Analysis Of Cellular Network Interference Based On Joint Probability Distribution Of Link Distance

In order to meet the demand of current communication service data volume,the traditional single-layer cellular network has gradually developed to multi-layer heterogeneous cellular network.The forms of interference links in heterogeneous cellular networks are more complex.Modeling and analyzing the communication and interference links in cells is very important to study the system performance.In the actual wireless network scenario,the communication and interference link distances are not independent of each other in the sense of probability.The joint Probability Density Function(PDF)of the two link distances is a prerequisite for analyzing the Key Performance Indicators(KPI)of cellular communication.However,the existing relevant studies roughly regard the above two link distances as independent to simplify the analysis.The analysis results are difficult to meet the requirements for accurate analysis of the5 th Generation Mobile Communication System(5G)heterogeneous network structure.This paper focuses on the 5g cellular network scenario,and analyzes the joint probability distribution of user terminal communication and interference link distance.Considering that the derivation of the strict closed expression corresponding to the distance distribution is extremely complex,it is appropriate to approximate it in the modeling process.Based on this,some performance indicators in cellular network are deduced and analyzed.The main research contents and innovations of this paper are as follows.(1)In view of the problem that considering the above two link distances as independent of each other will affect the KPI analysis accuracy of 5G cellular networks,geometric modeling of downlink communication and interference links when the out-of-cell interfering nodes in the cellular network are located on the diagonal extension of the hexagon.According to this,the mathematical expressions of the joint Cumulative Distribution Function(CDF)and joint PDF are deduced,and the obtained formulas are highly consistent with the statistical results of the Monte Carlo simulation.(2)Aiming at the problem that the obtained joint probability distribution formula is very complicated and inconvenient to apply,the hexagonal cell is approximated to simplify the probability distribution formula.Firstly,the hexagonal cell is approximated by concentric circles in the model,and then the joint distribution function of the distance between communication and interference links in the circular cell is derived as an approximation of the joint distribution function corresponding to the hexagonal cell.Secondly,based on the two metrics of Manhattan distance and Euclidean distance,use the golden section method to find the optimal radius of the approximate circle.The research results show that the optimal approximate circles based on the above two distance metrics are consistent.(3)Aiming at the problem that the interfering nodes outside the cell may not be located on the extended diagonal in the actual communication scenario,the difference of the joint distribution function obtained by the interfering nodes at different positions is analyzed to evaluate the universality of the formula obtained in part(1).Firstly,based on the statistical analysis of probability theory and mathematical geometry theory,it can be found that when the interfering nodes outside the cell are located on the vertical line and the extended diagonal line of a certain side of the hexagon,the difference between the two corresponding joint probability distributions is the largest;Secondly,deduce the joint CDF with the interfering nodes located on the mid-perpendicular line;Finally,when the interfering nodes outside the cell are located on the vertical line and the extended diagonal line respectively,the relationship between the difference between the two joint CDFs with the distance of the interfering node from the cell is analyzed.Theoretical analysis and Monte Carlo simulation results consistently show that in the general case where the base station in the neighboring cell is far away from the boundary of the cell,the joint probability distribution when the interfering node is located on the extended diagonal of the hexagon is regarded as an approximation of the corresponding joint probability distribution when the interfering node is located at any position outside the cell,which is completely feasible in engineering.(4)Based on the joint PDF of communication and interference link distances,some KPIs in the communication system are derived and analyzed.Signal-to-Interference Ratio(SIR),one of the communication performance indicators,is closely related to the link distance.Based on the joint PDF of the communication and interference link distances,the PDF of the SIR of the user terminal in the cell is derived,and then the outage probability based on SIR is derived.Finally,the correctness of the obtained SIR and outage probability is verified based on Monte Carlo simulation.