mathematical model, we can get the transmission time period, the local cache files at any time and the transmission rate of the base station and the small base station at any time. Research shows that, as the file skewness increases, the gain is greater.

In this paper, the study of the interior point penalty function method is used to study the composition of the penalty function and the selection of the unconstrained optimization algorithm. The effects of the penalty function and the reciprocal interior point penalty function, the gradient descent method and the Newton method on the interior point penalty function are studied respectively. The study shows that the Newtown method is superior to the gradient descent method with a proper selection of the initial point.

KEY WORDS: wireless cache networks, energy optimization, convex optimization, penalty function

目录

摘要...................................................................................................................................................I

Abstract.............................................................................................................................................II

第一章：绪论 1

1.1 引言 1

1.1.1 移动业务量激增 1

1.1.2 通信行业的节能要求 1

1.2 小型基站网络（Small Cell Network） 2

1.3 关键技术 3

1.3.1 主动缓存技术 3

1.3.2 预测技术 3

1.4 本文的研究目的和主要的研究内容 4

1.4.1 研究目的 4

1.4.2 主要的研究内容 4

第二章 数学基础 5

2.1 数学优化问题 5

2.1.1 数学优化 5

2.1.2 凸优化 5

2.1.3 凸集 6

2.1.4 凸函数 6

2.2 优化算法 7

2.2.1 无约束优化问题 7

2.2.2 约束优化问题：内点惩罚法 11

第三章 最小化能量消耗的小型基站无线回程链路缓存策略 14

3.1 引言 14

3.2 系统模型 14

3.3 联合最优策略 19

第四章 凸优化分析 23

4.1 构造惩罚函数 23

4.2 性能分析 24

4.3 结果分析 25

致谢................................................................................................................................................26

参考文献........................................................................................................................................27

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