Performance Analysis On Small Cell Networks Based On Fractal Characteristics

In order to meet the growing traffic demand,small cell networks,as one of the key technologies in the fifth generation(5G)cellular network architecture,have become a research hotspot of 5G communication.However,small cell networks are usually deployed in densely populated urban areas.Due to the diversity of topography,plants and buildings are unevenly distributed,and the atmosphere and weather environment are changing,wireless signals experience different signal attenuations in different propagation directions in complex transmission environments.Different signal attenuations are experienced in the direction of propagation,making the coverage boundary of the wireless small cell network irregular,which poses a challenge for the performance analysis such as coverage probability and average rate of 5G small cell networks.It has been documented that the coverage boundary of an actual small cell network has fractal characteristics.Pareto distribution is widely used to analyze the performance of small cell networks with heavy-tail and fractal characteristics,and has closed-form solution.Therefore,we assume that the distance from the coverage boundary to the base station follows the Pareto distribution.An anisotropy path loss model is proposed in thie paper.Coverage probability,average rate and area spectral efficiency of fractal small cell networks have been analyzed.The lower bound expression of the average rate is derived according to Jensen's inequality,and the influence of fractal parameters on the performance of small cellular networks is analyzed.We assume that the distance from the coverage boundary to the base station follows the Pareto distribution and users can associate with the base station if they fall within the coverage area of the fractal small cell network.However,in order to get better quality of service,the typical UE can associate itself with the SBS that provides the highest instantaneous received power.In this scenario,we are more concerned about the anisotropy of path loss,not the distribution of coverage boundary.We compare the probability density function(PDF)of the path loss exponent measured from the real-world data collected from the Zhangjiang Road at Shanghai city,China,with the Gamma distributions.The result shows the PDF curve of measured data almost matches with the PDF curve of the hypothetical Gamma distribution with the shape parameter 11.69 and the scale parameter 0.36.Thus,the path loss exponent is assumed to be governed by Gamma distribution,we assume that the typical user equipment associates itself with the small cell base station that provides the highest instantaneous received power,coverage probability,average rate and area spectral efficiency of the fractal small cell network with the MIMO technology.In this paper,MIMO technology is applied to fractal small cell networks for the first time and an anisotropic path loss model is proposed in this paper,which provides some guidelines for the research and performance analysis of fractal small cell networks.