【作者】 陈颖；

【导师】 张宏纲；

【作者基本信息】 浙江大学 ， 信息与通信工程， 2021， 博士

【摘要】 近十几年来,无线通信网络正在经历前所未有的飞速发展,学术界和工业界从各个角度对其进行设计和优化的成果层出不穷。鉴于网络拓扑是网络各种性能的决定性因素之一,通过优化拓扑来提高网络性能也成为了研究人员热切关注的问题。而要想对无线通信网络的拓扑架构进行最优设计,就需要我们对网络的现有拓扑特征和拓扑理论有全面深入的掌握。基于这种现状,本学位论文围绕“网络具有哪些拓扑特征”和“拓扑特征如何影响网络性能”这两大主题,利用代数拓扑工具,针对无线通信网络领域的具体场景进行了深入研究。针对“网络具有哪些拓扑特征”这一问题,本学位论文选择移动蜂窝网络中的基站分布作为具体研究场景。作为无线通信业务的最主要载体之一,基站的部署规模正在经历空前的爆炸式增长,如何通过对基站位置的合理分布来获得更加优越的网络覆盖性能已经成为一个非常具有挑战性的研究方向。在这样的目标指引下,获取对蜂窝网络拓扑的深层认知就成为了我们急需解决且意义重大的课题。本学位论文引入了 α-Shapes、Betti数、Euler示性数和Hurst系数等经典的代数几何工具,分别在国家范围和城市范围这两种不同的空间尺度下,独立地对多个具有代表性的欧洲和亚洲国家或者城市的真实基站位置数据进行了深入挖掘和分析。首先,基于Betti数和Hurst系数,本学位论文发现欧洲和亚洲国家或者城市的基站空间分布都表现出明显的分形特征。另外,基于Euler示性数来描述国家或者城市范围蜂窝网络的实际基站分布时,本学位论文发现对数正态分布是拓扑特性的最佳匹配。针对“拓扑特征如何影响网络性能”这一问题,本学位论文选择分形D2D(Device-to-Device)移动社交网络容量作为具体研究场景。随着互联网社交媒体的兴起,移动社交通信已经成为无线通信业务的重要组成部分。本学位论文分别在直接和分级社交通信两种情况下,研究了分形拓扑对网络容量上界的影响,其中移动社交网络的分形拓扑是由具有自相似性和反相关性的社交联接所决定的。首先,本学位论文推导并证明了对于直接社交通信场景下的分形D2D移动社交网络来说,如果用户根据随机分布从直接接触节点中选择一个目标用户并与之通信,那么网络的最大容量是(?),其中n代表整个网络的全部用户数量;如果用户根据幂律分布d-β从直接接触节点中选择一个目标用户并与之通信,那么网络的最大容量可到达(?),其中d表示一对社交接触节点之间的距离,β是频率参数。另外,考虑到除了和有直接社交联接的信任用户进行直接社交通信之外,用户也需要与不存在直接社交联接的其他用户进行分级社交通信,本学位论文进一步深入研究并推导了分形D2D移动社交网络在分级社交场景下的最大网络容量。本学位论文的结果表明,此时的网络容量主要受分形结构的相关指数ε所影响。与直接社交通信相比,如果2<ε<3,网络容量将以1/logn的比例下降,如果ε=3,下降因子则变为1/n。总的来说,本学位论文基于代表性代数拓扑工具,结合移动蜂窝网络的基站分布和分形D2D移动社交网络容量这两个具体场景,得到了一系列颇具价值的研究结果。我们相信,这些研究结果将为无线通信网络的精准建模和优化设计提供基础性的理论指导。更多还原

【Abstract】 Over the last decade or so,wireless communication networks(WCNs)have been experienc-ing an unprecedented boom,and fruitful findings on their design and optimization from various perspectives have been emerging in an endless stream from both academic and industrial domains.Since network topology is one of the critical factors of various network performances,its optimization has gained intensive attention from researchers as well.In order to optimize the topology of wireless communication networks,we need to have a comprehensive understanding of the existing topological characteristics and topological theories of the networks.In this regard,focusing on the two topics of ’what topological features the networks have’ and ’how topological features affect network performances’,this dissertation makes an indepth study on the specific scenarios in the field of WCNs by using algebraic topology tools.Aiming at the topic of ’what topological features the networks have’,this dissertation chooses the base station(BS)distribution in the mobile cellular networks as the study scenario.The deployment scale of the BSs,which is one of the main carriers of the wireless communication services,in the mobile cellular networks has been going through the ever-increasing trend.As a result,how to gain prominent network coverage performance by means of appropriate placements of BSs has become a challenging research orientation.In the guidance of this target,a deeper understanding of the cellular networks from the angle of topology is of great urgency and fundamental significance to be achieved.In our researches,under two different spacial scales,namely national and urban scopes,practical location data of BSs in twelve representative countries(six Asian and six European countries respectively)and eight representative cities(four Asian and four European cities respec-tively)are processed separately with classical algebraic geometric instruments,namely α-Shapes,Betti numbers,Euler characteristics,and Hurst coefficients.Firstly,the BS spatial distributions of both Asian and European countries or cities express fractal features based on the Betti numbers and the Hurst coefficients.Secondly,it is found out that the log-normal distribution presents the best match to the cellular network topology when the practical BS distribution under national or urban scope is characterized by the Euler characteristics.Regarding to the topic of ’how topological features affect network performances’,this disserta-tion chooses fractal D2D(Device-to-Device)mobile social network capacity as the study scenario.With the rise of the Internet social media,mobile social communication has become an important part of wireless communication services.Under both direct and hierarchical social communica-tion cases,the influence of the fractal topology on the maximum capacity of D2D mobile social networks is studied in this dissertation.Specifically,the fractal networks are characterized by the direct social connections with self-similarity and anti-correlation patterns.Firstly,for a fractal D2D mobile social network with direct social communications,it is derived and proved that the maxi-mum network capacity is(?)if a user communicates with one of his/her direct contacts in a random way,where n denotes the total number of users in the network,and the maximum net-work capacity can reach up to(?)if any pair of social contacts with distance d communicate according to the power-law probability in proportion to d-β,where β is the frequency parameter.Secondly,since users also need to get in touch with other users without direct social connections through multiple inter-connected users,the maximum capacity of a fractal D2D social network with hierarchical communications is further investigated and derived.Our results show that this network capacity is mainly affected by the correlation exponent ε of the fractal structure.The net-work capacity is reduced in proportional to 1/log n if 2<ε<3,while the reduction coefficient is 1/n if ε=3.In summary,this dissertation integrated representative algebraic topological tools into the analyses of two different WCN scenarios,namely the BS distribution of the mobile cellular networks and the transmission capacity of the fractal D2D mobile social networks,and plenty of valuable research results were obtained.We believe that these research results will provide fundamental theoretical guidance for the accurate modeling and optimal design of WCNs.更多还原