无线通信资源配置中的优化问题与方法  

Optimization problems and methods for resource allocation in wireless communications

作　　者：刘亚锋[1] 武哲宇 陈伟坤 戴彧虹[1] Ya-Feng Liu;Zheyu Wu;Wei-Kun Chen;Yu-Hong Dai

机构地区：[1]中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京100190 [2]中国科学院大学数学科学学院,北京100049 [3]北京理工大学数学与统计学院,北京100081

出　　处：《中国科学：数学》2023年第5期667-696,共30页Scientia Sinica：Mathematica

基　　金：国家优秀青年科学基金(批准号:12022116);国家自然科学基金(批准号:12021001,11991021,12288201和12101048)资助项目。

摘　　要：无线通信系统设计中的许多问题归根结底可建模为优化问题.一方面,这些优化问题常常具有高度的非线性性,一般情形下难于求解;另一方面,它们又有自身的特殊结构,如隐凸性和可分性等.利用优化的方法结合问题的特殊结构求解和处理无线通信系统设计问题是近年来学术界研究的热点.本文重点介绍和讨论无线通信系统设计中的最优资源配置(resource allocation)问题和相关优化方法.本文以优化方法为主线,着重介绍这些优化方法在求解无线通信资源配置优化问题中的应用,主要包括线性锥规划如何揭示非凸问题中的隐凸性,Lagrange对偶理论如何揭示相关问题最优解的结构,稀疏优化和整数规划技巧如何帮助建立相关问题的数学模型,以及半正定松弛、交替最优化和分式规划技巧如何快速求解相关问题.最后,本文展望无线通信系统优化设计研究中的一些研究方向和关键问题.Many problems arising from wireless communication system design can be formulated into optimization problems.On the one hand,these optimization problems are often highly nonlinear,and thus generally difficult to solve.On the other hand,they have their own special structures,such as hidden convexity and separability.Designing efficient optimization algorithms to solve these problems based on their special structure has been a hot research topic in recent years.In this paper,we focus on optimization methods for resource allocation problems in wireless communication system design.Taking optimization theories and algorithms as the main line,we introduce their applications in solving resource allocation problems,including how conic programming reveals the hidden convexity in specific non-convex problems,how Lagrangian duality helps to characterize the structure of their optimal solutions,how sparse optimization and integer programming techniques help to formulate the related problems,and how semidefinite relaxation,alternating optimization,and fractional programming help to design efficient algorithms.Finally,we give a prospect of some future research directions and the key problems in wireless communication system design.

关 键 词：半正定松弛 交替最优化 对偶理论 多用户干扰信道 分式规划 无线通信系统优化设计 稀疏优化 隐凸性 整数规划 

分 类 号：TN92[电子电信—通信与信息系统]