Performance Analysis Of Wireless Networks Using Stochastic Geometry And Queuing Theory

Wireless networks are in the midst of a profound evolution in which both opportunities and challenges coexist.In order to meet the exponential growth of traffic demands and provide ubiquitous connectivity for massive communication devices,the deployment of wireless networks is gradually tending toward densification and irregularization.Meanwhile,for the purpose of improving spectrum efficiency,the multiple access scheme is experiencing a paradigm shift from orthogonal mode to non-orthogonal mode.In the face of cutting-edge technologies,it is imperative to excavate the intrinsic relation between network parameters and network performance,and explore the variation law of network performance with the network parameters.However,in wireless networks,the network spatial topology has certain randomness,and the special implementation principle of the non-orthogonal multiple access technology results in huge difficulty in characterizing the network interference.In addition,due to the temporal traffic dynamics,the interaction between interference and queue status arises,which consequently render the analysis intractable.Therefore,how to integrate the above factors into the network performance evaluation model and reveal its vital mechanism of action on network performance is a problem worthy of further study.In view of this,by leveraging both stochastic geometry and queuing theory as mathematical tools,this thesis is devoted to investigate the performance of wireless networks based on two typical non-orthogonal multiple access schemes,i.e.,sparse code multiple access(SCMA)and power domain non-orthogonal multiple access(NOMA).Moreover,an analytical framework for large-scale random wireless networks incorporating the temporal traffic dynamics is proposed in this thesis.Specifically,the main contents and contributions are summarized as follows:1.In SCMA wireless networks,the bidirectional mapping relationship between SCMA codebook and physical time-frequency resource blocks highly complicates the characterization of the inherent relationship between interference and network performance.Aiming at this challenge,this thesis proposes a performance evaluation method by using stochastic geometry.Through this method,the performance of the SCMA wireless network can be analyzed from the perspectives of both the link successful transmission probability and the network area spectral efficiency.First,by taking the modeling of SCMA network interference as the entry point,the mathematical relationships between the interference and the successful transmission probability and the area spectral efficiency are established.The key enabling mechanism of SCMA consequently results in an intricate mathematical relation.For analytical tractability,this thesis obtains the closed-form expressions of the successful transmission probability and the area spectral efficiency in a matrix form through ingenious mathematical processing.Secondly,in order to theoretically reveal the impact of network parameters on network performance,this thesis strictly proves the scaling law of area spectral efficiency with transmitter density in SCMA wireless networks.The impact of the sparse structure of SCMA codewords(i.e.,codeword length and the number of non-zero elements in the codeword)on the maximum achievable area spectral efficiency and the optimal transmitter density is also analyzed.Finally,we study the trade-off between the successful transmission probability and the area spectral efficiency.By carefully tuning the probability that the transmitter accesses the SCMA codebook resource,the area spectral efficiency of the network area can be maximized under the condition that the successful transmission probability is guaranteed to meet certain constraints.The derived analytical results can provide helpful insight on the codebook design and resource optimization in SCMA wireless networks.2.In NOMA wireless networks,the impact of the temporal traffic dynamics on the network performance remains unexplored.Aiming at this problem,this thesis investigates the fundamental performance of uplink non-orthogonal multiple access(NOMA)transmissions,while taking into account the unsaturated traffic profile by using queuing theory.By utilizing tools from queuing theory,this thesis first explicitly characterizes the stable throughput region,which represents the region of traffic arrival rates on the condition that the queuing delay converges in distribution to a bounded random variable.In light of this,the critical condition under which NOMA can extend the stable throughput region of orthogonal multiple access(OMA)is derived.Then,incorporating the dynamic feature of queues,this thesis proposes an algorithmic solution to calculate the average delay incurred from both queuing and transmission.It is interestingly found that the superiority of NOMA over OMA in terms of average delay heavily hinges on the temporal traffic variations of each user.In order to further analyze the boundary performance of the average delay obtained by the algorithm,this thesis obtains closed-form expressions of the upper and lower bounds on the average delay by considering special queuing system.In addition,according to the implementation principle of NOMA,the receiver sequentially decodes and extracts the signals of each user by using the successive interference cancellation(SIC)method.However,in the traditional SIC strategy,when the signal with the highest decoding order cannot be successfully decoded,the receiver will directly abandon the decoding of the subsequent users,which definitely results in a loss of a certain decoding probability for the low-rank users.In light of this,this thesis also considers an improved SIC decoding strategy.The simulation results exhibit that the improved strategy can further extend the stable region of the system and reduce the average delay.The derived results quantitatively reveal the comparative advantages of NOMA under various traffic conditions,and demonstrate the prominent effect of the temporal traffic dynamics.3.In large-scale random wireless networks,the mutual interference is affected by the random distributed network node and the random arrived data traffic.Due to this fact,the mutual interference intercouples with both the spatial locations and temporal queue statuses,and hence poses a great challenge in evaluating the network performance.Aiming at this,by utilizing both stochastic geometry and queuing theory,this thesis proposes a performance analysis method for large-scale wireless networks while taking into account the random traffic arrival and queuing process.Firstly,by using stochastic geometry,this thesis characterizes the mathematical relationship between interference and average service rate,and obtain the closed-form expression for the average service rate.On the other hand,by leveraging queuing theory,this thesis proposes a simple yet accurate approximation method,which can effectively eliminate the impact caused by the interaction between queues.Then,combined with the above analysis from two different perspectives of stochastic geometry and queuing theory,a fixed-point equation for the queue status distribution is established,and the probability distribution of the queue status can be derived by solving the fixed-point equation.Based on the aforementioned analysis,this thesis obtains closed-form expressions for the average delay and its cumulative distribution function.Finally,in order to study the stability of queues in large-scale networks,this thesis proposes the concept of stability,under which the traffic arrival rate can be adjusted to ensure that the proportion of unstable queues in network is not more than .Based on this concept,this thesis further derives the sufficient and necessary conditions for the network to be in the state of stability.The derived results quantitatively demonstrate the impact of network parameters on the network delay and stability performance,which can provide guidance in network performance evaluation and network parameter configuration.