Modeling And Performance Analysis For Heterogeneous Cellular Networks Based On Stochastic Geometry

With the rapid increase of data traffic amount,mobile cellular networks have evolved from traditional single-tier macro cellular networks to multi-tier heterogeneous cellular networks(HCNs).The traffic is offloaded from macro base stations to small cells.The interference pattern in HCNs is so complex that the traditional grid model is not able to analyze it.How to accurately model and analyze HCNs is crucial to the design and deployment of the system.Stochastic geometry can be used to model and analyze HCNs as a powerful mathematical tool.By modeling the network nodes as a specific point process,the average performance metrics of the network can be derived based on the properties of the point process.Poisson point process(PPP)is the most popular point process due to its tractability.However,in real scenarios,small cells are more likely to cluster around hotspots,rather than completely uniformly distributed.Meanwhile,models based merely on stochastic geometry usually neglect the arrival process of data packets,and cannot describe the real dynamic traffic state in HCNs.To comfort to the clustered property of small cell deployment,this dissertation uses Matern cluster process(MCP)which is a kind of Poisson cluster process(PCP)to model HCNs.Average coverage probability and area spectrum efficiency(ASE)are analyzed and derived.Meanwhile,stochastic geometry is combined with queueing theory to discuss the dynamic traffic in HCNs.Average packet throughput and mean delay performances are analyzed and derived.The main achievements of this research are listed as below.(1)For a two-tier HCN composed of macro base stations(MBSs)and small cells,MCP is used to model and analyze the network.Locations of MBSs are modeled as a PPP,while small cells are modeled as a MCP to reveal the clustered property of small cells.Lcations of users are modeled as another independent PPP.Considering that small cells are more likely to be deployed away from MBSs,MBS exclusion region is introduced where small cells are not allowed to be deployed.Performances of two different scenarios are discussed and compared with each other,i.e.,the two-tier HCN with independent tiers(without MBS exclusion region)and the two-tier HCN with dependent tiers(with MBS exclusion region).The distribution functions of the serving distance given the typical user is located at several different positions are derived.Based on the probability generating functions of PPP and MCP,the Laplace transform of interference is derived.Finally,based on the total probability law,the average coverage probability and ASE are obtained.Simulation results show that the two-tier HCN with dependent tiers can have a better tradeoff between the average coverage probability and ASE.(2)MCP is used to model and analyze the D2 D networks.MCP is used to model the clustered D2 D devices.D2 D receiver(DR)selects its serving D2 D transmitter(DT)based on uniform choice strategy(the serving DT is uniformly selected from the same cluster)and nearest choice strategy(the DT which is the nearest to the typical DR from the same cluster is selected as its serving DT).The distribution functions of the serving and interference distances and the Laplace transforms of the intra-cluster and inter-cluster interference are derived for the two strategies,separately.The average probability and ASE are obtained for the two strategies.Simulation results show that for uniform choice case,there exists an optimal mean number of intra-cluster active DTs to maximize the ASE performance of the network.For nearest choice case,ASE increases linearly with the mean number of intra-cluster active DTs.For both cases,there exists an optimal signal-to-interference-ratio(SINR)threshold to maximize the ASE of the network.(3)In order to model the dynamic traffic scenario,a spatiotemporal network model is used to analyze the mean packet throughput of HCNs.By combining stochastic geometry and queueing theory,a K-tier spatiotemporal HCN model is proposed.Locations of base stations from each tier are modeled as an independent PPP.Locations of users are also modeled as another independent PPP.Each tier has a biased association factor,and each user is connected to the base station which can provide the maximum average biased received power.Orthogonal frequency reusing(each tier uses an orthogonal spectrum resource)and universal frequency reusing(all tiers share the same spectrum resources)are considered.Packets arrive at each user following an independent Bernoulli process.Assuming that different users have different packet arrival rates.Random scheduling(RS)and round robin(RR)scheduling schemes are used to manage traffic.The transmission success probability and base station active probability are decoupled.The mean packet throughputs of the HCN under the two frequency reusing methods are derived,separately.Simulation results show that there exist optimal bias association factors to maximize the mean packet throughputs.(4)The spatiotemporal network model is used to analyze the delay performances of the three scheduling schemes.By combining stochastic geometry and queueing theory,the delay performances of the following three scheduling schemes are analyzed: RS,RR and First input and first output(FIFO).Small cells are modeled as a PPP.Assuming there are multiple users inside each small cell,and each small cell uses one scheduling scheme to select a user to serve at each time slot.Packets arrived at each user follow an independent Bernoulli process.Retransmission of the failed packets is considered.Based on the Markov chain,the mean delay and the mean active probability of base stations are derived for each scheduling scheme,separately.Finally,the cumulative distribution function of the mean delay for each scheduling scheme is obtained.Simulation results show that in light traffic scenario,adopting FIFO can achieve the minimum mean delay.However,in heavy traffic scenario,adopting RR can obtain the best delay performance.The analysis provides guidance for the appropriate selection of scheduling schemes under different traffic load conditions.