Faced with the ever-increasing trend of the cellular network scale, how to quantitatively evaluate the effectiveness of the large-scale deployment of base stations (BSs) has become a challenging topic. To this end, a deeper understanding of the cellular network topology is of fundamental significance to be achieved. In this paper, @math -Shape, a powerful algebraic geometric tool, is integrated into the analysis of real BS location data for six Asian countries and six European countries, respectively. Firstly, the BS spatial deployments of both Asian and European countries express fractal features based on two different testifying metrics, namely 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 deployment is characterized by the Euler characteristics.
Understanding the network topology can prominently facilitate the design of efficient cellular networks, and pervasive applications depending upon the network topology have been found in the wireless communication field. For instance, the knowledge of network topology can be exploited to perform automatic computations for topology control in WSNs @cite_6 , investigate the pros and cons of BS switching on off scheme @cite_8 , develop energy-saving mechanism for green cellular networks @cite_25 , improve the spectral efficiency and reduce the bit error rate (BER) in space-time network coding (STNC) scheme @cite_40 , manage the interference and allocate spectrum resource for a femtocell-based cellular network @cite_20 and so on.
@cite_8 @cite_6 @cite_40 @cite_25 @cite_20
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Large-scale, self-organizing wireless sensor and mesh network deployments are being driven by recent technological developments such as The Internet of Things (IoT), Smart Grids and Smart Environment applications. Efficient use of the limited energy resources of wireless sensor network (WSN) nodes is critically important to support these advances, and application of topology control methods will have a profound impact on energy efficiency and hence battery lifetime. In this survey, we focus on the energy efficiency issue and present a comprehensive study of topology control techniques for extending the lifetime of battery powered WSNs. First, we review the significant topology control algorithms to provide insights into how energy efficiency is achieved by design. Further, these algorithms are classified according to the energy conservation approach they adopt, and evaluated by the trade-offs they offer to aid designers in selecting a technique that best suits their applications. Since the concept of "network lifetime" is widely used for assessing the algorithms' performance, we highlight various definitions of the term and discuss their merits and drawbacks. Recently, there has been growing interest in algorithms for non-planar topologies such as deployments in underwater environments or multi-level buildings. For this reason, we also include a detailed discussion of topology control algorithms that work efficiently in three dimensions. Based on the outcomes of our review, we identify a number of open research issues for achieving energy efficiency through topology control. This study considers an integrated topology control and routing problem in wireless sensor networks (WSNs), which are employed to gather data via use of sensors with limited energy resources. We employ a hierarchical topology and routing structure with multiple sinks and devise a topology control scheme via usable energy fraction at the sensors. We develop and examine three different mathematical models whose solutions prescribe clusterhead and sink locations and data routing from sensors to sinks in a period of a deployment cycle. We develop a heuristic solution algorithm which provides very small optimality gaps for the models. The approach utilizes two types of solution representations, a combination of multiple neighborhoods, and objective value-based cut inequalities for improving the evaluation of candidate solutions. We present extensive numerical test results and analysis of the models and the solution approach. We determine that our proposed model, which minimizes average energy usage and the range of remaining energy distribution at the sensors, captures important characteristics of topology control and routing integration in WSN design and exhibits significantly better performance than our benchmark models and a well-known protocol HEED in extending network lifetime. Topology Control (TC) is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption (which is essential to extend the network operational time) and radio interference (with a positive effect on the network traffic carrying capacity). The goal of this technique is to control the topology of the graph representing the communication links between network nodes with the purpose of maintaining some global graph property (e.g., connectivity), while reducing energy consumption and or interference that are strictly related to the nodes' transmitting range. In this article, we state several problems related to topology control in wireless ad hoc and sensor networks, and we survey state-of-the-art solutions which have been proposed to tackle them. We also outline several directions for further research which we hope will motivate researchers to undertake additional studies in this field. Heterogeneous cellular networks (HetNets) are to be deployed for future wireless communication to meet the ever-increasing mobile traffic demand. However, the dense and random deployment of small cells and their uncoordinated operation raise important concerns about various costs issues, among which notably is energy efficiency. Base station (BS) cooperation is set to play a key role in managing interference in HetNets. In this paper, we consider BS cooperation in the downlink HetNets where BSs from different tiers within the respective cooperative clusters jointly transmit the same data to a typical user, and in particular focus on the optimization of the energy efficiency performance. First, based on a proposed clustering model, we derive the spectral efficiency using tools from stochastic geometry. Furthermore, we formulate a power minimization problem with a minimum spectral efficiency constraint and derive the optimal received signal strength (RSS) thresholds under certain approximation. Building upon these results, we could address the problem of how to design appropriate RSS thresholds, taking into account the tradeoff between spectral efficiency and energy efficiency. Simulations show that the proposed clustering model is more energy-saving than the geometric clustering model, and deploying a multitier HetNet is significantly more energy-saving compared to a macro-only network.