Stochastic Analysis and Optimization of Heterogeneous Wireless Networks by Wei Bao A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto ⃝c Copyright 2016 by Wei Bao Abstract Stochastic Analysis and Optimization of Heterogeneous Wireless Networks Wei Bao Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2016 In order to improve the performance of mobile networks, one widely promoted approach is to install a diverse set of small-cells overlaying the current macrocell network to form a multi-tier heterogeneous wireless network (HWN). In this thesis, I propose new stochastic approaches to evaluate and design HWNs by investigating user load, interference patterns, and user mobility, the results of which provide new analytical insights and design guidelines to improve future HWNs. In the first part of this thesis, I focus on the evaluation of user load through characterizing the joint distribution of users in different cells in an HWN with arbitrary user movement trajectories and dependently distributed user channel holding times. Through developing a new stochastic network analysis framework, I derive a closed-form expression for the joint user distribution, which is only related to the average arrival rate and the average channel holding time of each cell, and hence it is irrelevant to the general user movement patterns and distributions of channel holding times. This property suggests that accurate evaluation of the user distribution and other associated metrics such as the system workload can be achieved with low complexity, without the need to collect a large amount of user location data. The multi-tier architecture of HWNs introduces complicated interference patterns in the system. In the second part of this thesis, I introduce a stochastic analytical framework to compare the performance of open and closed access modes in a two-tier network with macrocells and femtocells, with regard to uplink interference and outage at both the macrocell and femtocell levels. A stochastic geometric approach is employed as the basis for the analysis to characterize the distributions of uplink interference and the outage probabilities. I further derive sufficient conditions for open and closed access modes to outperform each other in terms of the outage probability at either the macrocell or femtocell level. This leads to closed-form expressions to upper and lower bound the difference in the targeted received power between the two access modes. In the third part of this thesis, I study the resource allocation and user association problem in HWNs with random distributed users and BSs for optimizing the average user data rate. Both the user load and interference patterns are considered. I first derive the average user data rate through stochastic geometric analysis. The expression is employed as the objective function of the optimization problem, which is ii non-convex in nature and cannot be solved with a standard method. Then, I propose an innovative approach, solving the optimization problem optimally for low user density, and asymptotically optimally for high user density. The deployment of small-cell BSs in HWNs leads to a higher user data rate, but it also introduces more handoffs to the users. In the fourth part of this thesis, I present a new stochastic geometric analysis framework on user mobility in HWNs, which captures the spatial randomness and various scales of cell sizes in different tiers. I derive analytical expressions for the rates of all handoff types experienced by an active user with arbitrary movement trajectory. Noting that the data rate of a user also depends on the set of cell tiers that it is willing to use, I also provide guidelines for tier selection under various user velocity, so that an optimal tradeoff between the handoff rate and the data rate can be achieved. iii Acknowledgements First, I would like to express my deepest gratitude to my supervisor, Prof. Ben Liang, for his patient guidance, constant encouragement, and excellent advice throughout my PhD study. Without his invaluable help, this work would not be possible. I would like to thank Prof. Wei Yu for being my thesis committee member and for his collaboration with me on part of my research. His suggestions significantly improved the quality of the thesis. I would also like to thank committee member Prof. J¨orgLiebeherr for his careful proof reading and insightful suggestions on this thesis. In addition, Prof. Jianping Pan graciously agreed to be my external examiner, and his feedback in the final stage was very helpful. I am also very grateful to Dr. Stefen Valentin, who offered me the precious research intern opportunity at the Bell Labs and helped a lot in my research. I am very grateful to Dr. Wei Wang for his help in improving my research skills and planning my future career. His strong support and encouragement kept me motivated and confident. I would also like to thank Dr. Yicheng Lin for his collaboration with me on our IEEE JSAC paper. His visions on future mobile networks greatly inspired me. Special thanks also go to Dr. Sun Sun, Jaya Prakash Champati, Yuhan Zhou, and Binbin Dai, who provided me with precious assistance during my PhD study. Thanks to all my colleagues who offered helpful discussions: Dr. Mahdi Hajiaghayi, Ali Ramezani, Meng-Hsi Chen, Dr. Ruhallah Ali Hemmati, Yujie Xu, Sowndarya Sundar, Qiang Xiao, Dr. Honghao Ju, Juan Wen, Caiyi Zhu, Wanyao Zhao, Samer Fouad Zakhary, and others. I must also mention the joy moments I had on weekends and holidays, such as badminton games, board games, travels, picnics, and so on. They will definitely become special memories of mine when looking back to my PhD life. Thanks to Dr. Wei Wang, Dr. Yicheng Lin, Yu Xiao, Binbin Dai, Dan Fang, Dr. Tony Liang Liang, Jessica Yihua Hu, Yuhan Zhou, Caiyi Zhu, Wanyao Zhao, Dr. Qi Zhang, and Siyu Liu who have brought happiness to my life. I must also mention Yifei Hao, Yu Xia, Dr. Wenbo Shi, Candy Tian Yu, and Yichun Qiu. Thanks for their encouragement, support, and most of all their humor. They kept things light and me smiling. I must acknowledge with tremendous thanks to my wife, Zhi Zeng. Through your love, patience, support, and unwavering belief in me, I've been able to complete my long PhD journey. Thank you with all my heart and soul. I love you and am forever indebted to you for giving me your love and heart. Finally, I take this opportunity to express my profound gratitude to my beloved parents for under- standing, support, and endless love during my study in Canada. To you I dedicate this thesis. This research was partially funded by Bell Canada and the Natural Sciences and Engineering Research Council (NSERC) of Canada. iv Contents 1 Introduction 1 1.1 New Challenges in Analysis and Design of HWNs . 1 1.1.1 Understanding User Distribution in HWNs . 1 1.1.2 Characterization of Interference Patterns . 2 1.1.3 Design of User Association Rules . 2 1.1.4 Quantification of Handoff Patterns . 3 1.2 Thesis Outline and Main Contributions . 4 1.2.1 User Distribution under General Mobility and Session Patterns . 4 1.2.2 Uplink Interference Comparison of Open Access and Closed Access . 5 1.2.3 Optimal Spectrum Allocation and User Association . 5 1.2.4 Handoff Rate Analysis in HWNs . 6 2 Related Works 7 2.1 User Mobility Model . 7 2.1.1 Queueing Networks Models . 7 2.1.2 Insensitivity Property of Queueing Networks . 7 2.1.3 Mobility Modeling with Cell Geometry . 8 2.2 Interference Analysis of HWNs . 8 2.2.1 Stochastic Geometry as a Basic Tool . 8 2.2.2 Downlink Interference . 8 2.2.3 Uplink Interference . 9 2.3 Spectrum Allocation and User Association . 10 2.4 A Brief Review on Queueing Networks . 11 2.4.1 Queueing Network under Consideration . 11 2.4.2 Routing Balance Equations . 11 2.4.3 Stationary Distributions of Jackson Networks . 11 2.5 A Brief Review on Stochastic Geometry . 12 2.5.1 Interference Analysis Based on Poisson Point Process . 12 2.5.2 Random Fibre Process . 13 2.6 Publications Related to this Thesis . 13 3 Insensitivity of User Distribution in HWNs 14 3.1 System Model . 14 3.2 Stationary User Distribution in Single-Route Network . 16 v 3.2.1 Queueing Network Model for Single-Route Network . 16 3.2.2 Reference Single-Route Memoryless Network . 17 3.2.3 Insensitivity of Single-Route Network . 18 3.3 Stationary User Distribution in Multiple-Route Network . 21 3.3.1 Queueing Network Model for Multiple-Route Network . 21 3.3.2 Insensitivity of π(x)................................... 21 3.3.3 Insensitivity of π1(y)................................... 22 3.4 Experimental Study . 23 3.4.1 Requirements and the Dartmouth Traces . 23 3.4.2 Data Preprocessing . 24 3.4.3 Trace Analysis . 24 3.4.4 Marginal User Distribution at a Single AP . 26 3.4.5 KL Divergence and Entropy Gap for Multiple APs . 26 3.5 Summary . 30 4 Uplink Interference Analysis: Open Access versus Closed Access 31 4.1 System Model . 31 4.1.1 Two-tier Network . 31 4.1.2 Open Access versus Closed Access . 32 4.1.3 Path Loss and Power Control . 33 4.1.4 Outage Performance . 33 4.2 Open Access vs. Closed Access at the Macrocell Level . 34 4.2.1 Open Access Case . 34 4.2.2 Closed Access Case . 36 4.2.3 Parameter Normalization . 37 4.2.4 Open Access vs. Closed Access . 37 4.3 Open Access vs.