On The Base Station Distribution And Transmission Capacity Of Wireless Communication Networks Based On Algebraic Topology And Fractality

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 ?-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-?,where ? 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 ? of the fractal structure.The net-work capacity is reduced in proportional to 1/log n if 2<?<3,while the reduction coefficient is 1/n if ?=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.