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University of Southern California Dissertations and Theses
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Enabling virtual and augmented reality over dense wireless networks
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Enabling virtual and augmented reality over dense wireless networks
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Enabling Virtual and Augmented Reality over Dense Wireless Networks by Po-Han Huang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Computer Engineering) August 2020 Copyright 2020 Po-Han Huang Dedication To my father, Yao-Huei Starsky Huang. ii Acknowledgements I want to express my sincere gratitude to many signicant individuals for your help through my PhD study. First, I would like to thank my advisor, Professor Konstantinos Psounis, for his guidance and feedback during my PhD study. He has encouraged me to develop independence in my academic life and has given me the freedom to explore any topics in which I am truly interested. Although I have kept changing my research areas, he has always given me helpful advice. I am grateful for the constant support he has provided throughout my time at USC. Besides my advisor, I would like to thank my dissertation committee, Professor Ramesh Govin- dan and Professor Bhaskar Krishnamachari, for their insightful comments and contributions to my research direction. I thank Professor C.-C. Jay Kuo and Professor Keith Chugg for serving on my qualifying exam committee and providing helpful feedback. I also thank Weng, Hang, Kaidong, Yonglong, Griey, Kwame, and Ting-Ru, for stimulating conversations and collaboration on my research work. I would like to thank my TA partners, my labmates in RTH 418, my labmates in NSL, and other friends at USC for many meaningful discussions on research and life. Each one of you has helped me to survive the PhD program in many ways. Finally, I want to dedicate this thesis to my wife, Wan-Rou, for her endless support and understanding, and to my family: my mother, Wei Kao, and my sister, Hsuan-Wen Huang, for instilling the values I needed for this incredible journey. I love you. iii Table of Contents Dedication ii Acknowledgements iii List Of Tables vii List Of Figures viii Abstract xi Chapter 1: Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Chapter 2: Optimal Backhauling for Dense Small-Cell Deployments Using mmWave Links 8 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 Hybrid Architecture for Wireless Backhaul . . . . . . . . . . . . . . . . . . 13 2.3.2 Channel Model in mmWave Communication . . . . . . . . . . . . . . . . . 15 2.3.3 Hybrid Beamforming Architecture . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.1 Modelling: Integer Linear Programming (ILP) . . . . . . . . . . . . . . . . 18 2.4.2 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 mmHAUL without Coverage Constraints . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5.1 Upper Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5.2 Rounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5.3 Greedy Knapsack Algorithm for Leftover Antennas . . . . . . . . . . . . . . 23 2.5.4 ClosURK: An Optimal Solution for mmHAUL without Coverage Constraints 24 2.5.5 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6 mmHAUL with Coverage Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6.1 Greedy Set-Cover Based Algorithm for Coverage Guarantee . . . . . . . . . 26 2.6.2 CovURK - An Approximation Algorithm . . . . . . . . . . . . . . . . . . . 27 2.6.3 CovURK Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.6.4 Feasibility Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.6.5 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.7 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.7.1 Small-Scale Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.7.1.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 31 iv 2.7.1.2 Simulation Results - mmHAUL without Coverage Constraints . . 32 2.7.1.3 Simulation Results - mmHAUL with Coverage Constraints . . . . 33 2.7.1.4 Topology of Cluster Heads . . . . . . . . . . . . . . . . . . . . . . 35 2.7.1.5 Statistical Signicance . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.7.2 Large-Scale Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.7.2.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.7.2.2 Varying Number of Small Cells and Antennas . . . . . . . . . . . 37 2.7.2.3 Comparison to Prior Work . . . . . . . . . . . . . . . . . . . . . . 39 2.8 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.8.1 Signaling and Computational Overhead . . . . . . . . . . . . . . . . . . . . 41 2.8.2 Partially-Connected Hybrid Beamforming Architectures . . . . . . . . . . . 42 2.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.10.1 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.10.2 Proof of Theorem 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Chapter 3: Ecient User-Cell Association for 360 Video Streaming over Wireless Networks 51 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.1 Caching Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.2 Multiple Description Video Streaming . . . . . . . . . . . . . . . . . . . . . 57 3.3.3 Unicast versus Multicast Transmissions . . . . . . . . . . . . . . . . . . . . 57 3.3.4 Wireless Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.4 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.4.1 Mixed Integer Linear Programming . . . . . . . . . . . . . . . . . . . . . . . 59 3.4.2 Problem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.2.1 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.2.2 Separability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.4.2.3 Enhanced Views Multicasting . . . . . . . . . . . . . . . . . . . . 63 3.5 Proposed Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.5.1 Optimal Solution - the Branch-and-Bound Method . . . . . . . . . . . . . . 64 3.5.1.1 Problem Transformation . . . . . . . . . . . . . . . . . . . . . . . 64 3.5.1.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.5.1.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.5.2 Submodular-Based Greedy Algorithm - ELVA . . . . . . . . . . . . . . . . . 66 3.5.2.1 Problem Transformation . . . . . . . . . . . . . . . . . . . . . . . 66 3.5.2.2 Evaluation Function . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.5.2.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.5.2.4 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.5.3 MKP-Based Greedy Algorithm - EVA . . . . . . . . . . . . . . . . . . . . . 70 3.5.3.1 Evaluation Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.5.3.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.3.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.6 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.6.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.6.2 Simulation Results - Small-Scale Study . . . . . . . . . . . . . . . . . . . . 75 3.6.2.1 Varying Number of Enhanced Views . . . . . . . . . . . . . . . . . 75 3.6.2.2 User Association and Resource Utilization . . . . . . . . . . . . . 76 3.6.2.3 Varying Number of Small Cells . . . . . . . . . . . . . . . . . . . . 76 v 3.6.2.4 Varying Number of Mobile Users . . . . . . . . . . . . . . . . . . . 77 3.6.2.5 Varying Parameter of p in EVA . . . . . . . . . . . . . . . . . . . 77 3.6.2.6 Varying Cache Size of a Small Cell . . . . . . . . . . . . . . . . . . 78 3.6.3 Simulation Results - Large-Scale Study . . . . . . . . . . . . . . . . . . . . 78 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Chapter 4: AutoCast: Scalable and Ecient Sensor Sharing between Autonomous Vehicles 81 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3 AutoCast Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4 Data Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.5 AutoCast Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.6 AutoCast Scheduler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.6.1 Problem Formulation - Markov Decision Process . . . . . . . . . . . . . . . 97 4.6.2 Scheduling Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.6.3 Scheduling Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.7 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.7.1 A Basic Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.7.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Chapter 5: Conclusion 114 Reference List 116 vi List Of Tables 1.1 Content-Specific Bandwidth Saving Methods . . . . . . . . . . . . . . . . . 3 2.1 System Model Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Simulation Paramters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1 Problem Formulation Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Settings for Simulation Experiments . . . . . . . . . . . . . . . . . . . . . . 72 3.3 Number of Small Cells with % of Total RBs . . . . . . . . . . . . . . . . . . . . . . 73 vii List Of Figures 1.1 Global mobile data trac over the years [18]. The number on the bar shows what percentage of mobile trac is video at that year. . . . . . . . . . . . . . . . . . . . 2 2.1 Hybrid architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Number of Required Antennas with Dierent Rate Requirement . . . . . . . . . . 15 2.3 Fully-Connected Hybrid Beamforming Architecture [87] . . . . . . . . . . . . . . . 16 2.4 System throughput of ClosURK v.s. number of small cells. . . . . . . . . . . . . . 30 2.5 System throughput of ClosURK v.s. number of antennas. . . . . . . . . . . . . . . 31 2.6 System throughput of CovURK v.s. number of small cells. (Note that ClosURK does not satisfy the coverage constraints and this is why it is above the Optimal.) . 33 2.7 System throughput of CovURK v.s. number of antennas. . . . . . . . . . . . . . . 33 2.8 Topology of cluster heads of ClosURK. . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.9 Topology of cluster heads of Optimal. . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.10 Topology of cluster heads of CovURK. . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.11 System throughput with 95% condence intervals v.s. number of small cells. . . . . 37 2.12 System throughput of ClosURK and CovURK v.s. number of small cells. . . . . . 37 2.13 System throughput of dierent architectures v.s. number of small cells. . . . . . . 38 2.14 System throughput of dierent architectures v.s. number of antennas. . . . . . . . 39 2.15 Signalling ow for mmHAUL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.16 Partially-Connected Hybrid Beamforming Architecture. . . . . . . . . . . . . . . . 44 3.1 Simple scenario for two-tier 360 video delivery over wireless networks. . . . . . . . 52 viii 3.2 Scenarios for small-scale study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3 Total rewards versus number of enhanced views. . . . . . . . . . . . . . . . . . . . 74 3.4 Comparison of unicasting and multicasting enhanced views. (Sec. 3.4.2.3) . . . . . 74 3.5 User association in Uniform/Uniform scenario. . . . . . . . . . . . . . . . . . . . . 75 3.6 Total rewards versus number of small cells. . . . . . . . . . . . . . . . . . . . . . . 77 3.7 Total rewards versus number of mobile users. . . . . . . . . . . . . . . . . . . . . . 77 3.8 Total rewards versus p value in EVA. . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.9 Total rewards versus cache size of a small cell. . . . . . . . . . . . . . . . . . . . . . 79 3.10 Large-scale simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1 AutoCast enables multiple vehicles to have extended LiDAR vision into occlusion and beyond sensing range by ecient sensor sharing. a) Left turn in an intersection. Yellow slices represent blocked views. b) The LiDAR data of the blue car. c) The LiDAR view of the blue car after merging neighboring vehicles views using AutoCast, which detects the incoming black car while achieving extended sensing range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 A highway scenario. The yellow views represent the blocked views by the nearby vehicles, and the blue views represent the line-of-sight views. . . . . . . . . . . . . 83 4.3 AutoCast System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 An illustration of view partition (V = 8). . . . . . . . . . . . . . . . . . . . . . . . 89 4.5 An example of the view partition and blocked view index. . . . . . . . . . . . . . . 89 4.6 Empty occupancy grids indicate occluded view partitions. . . . . . . . . . . . . . 89 4.7 An example of adjacent views when N = 2. Blocked view 8 (Red) increases the relevance of adjacent views (Yellow). . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.8 AutoCast Sharing Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.9 AutoCast Protocol (Intersection w/ RSU). . . . . . . . . . . . . . . . . . . . . . 95 4.10 An illustration of H (j;u) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.11 Total rewards v.s. number of available time slots (T ) . . . . . . . . . . . . . . . . . 102 4.12 Total rewards v.s. safety index (^ s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.13 Total rewards v.s. speed (km/h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 ix 4.14 Completeness and Situation Awareness: the Basic Scenario . . . . . . . . . . . . . 105 4.15 Vehicle Density vs. Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.16 Reward Ratio over Time (20 Vehicles). . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.17 Real-time 3D Object Region Proposal . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.18 Vehicle Density vs. U Cov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.19 Vehicle Density vs. U Loc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.20 Vehicle Density vs. U PP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.21 The physical DSRC radio device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.22 AutoCast's transmission latency for partitions that have dierent reward. . . . . 110 4.23 Distributed AutoCast Sharing Region. . . . . . . . . . . . . . . . . . . . . . . . . 111 4.24 Distributed Scheduling Results on Highway . . . . . . . . . . . . . . . . . . . . . . 112 x Abstract The advances of wireless virtual and augmented reality (VR/AR) are imperative not only be- cause of the expectation of portable VR headsets but also because of the requirement of the timely AR information sharing between mobile devices. Wireless VR/AR can then enrich the VR/AR user experience and thus provide the potential of attracting more users. However, the delivery of VR/AR applications over wireless networks introduces many technical challenges due to the associated high-bandwidth demand and the new, sophisticated data types, e.g., 360-degree videos, sensing data, and visual information represented by 3D point clouds or meshes. The next-generation wireless technologies, such as 5G and WiFi 6, are envisioned to increase wire- less bandwidth by dense base station deployments for high-demand applications, for example, VR/AR. Such deployments with a massive number of base stations require specic network sys- tem designs to support VR/AR applications. Particularly, an application-aware network system design is required for the backhaul systems between the core network and base stations, the ac- cess networks between base stations and VR/AR users, and the device-to-device communications among VR/AR users. In this thesis, we start our discussion with a dense wireless network architecture design. More specically, we study how to replace optical bers, which are the traditional yet expensive way to deploy backhaul networks, with millimeter-wave (mmWave) communications. We further demon- strate how to leverage the mmWave wireless backhauling to have high-data-rate access networks and/or to connect a large number of devices. Based on the network architecture, we switch our xi focus to application-aware algorithm designs in two dierent scenarios. In wireless access net- works, we consider how to improve the quality of experience of VR users by an intelligent and ecient user-cell association scheme. And, in device-to-device networks, we explore how to share visual and sensing information eciently among connected and autonomous vehicles. xii Chapter 1 Introduction 1.1 Motivation Mobile video trac has already represented more than 70% of the total wireless trac and is expected to grow further [18], as shown in Fig. 1.1. Virtual and augmented reality (VR/AR), e.g., multiplayer VR games, multi-agent AR systems, and mixed-reality-enabled mission drones, are gaining much attention and will exacerbate the challenges of serving such vast volumes of mobile video trac via wireless networks, especially 5G and WiFi 6 [58]. It is not only because of the increased volume but also because of the real-time nature of these applications that introduce timeliness constraints. VR, a technology making the users immerse themselves into a virtual world, has been widely used for entertaining and educational purposes [30]. However, it has its fundamental limitation because a VR headset should connect with a VR server with a \not-long-enough" cable. This limitation not only restricts the physical movement of a VR user but also connes the developing exibility of VR applications. Tethering VR headsets via wireless while providing the same video quality as via wire is one of the main goals for the next-generation wireless technologies. On the other hand, AR, a technology superimposing a computer-generated image on a user's view of the real world, has been adopted in many mobile games, such as Pok emon Go [20], Wizards Unite 1 2017 2018 2019 2020 2021 2022 Year 0 10000 20000 30000 40000 50000 60000 70000 80000 PB per month 59.3% 63.4% 67.5% 71.5% 75.2% 78.6% Global Mobile Data Traffic, 2017 - 2022 Video Non-Video Figure 1.1: Global mobile data trac over the years [18]. The number on the bar shows what percentage of mobile trac is video at that year. [19], etc., as well as in robotic networks and autonomous driving systems [104]. This application, however, has been circumscribed by inaccurate detection/positioning such that a generated image by one user cannot be superimposed precisely on another user's screen. Crowdsourcing might be a remedy to improve the performance, but ecient information sharing in resource-constrained wireless networks should be carefully investigated. What's more, both VR/AR applications are eager to support a number of users simultaneously, resulting in a more bandwidth-starved underlay network. VR/AR applications typically consist of two components (or two types of contents): 360- degree videos and augmented information (e.g., metadata, sensing data, and visual information). The 360-degree videos are used to construct a virtual world, and the augmented information is used to connect the physical world to the virtual world. Both components can be captured by xed on-site cameras, augmented with local information, downloaded from the cloud, augmented by applications like VR/AR games. They can also be obtained by navigation apps or wearable computer glasses with video processing functionality. For each of the components, many bandwidth-saving techniques are proposed to reduce wireless bandwidth requirements and are summarized in TABLE 1.1. More specically, the 360-degree 2 Table 1.1: Content-Specific Bandwidth Saving Methods 360-Degree Video Augmented Information General Two-tier streaming or Multi-tier streaming Multiple representations (full, dynamic objects, bounding boxes) User-Specic View partitioning Region-of-interest videos can be separated into multiple tier chunks to oer dierent resolutions (i.e., two/multi-tier streaming [43]) and also be separated into several partial views (i.e., view partitioning [102]). For example, consider a 360-degree video broken into north, south, west, and east view segments. These chunks/views can be stored in local caches of small cells (or access points) and controllers [33]. Users associate with small cells and download video chunks from the small cell that they are associated with depending on their interests, locations, and wireless channel condition. On the other hand, the augmented information, which is typically represented by point clouds or meshes, can be classied into multiple representations, such as full objects, dynamic objects, or bounding boxes [104]. For example, consider that a Light Detection and Ranging (Lidar) sensor obtains the 3D information of a person who is waving his/her hand. This sensor can share either the full information of the person or the moving hand only (i.e., dynamic object) with another device. The augmented information, as well as the partial views, can be further specied by the interests of the VR/AR users. Some examples dictating how interested a user is for a particular chunk of video or a piece of augmented information are the direction of movement of the users, the path and nal destination, the blocking of views from obstacles, their participation in specic VR/AR games, etc. These user interests may be communicated to the network, e.g., to controllers, which in turn may schedule the transmission of video chunks from small cells to users or the transmission of augmented information among users via device-to-device communications. To further reduce wireless bandwidth requirements, the overall system may choose to send full frames, partial views, dynamic objects, or even motion vectors and rely on users to reconstruct the video/information from prior frames locally. 3 In addition to the content-specic bandwidth saving methods mentioned above, we can, on the other hand, increase the total bandwidth by leveraging a so-called dense small-cell deployment [26, 62]. Such small cell architectures may support wireless VR/AR as their increased density, which can be up to 75-200 small cells per square km [9, 12, 5], can provide a signicantly higher system capacity by frequency reuse. Consider an enterprise WiFi network or a 5G cellular network where users wish to receive video streaming for VR/AR purposes. We consider medium and dense deployments of small cells, coupled with many controllers such that the network is capable of dealing with the increased demand for wireless bandwidth. Such networks can be found in city centers, airports and train stations, conference/convention centers, university and enterprise campuses, and other public venues. However, these densely deployed wireless networks could cause many technical challenges such as costly backhaul systems and suboptimal user-cell association schemes. The backhaul network should be re-designed because it would be too expensive to connect such a large number of access points via bers [4]. Traditional signal-to-interference-noise- based (SINR-based) user-cell association schemes may not be able to support VR/AR applications and meet the quality of experience expected by users [84]. Motivated by the issues thereof, we would like to investigate how to enable/service VR/AR applications over dense wireless networks. To achieve this goal, the following questions should be addressed: 1. Optimal wireless backhauling architectures are required to support high-demand applica- tions such as VR/AR. 2. Advanced user-cell association and fast roaming schemes are in place and focus on VR/AR- related aspects of the wireless system. 3. Ecient device-to-device aided multicasting scheduling methods should be studied to share the augmented information among connected devices. 4 More specically, in this thesis, we will investigate what kind of wireless backhauling architectures can optimally support the dense small-cell deployments, which can further support VR/AR ap- plications. In such deployments, We will then study ecient user-cell association schemes for VR streaming. Finally, we will consider how to multicast user interests and visual information e- ciently in dense autonomous systems for AR applications and use an autonomous-driving system as an example to study its performance. 1.2 Organization The rest of the thesis is organized as follows. In Chapter 2, we investigate optimal wireless backhaul architectures for dense small-cell de- ployments of 5G networks. We envision a wireless backhaul architecture where cells are grouped into clusters. One small cell per cluster plays the role of \cluster head" connecting to the BS via a millimeter wave (mmWave) multiple-input and multiple-output (MIMO) link; the rest of the small cells in the cluster will then connect to the \cluster head" to reach the BS. We formulate the problem of jointly selecting the cluster heads and the number of BS antennas dedicated to each mmWave MIMO link between the BS and each cluster head to maximize system throughput as an integer linear program (ILP) and prove its NP-hardness. We then propose anO(lnjSj) approx- imation algorithm, whereS is the number of small cells. We show via extensive simulations that the algorithm performs very close to the optimal in practice. Last, we show that the algorithm has, on average, more than 40% performance gain compared to previous work. In Chapter 3, we study ecient user-cell association schemes for 360 video streaming over wireless networks. The delivery of 360 videos for virtual and augmented reality presents many technical challenges especially in bandwidth starved wireless environments. Recently, a so-called two-tier approach has been proposed which delivers a basic-tier chunk and select enhancement- tier chunks to improve user experience while reducing network resources consumption. The video 5 chunks are to be transmitted via unicast or multicast over an ultra-dense small cell infrastructure with enough bandwidth where small cells store video chunks in local caches. In this setup, user-cell association algorithms play a central role to eciently deliver video since users may only download video chunks from the cell they are associated with. Motivated by this, we jointly formulate the problem of user-cell association and video chunk multicasting/unicasting as a mixed integer linear programming, prove its NP-hardness, and study the optimal solution via the Branch-and-Bound method. We then propose two polynomial-time, approximation algorithms and show via extensive simulations that they are near-optimal in practice and improve user experience by 30% compared to baseline user-cell association schemes. In Chapter 4, we explore the possibility of eciently multicasting visual/sensor information among connected and autonomous vehicles. Autonomous driving and advanced driving assis- tance systems leverage visual/sensor information to augment their vision. Sharing this kind of information among nearby vehicles improves visual perception, reliability and robustness, but re- quires signicant bandwidth resources. To enable ecient and scalable autonomous vehicle sensor sharing, we introduce AutoCast, a sensor sharing system that ensures the maximum amount of useful information is shared within a given timeframe. AutoCast reduces the volume of in- formation by spatially partitioning a vehicle's view in partial views and carefully assessing the signicance and relevance of each partial view before transmitting. Then, AutoCast optimally schedules partial views transmissions. Specically, motivated by a Markov decision process for- mulation solved via dynamic programming, it uses a greedy heuristic to eciently determine a near-optimal scheduling policy with maximizes the utility of the transmitted shared information. At the system level, AutoCast devises a novel interaction and clustering protocol that enables vehicles to exchange their states, receive a transmission schedule, and share visual information while avoiding channel interference and collisions. We implement AutoCast on Carla, one of the most realistic autonomous driving simulators. Extensive evaluation results under dierent scenarios show that the protocol operates as designed, the scheduling algorithm is near-optimal 6 with negligible computation overhead, and the system delivers 2 to 3x more useful information compared to sharing full views in a random order. Finally, we conclude this thesis in Chapter 5, with a summary of our contributions and a discussion of future work. 7 Chapter 2 Optimal Backhauling for Dense Small-Cell Deployments Using mmWave Links 2.1 Introduction To meet the high demand in 5G cellular networks, several research directions are explored to increase the capacity of both the access networks and the backhaul networks [110]. For wireless access networks, one promising solution is to use a highly dense base station deployment, which could enhance the whole system throughput by frequency reuse [62]. For example, recent industry reports [12, 5] envision that the number of small cells in a dense deployment will be more than 200 per square km. To support such a network deployment, the backhaul network should be re-designed because it would be too expensive to connect such a large number of access points via bers [4]. Millimeter Wave (mmWave) communication has recently matured thanks to hardware design advancements, and has been proposed to support the high bandwidth demand in 5G cellular networks [124]. The rationale behind using mmWave communication is to take advantage of higher frequency bands, e.g. from 30 GHz to 300 GHz, which could provide higher capacity with larger bandwidth than todays microwave bands. For this reason, mmWave communication is considered suitable for high-bandwidth backhaul connection of ultra-dense small cells [29]. 8 However, there are some fundamental challenges with mmWave communication, such as direc- tivity challenges, high pathloss, low penetration and more [130]. These challenges make mmWave communication only useful for short-range transmissions. To make mmWave links handle long- range transmissions, it has been recently proposed to use multiple-input and multiple-output (MIMO) beamforming [21]. This MIMO beamforming is not expected to incur signicant inter- antenna interference thanks to the intrinsic directional nature of the transmissions which has led researchers to model mmWave backhaul links as pseudo-wires without interference [127]. Motivated by this, [119, 139, 73, 126, 137, 143, 68, 131, 135, 49, 144, 70, 55, 111, 142, 146, 80, 37, 118] discuss how to use mmWave communication in wireless backhaul networks. Some of this work focuses on a distributed architecture (e.g., [119, 139, 73, 126]), where network operators deploy cluster heads connected with bers to the core network and provide mmWave backhaul connection for the rest of the small cells. Another approach is to use a centralized architecture (e.g., [137, 143, 68, 131, 135]), where a central node like a macro cell controls every small cell via a mmWave backhaul. However, neither architecture is particularly appealing for a dense network deployment. For example, the centralized architecture has too high of a signaling complexity, and the distributed architecture cannot handle well the uctuation of trac demand as the number of cluster heads is xed. To address those problems a hybrid architecture has been proposed, see, for example, [49, 144, 70, 55, 111, 142, 146, 80, 37, 118, 63], where a centralized node (e.g., macro cell) controls several cluster heads which are also small cells via mmWave communication, and these cluster heads provide wireless backhaul for the rest of the small cells. In this fully wireless backhaul network architecture, the macro cell only controls the cluster heads rather than all small cells, and there is great exibility for changing cluster heads if the trac demand uctuates. Still, due to the short range of mmWave communication, multi-hopping might be required, and, to avoid the performance issues of multi-hopping, e.g. latency [140], MIMO beamforming has been suggested to support long-range transmissions between the macro cell and the cluster heads [21]. 9 In the context of such a hybrid architecture with MIMO-enabled mmWave backhaul links, in this work we study how to optimally select cluster heads among the small cells and how to optimally select the link capacity of the backhaul links between the macro cell and the cluster cells, that is, how many antennas of the macro cell to dedicate at each backhaul link, to maximize the achieved system throughput. For this purpose, we formulate this problem into an integer linear program (ILP) and prove its NP-hardness by reducing it to a k-set cover problem. To solve the problem in polynomial time, we rst transform it into a simpler problem by allowing some cells to be out of range of all selected cluster heads and propose an optimal solution. We then require that all cells should be assigned to a cluster head and propose an approximation algorithm which uses the aforementioned optimal solution to solve the original problem, and show its near-optimality by simulation. The main contributions of this paper are as follows: 1. To the best of our knowledge, this paper is the rst work which jointly considers antenna partitioning and cluster heads selection in mmWave wireless backhauling under a hybrid architecture. 2. An optimal algorithm is proposed for the special case where there are no coverage constraints, i.e. some remote cells may not be covered by any cluster head. 3. The problem with coverage constraints is shown to be NP hard and an approximation algorithm is proposed and proved to be an O(lnjSj)-approximation where S is the number of small cells. 4. Extensive simulations show that the proposed algorithm is, in practice, within 5% o the optimal, and at least 40% superior than prior work [137]-[135] and [70]-[37]. The rest of the paper is organized as follows. Section 2.2 summarizes related work. Section 3.3 presents the system architecture that we consider. The objective of this work and a formal 10 problem description is presented in Section 4.6.1. In Section 2.5, we solve the problem without coverage constraints by an optimal solution. Then, an approximation algorithm for the original NP hard problem is discussed in Section 2.6. In Section 3.6 we evaluate the performance of the approximation algorithm using simulations and show that it outperforms previous works under a variety of realistic scenarios. Practical considerations are discussed in Section 2.8 and Section 4.9 concludes the paper. 2.2 Related Work We summarize prior work on backhaul design focusing on distributed, centralized, and hybrid architectures. Distributed Architecture. A distributed architecture was presented in [119, 139, 73, 126] with two types of nodes: anchored nodes and demand nodes, where anchored nodes were used for backhaul relaying and demand nodes were used for serving users. Note that anchored nodes connect to core networks via a wired backhaul and demand nodes connect to core networks with the help of anchored nodes via a wireless backhaul. [119] and [139] designed algorithms which minimize the deployment cost under a bandwidth resource constraint for a wireless small-cell backhaul network. The authors in [73] and [126] investigated how to select anchored nodes and where to place them while connecting them with wires for achieving high throughput. This line of prior work does not consider wireless backhauling between the anchored nodes and the macro cell. In contrast, we consider wireless backhauling between both small cells and cluster heads, and between cluster heads and the macro cell. Centralized Architecture. A centralized architecture was investigated in [137, 143, 68, 131, 135], where a central node like a macro cell controls every small cell via a mmWave backhaul. Some work in this line of research (e.g., [137] and [143]) focused mainly on how to eciently allocate antennas of the macro cell to provide a wireless backhauling solution towards all small cells. 11 Other works (e.g., [68]-[135]) discussed the role of MIMO beamforming methods for providing better performance under dierent scenarios. More specically, the authors in [68] took wind- induced beam misalignment into consideration, the authors in [131] addressed full-duplex small cells, and the authors in [135] considered both cell association and bandwidth allocation in their model. However, this prior work does not consider the option to select a subset of small cells to act as relays (cluster heads) for the rest of the small cells. Hybrid Architecture. A hybrid architecture has been recently introduced, see [49][144] and references therein, according to which a centralized node (e.g. macro cell) controls several cluster heads which are also small cells via mmWave communication, and these cluster heads provide wireless backhauling for the rest of the small cells. A number of associated problems have been studied, see [49, 144, 70, 55, 142, 111, 146, 80, 37, 118]. Specically, [70] and [55] study how to associate small cells with cluster heads subject to a predetermined number and location of cluster heads. In contrast, we study the optimal number and location of cluster heads. [111] studied dynamic radio resource management and transmission schemes to maximize the system throughput while maintaining low packet delay in the context of a xed wireless backhaul, whereas we consider dynamic wireless backhauling for performance reasons. [142] studied packet delay in wired and wireless backhauling technologies and proposed a backhaul-aware BS association policy to minimize the delay, whereas we focus on throughput. [146], [80], and [37] studied via heuristics how to t more network ows (video streams) in a hybrid architecture with bandwidth resource constraints, without providing any formal performance guarantees. Last, [118] studied inter- operator resource management for maximizing the average sum rate. Specically, the authors optimized the average sum rate and provided a cooperative and non-cooperative scheme to obtain a near-optimal performance. Note that all prior work on hybrid architectures does not take antenna partitioning into consideration, which has an impact on the system throughput. 12 Cluster heads (also small cells) Small cells Backhaul link between a cluster head and a macro cell Backhaul link between a cluster head and a small cell Figure 2.1: Hybrid architecture. In summary, dierent from prior work, this work takes advantage of both a fully-wireless backhaul and a dynamic selection of cluster heads to achieve higher throughput while providing optimal and approximation algorithms. 2.3 System Architecture 2.3.1 Hybrid Architecture for Wireless Backhaul According to the hybrid architecture of wireless backhaul design for small cell networks (see Fig. 2.1), packets travel between the core network and a macro base station (BS) via ber, then travel between the macro cell and a cluster head via mmWave communication, and last between a cluster head and the other small cell again via mmWave communication. The main assumptions that we make are as follows. First, similar to prior work [127], we assume that the communication between cluster heads and the macro cell, as well as the com- munication between small cells and cluster heads have small interference, because main lobes are narrow and only side lobes contribute to interference. That said, we do take this small interference into consideration in our analysis, see Eq. (2.1). 13 Second, note that beamforming will suer from alignment issues especially in a mmWave environment [68] whenever the antennas are recongured. For this reason, rapidly updating cluster heads is impractical and, instead, we assume that cluster heads change at much lower time scales than the duration of a transmission, such that the alignment issues can be addressed by standard schemes like the one presented in [68]. Another practical reason to change cluster heads at low time scales is the signicantly higher cost of advanced antennas that can support fast reconguration, and that the signaling overhead increases as the frequency of antenna recongurations increases, see Sec. 2.8 for a discussion on signaling overhead. Third, we assume that our network operates in the context of a half duplex communication system, and the scheduling con icts from the half duplex system can be avoided using con ict- free routing tables and dual egress congurations, see [98] and references therein for more details. Therefore, we can fully utilize the resources in both frequency and time domain. Last, we assume that every small cell always has packets to send, i.e. we operate in the saturated throughput regime. With this assumption in mind, the amount of trac between small cells and cluster heads is not the main focus because it is always conned by the link capacity between the cluster heads and the macro cell. The main goal is to select the optimal set of cluster heads among all small cells such that the capacity of the backhaul network is maximized, subject to the constraints of coverage and maximum number of available antennas. Note that a small cell which becomes a cluster head should not only deal with the data from its users, but also with the trac from the other small cells which use it as a relay. 14 0 100 200 300 400 500 Distance (m) 0 20 40 60 80 100 120 Number of Antenna Rate = 10 Gbps Rate = 9 Gbps Rate = 8 Gbps Rate = 7 Gbps Rate = 6 Gbps Rate = 5 Gbps Figure 2.2: Number of Required Antennas with Dierent Rate Requirement 2.3.2 Channel Model in mmWave Communication Let d i be the distance between the macro cell and small cell i. Then, the signal-to-noise ratio (SNR) without beamforming for small cell i can be obtained as follows, D i = P t H i d i N 0 W + ;8i2S; (2.1) whereP t is the transmission power, H i is the small scale fading, is the path-loss coecient, W is the bandwidth of a frequency slot, andN 0 is the noise power spectral density. In addition, captures the small interference from the side lobes of other links, which, following [28], equals: = X 8j2S;j6=i p t H j d j;i ; where p t is the transmission power of a side-lobe beam, H j is the small-scale fading, and d j;i is the distance between small cellj and small celli. Note that, as shown in [108], small-scale fading has a minor impact on the received power from LOS base stations when directional antennas are used in mmWave systems, but we include it for completeness nevertheless. 15 . . . . . . . . . RF Chain RF Chain . . . Baseband Precoder . . . Figure 2.3: Fully-Connected Hybrid Beamforming Architecture [87] Then, the backhaul capacity C i , achieved with N i transmitter antennas and one receiver antenna, can been shown to equal [22] C i (N i ;D i ) =W log 2 (1 +N i D i ): (2.2) This equation shows the relationship between three parameters: the distance between a small cell and the macro cell, the number of antennas for a mmWave link, and the capacity of the link. We illustrate this relationship in Fig. 2.2, where it is evident that to maintain the same capacity as the distance grows linearly we need an exponentially larger number of antennas. Note that the capacity model between the macro cell and a small cell only uses beamforming gain instead of multiplexing gain for MIMO beamforming. This is because multiplexing gains require a well-conditioned channel matrix from rich scattering. However, since rich scattering is typically unavailable in mmWave systems, the channel matrix is typically ill-conditioned, and beamforming gain is usually adopted in the model of mmWave MIMO beamforming, see [127, 22, 54, 87]. 16 2.3.3 Hybrid Beamforming Architecture We assume a fully-connected hybrid beamforming architecture, see Fig. 2.3 for a schematic representation. Note that a fully-connected hybrid beamforming architecture allows arbitrary partitioning of the antenna elements to RF chains. Since narrow beams are usually found in mmWave setups, it is beamforming rather than multiplexing gains that are used in our context. Therefore, each cluster head should be associated with one or more RF chains / antenna elements (depending on the number of antennas and clusters heads) and each RF chain should transmit useful signal to one cluster head only. Besides fully-connected hybrid beamforming architectures, there is a plethora of partially-connected hybrid beamforming architectures aiming to reduce the cost at the expense of less exibility. We discuss how to apply our work to partially-connected hybrid beamforming architectures in Sec. 2.8.2. 2.4 Problem Formulation In this section, we formulate the problem of mmWave Wireless Backhauling for Hybrid Architecture ULtra-Dense Networks (mmHAUL) using integer linear programming (ILP). Specically, we want to determine which small cells become cluster heads, which small cells connect to these cluster heads while maximizing the system throughput and ensuring connectivity for every small cell, and how many antennas of the macro cell are allocated to the connection between the macro cell and each cluster head. TABLE 2.1 lists useful notation. 17 Table 2.1: System Model Notation Description Notation Decision variable for establishing connection between cluster head i and small cell j y i;j The set of small cells S Distance between macro cell and cluster head i d i Transmission power of macro cell P t Small-scale fading from macro cell to small cell i H i Bandwidth of a frequency slot W Noise power spectral density N 0 Path loss exponent Signal-to-noise ratio between macro cell and cluster head i D i Number of antennas for backhauling of cluster head i N i Backhaul capacity for cluster head i C i (N i ;D i ) Maximum number of available antennas in macro cell N MAX Adjacency matrix and its elements A :a i;j 2.4.1 Modelling: Integer Linear Programming (ILP) Given the set of small cellsS, the adjacency matrix A = 2 6 6 6 6 6 6 4 a 1;1 a 1;jSj . . . . . . . . . a jSj;1 a jSj;jSj 3 7 7 7 7 7 7 5 ; which indicates whether small cell i and j are within range or not, and the number of available antennas at the macro cell N MAX , we want to determine the values of the following decision variables: y i;j which indicates whether small cell j connects to cluster head i, and, N i which indicates the number of antennas used for the link between the macro cell and the small cell i. Note that N i > 0 indicates small cell i is selected to act as a cluster head. Under the saturation regime, the amount of trac between the small cells and the cluster heads is eventually conned 18 by the link capacity between the cluster heads and the macro cell. This is so because, by design, the link capacity between a cluster head and the macro cell would be less than the sum of the link capacities between the cluster head and the small cells it is serving, in order to take advantage of statistical multiplexing. Hence, under a saturation regime where all small cells are fully loaded, the bottleneck is the link between the cluster head and the macro cell, and not the links between a small cell and its cluster head. Therefore, the main goal of this problem is to select the right set of cluster heads and allocate to each of them the right number of antennas which would dictate the capacity of the backhaul links between cluster heads and the macro cell. We formulate this problem as follows. Q1 : max yi;j;Ni X 8i2S C i (N i ;D i ) (2.3) s.t. y i;j N i a i;j ;8i;j2S (2.4) X 8i2S y i;j = 1;8j2S (2.5) X 8i2S N i N MAX ; (2.6) y i;j =f0; 1g;8i;j2S N i 2Z+;8i2S The rationale behind this model is as follows. Objective (2.3) aims to maximize the system throughput by deciding the allocation of antennas and the associations between the cluster heads and the rest of small cells. Note that even though the objective function does not depend on the allocation variable y i;j , we need the allocation variable y i;j in the constraints to ensure coverage (see below). (2.4) represents that the connection y i;j can be chosen if small cells i and j are adjacent to each other (i.e., a i;j = 1) and small cell i has been chosen as a cluster head (i.e., N i > 0). (2.5) guarantees that every small cell connects to one cluster head. Last, (2.6) guarantees 19 that the total number of used antennas for the links between cluster heads and the macro cell cannot exceed the number of available antennas at the macro cell. 2.4.2 Complexity Analysis In this section, we show that mmHAUL is NP-hard by reducing it to a k-set cover problem. We start by dening the k-set cover problem and then we prove NP-hardness. Denition 1. (k-Set Cover Problem) Given a universeU, an integerk, and a familyT of subsets ofU, a cover is a subfamilyCT of sets whose union isU, andjCjk. Theorem 1. mmHAUL is NP-hard Proof. Consider that N i =f0; 1g;8i2S. We can transform our problem to the standard form of the k-set cover problem by the following steps. (i) Since N i =f0; 1g;8i2S, we can get C MAX = C i (1;D max ), where D max denotes the maximum SNR value. With C MAX , we can render (2.3) into a minimization problem: min Ni;yi;j P 8i2S (CC MAX )N i (ii) The constraints (2.4) and (2.5) are the typical coverage constraints in the k-set cover problem. (Note that (2.5) is usually expressed as a inequality rather than an equality but the solution is the same in our case.) (iii) Let k =N MAX , (2.6) becomes P 8i2S N i k, which is the standard form of the k-set cover problem. From this, it is evident that the k-set cover problem is a special case of our problem. It is obvious that our problem is more complicated than the k-set cover problem because ourN i ;8i2S can be any positive integers. Since the k-set cover problem is known to be NP-complete, our problem is NP-hard. 2.5 mmHAUL without Coverage Constraints Since this problem is NP-hard, our rst attempt to solve it eciently assumes that every small cell is within range of any other small cell. Therefore, we reformulate the original problem (Q1) by 20 assuming that the aforementioned adjacency matrix is full of ones. Note that in the next section we solve the original problem (Q1) using as part of the solution the methods developed in this current section. Given the full connectivity assumption, (2.4) and (2.5) are always satised. Thus, these two constraints and the decision variable y i;j can be eliminated. Still, we have to decide which small cells should become cluster heads for maximizing the system throughput, and, the rest of the small cells will associate with a cluster head near them. With the above in mine we reformulate the problem as follows. Q2 : max Ni X 8i2S C i (N i ;D i ) (2.7) s.t. X 8i2S N i N MAX : (2.8) N i 2Z+;8i2S In the following subsections, we propose a polynomial time algorithm to obtain the optimal solution ofQ2. The algorithm consists of three steps which we discuss separately in the following subsections. 2.5.1 Upper Bound The rst step to solve this problem is to reformulate it from ILP to linear programming (LP). In particular, the relaxed problem is the same as Q2, but now N i is a real number instead of an integer. 21 Since it is an LP with one objective function and one constraint, we can use Lagrangian relaxation to solve it as follows: max Ni X 8i2S [C i (N i ;D i )N i ] +N MAX (2.9) s.t. N i 2R+;8i2S where is the Lagrangian multiplier. Using the Karush-Kuhn-Tucker (KTT) conditions, we get the following, which, interestingly, resembles the KTT conditions for the well know waterlling problem [101]. dCi(Ni;Di)Ni dNi = 0 ( P 8i2S N i N MAX ) = 0 0 9 > > > > > > = > > > > > > ; KKT conditions. Then, we have the allocation policy as follows, ( W 1 D i ) + =N i ;8i2S (2.10) X 8i2S N i =N MAX ; (2.11) Once this algorithm is performed, the optimal solution of the relaxed problem can be obtained, which is an upper bound of Q2, since N i is not an integer value in Q2. 22 2.5.2 Rounding In this step we simply round the real valued N i to the largest integer less than or equal to N i using the oor function, i.e., ~ N i =bN i c;8i2S: (2.12) 2.5.3 Greedy Knapsack Algorithm for Leftover Antennas After rounding, there will be some left over antennas, which allows us to assign more antennas to some links. Note that we do not assign more than one antenna to a small cell before going over all small cells because of the logarithmic objective function (see (2.7) and (2.2)). Therefore, starting with ~ N i , we dene a binary decision variable b i to decide whether small cell i can have one more antenna or not. We solve the following problem: Q3 : max bi X 8i2S C i ( ~ N i +b i ;D i ) (2.13) subject to X 8i2S b i ~ N MAX ; (2.14) b i =f0; 1g;8i2S where ~ N MAX =N MAX P 8i2S ~ N i . Q3 is a standard binary Knapsack problem, and we can use a greedy algorithm [93] to get a polynomial-time solution. Specically, at each step we select the small cell i with the largest 23 value ofD i (i.e., the best SNR or the closest one) to give one antenna, and subtract one antenna from ~ N MAX until ~ N MAX 0. Please see Algorithm 1 for more details. Algorithm 1 Greedy Knapsack Algorithm for Q3 Input: ~ N i ;8i2S, D i ;8i2S, and ~ N MAX . Output: b i ;8i2S. 1. Initialize b i ;8i2S =f0;:::; 0g 2. Sort8i2S by D i in descending order with new index ^ i. 3. for8 ^ i2S do 4. if ~ N MAX 0 then 5. b ^ i = 1 6. ~ N MAX = ~ N MAX b ^ i 7. end if 8. end for Notice that it is straightforward to show that the Greedy Knapsack Algorithm is the optimal solution for Q3: Theorem 2. Greedy Knapsack Algorithm is the optimal solution for Q3. Proof. Greedy Knapsack Algorithm is the exact optimal solution for Q3 since all variables have the same weight (i.e., 1) according to the results in [93]. 2.5.4 ClosURK: An Optimal Solution for mmHAUL without Coverage Constraints We put everything together and propose an algorithm we referred to as ClosURK (Closest-selected algorithm with Upper bound, Rounding, and greedy Knapsack) which optimally solves Q2. The algorithm obtains the upper bound rst, then performs rounding, and nally uses the Greedy Knapsack Algorithm. The details of ClosURK are shown in Algorithm 2. The following theorem proves that ClosURK nds an optimal solution to Q2. Theorem 3. Given D i 1;8i2S, ClosURK is the optimal solution of Q2. Proof. Please see Sec. 2.10.1. 24 Algorithm 2 ClosURK for mmHAUL without Coverage Constraints Input: D i ;8i2S and N MAX . Output: N i ;8i2S. 1. N i Upper Bound (D i ;N MAX ); 2. ~ N i Rounding (N i ;D i ;N MAX ); 3. b i Greedy Knapsack Algorithm ( ~ N i ;D i ; ~ N MAX ); 4. N i = ~ N i +b i ; Remark. The intuition of this algorithm is quite straightforward. The rst two steps (i.e., upper bound and rounding) are used to obtain the initial allocation of antennas and access the number of leftover antennas. Because of the logarithmic objective function, allocating additional antennas one by one to each small cell is better than allocating all antennas to one small cell. Therefore, for the leftover antennas, we allocate one more antenna to each small cell starting from the closest one to the macro cell with the highest SNR value and proceeding in decreasing order of SNR. 2.5.5 Complexity Analysis What remains is to prove that the algorithm can run in polynomial time. Theorem 4. Given D i 1;8i2S, ClosURK runs in polynomial time. Proof. Since the upper bound of Q2 can be obtained in polynomial time based on [101], the rst part of ClosURK runs in polynomial time. Rounding can run in linear time as we can examine every small cell once. Greedy Knapsack Algorithm runs in O(jSj log(jSj)), which is indeed polynomial time. In conclusion, ClosURK runs in polynomial time. 2.6 mmHAUL with Coverage Constraints In this section, we propose an approximation algorithm to solve mmHAUL with coverage con- straints. We develop this algorithm based on ClosURK while taking coverage constraints into account simultaneously. In addition, we provide a formal proof for its performance guarantee. 25 Following the remark in Sec. 2.5, as long as the coverage constraints are satised, we can perform ClosURK to get the optimal solution. Therefore, our approach to solve mmHAUL is to satisfy the coverage constraints rst with the minimum number of antennas, and then use ClosURK to get the maximum throughput with the remaining antennas. (Notice that in the following discussion, we assume that the coverage constraints can always be satised. Otherwise, no algorithm can solve this problem. We discuss how to check the feasibility of the problem in Sec. 2.6.4.) 2.6.1 Greedy Set-Cover Based Algorithm for Coverage Guarantee To take care of the coverage constraints with the minimum number of antennas, we develop an algorithm based on the solution for the k-Set Cover Problem. Thus, we propose a Greedy Set- Cover based Algorithm, which can eciently satisfy the coverage constraints by greedily choosing cluster heads. At each step of a greedy procedure we select the small cell i with the smallest K i = 1 jSij to become cluster head, whereS i is the set of small cells that can be covered by cluster head i, andjj denotes the cardinality of that set. In other words, we select the small cell that can cover the most number of small cells at each step, see Algorithm 3 for more details. Algorithm 3 Greedy Set-Cover based Algorithm Input: D i ;8i2S and N MAX . Output: x i ;8i2S. 1. Initialize x i ;8i2S =f0;:::; 0g. 2. CalculatejS i j;8i2S. 3. whilejSj! = 0 do 4. ~ i = arg max 8i2S K i = Ni jSij 5. x ~ i = 1 6. S S ~ i 7. UpdatejS i j;8i2S. 8. end while 26 2.6.2 CovURK - An Approximation Algorithm We propose an approximation algorithm which we refer to as CovURK (Coverage aware algorithm with Upper bound, Rounding, and greedy Knapsack algorithm) to solve the original mmHAUL problem. CovURK rst checks whetherjSj N MAX orjSj > N MAX , and then operates dif- ferently depending on the condition. In the rst case, all small cells will become cluster heads (though they will be a cluster on their own) and there are no coverage constraints. Thus, we can just run ClosURK. In the second case, the basic idea of CovURK is to rst run the Greedy Set- Cover based Algorithm to satisfy the coverage constraints and then run ClosURK to achieve the maximal throughput by allocating antennas appropriately, see Algorithm 4 for more details. In the following section, we prove that this algorithm provides an O(lnjSj) performance guarantee. Algorithm 4 CovURK for mmHAUL Input: D i ;8i2S and N MAX . Output: N i ;8i2S. 1. ifjSjN MAX then 2. N i ClosURK (D i ;N MAX ); 3. else 4. N i Greedy Set-Cover (D i ;N MAX ); 5. N i ClosURK (N i ;D i ;N MAX ); 6. end if 2.6.3 CovURK Performance Analysis We rst analyze the optimality of CovURK whenjSjN MAX and the whenjSj>N MAX . Theorem 5. Given D i 1;8i2S andjSjN MAX , ClosURK is the optimal solution of Q1. Proof. SincejSjN MAX , every small cell will have N MAX jSj antennas. Also, because N MAX jSj 1, this implies every small cell is covered, i.e., (2.4) and (2.5) are satised. Then, from the conclusion of Theorem 3, ClosURK is the optimal solution of Q1 in this case. Denition 2. For a given topology, let L = C i (N i ;D min ) denote the lowest throughput and U = C i (N i ;D max ) denote the highest throughput between the macro cell and a small cell, where 27 D min is the minimum SNR value in the given topology, and D max is the maximum SNR value in the given topology. Theorem 6. For a given topology and D i 1;8i2S, CovURK is an 1 + (lnjSj 1) U L approxi- mation algorithm whenjSj>N MAX . Proof. Please see Sec. 2.10.2. The approximation ratio depends on how we (approximately) solve the set cover problem and there are several ways to solve it, see [42] and references therein. For example, we could get a tighter bound if we use the analysis in [42] or we could use a more complicated approximation algorithm than the greedy one we use, to get an O(lnf)-approximation algorithm, where f is the maximum number of sets in which any element appears. Furthermore, the approximation ratio depends on the lowest throughput L and the highest throughput U in the given topology. If we have a hotspot network topology, where all small cells are distributed in a small area, the values of L and U will be closer and the bound will become tighter. Otherwise, if we have a uniform network topology, where small cells are evenly distributed within a macro cell, the values of L and U will diverge more and the bound will become looser. 2.6.4 Feasibility Check We use results from [64][114] to check whether the coverage constraints are satisable. We start by stating two useful facts: 1. If any row ofA has all 0's, obviously the coverage constraint cannot be satised. 2. Dene a dominated set as follows: a row ofA where there is only one 1 among its entries. If the number of dominated sets are larger than lnjSjN MAX , the coverage constraints might not be satised by the Greedy Set-Cover based Algorithm. 28 It takes a polynomial time to check both facts above. Clearly, if the rst fact holds, there is no solution to the problem. Every time we choose a small cell to be the cluster head we check whether the second fact holds, and, if yes, we conservatively don't select the small cell as a cluster head as it wouldn't be guaranteed that the Greedy Set-Cover based Algorithm could satisfy the coverage constraints. 2.6.5 Complexity Analysis What remains is to prove that the algorithm can run in polynomial time. Theorem 7. Given topology and D i 1;8i2S, CovURK runs in polynomial time. Proof. The approximation algorithm requires two algorithms: one is Greedy Set-Cover based Algorithm and the other is ClosURK. Since the algorithm for mmHAUL without coverage con- straints has been proved to be run in polynomial time in Theorem 4, the remaining part of this proof is that Greedy Set-Cover based Algorithm runs in polynomial time. Based on the results in [42], we know that the time complexity of Greedy Set-Cover based Algorithm is O(jSj 2 logjSj), which is indeed polynomial time. Therefore, the approximation algorithm runs in polynomial time. 2.7 Performance Evaluation We study the performance of various schemes via simulations under two network scales: A) In a small-scale scenario (i.e., when the network consists of a small number of small cells and antennas), mmHAUL without and with coverage constraints are investigated to study the optimality of ClosURK and the performance guarantee of CovURK, respectively. B) In a real-life large-scale scenario (i.e., on a network with a large number of small cells and antennas), we use the same process to test how ecient both algorithms are when the size of the network scales up. 29 Table 2.2: Simulation Paramters Parameters Values Small-scale Large-scale Radius of the macro cell 200 m 500 m Radius of a small cell 100 m 200 m Transmission power of the macro cell 30 dBm 46 dBm Transmission power of a small cell 27 dBm 30 dBm Carrier frequency 60 GHz Available bandwidth 1 GHz Bandwidth for a frequency slot 100 MHz Antenna gain 5 dBi Noise power spectral density -174 dBm/Hz Path loss exponent 5 0 5 10 15 20 Number of Small Cells 0 50 100 150 200 250 300 350 System Throughput (Gbps) Upper_Bound Optimal_woSC ClosURK Rounding Figure 2.4: System throughput of ClosURK v.s. number of small cells. We use the following legends to label various algorithms. For mmHAUL without coverage constraints (Q2), we use \Upper Bound" to refer to the upper bound of this problem (see Sec. 2.5.1). We use \Rounding" to refer to the algorithm in Sec. 2.5.2. Last, we use \Optimal woSC" to refer to the optimal values for Q2. For mmHAUL with coverage constraints (Q1), we use \Optimal" to refer to the optimal values forQ1. Note that the optimal values of \Optimal woSC" and \Optimal" are obtained by CVX in MATLAB with Gurobi as the optimal solver. 30 1 2 3 4 5 6 7 8 9 10 Number of Antennas 0 10 20 30 40 50 60 System Throughput (Gbps) Upper_Bound Optimal_woSC ClosURK Rounding Figure 2.5: System throughput of ClosURK v.s. number of antennas. 2.7.1 Small-Scale Simulations First, we study the system throughput under a varying number of small cells and a varying number of antennas on the macro cell for mmHAUL without coverage constraints. Specically, we vary the number of small cells from 1 to 20, and we vary the total number of antennas from 1 to 10. Second, we study the system throughput under the same simulation settings and varying parameters for mmHAUL. Finally, we plot the cluster head distribution for ClosURK, Optimal, and CovURK to discuss how the selection of clusters aects performance. 2.7.1.1 Simulation Settings The parameters used for the simulation are based on [126], [40], and [14], and are listed in TABLE 2.2. The backhaul system is operated in 60 GHz. The transmission power of the macro cell is 30 dBm, the transmission power of a small cell is 27 dBm, the bandwidth of a frequency slot is 100 MHz, and the total available bandwidth is 1 GHz. The path-loss coecient is 5, and the noise power equals -174 dBm/Hz. In this scenario, small cells in the network are uniformly distributed within the range of a macro cell. The radius of the macro cell and the small cells is 200 m and 100 m respectively. 31 2.7.1.2 Simulation Results - mmHAUL without Coverage Constraints We rst examine the performance for mmHAUL without coverage constraints (Q2). In Fig. 2.4, we show the results of ClosURK, Upper Bound, Rounding, and Optimal woSC in terms of the total system throughput under a varying number of small cells. For now we assume that there are 5 antennas on the macro cell. First, whenjSjN MAX , all of the algorithms perform similarly: Rounding has the smallest throughput, and ClosURK and Optimal woSC have the same throughput in the middle of Up- per Bound and Rounding. The throughput dierence between Upper Bound and Rounding is a insignicant 0.2%. This is because the dierence of the allocated number of antennas between before and after taking the oor function is less than 1, considered to be small in terms of the total system throughput. Second, we analyze the performance of the algorithms whenjSj > N MAX . a) Upper Bound keeps increasing when the number of small cells increases since it allows fractional number of antennas allocated in each cluster head. b) The performance of Rounding drops drastically: N i ;8i 2 S obtained from Upper Bound is less than 1, which becomes 0 after Rounding. c) ClosURK and Optimal woSC have the same performance no matter how many small cells are in the system. Last, the system throughput of ClosURK and Optimal woSC increases more slowly than that of Upper Bound when the number of small cells increases. This shows the impact of linear programming relaxation in the algorithm. In the gure, the integrality gap in the algorithm is proportional to the number of small cells. In other words, the more small cells in the system, the harder it is to achieve the upper bound. Fig. 2.5 shows the results of ClosURK, Upper Bound, Rounding, and Optimal woSC in terms of the system throughput under a varying number of antennas. We assume there are 3 small cells in the setting. In this gure, the performance of Rounding diers from that of the rest of the 32 0 5 10 15 20 Number of Small Cells 0 20 40 60 80 100 120 140 System Throughput (Gbps) ClosURK Optimal CovURK Theoretical Bound Figure 2.6: System throughput of CovURK v.s. number of small cells. (Note that ClosURK does not satisfy the coverage constraints and this is why it is above the Optimal.) 1 2 3 4 5 6 7 8 9 10 Number of Antennas 20 25 30 35 40 45 50 55 60 System Throughput (Gbps) ClosURK Optimal CovURK Theoretical Bound Figure 2.7: System throughput of CovURK v.s. number of antennas. algorithms. When the number of antennas is a multiple of the number of small cells, the results of Rounding are the same as ClosURK and Optimal woSC. Otherwise, there are gaps between Rounding and Optiaml woSC. Notice that Greedy Knapsack Algorithm in ClosURK is the key step to ll those gaps, and to make ClosURK be the optimal solution of Q2. 2.7.1.3 Simulation Results - mmHAUL with Coverage Constraints In this section, we turn our focus on the original problem: mmHAUL (Q1). Fig. 2.6 shows the system throughput of ClosURK, Optimal, CovURK, and the theoretical lower bound under a 33 -200 -100 0 100 200 -200 -100 0 100 200 ClosURK Figure 2.8: Topology of clus- ter heads of ClosURK. -200 -100 0 100 200 -200 -100 0 100 200 Optimal Figure 2.9: Topology of clus- ter heads of Optimal. -200 -100 0 100 200 -200 -100 0 100 200 CovURK Figure 2.10: Topology of cluster heads of CovURK. varying number of small cells. Note that ClosURK does not satisfy the coverage constraint and thus is not a solution to Q1. We include it in this plot for reference only. Initially, we assume there are 5 antennas in the macro cell. Some observations can be summarized as follows. First of all, whenjSjN MAX , then CovURK, ClosURK, and Optimal have the same values of the system throughput. In other words, CovURK reaches the optimal values in this case. This result is expected since CovURK performs like ClosURK whenjSjN MAX , and ClosURK is the optimal solution from Theorem 5. WhenjSj > N MAX , the performance dierence between ClosURK and Optimal is between 2.58% and 30.80%. Since ClosURK is the optimal solution of mmHAUL without coverage con- straints and Optimal is the optimal value of mmHAUL with coverage constraints, this dierence clearly shows the impact of the coverage constraints in the problem. The gure also shows that this dierence is proportional to the number of small cells: more small cells require to be covered when the number of small cells increases, the performance therefore is sacriced when selecting more cluster heads with poor SINR. This result was expected. Third, the performance dierence between CovURK and Optimal is between 1.06% and 11.4% as the number of small cell increases. This shows that the approximation algorithm is near-optimal in most cases. Interestingly, in this gure, the total system throughput of Optimal converges to 100 Gbps when the number of small cells increases. This is because the coverage constraints force the system to select the cluster heads that are relatively far from the macro cell such that trac from 34 remote small cells is relayed, resulting in a smaller total system throughput from these cluster heads as the number of small cells increases. Although there are still some leftover antennas to be allocated, because most of the antennas have already been used to satisfy the coverage constraints, the system cannot get a signicant gain from these leftover antennas. Moreover, the total system throughput of CovURK slightly decreases when the number of small cells increases. This is consistent with the fact that the performance bound of CovURK is proportional to the number of small cells: as the number of small cells increases, the Optimal converges to a xed value, the distance between the optimal and CovURK increases and, thus, CovURK's performance decreases. Lastly, based on our proof, the theoretical bound is inversely proportional to the number of small cells. In Fig. 2.6, the dierence between Optimal and the theoretical bound is between 44.18% and 66.61% in the worst scenario when the number of small cells increases. Note that we can improve these results by implementing other algorithms for the Set Cover Problem as discussed in Sec. 2.6.3. In Fig. 2.7, we show the results of ClosURK, Optimal, CovURK, and the theoretical bound in terms of the system throughput under a varying number of antennas. We assume 3 small cells in the simulation. In this gure, as expected, when the number of antennas increases, the performance also increases. 2.7.1.4 Topology of Cluster Heads Fig. 2.8, 2.9, and 2.10 illustrate the topology of cluster heads of ClosURK, Optimal, and CovURK respectively, to present their choices of the cluster heads. Note that in this simulation there are 5 antennas and 10 small cells in the range of the macro cell. The orange circle is the range of the macro cell, the blue small circles are the positions of small cells, and the red, pink, black stars are the positions of the cluster heads of ClosURK, Optimal, and CovURK, respectively. We run the same setting for 10 times. At each iteration, there are 5 small cells selected to be the cluster heads 35 in ClosURK, Optimal, and CovURK. In Fig. 2.8, only the small cells in the middle, i.e., around the macro cell, are selected to be the cluster heads. As expected, since the small cells \close" to the macro cell have higher SNR values, we end up selecting them as cluster heads to maximize the system throughput. In Fig. 2.9 and 2.10, the results show that although both Optimal and CovURK have the same number of cluster heads in their networks, they select dierent sets of small cells to be the cluster heads. Specically, Optimal selects the cluster heads closer to the macro cell whereas CovURK selects the cluster heads farther from the center. The main reason leading to this is that Greedy Set-Cover based Algorithm in CovURK is an approximation algorithm, not the optimal solution for satisfying the coverage constraints. Moreover, both gures produce dierent results compared to ClosURK since both algorithms need to take care of the coverage constraints. 2.7.1.5 Statistical Signicance Fig. 2.11 shows condence intervals for ClosURK, Optimal, and CovURK. Note that the simu- lation settings are the same as Fig. 2.6. As shown in the gure, the 95% condence intervals of ClosURK, Optimal, and CovURK are 1 Gbps which corresponds to about 1% of variation o the mean. Thus, the average values of the performance for all the algorithms are representative, and, in the following sections we only present the average values. 2.7.2 Large-Scale Simulations In this section, rst, we study the system throughput under a varying number of small cells and a varying number of antennas on the macro cell for both ClosURK and CovURK. Specically, we vary the number of small cells from 100 to 500, and we vary the total number of antennas from 100 to 500. Then, we compare ClosURK and CovURK with the algorithms of prior work to show how ecient our algorithms are. 36 5 10 15 20 Number of Small Cells 80 90 100 110 120 130 140 System Throughput (Gbps) ClosURK Optimal CovURK Figure 2.11: System throughput with 95% condence intervals v.s. number of small cells. 100 150 200 250 300 350 400 450 500 Number of Small Cells 1000 2000 3000 4000 5000 6000 7000 8000 System Throughput (Gbps) ClosURK (N MAX = 100) CovURK (N MAX = 100) ClosURK (N MAX = 200) CovURK (N MAX = 200) ClosURK (N MAX = 300) CovURK (N MAX = 300) ClosURK (N MAX = 400) CovURK (N MAX = 400) ClosURK (N MAX = 500) CovURK (N MAX = 500) Figure 2.12: System throughput of ClosURK and CovURK v.s. number of small cells. 2.7.2.1 Simulation Settings The same settings as in the small scale simuations are used, except that now the macro cell has a radius of 500 m and transmits with power 46 dBm, and each small cell has a radius of 200 m and transmits with power 30 dBm, see TABLE 2. 2.7.2.2 Varying Number of Small Cells and Antennas In Fig. 2.12, we plot the performance of ClosURK and CovURK for a varying number of small cells and antennas together. As expected, the more antennas in the system, the higher system 37 100 150 200 250 300 350 400 450 500 Number of Small Cells 1000 1500 2000 2500 3000 3500 System Throughput (Gbps) ClosURK CovURK Centralized Hybrid Figure 2.13: System throughput of dierent architectures v.s. number of small cells. throughput we can obtain. Also, the most important observation from this gure is that CovURK has near-optimal performance in large-scale simulation. Note that the optimal values are in the middle of ClosURK and CovURK. Since the performance of CovURK is close to that of ClosURK as well as the optimal values, we conclude ConURK is near optimal. In addition to the above-mentioned results, some observations are summarized as follows. First, for every pair of ClosURK and CovURK with the same number of antennas, there is a performance dierence between these two algorithms when the number of small cells is larger than the number of antennas. Moreover, in the more constrained setting (i.e., a network with less antennas and more small cells), the performance dierence becomes larger since the cluster heads selection by Greedy Set-Cover based Algorithm is more dierent from ClosURK and CovURK. Second, for both ClosURK and CovURK with the same number of antennas, the throughput increases slowly as long as the number of small cells is larger than the number of antennas. This is because every small cell can only get one antenna in that case. Note that in this case the system throughput will converge to the upper limit, UN MAX , where U is the maximum SINR in Denition 2. 38 100 150 200 250 300 350 400 450 500 Number of Antennas 1000 1200 1400 1600 1800 2000 2200 2400 System Throughput (Gbps) ClosURK CovURK Centralized Hybrid Figure 2.14: System throughput of dierent architectures v.s. number of antennas. 2.7.2.3 Comparison to Prior Work Last, we study the performance of ClosURK and CovURK compared with the following prior studies under a varying number of small cells and a varying number of antennas in Fig. 2.13 and Fig. 2.14, respectively. • Centralized architectures (\Centralized", [137]-[135]): In the case ofjSjN MAX , Centralized evenly distributes its antennas to each cluster head. Moreover, in the case of jSj>N MAX , Centralized makes its small cells use one antenna in turns. • Hybrid architectures (\Hybrid", [70][37]): Hybrid has the same steps of CovURK: Greedy Set-Cover based Algorithm and the throughput enhancement. Instead of using Greedy Knapsack Algorithm for the throughput enhancement like CovURK, Hybrid uses random antenna allocation. Fig. 2.13 shows the performance of ClosURK, CovURK, Centralized, and Hybrid under a varying number of small cells. We assume that the macro cell has 200 antennas in the simulation. As shown in the gure, CovURK outperforms the others in most cases. As expected, Hybrid's performance is lower than that of ClosURK and CovURK since we choose the best way to allocate the antennas instead of randomly allocating them. In particular, CovURK can have a 30%-43% performance 39 gain compared with Hybrid. When the number of small cells increases, the gap between Hybrid and ClosURK/CovURK becomes larger. This is because the probability that Hybrid has the same set of cluster heads as ClosURK and CovURK is smaller when there are more small cells in the network. In addition, Centralized has the same performance as ClosURK and CovURK when jSj N MAX because in this case all the algorithms distribute the antennas evenly. However, when the number of small cells is larger than the number of antennas, small cells under the Centralized approach use the antennas in turns. When there are more small cells in the network, the performance cannot be more improved. Fig. 2.14 shows the performance of ClosURK, CovURK, Centralized, and Hybrid under a varying number of antennas. We assume there are 200 small cells in the simulation. Similarly to before and as shown in the gure, CovURK outperforms the other algorithms in most cases. As expected, the system throughput of Hybrid will be closer to ClosURK and CovURK when the number of antennas increases since the probability that Hybrid has a similar trend as our schemes becomes larger. The performance gain of CovURK is 2%-46%. On the other hand, Centralized has the similar trend like ClosURK and CovURK whenjSjN MAX because all of these algorithms evenly distribute the antennas to the cluster heads. The performance gain of CovURK is 43.61% compared with Centralized whenjSj>N MAX . The results establish that CovURK outperforms prior suggested algorithms by more than 40% depending on various scenarios. 2.8 Practical Considerations In this section we discuss practical issues related to the signaling between BSs and the compu- tational requirements to run our algorithms in a real world context that would implement our schemes, and to the cost and availability of various hybrid beam-forming architectures. 40 Macro Cell Small Cells (Cluster Heads) Small Cells Provide the required information to macro cell Cluster head decision Establish the link Broadcast to all the remaining small cells Cluster-head phase Small-cell phase Establish the link Connection decision Figure 2.15: Signalling ow for mmHAUL. 2.8.1 Signaling and Computational Overhead We adopt the structure of the existing 5G signaling ow [110, 62]. Fig. 2.15 provides the detail procedure of the information exchange between the macro cell and small cells/cluster heads. There are two parts in the signaling ow: the cluster-head phase, which connects the macro cell to cluster heads, and the small-cell phase, which connects the remaining small cells to cluster heads. The cluster-head phase executes either the CovURK or the ClosURK algorithms by proceeding as follows: 1) The beacons which are broadcasted by small cells are used by the macro cell to estimate the channel between small cells and itself. 2) The macro cell jointly decides the cluster head selection and antenna allocation on the links between itself and the cluster heads. 3) The macro cell broadcasts the decision to every small cell under its coverage and the links between the cluster heads and the macro cell are established. Then, the small-cell phase proceeds as follows: 1) The cluster heads broadcast the capacity of their link to the macro cell, and the number of already connected small cells, to all the remaining small cells. 2) The unconnected small cells make a connection to the cluster head that they prefer. Note that the small-cell phase is very similar to the well know user-cell association problem in the context of a multi-cell network, see, for example [23, 27], and thus we do not investigate it in this paper. It is worth to mention however that to tackle this problem one may use a centralized 41 approach, where the macro cell optimally allocates unconnected small cells to cluster heads, or a distributed approach, where unconnected small cells pick the cluster head of their choice. In the later case, which we adopt here for scalability reasons [23], the ordering by which unconnected small cells select cluster heads aects the nal outcome. To see this, when a new/unconnected small cell picks a cluster head, its decision will depend on the number of already connected small cells to this cluster head, as it would have to share the capacity of the cluster head with the rest of the connected small cells. As a last point, recall from Section 3.3 that we keep the same cluster heads for a period of time given that changing cluster heads takes time due to beam alignment challenges. Hence, the cluster-head phase described above won't be repeated every time a new small cell joins the network, whereas the small-cell phase will obviously be executed. We nish this section with a discussion on the computational overhead to run our algorithms. We have recorded the time that it takes to run ClosURK and CovURK on a MacBook Pro and it takes less than 1 second to run either one of them for large scale scenarios involving hundreds of antennas and hundreds of small cells. Specically, it takes about 0.6 seconds to run ClosURK and 0.9 to run CovURK. Today's macro BSs have far larger larger computational and storage capacity than a MacBook Pro, and the same will be true for upcoming cloud based BSs [117]. What is more, the antenna partitioning and cluster head selection decisions are expected to be updated at hourly timescales [138]. Thus, the computational overhead of our schemes is negligible. 2.8.2 Partially-Connected Hybrid Beamforming Architectures Fully connected beamforming architectures (see Fig. 2.3) are becoming available but are rather costly and 5G providers may choose to avoid them in the context of small cells, at least till they become more aordable. Motivated by this, we discuss partially-connected hybrid beamforming architectures and how the problem under study would modied in this case. There are clearly many ways one can design a partially-connected hybrid beamforming architecture. For the shake of discussion, we consider the simplest and thus least expensive one, which is oered by many 42 antenna manufacturers today: each RF chain is connected to a disjoint subset of the complete set of antenna elements. Specically, let B MAX be the total number of RF chains and recall that N MAX denotes the total number of antenna elements. As shown in Fig. 2.16, under the partially-connected architecture we consider, each RF chain connects tok antenna elements withkB MAX =N MAX . Now, letB i be a decision variable of how many RF chains are used in small celli. We can formulate the problem under study as follows: Q4 : max yi;j;Ni;Bi X 8i2S C i (N i ;D i ) (2.15) s.t. y i;j N i a i;j ;8i;j2S (2.16) X 8i2S y i;j = 1;8j2S (2.17) X 8i2S N i N MAX ; (2.18) X 8i2S B i B MAX ; (2.19) kB i N i k(B i + 1); (2.20) y i;j =f0; 1g;8i;j2S N i 2Z+;8i2S B i 2Z+;8i2S where (2.16) - (2.18) are exactly the same as (2.4) - (2.6), (2.19) guarantees that the total number of used RF chains for the links between cluster heads and the macro cell cannot exceed the number of available RF chains at the macro cell, and (2.20) assures that there are sucient number of RF chains to support the number of required antennas for small cell i. Note that Q4 is, as expected, again an NP-hard problem. In the following discussion, we provide a polynomial-time solution which reuses the CovURK algorithm and a modied version 43 . . . . . . . . . RF Chain RF Chain . . . Baseband Precoder . . . k k Figure 2.16: Partially-Connected Hybrid Beamforming Architecture. of the ClosURK algorithm introduced before. The modied ClosURK algorithm has three steps like the original: Upper Bound, Rounding, and Greedy Knapsack Problem, and tries to solve the following problem: Q5 : max Bi X 8i2S C i (kB i ;D i ) (2.21) s.t. X 8i2S B i B MAX ; (2.22) B i 2Z+:8i2S The idea is to allocatek antenna elements when applying the waterlling algorithm in the Upper Bound step and to leverage the rest of the steps in ClosURK as before (see Sec. 2.5.1). Then, the clustering part is still solved by CovURK. Note that there is no performance guarantee for the solution since the modied ClosURK does not necessarily nd the optimal antenna partition in this case. 44 2.9 Conclusion Connecting densely-deployed small cells with a macro cell in the context of future 5G networks is a challenging problem. We use a mmWave wireless backhauling network to do so. Specically, we create an intermediate relay of cluster heads for the small cells to connect to the macro cell via these cluster heads. We jointly optimize the selection of cluster heads and the allocation of antennas of the macro cell to the mmWave links between the macro cell and the cluster heads to maximize the throughput. We introduce an approximation algorithm, CovURK, which can solve this problem in polynomial time. Compared to pervious works, CovURK demonstrates an overall performance gain of 40% . 2.10 Appendix 2.10.1 Proof of Theorem 3 We rst analyze some properties of the logarithmic objective function in this problem. Then, based on these properties, we prove the optimality of ClosURK. The following proofs are based on the fact that D i 1;8i2S for mmWave communication. Lemma 1. Given D i 1;8i2S, and D i D j ;8i;j2S, and i6=j, C(N;D i )C(N 1;D i )>C(N + 1;D j )C(N;D j ). 45 Proof. We prove this lemma by contradiction. Assume givenD i 1;8i2S, andD i D j ;8i;j2 S, and i6=j, we examine the relation below. C(N;D i )C(N 1;D i )C(N + 1;D j )C(N;D j ) =) W log 2 (1 +ND i )W log 2 (1 + (N 1)D i ) W log 2 (1 + (N + 1)D j )W log 2 (1 +ND j ) =) log 2 ( 1 +ND i 1 + (N 1)D i ) log 2 ( 1 + (N + 1)D j 1 +ND j ) =) 1 +ND i 1 + (N 1)D i 1 + (N + 1)D j 1 +ND j =) D i D j D j D i SinceD i andD j are larger than or equal to 1, the left-hand-side is always larger than or equal to 1. Also, sinceD i D j , the right-hand-side is always less than or equal to 0. The above relation is impossible to be true. Therefore, it reaches to the contradiction, and the lemma holds. Lemma 2. Given D i 1;8i2S, and D i <D j ;8i;j2S, and i6=j, C(N;D i )C(N 1;D i )>C(N + 1;D j )C(N;D j ). 46 Proof. We prove this lemma by contradiction. Assume givenD i 1;8i2S, andD i <D j ;8i;j2 S, and i6=j, we examine the relation below. C(N;D i )C(N 1;D i )C(N + 1;D j )C(N;D j ) =) W log 2 (1 +ND i )W log 2 (1 + (N 1)D i ) W log 2 (1 + (N + 1)D j )W log 2 (1 +ND j ) =) log 2 ( 1 +ND i 1 + (N 1)D i ) log 2 ( 1 + (N + 1)D j 1 +ND j ) =) 1 +ND i 1 + (N 1)D i 1 + (N + 1)D j 1 +ND j =) D i D j D j D i =) D i 1 D i D j (*D j 1) Since D i are larger than or equal to 1, the left-hand-side is always larger than or equal to 1. Also, since D i <D j , the right-hand-side is always less than or equal to 1. The above relation is impossible to be true. Therefore, it reaches to the contradiction, and the lemma holds. Based on the lemmas, given D i 1;8i2S, the following statement is always true. Corollary 1. Suppose all small cells are assigned with N antennas each and there are n leftover antennas, where njSj. Then, the policy that allocates N + 1 antennas to exactly n small cells is better than a policy which, among these n small cells, allocates N + 2 antennas in one cell, N antennas in another, and N + 1 in the rest of them. Proof. Assume we arbitrarily choosen small cells to be withN + 1 antennas and the rest of small cells withN antennas. Based on the results of Lemma 1 and 2, we know that givenD i 1;8i2S, C(N +1;D i )C(N;D i )>C(N +2;D j )C(N +1;D j ). This tells us that we cannot improve the performance by moving one antenna from one of thesen small cells to another small cell of thesen small cells. More specically, the performance reduction by removing one antenna from small celli 47 isC(N +1;D i )C(N;D i ), and the performance gain by allocating one more antenna to small cell j isC(N +2;D j )C(N +1;D j ). SinceC(N +1;D i )C(N;D i )>C(N +2;D j )C(N +1;D j ), the performance gain will not be larger than or equal to the performance reduction. Therefore, the policy that exactly n small cells have N + 1 antenna is better than the policy that, among these n small cells, one of them has N + 2 antennas, one of them has N antenna, and the rest of them have N + 1 antenna. Theorem 3. Given D i 1;8i2S, ClosURK is the optimal solution of Q2. Proof. Based on the result of Corollary 1, we know that before every small cell has the same number of antennas, we should not give any small cells more antennas than the maximum allocated number of antennas for each small cell. This implies that every small cell has at leastb N MAX jSj c antennas in the optimal solution, which is also the same as the results obtained from Rounding. Because 0 1 Di 1 in (2.10) and (2.11) (D i 1), the dierence of 1 Di does not exceed 1, which makes all ~ N i =b N MAX jSj c after we execute Rounding. Therefore, Q2 can be reduced to Q3 after Step 2 in ClosURK. The only unsolved problem is how to allocate the leftover antennas, i.e., N MAX b N MAX jSj cjSj. Based on Theorem 2, Greedy Knapsack Algorithm is the optimal solution of Q3, which is also the optimal solution of Q2. In conclusion, ClosURK is the optimal solution of Q2. 2.10.2 Proof of Theorem 6 Denition 3. LetOPT denote the maximum sum rate of mmHAUL (Q1), andCovURK denote the sum rate obtained by CovURK. Denition 4. Let n OPT denote the number of small cells allocated one antenna by the optimal solution whenjSj > N MAX , and ~ n OPT denote the number of small cells allocated one antenna for covering the other small cells whenjSj>N MAX . 48 Note that whenjSj > N MAX , every small cell can only get one antenna. In other words, n OPT =N MAX . Lemma 3. For a given topology and D i 1;8i2S, Ln OPT OPTUn OPT . Proof. We can directly get this result by Denition 2, 3, and 4. Lemma 4. For a given topology and D i 1;8i2S, Ln OPT CovURK. Proof. WhenjSj>N MAX , every small cell in either OPT or CovURK can only get one antenna. Therefore, n CovURK = n OPT = N MAX . With the results of Denition 2, 3, and 4, Ln OPT CovURK can be easily stated. Theorem 6. For a given topology andD i 1;8i2S, CovURK is 1+(lnjSj1) U L approximation algorithm whenjSj>N MAX . Proof. We prove this by construction. We use the general result of set cover problem, and then based on this result, provide the performance guarantee for CovURK. In the worst case scenario, i.e., none of the cluster heads selected by CovURK are the cluster heads for OPT. Recall that the number of cluster heads selected by the optimal solution ~ n OPT . Based on [42], the number of 49 cluster heads selected by CovURK is at most lnjSj~ n OPT since CovURK uses Greedy Set-Cover based Algorithm. Then, we can give the proof as follows. OPTCovURKClosURK(n OPT ~ n OPT ) ClosURK(n OPT lnjSj~ n OPT ) (a) (n OPT ~ n OPT )U (n OPT lnjSj~ n OPT )U (b) = (lnjSj~ n OPT ~ n OPT )U = (lnjSj 1)~ n OPT U (lnjSj 1)n OPT U = (lnjSj 1) U L n OPT L (lnjSj 1) U L CovURK (c) =) OPT 1 + (lnjSj 1) U L CovURK (a) follows the results of Theorem 3, (b) follows the results of Lemma 3, and (c) follows the results of Lemma 4. 50 Chapter 3 Ecient User-Cell Association for 360 Video Streaming over Wireless Networks 3.1 Introduction Delivering 360 video streaming for virtual and augmented reality (VR/AR) is the next big chal- lenge in wireless networks due to the associated high-bandwidth demand and the dynamic nature of such applications [132, 26]. To make this come true, several research directions have been investigated, the most promising ones being the reduction of the amount of data for delivery and the increase of the available bandwidth via new wireless technologies. To reduce the amount of data for delivery, two-tier 360 video systems and tile-based 360 video streaming have been recently proposed in [103, 35, 33, 51, 43, 39, 129]. The main idea of these technologies is to divide the whole video into a basic-tier chunk and multiple enhancement-tier chunks (or tiles), and deliver the basic-tier chunk and a portion of enhancement-tier chunks to the users based on their specic requirements and the placement of the enhancement-tier chunks. The basic-tier chunk is used to ensure video availability from any angle while the enhancement-tier chunk is used to improve user experience. To increase wireless bandwidth the industry is envisioning 5G systems with dense base station deployments. Such small cell architectures may support wireless virtual reality [26, 63, 65] as their 51 VR/AR VR/AR VR/AR Basic Enhancement {1, 3} Basic Enhancement {2,3,4} I’m satisfied I’m satisfied I’m NOT satisfied Wasted Small cell 1 Small cell 2 VR/AR user1 VR/AR user2 VR/AR user3 Requirement {1, 3} Requirement {1, 4} Requirement {3} Figure 3.1: Simple scenario for two-tier 360 video delivery over wireless networks. increased density, which can be up to 75-200 small cells per square km, see, for example, reports from the 5G America/Small Cell Forum [9, 12], can provide a signicantly higher system capacity by frequency reuse. A major challenge in such ultra dense deployments is user-cell association due to high trac variability [84, 56, 46, 136, 116, 25], a problem exacerbated by VR/AR applications. Traditional signal-to-interference-noise-based (SINR-based) user-cell association schemes may not be able to support this kind of applications and meet the quality of experience expected by users. Consider Fig. 4.2 as a simplied example. There are two small cells with some cache capacity which are connected to a content server, and, there are three VR/AR users requiring some video. Since the small cells have limited capacity, assume small cell 1 has stored in its cache the basic view (basic-tier chunk) and enhanced views (enhanced-tier chunks) 1 and 3, and small cell 2 has the basic view and enhanced views 2, 3, and 4. The three users may require dierent enhanced views depending on their interests, direction of walking/gaze, etc. For example, say user 1 wants views 1 and 3, user 2 wants views 1 and 4, and, user 3 wants view 3 only. It is easy to see that SINR-based user-cell association may result in suboptimal operation as it is agnostic to the cache content of the various small cells. In our example, users 1 and 2 obtain service from small cell 1, user 3 obtains service from small cell 2, and while users 1 and 3 can receive their required views 52 user 2 can only receive one of his/her required views, even though the system has enough capacity to satisfy all users. There are real world VR/AR applications which are expected to have this challenge at a much larger scale. For example, the National Basketball Association (NBA) would like to have VR support in each game [15], where typical stadiums have tens of thousands of seats over tens of thousands of square meters, e.g., the Staples Center has 21,000 seats in 88,257.9 m 2 . As another example, augmented vehicular reality (AVR) [104] aims to make autonomous driving safer by extending vehicle's visual horizon via sharing visual information with other nearby vehicles. These examples require to understand how to associate every user/vehicle with appropriate cells/content proxies given communication bandwidth limitations. Motivated by the above, in this paper we investigate user-cell association schemes for 360 video streaming applications, where basic-tier and enhanced-tier video chunks are transmitted via broadcast, multicast or unicast transmissions from small cells to users. Since users can only receive data from the cell they are associated with and dierent cells will cache dierent content, it is evident that a joint optimization of user-cell association, video chunk placement, and selection of the enhanced views to be transmitted to users under a bandwidth constraint, is required to maximize the user experience. Also, since 360 video, when available, will be the main bandwidth consumer, it is reasonable to consider it in the user-cell association decisions. We formulate the associated joint optimization problem as a mixed integer linear programming and prove its NP- hardness by reducing it to a binary multiple knapsack problem (MKP). We then propose three algorithms to solve the problem: one based on the Branch-and-Bound method (BB) which yields the optimal solution, and two polynomial-time approximation algorithms, a submodular-based greedy algorithm which we refer to as Ecient Layered Video delivery Algorithm (ELVA), and an MKP-based greedy algorithm which we refer to as Ecient Video delivery Algorithm (EVA). We show that ELVA is a(1 1 e )-approximation algorithm, where is given by the network topology, and EVA is a 1 2 -approximation algorithm. Simulation results from both small-scale settings and 53 large-scale settings show that both algorithms outperform baseline user-cell association schemes in all scenarios. Noteworthy, ELVA has a near-optimal performance and can increase the quality of the user experience by 30% compared to SINR-based user-cell association. The rest of this paper is organized as follows. Section 4.2 summarizes the related work, Section 3.3 presents the system architecture and the main assumptions of our model, Section 4.6.1 formulates the problem at hand, Section 3.5 presents the three aforementioned algorithms and formally studies their performance, and Section 3.6 evaluates the performance of the proposed algorithms using simulations under a variety of realistic scenarios. Last, Section 4.9 concludes the paper. 3.2 Related Work VR/AR Content Delivery over Wireless Networks: The ecient delivery of mobile video content is becoming one of the highest priorities for the emerging ultra-dense small-cell deploy- ments [26]. Especially for VR/AR applications, a cellular-friendly streaming scheme was studied in [103], where the authors demonstrated that delivering only the visible portion of views can reduce bandwidth consumption without signicant degradation of the user experience. Based on the above idea, the authors in [35] proposed a resource management mechanism to further improve user experience. Then, the authors in [33] investigated how to place caches in the cells such that performance (measured in rewards earned by the service provider) is maximized. Multi-Tier Video Streaming: There are two approaches to deal with head movement, a key challenge in 360-degree video delivery. The rst is to predict users' behavior and thus upcoming head movement, see, for example, [103, 102, 99], such that the system can proactively download future video angles. The second is to use a multi-tier 360 video system, see, for example, [51, 43, 39, 129, 81], such that a low resolution basic-tier 360-degree video is always available for all angles, giving to the system more time to download enhanced video chunks for specic view 54 angles. The two approaches are complementary. Our work reduces network resource consumption and thus applies to both approaches. Since the later approach tends to have higher bandwidth requirements, we use it as our use-case application. User Association: Many prior works suggested that instead of SINR-based user-cell association (to be referred to as user association for brevity henceforth), application-aware or resource-aware user association scheme could improve user experience [84, 56]. For example, joint resource allocation and user association was investigated in [46] and a signicant gain in terms of system throughput has been shown. As another example, cache-aware user association was studied in [136] with the goal to minimize delay. Moreover, joint optimization of user association and dynamic TDD was discussed in [116] where the authors showed that the system could achieve higher throughput for both downlink and uplink trac by optimizing the TDD schedule and the user association at the same time. Hybrid Multicast/Unicast in Wireless Networks: Evolved Multimedia Broadcast Multi- cast Services (eMBMS) was standardized in LTE network [6] using a xed number of resources. Recently, many studies have proposed unicast services and dynamic resource allocation for eM- BMS to enhance resource utilization and system performance. For example, [96] studied dynamic eMBMS for speeding up le delivery, [34] proposed an ecient user grouping mechanism in the presence of hybrid multicast and unicast eMBMS services to achieve better system throughput, and [60] investigated a hybrid multicast and unicast service for a VR application where the au- thors proposed a novel hyper-cast approach to reduce total bitrate and save wireless network bandwidth. Despite the large body of work in the aforementioned distinct research areas, the performance of the overall multi-tier video delivery system jointly depends on user-cell association, as users can only receive data from their cell, cache and content placement, as cells cannot realistically store the basic and all enhanced views of all videos of interest, bandwidth resource allocation, as wireless bandwidth and the associated resource blocks are limited, and the selection of enhanced 55 views to be transmitted to users via multicasting or unicasting. This joint optimization problem is the topic of this work. 3.3 System Architecture 3.3.1 Caching Model Motivated by practical considerations, we assume every small cell within the neighborhood of some view, e.g. a store front, has a copy of the basic view. This provides fault tolerance against system/cell failures without much cost as the size of the basic view is typically small compared to the enhanced view (e.g. 0.57/0.42 Mb/s for raw/compressed 1080p resolution video and 2.3 Mb/s for 2K resolution video [100]). What is more, since VR/AR users are usually in the same immersive environment, e.g., playing the same VR game, watching the same NBA game, etc., the basic view is indeed common to all whereas the enhanced views are usually personalized due to user-specic interests and/or the eld of view in the users' head-mounted display (HMD). As a consequence, a user can always get the content of the basic view from the small cell one associates with. LetK be the maximum size of the cache in a small cell, measured by the number of enhanced views that may t in a small cell. For example, in Fig. 4.2, K = 2 for small cell 1, and K = 3 for small cell 2. For the enhanced views caching placement, we can apply any schemes proposed by prior work, e.g., [121, 76, 24, 92, 90, 82]. Under a given placement of enhanced views to caches and given bandwidth constraints, our goal is to jointly optimize user-cell association and the selection of enhanced views to be transmitted (via multicast or unicast) to users, such that user experience is maximized (see later for a formal denition). Note that the caching placement and the user-cell association are typically on dierent time scales. Cellular service providers will infrequently reallocate enhanced views among 5G small cell caches due to the associated cost and 56 latency to transfer these data among small cells or download them from the cloud, whereas user- cell association is expected to change frequently in the context of 5G ultra dense networks, see, for example [56, 69, 79]. For this reason, we jointly optimize the user cell association and enhanced views transmission scheduling given a caching placement, rather than also jointly optimizing the later. 3.3.2 Multiple Description Video Streaming We adopt the model of multiple description coding (MDC) in [145] for enhanced views, which is widely used for mobile clients. With MDC, a small cell receives an enhanced view k whose highest resolution version is of size E k , as well as lower resolutions of the same enhanced view. To simplify notation, instead of indexing the dierent resolution versions of k, we use a number between 0 and 1 to indicate the size of a lower resolution version of k as a fraction of E k , e.g. 0.5E k . Clearly, the user experience is proportional to the resolution of the enhanced view that a user receives [125, 50, 74]. 3.3.3 Unicast versus Multicast Transmissions Whether one may unicast or multicast enhanced views depends on the application. To see this, note that for VR/AR applications, it is common that the system fuses user-specic informa- tion/metadata into an enhanced view. For example, if a user is playing a game in a zombie mode which all the characters in the game are zombies, and another user is playing in an elf mode which all the characters in the game are elves, both users are seeing the same game object but with dierent styles. As another example, students may read the same material with a cus- tomized presentation style in an immersive classroom, see [60]. Since the image transfer/fusion is a computation-intensive task which VR devices (e.g., HMDs) do not support, a small cell with edge computing capabilities should take care of this. Hence, it makes more sense for a small cell to unicast the fused enhanced views to each user. That said, there is always a case that several 57 users share the same metadata, or that there are no metadata to be fused with an enhanced view, in which case it makes sense to multicast the enhanced view. We start the analysis by considering unicast mode (Section 3.4.1) and extend it to cover multicast (Section 3.4.2.3). 3.3.4 Wireless Model The data rate from small cell j to mobile user i is dened as follows, R i;j =W log 2 1 + P tj g i;j (d i;j ) N + P n:n6=j P tn g i;n (d i;n ) ! ; (3.1) where W is the size of the operational bandwidth, P tj is the transmission power of small cell j, g i;j () is the channel gain, which is a function of the Euclidean distance, d i;j , between mobile user i and small cell j, andN is the noise power. In the context of cellular networks, data are transmitted via resource blocks (RBs) whose duration of transmission, , is xed. Thus, depending on the data rate, a dierent number of bits, R i;j , gets transmitted per resource block. Then, if B is the size of a basic view measured in bits, it follows that the required number of RBs to deliver a basic view to user i from small cell j, N b i;j , equals N b i;j =d B Ri;j e =d B Ri;j e, assuming = 1 to simplify the notation and without loss of generality. Similarly, the required number of RBs to deliver enhanced view k at the highest resolution to user i from small cell j, N e i;j;k , equals N e i;j;k =d E k Ri;j e. As already discussed, depending on the application, enhanced views may be unicast to a specic user or multicast to a group of users. In what follows we rst consider the case where the system broadcasts the basic view to every user and unicasts user-specic enhanced views to dierent users and then extend the model and algorithms to account for a system which multicasts common enhanced views when they are requested by several users on the same cell. 58 3.4 Problem Formulation We wish to study the problem of optimal user association and resource allocation for two-tier 360 video delivery. With this in mind, we formulate the problem via mixed integer linear program- ming and prove its NP-hardness, and establish that the problem can be separated into smaller subproblems. 3.4.1 Mixed Integer Linear Programming LetM =f1;:::;Mg be the set of mobile users, S =f1;:::;Sg be the set of small cells, and E =f1;:::;Eg be the set of enhanced views corresponding to a 360 degree basic view (e.g. for 45 degree enhanced views with no overlap, E = 8). Also, let w i;j;k =f0; 1g be an indicator function showing if the desired enhanced view k of user i is in small cell j, where for every small cell j with cache size K, it must be that X 8k2E 1 Y 8i2M (1w i;j;k ) ! K to satisfy the cache size constraint. Further, let N j be the total number of RBs available to small cell j at each timeframe. Last, let x i;j =f0; 1g indicate if user i is associated with small cell j, and y i;j;k 2 [0; 1] indicate the resolution in which user i receives enhanced view k from small cell j assuming that the user is associated with this base station. Note that y i;j;k is by denition 0 if user i is not associated with small cell j. If the user is associated with the small cell, a 0 value indicates no reception of the enhanced view while a 1 value indicates reception at the highest possible resolution. TABLE 3.1 summarizes the notation. Upon delivery of a desired enhanced view at resolutiony i;j;k , the user receives a reward propor- tional to the resolution. Our objective is to maximize the total reward from delivering enhanced views at select resolution levels to users. With all the above in mind, we use mixed integer linear programming and formulate the problem as follows: 59 max xi;j;y i;j;k X 8i2M X 8j2S X 8k2E y i;j;k w i;j;k subject to: X 8j2S x i;j = 1; 8i2M; y i;j;k x i;j w i;j;k ; 8i2M;8j2S;8k2E; max 8i2M x i;j N b i;j + X 8i2M X 8k2E y i;j;k N e i;j;k N j ;8j2S; x i;j =f0; 1g;8i2M;8j2S; y i;j;k 2 [0; 1]; 8i2M;8j2S;8k2E: (3.2) The optimization is over x i;j , i.e. user-cell association, and y i;j;k , i.e. the selection and resolution of the enhanced views to be transmitted to users, given which enhanced views each small cell has on its cache, and the available RBs (wireless bandwidth) for each cell. The rst constraint in the above formulation is used to indicate that a user can only associate with one small cell. The second constraint is to assure that the portion of an enhanced view can only be delivered when the user decides to associate with the small cell and the small cell has the enhanced view. The third constraint is to assure that the total number of required RBs to transmit the basic views (rst term in the constraint where broadcasting is used) and the enhanced views at the select resolution levels (second term in the constraint where unicast is used) can not exceed the total number of RBs available to the small cell. 3.4.2 Problem Analysis 3.4.2.1 Complexity Analysis We prove that the problem is NP-hard by reducing it to a 0-1 Multiple Knapsack Problem. 60 Table 3.1: Problem Formulation Notation Description Notation Decision variable for establishing connection between user i and small cell j x i;j Decision variable for determining the resolution in which user i receives enhanced view k from small cell j y i;j;k A set of VR users M A set of small cells S A set of enhanced views E Indication if the desired enhanced view k of user i is in small cell j w i;j;k The maximum size of the cache in a small cell K Number of RBs for user i to get the basic view from small cell j N b i;j Number of RBs for user i to get enhanced view k at highest resolution from small cell j N e i;j;k Total number of RBs for small cell j of each timeframe N j Denition 5. (0-1 Multiple Knapsack Problem [94]) Given a set of n items and a set of m knapsacks, let f v (j) be the prot of item j, f w (j) be the weight of item j, and C i be the capacity of knapsack i. The problem is to select m disjoint subsets of items so that the total prot of the selected items is maximized, and each subset can be assigned to a corresponding knapsack whose capacity is no less than the total weight of the items in the subset. Formally, max ui;j X 8i X 8j f v (j)u i;j subject to: X 8i X 8j f w (j)u i;j C i ;8i2f1;:::;mg X j u i;j 1;8j2f1;:::;ng u i;j =f0; 1g;8i;8j: (3.3) Lemma 5. Problem (3.2) is NP-hard. 61 Proof. We rst show that a simplied version of Problem (3.2) is NP-hard and then argue that Problem (3.2) is also NP-hard. Consider that N b i;j = N b ;8i 2 M;8j 2 S, thus obviously maxfN b i;j g = N b . In addition, consider that P 8k2E y i;j;k N e i;j;k = N e i;j ;8i2M;8j 2S, and P 8k2E y i;j;k w i;j;k =w i;j ;8i2M;8j2S with y i;j;k = 1 if x i;j = 1. We can transform our prob- lem to the standard form of MKP by the following steps. a) The rst constraint in Problem (3.2) is the same as the second constraint in Problem (3.3) when x i;j = u i;j . b) The third constraint in Problem (3.2) can be simplied as: P 8i2M P 8j2S N e i;j x i;j N j N b , which is the same as the rst constraint in Problem (3.3) with x i;j = u i;j , C i = N j N b , and f w (j) = N e i;j . c) The objective function in Problem (3.2) can be simplied as: P 8i2M P 8j2S w i;j x i;j , which is the same as the objective function in Problem (3.3) with x i;j = u i;j and f v (j) = w i;j . From this, it is evident that the MKP is a special case of Problem (3.2). It is obvious that Problem (3.2) is more complicated than MKP because N b i;j can be any positive number as well as there is one more decision variable y i;j;k involved in the problem. Since MKP is known to be NP-complete, Problem (3.2) is NP-hard. Since Problem (3.2) is NP-hard, there is no polynomial-time algorithm to solve this problem optimally. 3.4.2.2 Separability When we x x i;j , the problem for each small cell j becomes as follows: U j (M j ) = max y i;j;k X 8i2Mj X 8k2E y i;j;k w i;j;k subject to: y i;j;k w i;j;k ; 8i2M j ;8k2E; X 8i2Mj X 8k2E y i;j;k N e i;j;k N j ; y i;j;k 2 [0; 1]; 8i2M j ;8k2E; (3.4) 62 whereM j =fi2Mj x i;j = 1g and N j = N j max 8i2Mj N b i;j (note that x i;j = 1 for all i2M j ). Therefore, Problem (3.2) is separable for each small cell j. Note that Problem (3.4) is a convex optimization problem and is in a standard form of fractional Knapsack problem. Therefore, it can be easily solved by a standard greedy algorithm which picks the element with the highest value of w i;j;k N e i;j;k iteratively until the second constraint becomes an equality. 3.4.2.3 Enhanced Views Multicasting To model the case where some of the enhanced views can be multicast and some cannot, we change the third constraint in Problem (3.2) as follows: max 8i2M x i;j N b i;j + X 8k2E 8 < : max 8i2M k y i;j;k N e i;j;k + X 8i2MnM k y i;j;k N e i;j;k 9 = ; N j ;8j2S; whereM k is the set of mobile users sharing enhance viewk. The rst term of the new constraint is the number of RBs required to broadcast the basic view, the second term is the number of RBs required to multicast enhanced view k to a specic group of users, and the third term is the number of RBs required to unicast enhanced viewk to the rest of the users that wish to receive it. Clearly, multicasting some of the enhanced views can benet the system because of the reduction of RBs usage, which we show via simulations later. 3.5 Proposed Algorithms We start with the optimal solution and then propose polynomial time approximation algorithms. 63 3.5.1 Optimal Solution - the Branch-and-Bound Method 3.5.1.1 Problem Transformation Recall that the original problem can be decomposed into many small problems (Problem (3.4)) when x i;j is xed, and each small problem is a convex optimization problem (see Sec. 3.4.2.2). Therefore, the remaining task is to determine the optimal value of x i;j , i.e., the optimal small cell association for every user. We have the following binary integer programming: max xi;j X 8j2S U j (M j ) subject to: X 8j2S x i;j = 1;8i2M M j =fi2Mj x i;j = 1g x i;j =f0; 1g;8i2M;8j2S: (3.5) 3.5.1.2 Algorithm Since Problem (3.5) is a binary integer programming, we can use the Branch and Bound method [115] to nd the optimal solution. We dene two new variables for this algorithm,M C =M [ 8j2S M j andS C i =fj2Sj j can be selected by ig. The algorithm proceeds as follows: 1. (Initialization) SetM j =;;8j2S,M j =;;8j2S,S C i =S;8i2M, andV =1. 2. (Branching) Evaluate the potential P = X 8i2M C ( max 8j2S C ( X 8k2E w i;j;k )) of this node. 64 IfP >V P 8j2S U j (M j ), setx i ;j = 1 for whichfi ;j g = arg max i2M C ;j2S C i f P 8k2E w i;j;k g andM j fi g. Otherwise, go to Step 4. If the rst constraint in Problem (3.5) is satised, i.e., P j2S x i;j = 1;8i2M, go to Step 3. Otherwise, repeat Step 2. 3. (Updating) Solve Problem (3.4) based onM j . If P 8j2S U j (M j )V , setV = P 8j2S U j (M j ) and setM j =M j . Otherwise, go to Step 4. 4. (Backtracking) Choose the lastly joined user i. Remove i fromM j , remove j fromS C i , set S C i =S;8i2M; where i6= i, and set x i;j = 0;8j2S. If there is no lastly joined user, stop. Otherwise, go to Step 2. The idea of this algorithm is eciently going through all the user-association combinations by evaluating the potentialP of the current state (x i;j ). If there exists a branch having potential to increase the value, the Branch-and-Bound method should proceed going through the user- association combinations based on the current state. Otherwise, if the result of the potentialP is bounded by the current maximum valueV , it is unnecessary to evaluate the rest of combinations based on the current state. In this case, the algorithm goes back to the previous state and tries to branch other possible combinations which have not been visited yet. 3.5.1.3 Performance Analysis We analyze the time complexity of the Branch-and-Bound method in the following lemma. Lemma 6. The time complexity of the Branch-and-Bound method is O(jMj jSj jSjjMj log(jMj)). Proof. First of all, since Problem (3.4) is a fractional Knapsack problem, the time complex- ity to solve every subproblem (i.e., Problem (3.4)) is O(jMj log(jMj)). Moreover, since there arejSj subproblems, the time complexity of obtaining the value of P 8j2S U j (M j ) in Step 2 in the algorithm is O(jSjjMj log(jMj)). Then, because the worst case of the algorithm is to traverse every possible combination, which isjMj jSj , the time complexity of the algorithm is O(jMj jSj jSjjMj log(jMj)). 65 3.5.2 Submodular-Based Greedy Algorithm - ELVA In this section we introduce a (1 1 e )-approximation algorithm which we refer to as Ecient Layered Video delivery Algorithm (ELVA). (Note that the value of is dened later in Lemma 10.) Note that Problem (3.2) in Sec. 4.6.1 is neither submodular nor monotone because of the term max 8i2M x i;j N b i;j in the third constraint (i.e., multicasting the basic view). However, based on the layered structure of the problem setting (i.e., two-tier video), we can transform Problem (3.2) to a monotone submodular maximization problem and use a standard greedy approach for monotone submodular maximization problems to solve it. 3.5.2.1 Problem Transformation We dene the new monotone submodular maximization problem over a matroid constraint by replacing U j () with e U j () in Problem (3.5), where e U j () is dened as follows: e U j (M j ) = max y i;j;k X 8i2Mj X 8k2E y i;j;k w i;j;k subject to: y i;j;k w i;j;k ; 8i2M j ;8k2E; X 8i2Mj X 8k2E y i;j;k N e i;j;k e N j ; y i;j;k 2 [0; 1]; 8i2M j ;8k2E: Note that e N j = N j N b , where N b is given by N b = B Rmax min , and R max min is obtained by rst nding d max min = max i fmin j fd i;j gg and then using Eq. (3.1) to nd the corresponding R max min . Note that the above max-min problem can be solved in polynomial time by applying 66 the divide-and-conquer algorithm for the closest pair of points problem [120]. Then, we have the following problem: max xi;j X 8j2S e U j (M j ) subject to: X 8j2S x i;j = 1;8i2M M j =fi2Mj x i;j = 1g x i;j =f0; 1g;8i2M;8j2S: (3.6) 3.5.2.2 Evaluation Function To greedily solve this problem as a monotone submodular maximization problem, we rst intro- duce a so-called evaluation function. Q i;j ( b N j ) = minf N b N b i;j ; 0gT +G i;j ( b N j ); (3.7) where T is an arbitrary big number, and G i;j ( b N j ) is obtained by solving the following linear programming, where b N j is the current available RBs (this value will be updated at every iteration): G i;j ( b N j ) = max y i;j;k X 8k2E y i;j;k w i;j;k subject to: X 8k2E y i;j;k N e i;j;k b N j ; y i;j;k 2 [0; 1]; 8k2E: (3.8) We then use this function to select an element and update the value of the function iteratively until every element has been visited once. 67 3.5.2.3 Algorithm The algorithm leverages the submodularity and monotonicity of Problem (3.6). With these two properties, we can directly apply the standard greedy algorithm for monotone submodular max- imization problems, which always chooses the user-cell association with the maximal marginal value (Q i;j ( b N j )) based on the current available resources, see Algorithm 5 for more details. Algorithm 5 Submodular-Based Greedy Algorithm - ELVA Input: N e i;j;k 2R, w i;j;k =f0; 1g, N j 2R, and N b i;j 2R. Output: x i;j and y i;j;k . 1. Initialize x i;j = 0, y i;j;k = 0, b N j =N j N b . 2. whileM6=; do 3. Calculate Q i;j ( b N j ) for every i and j. 4. x i;j = 1 with the highest value of Q i;j ( b N j ). 5. i =i and j =j. 6. Sort8k2E by w i ;j ;k N e i ;j ;k in descending order (k ). 7. for8k 2E do 8. y i ;j ;k = min n b N j N e i ;j ;k ; 1 o 9. b N j = b N j y i ;j ;k N e i ;j ;k 10. end for 11. M Mnfi g 12. end while 13. Solve Problem (3.4) based on x i;j . Note that since after Step 1 - Step 12 maxfx i;j N b i;j g might be smaller than N b , Step 13 helps allocate the remaining unused resources for maximizing the number of total rewards. Also note that if there are two or more choices with the same value of Q i;j , the algorithm will break the tie based on the best SINR. 3.5.2.4 Performance Analysis We establish an approximation ratio for ELVA. First, we prove that Problem (3.6) is a monotone submodular maximization problem. Second, we prove that ELVA can always be better than any algorithms for Problem (3.6), and has the approximation ratio (1 1 e ). Then, we show that ELVA can be performed in polynomial time. 68 Denition 6. (Submodularity [97]) A set function f : 2 X !R is submodular if, for allA;BX withAB, and for all i2XnB, f(A[fig)f(A)f(B[fig)f(B). Lemma 7. e U j () in Problem (3.6) is submodular. Proof. To prove this, we need to show that e U j (A[fig) e U j (A) e U j (B[fig) e U j (B) where ABM j and i2M j nB. The proof is by illustrating all of the cases in the problem. Let d N X j = e N j P i2X P k2E y i;j;k N e i;j;k . GivenAB, we have d N A j d N B j . Case 1: Suppose e U j (A) e U j (B). There exists an element i2M j nB. If i does not aect the ranking of bothA andB, we have e U j (A[fig) e U j (A) = e U j (B[fig) e U j (B) = 0. If i aects the ranking ofA, but not the ranking ofB, we have e U j (A[fig) e U j (A) e U j (B[fig) e U j (B) = 0. Note that the case when i aects the ranking ofB, but not the ranking ofA will not happen. Case 2: Suppose e U j (A) > e U j (B). We don't need to discuss this because it won't happen. Therefore, based on Denition 6, e U j () in Problem (3.6) is submodular. Denition 7. (Monotonicity [97]) A submodular function f is monotone if for everyAB, we have that f(A)f(B). The following lemma follows directly from the fact that e U j () is a linear function wherew i;j;k 0. Lemma 8. e U j () in Problem (3.6) is monotone. From the above, Problem (3.6) is a monotone submodular maximization with a matroid con- straint or knapsack constraints [97]. Let OPT1 be the optimal value of Problem (3.2) and OPT2 be the optimal value of Problem (3.6). Lemma 9. ELVA (1 1 e )OPT2. Proof. Since ELVA uses the greedy algorithm for monotone submodular maximization problems in [97] and Problem (3.6) is a monotone submodular maximization problem from Lemma 7 and 8, we can directly get the result from [97]. 69 Lemma 10. OPT1 OPT2, where = e Nj Nj . Proof. Lety 1 i;j;k be the solution obtained by OPT1. There are two things that need to be proved. First, we have to prove that y 1 i;j;k is also a solution of Problem (3.6) which is easy to see directly. Second, we have to prove that maxfx i;j N b i;j g from OPT1 is smaller than or equal to N b which follows directly considering how we obtain N b (see Problem Transformation subsection above). From Lemmas 9 and 10 it follows directly that: Theorem 8. ELVA is a (1 1 e )-approximation algorithm. Lemma 11. ELVA is a polynomial-time algorithm. Proof. First, to calculate the evaluation function (3.7), it takesO(jSjjMj) computation. Then, to nd the maximum value of (3.7), it requires the time complexity of O(jSjjMj log(jSjjMj)). The above two steps should be done for every mobile user (i.e.,jMj) so that the time complexity of ELVA is O(jSjjMj 2 +jSjjMj 2 log(jSjjMj)): 3.5.3 MKP-Based Greedy Algorithm - EVA The idea in this section is to use the greedy algorithm for MKP to solve our problem. We rst state the evaluation ratio to be used by the algorithm. 3.5.3.1 Evaluation Ratio A i;j = ( P 8k2E w i;j;k ) p N b i;j ; (3.9) wherep is a term to tradeo the importance of resource blocks represented byN b i;j versus rewards represented by the weights w i;j;k . Note that in the performance evaluation section we will also consider the standard SINR-based greedy scheme, which can be obtained by simply setting p to zero. 70 3.5.3.2 Algorithm We introduce Ecient Video delivery Algorithm (EVA), which is an algorithm that uses (3.9) to rank the choice for every user. Then, the algorithm greedily chooses user-association pairs based on the maximum value of (3.9) iteratively, see Algorithm 6 for more details. Algorithm 6 MKP-Based Greedy Algorithm - EVA Input: N e i;j;k 2R, w i;j;k =f0; 1g, N j 2R, and N b i;j 2R. Output: x i;j and y i;j;k . 1. Initialize x i;j = 0, y i;j;k = 0, and N b j = 0. 2. Sort8i2S by A i;j in descending order. 3. for8i2M do 4. x i;j = 1 with the highest value of A i;j . 5. N b j = maxfN b i;j x i;j ; N b j g 6. end for 7. for8j2S do 8. N j =N j N b j 9. end for 10. for8i2M do 11. Sort8k2E by w i;j;k N e i;j;k in descending order. 12. for8k2E do 13. y i;j;k = min n Nj N e i;j;k ; 1 o 14. N j =N j y i;j;k N e i;j;k 15. end for 16. end for 3.5.3.3 Performance Analysis The following result about EVA's approximation ratio follows directly from the results in [123]. Theorem 9. EVA is a 1 2 -approximation algorithm. Lemma 12. EVA is a polynomial-time algorithm. Proof. To calculate the evaluation ratio (3.9) it takes O(jSjjMj) computation. Then, to nd the maximum value of (3.9), the time complexity is O(jSjjMj log(jSjjMj)). The other steps require only linear time. Putting it all together, the time complexity of EVA isO(jSjjMj log(jSjjMj)). 71 Table 3.2: Settings for Simulation Experiments Description Notation Small-scale Large-scale Default number of VR users jMj = 50 jMj = 500 Default number of small cells jSj = 10 jSj = 100 Default number of enhanced views jEj = 5 jEj = 20 Total number of RBs for small cellj of each timeframe N j = 50; 000 Size of a basic view B = 2 Mb Size of an enhanced view E k = 2 Mb Carrier frequency f c = 5 GHz Transmission power P t = 1 Watt Noise power N =174 dBm/Hz Map Range 1; 000 m 3.6 Performance Evaluation In this section, we compare dierent algorithms in a small-scale and a large-scale network to study their performance. We use the following legends to label various algorithms: \Optimal" for the optimal solution obtained by CVX [13], \BB" for the Branch-and-Bound Method, \ELVA" for the submodular-based greedy algorithm, \EVA" for the MKP-based greedy algorithm (with a default value of p equal to one), and \SINR" for the SINR-based greedy algorithm. 3.6.1 Simulation Settings We consider a network of small cells and VR users in a circle with a radius of 1,000 m. The path loss for the following simulations is based on WINNER-II model. According to this model, g ij is given in dB from the formula below: g i;j (d i;j ) =a log 10 (d i;j ) +b +c log 10 (f c =5) +X; (3.10) wherea,b,c, andX are parameters related with scenarios which can be found in [95]. The carrier frequency (f c ) is 5 GHz, the transmit power of a small cell (P t ) is 1 Watt, and the background noise power (N ) is assumed to be -174 dBm/Hz. We assume every small cell has 50,000 RBs per 72 -1000 -500 0 500 1000 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 Hotspot/Uniform (Iteration = 10) (a) Hotspot/Uniform -1000 -500 0 500 1000 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 Uniform/Uniform (Iteration = 10) (b) Uniform/Uniform Figure 3.2: Scenarios for small-scale study. Table 3.3: Number of Small Cells with % of Total RBs RU (%) 0-20% 21-40% 41-60% 61-80% 81-100% Optimal/BB 0 0 0 0 10 ELVA 2 3 2 1 2 EVA 9 1 0 0 0 SINR 10 0 0 0 0 second, where one RB is 180 KHz 0.5 ms, and the total available bandwidth of the system is 100 MHz. The above parameters are set according to [7, 134, 61]. We assume that w i;j;k = 1;8i;j;k, the number of enhanced views complementing a basic viewjEj varies between 5 and 20, and the cache size K default value isd jEj 2 e. We apply a caching placement scheme based on [121, 24] to allocate enhanced views to small cell caches. The main idea of the scheme if to allocate enhanced views based on long term statistics about what users tend to request depending on their current position while guaranteeing that each enhanced view will be present in at least one cache. The size of a basic view is 2 Mb (2.3Mb) and the size of an enhanced view is 2 Mb (for every 90 ) based on [100, 38] and the recommendation of YouTube [141] for one-second 2K video and 4K 360 video, respectively. Last, the default number of small cells is, enhanced views and VR users depends on the considered scenarios. TABLE 3.2 summarizes the simulation parameters. 73 1 2 3 4 5 Number of Enhanced Views 0 50 100 150 200 Total Rewards Optimal BB ELVA EVA SINR (a) Hotspot/Uniform 1 2 3 4 5 Number of Enhanced Views 20 40 60 80 100 120 140 160 180 Total Rewards Optimal BB ELVA EVA SINR (b) Uniform/Uniform Figure 3.3: Total rewards versus number of enhanced views. 1 2 3 4 5 Number of Enhanced Views 0 50 100 150 200 Total Rewards Optimal (unicasting all enhanced views) Optimal (multicasting all enhanced views) (a) Hotspot/Uniform 1 2 3 4 5 Number of Enhanced Views 0 50 100 150 200 Total Rewards Optimal (unicasting all enhanced views) Optimal (multicasting all enhanced views) (b) Uniform/Uniform Figure 3.4: Comparison of unicasting and multicasting enhanced views. (Sec. 3.4.2.3) 74 -1000 -500 0 500 1000 -1000 -500 0 500 1000 Topology (a) Topology -1000 -500 0 500 1000 -1000 -500 0 500 1000 OPT (b) Optimal/BB -1000 -500 0 500 1000 -1000 -500 0 500 1000 ELVA (c) ELVA -1000 -500 0 500 1000 -1000 -500 0 500 1000 EVA (d) EVA -1000 -500 0 500 1000 -1000 -500 0 500 1000 SINR (e) SINR Figure 3.5: User association in Uniform/Uniform scenario. 3.6.2 Simulation Results - Small-Scale Study For the small-scale setup the default number of small cells is 10, the default number of enhanced views is 5, and the default number of VR users is 50. (Thus, on average, there are about 5 users per small cell, and hence 25 enhanced views of interest to those 5 users. As a result, each small cell cache would store on average about 10% of the enhanced views of interest.) We study two scenarios in the small-scale network: (i) small cells are \normally" distributed with mean of (0; 0) and variance of 200 m in the given area, and VR users are uniformly distributed in the given area (\Hotspot/Uniform"), see Fig. 3.2 (a)), and (ii) both small cells and VR users are uniformly distributed in the given area (\Uniform/Uniform"), see Fig, 3.2 (b)). 3.6.2.1 Varying Number of Enhanced Views Fig. 3.3 and 3.4 plot the total rewards as the number of enhanced views varies from 1 to 5. In Fig. 3.3, when the number of enhanced views increases, the total rewards of all algorithms increase as expected. \Optimal" and \BB" have the same performance, which validates the opti- mality of the Branch-and-Bound Method. \ELVA" is near-optimal, with only 1%3% dierence from \Optimal". \EVA" has20% dierence from \Optimal", and \SINR" has40% dier- ence from \Optimal. In Fig. 3.3 (a) and (b), the dierence between \EVA" and \SINR" in \Uniform/Uniform" is smaller than the dierence in \Hotspot/Uniform", since the SINR values of cell-user pairs are closer in the former case. Fig. 3.4 depicts the advantage of multicasting enhanced views (see Sec. 3.4.2.3). In addition, as expected, when the number of enhanced views increases, the benet becomes noticeable. 75 3.6.2.2 User Association and Resource Utilization We plot the resulting user association and resource utilization when using each algorithm to understand the reason for their performance gap. We measure resource utilization (RU) by the number of used RBs over the number of total RBs in a small cell. First, we plot the user association of every algorithm under the \Uniform/Uniform" scenario in Fig. 3.5. For reference only, Fig. 3.5 (a) depicts the topology before we perform any algorithms. As shown in Fig. 3.5 (b) and (c), \ELVA" makes similar choices for user association as \Optimal/BB", explaining why \ELVA" has a near-optimal performance. Moreover, in Fig. 3.5 (d) and (e), \EVA" makes similar choices for user association as \SINR" which connects users to the nearest cell, and, consistent with the discussion in the previous section, \EVA" and \SINR" have similar performance in the uniform topology of small cells. Second, we present the number of small cells with dierent levels of RU in TABLE 3.3. All of the small cells in \Optimal/BB" fully utilize their resources as expected, whereas the small cells in \ELVA" partially utilize their resources, because some mobile users of \ELVA" choose dierent small cells to obtain the enhanced views. Moreover, the small cells in \EVA" and \SINR" underutilize their resources depending on their user-association. Although their mobile users connect to the nearest small cells, these mobile users cannot obtain more enhanced views from the small cells. 3.6.2.3 Varying Number of Small Cells Fig. 3.6 plots the total rewards versus the number of small cells which varies from 1 to 10. As expected, when the number of small cells increases, the total rewards of \Optimal", \BB", \ELVA", and \EVA" increase. \SINR" stays stable, since it only considers distance as a metric to make association decisions. 76 2 4 6 8 10 Number of Small Cells 50 100 150 200 Total Rewards Optimal BB ELVA EVA SINR (a) Hotspot/Uniform 2 4 6 8 10 Number of Small Cells 50 100 150 200 Total Rewards Optimal BB ELVA EVA SINR (b) Uniform/Uniform Figure 3.6: Total rewards versus number of small cells. 10 20 30 40 50 Number of Mobile Users 0 50 100 150 200 Total Rewards Optimal BB ELVA EVA SINR (a) Hotspot/Uniform 10 20 30 40 50 Number of Mobile Users 20 40 60 80 100 120 140 160 180 Total Rewards Optimal BB ELVA EVA SINR (b) Uniform/Uniform Figure 3.7: Total rewards versus number of mobile users. 3.6.2.4 Varying Number of Mobile Users In Fig. 3.7, the total rewards are depicted versus the number of mobile users which varies from 10 to 50. As expected, when the number of mobile users increases, the total rewards of all algorithms increase. 3.6.2.5 Varying Parameter of p in EVA In Fig. 3.8, we plot the total rewards versus the p value in (3.9) which varies between 1 and 5. Note that with the larger p value, \EVA" puts more emphasis on the \weight" than on SINR. We observe that as the p value increases, the performance of \EVA" is a concave function, which 77 1 2 3 4 5 p value 50 100 150 200 Total Rewards Optimal BB ELVA EVA SINR (a) Hotspot/Uniform 1 2 3 4 5 p value 50 100 150 200 Total Rewards Optimal BB ELVA EVA SINR (b) Uniform/Uniform Figure 3.8: Total rewards versus p value in EVA. implies that focusing on the rewards more and more (At the expense of SINR) doesn't necessarily improve performance. More specically, the best value of p is 3 in \Hotspot/Uniform, and the best value of p is 4 in \Uniform/Uniform". 3.6.2.6 Varying Cache Size of a Small Cell In Fig. 3.9 the total rewards are depicted as the cache size of a small cell varies from 1 to 10. We set the number of enhanced views to 10 (i.e.,jEj = 10), and the number of required enhanced views for every user is 2. Note that since the number of desired enhanced views for every user is 2, the maximum total reward in this case is 100. When the cache size of a small cell increases, the total rewards of all schemes increase as expected. 3.6.3 Simulation Results - Large-Scale Study For the large-scale setup the default number of small cells is 100 (which corresponds to about 35 small cells per square km, a dense deployment which is nevertheless less than the 75-200 small cells per km envisioned by industry [9, 12]), the default number of enhanced views is 20, and the default number of VR users is 500. The same scenarios are considered as those in the small-scale network: \Hotspot/Uniform" and \Uniform/Uniform". 78 2 4 6 8 10 Cache Size of a Small Cell 0 20 40 60 80 100 Total Rewards Optimal BB ELVA EVA SINR (a) Hotspot/Uniform 2 4 6 8 10 Cache Size of a Small Cell 0 20 40 60 80 100 Total Rewards Optimal BB ELVA EVA SINR (b) Uniform/Uniform Figure 3.9: Total rewards versus cache size of a small cell. 5 10 15 20 25 30 35 40 Number of Enhanced Views 0 2000 4000 6000 8000 10000 Total Rewards ELVA (Hotspot/Uniform) EVA (Hotspot/Uniform) SINR (Hotspot/Uniform) ELVA (Uniform/Uniform) EVA (Uniform/Uniform) SINR (Uniform/Uniform) (a) Total rewards versus number of enhanced views. 50 100 150 Number of Small Cells 0 1000 2000 3000 4000 5000 6000 Total Rewards ELVA (Hotspot/Uniform) EVA (Hotspot/Uniform) SINR (Hotspot/Uniform) ELVA (Uniform/Uniform) EVA (Uniform/Uniform) SINR (Uniform/Uniform) (b) Total rewards versus number of small cells. 200 400 600 800 1000 Number of Mobile Users 0 2000 4000 6000 8000 10000 12000 Total Rewards ELVA (Hotspot/Uniform) EVA (Hotspot/Uniform) SINR (Hotspot/Uniform) ELVA (Uniform/Uniform) EVA (Uniform/Uniform) SINR (Uniform/Uniform) (c) Total rewards versus number of mobile users. Hotspot/Uniform Uniform/Uniform 0 0.2 0.4 0.6 0.8 1 Jains Fairness Index ELVA EVA SINR (d) Jain's fairness index in the default settings. Figure 3.10: Large-scale simulation. 79 We vary the number of enhanced views from 5 to 40 in Fig. 3.10 (a), the number of small cells from 50 to 150 in Fig. 3.10 (b), and the number of mobile users from 100 to 1000 in Fig. 3.10 (c). As shown in the gures, the trend of the total rewards under dierent varying parameters in the large-scale study is the same as those in the small-scale study. This implies that the study in the small-scale study is directly applicable to that in the large-scale study. In Fig. 3.10 (d), we evaluate the fairness of the users using Jain's index [71] in the default settings. As expected, \ELVA" outperforms \EVA" and \SINR" because some users in \EVA" and \SINR" are more likely to receive small rewards. In summary, it is evident that SINR-based user association is not the best strategy for two- tier 360-degree video delivery, and the proposed polynomial time \ELVA" algorithm achieves a near-optimal performance in all the scenarios. 3.7 Conclusion We jointly optimized user-cell association and resource allocation for delivering two-tier 360 video in wireless virtual/augmented reality. We formulated the problem using mixed integer linear programming, proved it is a NP-hard, described an optimal algorithm and proposed a polynomial time approximation algorithm which was shown to be near optimal in practice. Simulation results also established that the proposed algorithm can boost user experience by at least 30% compared to baseline user association schemes. 80 Chapter 4 AutoCast: Scalable and Ecient Sensor Sharing between Autonomous Vehicles 4.1 Introduction Self-driving cars use advanced sensors, such as LiDar and stereo cameras, to permit vehicles to accurately position themselves with respect to the surrounding environment and to recognize dangers in it. To further improve these goals, cooperation and information sharing between autonomous vehicles is a key component of future intelligent transportation systems (ITS). To leverage this visual information to enhance reliability, \see-through" systems [52] and \augmented vehicular reality" systems (AVR, [104]) have been recently proposed. These technologies, which allow two vehicles to exchange sensor information, address the challenges of limited range and line-of-sight requirement. Several safety hazards can be avoided in the presence of such sharing. Prior work has not considered sharing visual information among multiple vehicles, for example, in a busy intersection or a highway segment. By sharing visual information with multiple vehicles, one can achieve enhanced situation awareness to make more informed decisions in a complex scenario. For example, Figure 4.1 shows that the blue car may receive LiDAR visual information from neighboring vehicles so that its driving algorithm can see the black and other cars. As another example, Figure 4.2 shows two cars in the outside lanes of a three lane road attempting 81 b) Single Vehicle LiDAR (Blue) c) AutoCast LiDAR (Blue) a) Unprotected Left Turn Occluded Area Detected Vehicle Range Limited Range Extended 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Figure 4.1: AutoCast enables multiple vehicles to have extended LiDAR vision into occlusion and beyond sensing range by ecient sensor sharing. a) Left turn in an intersection. Yellow slices represent blocked views. b) The LiDAR data of the blue car. c) The LiDAR view of the blue car after merging neighboring vehicles views using AutoCast, which detects the incoming black car while achieving extended sensing range. 82 4 5 6 7 8 1 2 3 4 5 6 7 8 N 1 2 3 Figure 4.2: A highway scenario. The yellow views represent the blocked views by the nearby vehicles, and the blue views represent the line-of-sight views. to merge in the middle lane concurrently. Due to limited visibility, lane-changing vehicles are not aware of each other. Sharing the vision of the middle lane vehicle would allow cooperative driving to avoid the potential collision. Share visual information among multiple vehicles over a wireless network is quite demanding due to latency constraints and bandwidth limitations. To see this, a 64-beam LiDAR can generate up to 2.2 million points per second [3]. Exchanging such sensor data among only a few vehicles could well exceed the bandwidth available for vehicle-to-vehicle communication or it could take too long for the shared data to be relevant. We use two key ideas to reduce the volume of information: (a) we spatially partitioning a vehicle's view into partial views; (We consider two spatial partitions, tiles of the full view whose union yields the full view and objects of interest, e.g. vehicles or obstacles.); (b) we access the relevance of partial views for vehicles and only send relevant partitions to receivers. With this basic approach, we then ask: how can we schedule transmissions so that the maximum amount of useful information is transmitted within a given time-frame. In this paper, we propose AutoCast, a system that enables vehicles to eciently and co- operatively exchange important sensor data in time while eliminating duplicate and redundant 83 sharing. To achieve this, AutoCast must solve several challenging problems: how to assess the importance of the sensor data, how to enable the right group of vehicles to cooperate in a highly dynamic environment, and how to schedule wireless sharing without introducing latency or transmission collisions. Contributions. To address these challenges, the paper makes three contributions (§4.3). First, AutoCast partitions sensor data into partial views and devises a novel data assessment method- ology (§4.4) to gauge the signicance of each partial view. View partitioning has been introduced in the context of tile-based virtual reality (VR [59, 66, 67]), however in our context one needs to prioritize the importance of partial views based on future vehicle trajectories (e.g. upcoming turns), view blockage (e.g. from other cars or high rise buildings), emergency situations (e.g. pedestrians or cyclists), etc. As an example, see Figure 4.2, where a dierent set of partial views of the middle-lane car are of interest for neighboring cars. (Partial views of interest are indicated by yellow.) Second, vehicles need appropriate handshake to start cooperation. AutoCast proposes a novel interaction and clustering protocol (§4.5). The protocol enables vehicles to exchange their states and express the view requests through a compact beacon before sharing the actual sensor data. The beacon also informs the scheduler about necessary metadata to make optimal scheduling decisions. Finally, the protocol also functions as admission control to automatically form vehicle clusters for sensor sharing while avoiding channel interference. Third, AutoCast scheduler leverages a Markov Decision Process (MDP) to formulate the associated problem of multicast scheduling (§4.6.2). We propose a dynamic-programming-based algorithm, which can solve the problem optimally. We also propose a near-optimal greedy heuristic to eciently compute a schedule with negligible latency. We implement AutoCast (the protocol operations and scheduler) in CarLA [41], a state-of- the-art autonomous vehicle simulator. Our evaluation results (§4.7) shows that AutoCast can achieve a 200% gain in data sharing utility compared to a system which attempts to share the full 84 visual information of each car in a round robin fashion. AutoCast enables clusters of vehicle to achieve nearly 300% sensing area extension, and scales gracefully with the vehicle density. 4.2 Related Work Connected Vehicles and Infrastructure: Connected vehicles promise great opportunity to im- prove the safety and reliability of self-driving cars. Vehicle-to-vehicle (V2V) communications and vehicle-to-infrastructure (V2X) communications both play an important role to share surround- ing information among vehicles. Communication technologies, e.g.,, DSRC [75] and LTE-Direct [47, 106], provide capabilities to exchange information among cars by dierent types of trans- mission, i.e.,, multicasting, broadcasting, and unicasting. Automakers are deploying V2V/V2X communications in their upcoming models [8, 16]). The academic community has started to build city-scale advanced wireless research platforms (COSMOS [1]) as well as large connected vehicle testbed in the U.S. (MCity [17]) and Europe (DRIVE C2X [128]), which gives an opportunity to explore the application feasibility of connected vehicles via V2V communications in practice. Sensor/Visual Information: Collecting visual information from sensors (e.g., LiDAR, stereo cameras, etc.) is a major part of autonomous driving systems. These systems rely on such infor- mation to make a proper on-road decisions for detection [36], tracking [88], and motion forecasting [89]. In addition, there is a large body of work that explores vehicle context and behavior sensing [48, 112, 105] to enhance vehicular situational awareness. Thanks to advanced computer vision and mobile sensing technologies, all the sensing capability can already be leveraged eciently in a single car setting [86]. This work, and several related works discussed below, take the next step of designing how to share this information among nearby vehicles. Vehicle Sensor Sharing: Past research has attempted to realize some form of context sharing among vehicles. Rybicki et al. [113] discuss challenges of VANET-based approaches, and propose to leverage infrastructure to build distributed, cooperative Trac Information Systems. Other 85 work has explored robust inter-vehicle communication [109, 78], an automotive ontology for intel- ligent vehicles [44], principles of community sensing that oer mechanisms for sharing data from privately held sensors [77], and sensing architectures [85] for semantic services. Motivated by the \see-through" system introduced in [52], several prior works on streaming video from a leader to a follower for enhanced visibility have been proposed [32, 107, 45, 72, 83]. The above line of work has focused on scenarios with two cars, where a leader car delivers its whole video to a follower vehicle. As previously discussed, there are many examples where this leader-follower approach is not sucient. In this work, we focus on enabling clusters of vehicle to share sensor information at scale. Moreover, we design an optimal policy to compute when, which views, and to which cars to deliver views over time. 4.3 AutoCast Overview AutoCast enables scalable and ecient sensor sharing between autonomous vehicles. In Auto- Cast, vehicle sensor sharing happen in two cases: a) vehicle requesting extra information to make driving decisions (e.g., an occluded area on the planned path) [104]; b) vehicle sharing its own sensor to alert neighbors' attention (e.g., pedestrian crossing, potholes, temporary construction zones, etc.). Figure 4.3 illustrates the system architecture. For each sensor frame, AutoCast rst partitions the frame into several view segments. Then, AutoCast analyzes the view primi- tively (§4.5) to identify occlusion area of interest to request (pull) and objects/events of interest to share (push). The analysis result together with the vehicle state (e.g., pose, velocity, etc.) is combined into an AutoCast beacon. The vehicle registers the beacon to the scheduler, which can either be a Road-side Unit (RSU) or a participating vehicle (further discussed in §4.5). The scheduler assesses the relevance and importance of each view of each vehicle based on all push 86 Vehicle 1 Vehicle N Data Channel Control Channel Beacon & Schedule Update Sensor Exchange View Partitioning & Assessment Sensor Intergration Autonomous Driving or ADAS 3D Frames ... AutoCast Scheduling Data Assessment AutoCast Scheduler Figure 4.3: AutoCast System Architecture and pull requests collected from all surrounding vehicles. Using the assessment result, the sched- uler computes a transmission schedule prioritizing the importance and signicance of views while optimizing the total bandwidth utilization among all sharing vehicles. Finally, the schedule is broadcasted to every participating vehicle, which transmits sensor data following the schedule through Vehicle-to-Vehicle (V2V) communication channel. Received sensor data can be merged and further integrated to make more informed autonomous driving decisions. In the following, we discuss the three major components of AutoCast: View Partitioning and Data Assessment, Beacon and Clustering Protocol and Scheduling. View Partitioning and Data Assessment(§4.4). To enable exible selective sharing, for each sensor frame,AutoCast partitions the data into several view segments. Motivated by tiled representations in mobile VR applications [59], each view segment is set to a xed horizontal angle of view. To assess the signicance of a view,AutoCast data assessment has two parts, one computed locally and one on the scheduler. In local computation, AutoCast leverages several 87 information, such as whether the view is occluded by a neighboring truck, if the vehicle is making a turn or lane change, or if the view contains objects of a particular interest (e.g., pedestrian crossing, red light violation), etc. to decide if the vehicle wants to pull or push a view. The scheduler, on the other hand, synthesizes all push and pull requests to assess the view relevance to all vehicles in the vicinity. AutoCast Beacon and Clustering Protocol. In order for the scheduler to synthesize the assessment and make optimized decisions, participating vehicles need to register their push and pull requests of their own views to the scheduler. To this end, AutoCast design a novel beacon protocol to enable the interaction between autonomous vehicles and the scheduler. Moreover, based on the beacon messages, AutoCast tracks the position and motion of the vehicles and automatically denes the cluster of vehicles that are eligible to participate in the sharing to ensure data delivery and maximum bandwidth utilization. In §4.5, we rst introduce a basic version of the protocol that operates in and around an intersection area where an RSU is available. Next, we extend the protocol to any location without RSUs where vehicles can dynamically form clusters avoiding channel interference. Remark: We discuss a decentralized AutoCast where a scheduler is embedded in each vehicle to assess data and compute the schedule locally with consistent states in §4.8. Scheduler. Once the cluster and all participants are dened,AutoCast can compute the trans- mission schedule. We formulate the scheduling problem as a Markov Decision Process (MDP), which makes an optimal policy to decide which vehicle, at what time, transmits which view(s), to benet which vehicle(s). We study the optimal performance using dynamic programming, and design a greedy scheduler to decide, with negligible latency in V2V scenario, a schedule among vehicles with near-optimal eciency. 88 1 2 3 4 5 6 7 8 N Figure 4.4: An illustration of view partition (V = 8). MobiSys ’18, June 10–15, 2018, Munich, Germany H. Qiu et al. Sparse HD Map Sparse HD Map Sparse HD Map Sender Receiver Feature Extraction Dynamic Object Extraction Point Cloud Compression Motion Vector Estimation Relative Localization Relative Localization Feature Extraction Perspective Transformation Reconstruction Autonomous Driving or ADAS 3D Frames 3D Frames Camera Coordinates Object Point Clouds Motion Vectors Figure 3—AVR sender and receiver side components. systems. For AVR, such a sparse map su ces for relative positioning. As we describe later, the sparse 3D map can be constructed o ine, and potentially crowd-sourced. With this sparse map, the sender processes 3D frames from its camera and extracts features within the 3D frames, then uses some of these features to position its own camera relative to the sparse 3D map. The sender sends its position and a compressed (see below) representation of the 3D frame to the receiver. The receiver uses the sender’s camera coordinates, features extracted from its own 3D sensor, and its own copy of the sparse 3D map to estimate its position relative to the sender. After decompressing the received point clouds of dynamic objects, the receiver applies a perspective trans- formation to these objects to position them within its own coordinate frame of reference. Second, if AVR were to transmit 3D frames at full frame rates, the bandwidth requirement could overwhelm current and future wireless technologies. Fortunately, successive 3D frames contain significant redundancy: static objects in the environmentmay,inmostcases,notneedtobecommunicated between vehicles, because they may already be available in precomputed HD maps. For this reason, an AVR sender can also, instead of sending full frames, transmit point clouds representing dynamic objects (e.g., cars, pedestrians) within its field of view, and also the motion vector of these dynamic objects. The receiver uses the object’s motion vectors to reconstructtheobjectposition,andsuperimposesthereceived object’s point cloud onto its own 3D frame. Third, many of the 3D sensor processing algorithms are resource-intensive, and this impacts AVR in two ways. It can limit the rate at which frames are processed (the throughput), and lower frame rates can impact the accuracy of algorithms that detect and track objects or that estimate position. It can also increase the latency between when a 3D frame is captured and when the corresponding point cloud is received at another vehicle. AVR selects, where possible, lightweight sensor processing algorithms, and also optimizes the process- ing pipelines to permit high throughput and low end-to-end latency. Its motion vectors permit receivers to hide latency, as described later. A complete realization of AVR must include mechanisms that prevent or detect sensor tampering and protect the Figure 4—The green dots represent static features that are used to construct the sparse HD map, while features from the moving vehicle are filtered out. privacy of participants who share sensor data (§7). We have left such mechanisms to future work. OurinitialdesignofAVRisbasedonrelativelyinexpensive (2 orders of magnitude cheaper than high-end LiDARs) o - the-shelfstereocameras,butwealsopresentsomeevaluations with a LiDAR device. 3.1 Relative Localization In AVR, a receiver needs to be able to estimate its position relativetothesender.AbsolutepositionsfromGPSwouldsuf- fice for this, but GPS is known to exhibit high error especially in urban environments, even with positioning enhancements [28]. Specialized ranging hardware can estimate distance and relative orientation between the vehicles, but this would add to the overall cost of the vehicle. The depth perception from the 3D sensors can estimate relative position between the sender and receiver, but, in AVR, the sender and receiver need not necessarily be within line-of-sight. Key idea. Instead, AVR uses prior work in stereo-vision based simultaneous localization and mapping (SLAM, [38]). This work generates sparse 3D features of the environment (called ORB features [38]), where each feature is associated with a precise position relative to a well-defined coordinate frame of reference. AVR uses this capability as follows. Suppose car A drives through a street, and computes the 3D features of the environment using its stereo vision camera. These 3D features contribute to a sparse 3D map of the environment and each feature has a position relative to the position of A’s camera at the beginning of A’s scan of the street (we call this A’s coordinate frame). Another car, B, if it has this static map, can use this idea in reverse: it can determine 3D features using its stereo camera, then position those features in car A’s coordinate frame by matching the features, thereby enabling it to track its own camera’s position. A third car, C, which also shares A’s map, can position itself also in A’s coordinate frame of reference. Thus, B and C can each position themselves in a consistent frame of reference, so that B can correctly determine its position relative to C, and correctly overlay C’s shared view over its own. To our knowledge, this is a novel use of stereo-vision based SLAM. Generating the sparse 3D map. As a car traverses a street, all stable features on the street, from the buildings, the tra c signs, the sidewalks, etc., are recorded, together with their coordinates, as if the camera were doing a 3D scan of the 2 3 4 5 2 3 7 8 1 2 Figure 4.5: An example of the view partition and blocked view index. Figure 4.6: Empty occupancy grids indicate occluded view par- titions. 89 4.4 Data Assessment In this section, we introduce a way to do view partition and a method do data assessment. View Partition. To handle the huge amount of visual information, and to enable view assessment and exible scheduling, we propose a new 3D sensor data representation, partial views. As shown in Figure 4.4, the 360 degrees view of a car is partitioned intoV partial views (in this caseV = 8). LetV be the set of views. Let K be the total number of vehicles considered andK be the set of vehicles. We further assume that with the use of a compass, a coordination system at each vehicle numbers partial views clockwise, with the direction between view 1 and view V pointing towards the north, as shown in the gure. As mentioned previously, one of the challenges of this work is to design a method to properly assign the signicance of each view (of a car) for some other car, which we will refer to as the reward. A reward is earned when this view (or objects of interest in this view) is transmitted successfully to the car that is interested in it. For this purpose, we introduce an assessment policy which is based on four practical features that we further elaborate below: blocked views, view relevance to navigation, complement views, and safety incidents. Blocked View Index. The blocked view index of vehicle i is used to indicate whether vehicle j blocks viewv of vehiclei. In this case, vehicle i would like to receive views of vehicle j to extend its visibility on its view v. An example is shown in Figure 4.5. We dene the blocked view index (b (i;v);j ) as follows, b (i;v);j = 8 > > < > > : 1 , if car j blocks view v of car i; 0 , otherwise. (4.1) To obtain the occlusion information, AutoCast converts a 3D point cloud into a 2D occupancy grid, and uses empty grids to indicate occluded partitions (Figure 4.6). Navigation Index. Depending on the future trajectory of the vehicle, some views may be more important than others. For example, a car passing in the next lane may be more relevant to a lane-changing vehicle than a lane-keeping one. A pedestrian crossing a perpendicular road may be 90 more important to a turning vehicle than a vehicle going straight. Based on the motion direction and the navigation routes of the vehicle, we dene a navigation index that species which views are relevant to the vehicle. Specically, in the case ofV = 8 (Figure 4.4), if vehiclei goes forward and northbound, view 1 and 8 are of more relevance. To indicate whether a particular view is of relevance, we rst dene view sets corresponding to forward movement, backward movement, right turn movement, and left turn movement by D f =f1;::; V 4 ; 3V 4 + 1;:::;Vg, D b =f V 4 + 1;:::; 3V 4 g, D r =f1;:::; V 2 g, and D l =f V 2 + 1;:::;Vg, respectively. For example, for V = 8, D f does specify views 1, 2, 7 and 8 as the relevant views for a forward movement. We then dene the direction of movement index (d (i;v) (x;z)) as follows, d (i;v) (x;z) = 8 > > > > > > < > > > > > > : 1 , for view v = ((e 1 +x)%V ) + 1; ;8e2D z 0 , otherwise, (4.2) where % indicates the modulo operation, x is used to specify the current direction of a vehicle, specicallyx = 0; V 4 ; V 2 ; and 3V 4 for a northbound, an eastbound, a southbound, and a westbound moving vehicle, respectively, and z is used to indicate whether the vehicle will continue going forward, or it will go backwards, turn right, or turn left, specically, z =ff;b;r;lg for specifying which view set is to be used. For example, if V = 8, x = 0 (going northbound) and e2 D r = f1; 2; 3; 4g (turning right), the direction of movement index does specify views 1,2,3,4 as those of relevance. Note that the information required to compute the direction of movement index can be collected by compasses and navigation systems. Complement Index. Consider Figure 4.5. Car 2 is blocking view 8 of the car under consideration (car 1). However, for the car 1 to get information about white car 3, it is not enough to get view 8 of car 2, view 7 of car 2 is of essence. Essentially, because the coordinate systems at each car have a dierent origin, when a view is blocked, it could be the case that it is not enough to acquire 91 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Figure 4.7: An example of adjacent views when N = 2. Blocked view 8 (Red) increases the relevance of adjacent views (Yellow). this view (same view index) from another vehicle, but instead, adjacent views might be of interest too to complement the blocked view. Motivated by this, we use the complement index to specify which adjacent/neighboring views in vehiclej can benet viewv in vehiclei in addition to viewv of vehicle j. Specically, we use a parameter N to specify how many adjacent/neighboring views of the blocked view v will be considered of interest. As an example, for N = 2, Figure 4.7 shows that views 1, 7, and 8 of the leader car might benet/complement view 8 of the follower car (2 adjacent views, views 1 and 7, are considered in addition to view 8). Formally, we dene the complement index (c (i;v);(j;u) ) as follows, c (i;v);(j;u) = 8 > > < > > : 1 , for view u = ((v 1n)%V ) + 1; 0 , otherwise, (4.3) where n =f0;::; N 2 g and N, as already stated, is a predened parameter denoting how many neighboring views are included. Note that for a xed N, it is easy for a vehicle to specify the indices of views of interest using blocked views indices and the convention used to index views, see coordination system discussion in §4.4. 92 Safety Index. The safety index is used to indicated whether there are any important incidents in this view (e.g., pedestrians and police ocers) or not. We dene the safety index (s (j;u) ) as follows, s (j;u) = 8 > > < > > : ^ s , if there is an important incident in the view; 0 , otherwise, (4.4) where ^ s is a number to weight the importance of the safety index. For example, ^ s = 1 means no matter how many incidents or dynamic objects in a view, we give it a weight 1. ^ s can be the total number of dynamic objects in a views to give this view more attention. Similar to the blocking view, this information can be collected by stereo cameras and LiDAR assuming adequate software which analyzes an image and identies safety incidents. Putting Everything Together. We deney (i;v);(j;u) as the reward for viewv of vehiclei when view u of vehicle j is transmitted successfully to vehicle i as follows: y (i;v);(j;u) =b (i;v);j c (i;v);(j;u) (d (i;v) (x;z) +s (j;u) ): (4.5) The rationale behind this equation is that vehicle i is interested in a view u of car j if (i) car j is blocking one of its views v (b (i;v);j ), (ii) the view u of car j is complementing view v, that is, it either has the same index as v or it is adjacent to it (c (i;v);(j;u) ), and (iii) either this is a view where an important safety incident is taking place (s (j;u) ), or this view is in the future direction of car i (d (i;v) (x;z)), or both (in which case the reward is maximized). Note that car i uses this assessment method to implicitly prioritize the view that it wants rst by summing up all its views: X 8v y (i;v);(j;u) : (4.6) The higher the value of Eq. (4.6), the higher the chance that it will be delivered rst. 93 Figure 4.8: AutoCast Sharing Region. 4.5 AutoCast Protocol In this section, we describe the protocol design for vehicles to exchange states for the scheduler to compute and optimize the transmission schedule. We focus on introducing the protocol design for the intersection scenario where an RSU is available, while leaving the discussion of a distributed AutoCast without RSU support at any location in §4.8. Denitions. In AutoCast, vehicle sensor sharing happen in two cases: a) vehicle requesting extra information to make driving decisions (e.g., an occluded area on the planned path) [104]; b) vehicle sharing its own sensor to alert neighbors' attention (e.g., pedestrian crossing, potholes, temporary construction zones, etc.) [86]. We dene the view of the information described in the above two cases as pulling views and pushing views. In AutoCast, vehicles put a view request and express sharing intentions to the scheduler by sending the local data assessment result (§4.3) via a beacon. Since vehicle sensor sharing happen in a highly dynamic environment with all vehicles and other trac participants moving, AutoCast computes and updates schedules frequently. We dene a sharing session as the time period in which each schedule is carried out. We also dene a sharing region where vehicles carry out a sharing session. 94 Beacon (Push and Pull Partitions, etc.) Multicasting Schedule Updated Information Partitions Delivery RSU Transmitter Receiver Figure 4.9: AutoCast Protocol (Intersection w/ RSU). Single Intersection w/ RSU. Intersections are one of the most dangerous hazards where V2V communication can help [53]. Figure 4.9 illustrates AutoCast protocol for the intersection scenario. In AutoCast, vehicles come close to an intersection within a radio range R will broadcast beacons to the RSU. The beacon includes information such as vehicle id, GPS, vehicle pose(translation and rotation), velocity, timestamps, pulling views, and pushing views, and sizes. The RSU uses this information to compute the schedule. For each sharing session, the RSU selects, among all registered (beacon received) vehicles, only those within half radio range R/2 of the intersection center (sharing region) to participate so that all participants can hear each other during the sharing session. Figure 4.8 shows an example of the sharing region. Depending on the duration of the sharing session and the speed limit, AutoCast applies a guarding margin to ensure that participating vehicles will not move out of the sharing region until the session ends. For example, vehicles cruising at 40 mph will move 1.79 m during an LTE frame duration of 100 ms [11]. Using only the beacons of vehicles within the sharing region, the scheduler computes upto the duration of the sharing session based on the view sizes and the bandwidth available. Finally, the RSU broadcast the transmission schedule to every participant. Depending on which V2V technology is used ( e.g., DSRC, LTE-V), AutoCast protocol has dierent PHY layer implications, which we will discuss in §4.8. 95 The protocol naturally extends to any location with an RSU, as long as the RSU specify a sharing region to compute the schedule. Next, we discuss a single intersections w/o RSU, and any location w/o RSU. Remark: when beacons are reliably delivered, every participant should have consistent states within the sharing region. Instead of relying on a central scheduler, each vehicle can compute full data assessment result as well as the schedule individually. The sharing session can then be triggered by a random leader. We discuss a distributed AutoCast in §4.8. 4.6 AutoCast Scheduler In this section, we discuss the AutoCast scheduler. We rst dene notation and basic assump- tions, then formulate the problem as a Markov decision process (MDP), and last propose two algorithms to solve it. Notation and Assumptions The scheduler species the order by which partial views are trans- mitted during a sharing session. Call a time slot the time it takes to transmit a partial view and let T be the number of available time slots for view delivery during a sharing session, andT be the set of time slots. Also, let B be the operational bandwidth and let d be the size of a time slot. The value of these parameters depend on the PHY technology. There are two technologies available today, DSRC and LTE-V (which is a variant of LTE direct), and we discuss more about the implications from choosing one over the other in §4.8. The rest of the discussion applies to both technologies. We assume the PHY layer uses QPSK as per common practice in car communication systems due to the challenging channel [10, 11]. Thus, in a time slot the system can deliver L =Bd 96 log(1 + QPSK ) bits, where QPSK is the SINR value required by QPSK. Then, we can dene the channel matrix as follows, P = 2 6 6 6 6 6 6 6 6 6 6 4 p 11 p 12 p 13 ::: p 1K p 21 p 22 p 23 ::: p 2K . . . . . . . . . . . . . . . p K1 p K2 p K3 ::: p KK 3 7 7 7 7 7 7 7 7 7 7 5 ; (4.7) where p i;j 2 [0; 1] indicates the successful probability of delivery from vehicle j to vehicle i, 8i;j2K. 4.6.1 Problem Formulation - Markov Decision Process We describe below the state, action, and reward for the MDP that we use to model the problem at hand. System States. Let h t i;(j;u) =f0; 1g indicate whether car i has received view u from car j by time slot t and let q t i =fh t i;(j;u) ;8j2K;8u2Vg be the reception vector of car i, whereK andV denote the set of all cars and views respectively. We dene the state of the system at time slot t by S t =fq t 1 ;q t 2 ;:::;q t K g;8t2T , where S t 2S, withS denoting the state space. System Actions. The RSU (or the leader if there is no RSU) will decide which vehicle will transmit which view. Let a t j;u =f0; 1g indicate whether vehicle j transmits view u at time slot t and A t =fa t j;u ;8j2K;8u2Vg denote the action taken at time slot t, where A t 2A, withA denoting the action space. 97 Reward Function. To maximize the total rewards the system needs to carefully decide the action (A t ) based on the current state (S t ). When the action is decided, the reward can be calculated as follows: R t (S t ;S t+1 ;a t j;u ) = X 8i2K;i6=j X 8v2V a t j;u (h t+1 i;(j;u) h t i;(j;u) )y (i;v);(j;u) : (4.8) Transition Probabilities. All cars in a sharing region are within range of each other, thus a transmitted view may be received by any car in the region depending on whether the wireless channel transmission results in a successful reception or not. Thus, the transmission probability from one state to another based on action a t j;u can be computed as follows: P a t j;u S t ;S t+1 = Y 8i2F1;i6=j p i;j Y 8i2F0;i6=j (1p i;j ); (4.9) where p i;j denotes the successful transmission probability dened in (4.7), F 1 = fijh t+1 i;(j;u) = 1 and h t i;(j;u) = 0g, andF 0 =fijh t+1 i;(j;u) = 0 and h t i;(j;u) = 0g. The conditionh t+1 i;(j;u) =f0; 1g and h t i;(j;u) = f0; 1g is used to represent all the possible combinations of events with respect to which subset of cars successfully receive the transmitted view. (The condition h t+1 i;(j;u) = 1 and h t i;(j;u) = 1 is not of interest to us, and the condition h t+1 i;(j;u) = 0 and h t i;(j;u) = 1 is impossible to happen.) MDP. With the above information, a nite-horizon MDP is dened as a tupleM = (S;A;P S t ;S t+1;R t ). Note that in this problem, our goal is to maximize the total rewards in a given period of time. (The model can be transformed to minimize the period of time required to successfully transmit a specic set of views and thus gain the corresponding rewards.) Policy and Value Function. To solve MDP, we should nd value functions to measure the goodness of a particular state under a policy, and nd optimal value functions to measure the best possible goodness of states under an optimal policy. For this purpose, we rst introduce the denition of a policy for MDP. 98 Algorithm 7 Dynamic Programming Input: h i;(j;u) , y (i;v);(j;u) ,P, and T Output: (S t ) 1. Initialize S 0 by calculating h i;(j;u) = 0, state stack =;, and t = 0. 2. state stack (S 0 ; 0) 3. t t + 1 4. while state stack6=; and t<T do 5. current state = state stack.pop() 6. for a j;u ;8j2K;8u2V do 7. Generate possible transitions and create corresponding new states S t+1 from cur- rent state (S t ) and the action (a j;u ) if they do not exist. 8. state stack (S t ;t) 9. end for 10. t t + 1 11. end while 12. InitializeV(S T ) = 0. 13. for all states in descending order of t do 14. Calculate (4.11) and the corresponding policy ( (S t )) at this state. 15. end for Denition 8. (Policy) At time t2T , a decision rule (S t ) is a mapping from states to actions. Then, the value function of every state (U (S t )) can be written as follows: U (S t ) = X 8S t+1 2S P (S t ) S t ;S t+1 (R t (S t ;S t+1 ;(S t )) + U (S t+1 )); (4.10) where (S t )2A is the action based on a policy . The goal of MDP is to obtain an optimal policy, where a = (S t )2A from solving the Bellman optimality equation [31] below: U (S t ) = max 8a t j;u 2A f X 8S t+1 2S P a t j;u S t ;S t+1 (R t (S t ;S t+1 ;a t j;u ) + U (S t+1 ))g: (4.11) 4.6.2 Scheduling Algorithms We introduce an optimal dynamic programming solution, an ecient greedy algorithm, and a baseline algorithm for comparison purposes. Dynamic Programming (DP) - Optimal Solution. There are three phases in dynamic programming (see Algorithm 7): initialization (Steps 1-3), state exploration (Steps 4-11), and 99 value updates (Steps 12-15). In the initialization phase, we initialize state stack, which keeps track of the next exploring state, the time, and the rst state (S 0 ). Next, in the state exploration phase, we explore all possible next states from the current state, and store these unvisited states into state stack for later exploration. If all possible next states are visited or t =T , we stop this procedure and go to the next phase. Otherwise, we pop up the next visiting state from the stack, and continue the state exploration phase. Finally, in the value updates phase, we initialize the value function of the last explored states to 0, and update the value function from the states at time T to the states at time 0 by solving (4.11). The DP algorithm can achieve the optimal values for a nite-horizon MDP [31]. Although DP can be used to solve MDP optimally, the time complexity of DP is exponential, which motivates us to introduce a greedy approach. 1 2 1,1 1,2 ,2 1,3 ,3 ,1 & !,# , $,$ ×(1−ℎ !, $,$ )× !,$ #∈ $,$ Figure 4.10: An illustration of H (j;u) . 100 Greedy Algorithm We propose an ecient greedy algorithm with near-optimal performance (see simulation results in §4.6.3). We start by dening the weighted preference (H (j;u) ) of a view to be the total rewards gained by the system if the view is delivered to all interested cars: H (j;u) = X 8i2K;i6=j X 8v2V y (i;v);(j;u) (1h i;(j;u) )p i;j : (4.12) To understand the rational of the formula, recall Eq. 4.5 and consider Fig. 4.10 where a bipartite graph has vehicles on the left and views on the right. The weight of each edge between a vehicle and a view corresponds to the total reward if the vehicle receives the view, where h i;(j;u) = 0 means vehiclei has not already received viewu from vehiclej. Then,H (j;u) can be computed by summing up the weights of the edges connecting to the (j;u) node. The algorithm is described in Algorithm 8. The main idea is to choose vehicle (j ) to deliver view (u ) leading to the highest weighted preference at every time slot. We then update the state based on the policy (j ;u ) until there is nothing to deliver or the system runs out of time (i.e., t =T ). Algorithm 8 Greedy Algorithm Input: h i;(j;u) , y (i;v);(j;u) ,P, and T Output: (S t ) 1. Initialize S 0 by calculating h i;(j;u) , and t = 0. 2. for t =T do 3. Calculate H (j;u) from (4.12) based on h i;(j;u) . 4. (j ;u ) = arg max (j;u) H (j;u) 5. h i;(j ;u ) = 1;8i2K 6. Update S t by the new h i;(j;u) . 7. (S t1 ) =a (j ;u ) 8. end for The complexity of the greedy algorithm isO(KV +KV ) =O(KV ). The rst term is from Step 3, where we need to calculateH (j;u) ;8j2K;8u2V. The second term is from Step 4, where we need to nd the maximum H (j;u) . 101 2 4 6 8 10 Number of Available Time Slots (T) 0 10 20 30 Total Rewards Optimal Greedy Agnostic Figure 4.11: Total rewards v.s. number of available time slots (T ) 0 1 2 3 4 Safety Index 0 20 40 60 80 Total Rewards Optimal Greedy Agnostic Figure 4.12: Total rewards v.s. safety index (^ s) 20 40 60 80 100 Speed (km/h) 5 10 15 20 25 30 Total Rewards Optimal Greedy Agnostic Figure 4.13: Total rewards v.s. speed (km/h) Baseline: Agnostic Scheduler. As a baseline, we introduce an \agnostic" scheduler for the purpose of comparison. The agnostic scheduler does not take into consideration rewards, dynamic objects, etc. Instead, it schedules for transmission the full view of each car in a round robin fashion (one car at a time), see [52] and [104]. 4.6.3 Scheduling Simulation Results In this section, we compare the proposed algorithms in a small-scale scenario to study their performance. We use the following legends to label the algorithms: \Optimal" for the optimal solution obtained by DP, \Greedy" for the proposed greedy algorithm, and \Agnostic" for the baseline. The channel matrix ( 4.7) is obtained from [10, 11], and is varied according to the speed and the distance between two vehicles. The size of a view is70kb 1 which can be transmitted in a 10-ms time slot, assuming a typical LTE direct data rate of 7.2Mbps [47] which would allow to transmit up to L = 72kb in a time slot. We consider 4 cars on a 2-lane road, two each lane. Varying Number of Available Time Slots. Figure 4.11 plots the total gained rewards as the number of available time slots varies from 1 to 10, where the speed of all cars is 90 km/h, the number of neighboring views is 2 (N = 2), and the safety index s (j;u) = 0;8j2K;8u2V. As expected, when the number of available time slots (T ) increases, the number of rewards increases. More specically, \Greedy" has less than 2% dierence from \Optimal" while \Agnostic" has a 1 Typically, a partial view of a 32-beam LiDAR has 700 point clouds (5,600 point clouds in a 360-degree full view partitioned in 8 partial views) and every point cloud is 32 3 = 96 bits (three oat numbers for x, y, and z). Hence, the size is67kb. 102 60% dierence from \Greedy". Note that in the scenario under study there are a total of 30 available rewards if all partial views of interest are successfully received, and the performance of optimal and greedy approach this number. Varying Safety Index. Figure 4.12 plots total rewards results after 10 time slots under a non- zero safety index. Specically, if u = v, then the safety index s (j;u) =f1; 2; 3; 4g. (This assigns more importance to obtaining front views). As shown in the gure, \Greedy" is still near-optimal, and has a 44% gain compared to \Agnostic". Varying Speed. Figure 4.13 plots the total rewards as the speed varies from 30 km/h to 90 km/h, where the number of available time slots is 10, the number of neighboring views is 2, and s (j;u) = 0;8j2K;8u2V. As expected, when the speed increases, the number of rewards decreases because the successful probability in (4.7) becomes smaller. 4.7 Performance Evaluation In this section, we evaluate AutoCast end-to-end under realistic environments. Evaluation of systems like AutoCast poses signicant challenges in practice. In order for AutoCast to op- erate at scale, it requires a eet of autonomous vehicles, each equipped with advanced sensors and V2V communication devices, of which the cost has yet to be amortized in mass produc- tion. However, both the academia and autonomous vehicle industry have been experimenting in near-realistic autonomous driving simulators, among which, one of the most representative platforms is CarLA [41]. CarLA is widely considered to be the leading simulation platform for autonomous driving and is supported both by car manufacturers as well as major players in the computing industry. CarLA can simulate multiple vehicles driving through realistic environments; the simulator has built-in 3D models of several environments including freeways, suburban areas, and downtown streets; the simulator can spawn vehicles with advanced sensors, such as LiDAR, Camera, Depth Sensor, etc.. 103 Setup. We implement the whole stack of AutoCast in CarLA and conduct our evaluation in various settings and scenarios. In our evaluation, each vehicle is equipped with a 32-beam LiDAR device on top of its roof, which has a sample rate of 10 fps, a vertical eld of view (FoV) of 30° and 360° horizontally. The vehicle is set to autopilot mode which cruises at the speed limit of the road. We use both local and highway scenarios to comprehensively investigate the performance. We simulate V2V channel loss in both scenarios referencing 3GPP standards [10, 11]. We use a peak rate of 7.2 Mbps (LTE-Direct QPSK with 10 MHz bandwidth [47]) in the simulation. The sharing region range (§4.5) is dened as half of the radio range R/2. Existing experimental tests with DSRC radios demonstrate a reliable transmission range of 100m [57] (<10% packet error rate). We set R = 100m and the sharing region radius to be 50 m. The sharing session duration is defaulted to 100 ms (LTE frame duration [10]) to be compatible to both technologies (further discussed in §4.8). To validate the results from CarLA, we also implementedAutoCast protocol andAutoCast scheduler using three iSmartWays DSRC radios [2]. Scheduling Algorithms. Two scheduling algorithms are compared: one isAutoCast's Greedy Algorithm described in§4.6.2, and the other is Agnostic, where cars within range will deliver their full view in turns. We do not consider DP here due to its very high complexity but have discussed its optimality in §4.6.2. Representations. 3D sensors, such as LiDAR, RADAR, stereo camera, often use point cloud data, either sensed or reconstructed, to build a representation to model the surrounding environ- ment. Each point in a point cloud has its 3D coordinates and other attributes such as color or re ection intensity depending on the sensor type. Autonomous vehicles use these 3D sensor data to match with a pre-loaded high denition base map to localize itself with respect to points and landmarks in the map. However, due to occlusion, not all points from the sensor can be matched to those in the base map. For example, the points modeling a nearby object (e.g.,, vehicle, cyclist, 104 Reward Ratio View Ratio 0 50 100 150 Ratio (%) AutoCast (Partition) Agnostic (Partition) AutoCast (Object) Agnostic (Object) Coverage Points Objects 0 100 200 300 400 500 Ratio (%) AutoCast (Partition) Agnostic (Partition) AutoCast (Object) Agnostic (Object) Figure 4.14: Completeness and Situation Awareness: the Basic Scenario 5 10 20 Number of Vehicles 0 50 100 150 200 Reward Ratio (%) AutoCast (Partition) Agnostic (Partition) AutoCast (Object) Agnostic (Object) 5 10 20 Number of Vehicles 0 50 100 150 200 View Ratio (%) AutoCast (Partition) Agnostic (Partition) AutoCast (Object) Agnostic (Object) Figure 4.15: Vehicle Density vs. Completeness 0 2 4 6 8 10 12 Elapsed time (s) 0 50 100 150 200 Reward Ratio (%) AutoCast (Partition) Agnostic (Partition) AutoCast (Object) Agnostic (Object) Figure 4.16: Reward Ratio over Time (20 Vehicles). 105 Figure 4.17: Real-time 3D Object Region Proposal pedestrian) can not be matched to the HD map. We dene these points as the points of dynamic objects. To further reduce the bandwidth requirement, we dene two representations when views are being shared: Partition and Object. In the Partition representation, when a car delivers a partial view, it transmits all of the point cloud of the partial view. whereas in the Object representation, a car only transmits point clouds of the dynamic objects in the view. We use a state-of-the-art point-cloud-based 3D object detector, PointRCNN [122], to detect the 3D regions of surrounded trac participants. Figure 4.17 visualizes the detection results of vehicles in the point cloud extracted from CarLA. In general, the size of a view in Object is much smaller than that in Partition, which permits more complete object awareness under the same bandwidth constraint. Metrics. Five metrics are discussed here to evaluate how AutoCast can give vision to occluded area, extend the sensing range, and enhance situation awareness. Reward Ratio. The total number of received rewards over the total number of desired rewards (§4.4). This metric shows how much more sharing demands can AutoCast fulll under the same network conditions. View Ratio. The total number of received views over the total number of desired views. This metric shows how many desired views are actually delivered. 106 5 10 20 Number of Vehicles 0 200 400 600 Coverage (%) 80 100 120 140 160 180 200 Coverage Area (m 2 ) AutoCast (Partition) Agnostic (Partition) AutoCast (Partition) Agnostic (Partition) Figure 4.18: Vehicle Density vs. U Cov 5 10 20 Number of Vehicles 0 100 200 300 Points (%) 6000 7000 8000 9000 Received Point Size AutoCast (Partition) Agnostic (Partition) AutoCast (Partition) Agnostic (Partition) Figure 4.19: Vehicle Density vs. U Loc 5 10 20 Number of Vehicles 0 50 100 150 200 Objects(%) 0 2000 4000 6000 8000 10000 Received Object Point Size AutoCast (Object) Agnostic (Object) AutoCast (Object) Agnostic (Object) Figure 4.20: Vehicle Density vs. U PP Coverage. The extra area that the merged view covers over the total area covered by the receiver's own sensor data. This metric shows how much more area the merged view could give vision to. Points. The total number of received points over the total number of points generated by the receiver itself. This metric shows, on average, how much more data point can a receiver use. For applications like simultaneous localization and mapping, vehicles can use extra data to identify its relative location with respect to its surroundings while mapping its surroundings. Objects. The total number of received points of dynamic objects over the total number of points of dynamic objects generated by the receiver itself. This metric evaluates, on average, how much more dynamic objects data can a receiver use in AutoCast. For applications like path planning, a vehicle only needs the information of dynamic objects, on top an HD base map, to calculate the best route. 4.7.1 A Basic Scenario We start the evaluation of AutoCast from a basic scenario where there are 10 cars, on autopilot mode, joining and leaving an intersection from all directions. Completeness. Figure 4.14 shows both of the completeness metric: the average reward ratio and view ratio per sharing session with 95% condence interval. Four modes are plotted: AutoCast 107 with Partition (dark blue), Agnostic with Partition (light blue), AutoCast with Object (green), and Agnostic with Object (yellow). As shown in the gure, in the case of transmitting full partitions,AutoCast outperforms Ag- nostic by over 40% in terms of reward ratio by prioritizing important views and careful scheduling to transmit almost 20% more views. When transmitting only the dynamic objects, both Auto- Cast and Agnostic can saturate 100% reward/view ratio. This shows that the assumed bandwidth is sucient for sharing sessions of 10 vehicles. Figure 4.16 shows a detailed plot of the reward ratio metric over time. As vehicles join the intersection, and leave the intersection, the reward ratio changes for every sharing session duration of 100 ms. Situation Awareness. Depending on what algorithm is taking the received data, AutoCast can serve in dierent representations. Figure 4.14 shows that transmitting full partitions can, on average, give a receiving vehicle more than 140% more points than it can percept itself. Transmitting only objects, though fullls all views desired, only supply around 25% more points. It also shows that the total size of all dynamic objects is way smaller than that of views, which validates that delivering the information of dynamic objects can signicantly save the bandwidth. However, this compact representation might not be a good choice for localization purpose which could benet from more static background information. Moreover, in Partition mode, AutoCast is able to deliver 20% more points from objects than Agnostic, which re ects the impact of the safety index to the schedule. When AutoCast assigning more weights to views with dynamic objects, these views are transmitted in higher priority yielding a higher utility for localization (number of received dynamic object point). For the same reason, AutoCast outperforms Agnostic in terms of Utility for Path Planning when transmitting full partitions since AutoCast put more emphasis on a view with dynamic objects. Nevertheless, transmitting only the object in the same sharing session results in more than 20% gain than Partition mode. 108 Figure 4.21: The physical DSRC radio device Latency and Staleness. With physical DSRC radio devices (as shown in in Figure 4.21), we measured the end-to-end latency for each partition. We feed the point cloud stream from CarLA to a random radio controller, which acts as the wireless interface to other vehicles and data streams. The latency is measured by calculating the duration from the start of the transmission period (every 100ms) to the time that the partition is received by the last car. Figure 4.22 shows the transmission latency of each partition in 5,10,20 cars scenario. The latency is sorted by the partition's reward, and the reward on the x-axis is normalized by the maximum partition reward for each scenario. The average delay of a partition is less than 50 ms when there are 20 vehicles. AutoCast can always schedule and send high-rewarding partitions sooner than others. 4.7.2 Sensitivity Analysis Vehicle Density. We vary the number of vehicles in the same intersection scenario to investigate how many cars can AutoCast accommodate with the assumed bandwidth. Figure 4.15 shows that the completeness of Partition almost linearly degrades as the number of cars increases, since the bandwidth is fully utilized in all cases. However, the more vehicles there are, the more gain 109 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Reward per Partition 0 25 50 75 100 Latency (ms) 5-Car 10-Car 20-Car Figure 4.22: AutoCast's transmission latency for partitions that have dierent reward. AutoCast achieve compared to Agnostic, because when there are fewer views, Agnostic has a higher chance to deliver those views with high rewards. Also, it is interesting to see Object starts to fall below 100% when 20 vehicles are present. When the bandwidth is stressed, the optimality of AutoCast reveals: AutoCast achieves on average 25% more reward while transmitting on average nearly 20% more views of objects. Figure 4.18, Figure 4.19 and Figure 4.20 shows the coverage results and the utility for localiza- tion and path planning under dierent vehicle density scenarios. While showing the ratio, we also plot the corresponding absolute number (i.e.,. the actual geographic area covered, the number of points received, and the number of points of objects received) on the right y axis (red). The methodology to calculate the area coverage is as follows. The surrounding area is converted into an occupancy grid of 10cm 10cm, where each grid is marked occupied if there are data points received in that grid. Since Figure 4.14 already illustrates that extra coverage and received points benets from Partition mode while received objects benets from Object mode. We only plot the result of the corresponding mode for each metric, respectively. When transmitting full partitions, the received points (Points in Figure 4.19) of AutoCast is very insensitive to the vehicle density, always fully utilizing the available bandwidth. Even when the bandwidth is signicantly stressed, the vehicle is constantly aware of around 140% more points of its surroundings. Correspondingly, the 140% more points translates to 84 m 2 (222%), 106.22 110 Channel 1 Channel 2 Channel 2 Guarding Margin in Forward Direction Figure 4.23: Distributed AutoCast Sharing Region. m 2 (283%), 127.86m 2 (373%) more coverage of the sensing area (Figure 4.18). However, Agnostic performs poorly, with the extra area almost being constant even in the 20 vehicle scenario. This proves that, in terms of coverage extension,AutoCast scales gracefully with vehicle density upto 20 vehicles in an intersection. Similarly, when transmitting objects only (Figure 4.20), AutoCast is able to deliver almost all dynamic object points in all scenarios (upto 6000 points in the 20 vehicles case). Agnostic fails slightly over 4% in terms of extra point ratio. 4.8 Discussion Distributed AutoCast. Since beacons are broadcasted, all vehicles in the sharing region (R/2 to the intersection center) are able to receive beacons from vehicles who are eligible to participate. In case an RSU is not available, vehicles can follow a cluster head selection protocol [91, 133] to select a leader to be the scheduler. The primary requirement for the leader selection is consistency and latency. In order to design a distributed protocol to operate at any location without RSU support, AutoCast needs to carefully and dynamically allocate dierent channels to sharing regions to avoid co-channel interference. Specically, AutoCast marks the map with grids of size RR. Neighboring grids are assigned alternating channels. Since autonomous vehicles are equipped with 111 0 2 4 6 8 10 12 Elapsed time (s) 0 50 100 150 200 Reward Ratio (%) AutoCast (Partition) Agnostic (Partition) AutoCast (Object) Agnostic (Object) Figure 4.24: Distributed Scheduling Results on Highway advanced 3D sensors (e.g., LiDAR, Stereo Camera) and are therefore capable to precisely localize with an error of around 10 cm, it is now possible to choose which channel to transmit based on the vehicle location. In other words, vehicles in each grid are allowed to send their beacons using only the designated channel (Figure 4.23). When a cluster leader is selected, the sharing region is centered at the leader's location at the time it is selected. The leader can compute the schedule using consistent information within the sharing region as discussed above. We implement distributed AutoCast in CarLA on a highway. In this scenario, we put 10 cars on autopilot mode. Figure 4.24 shows that AutoCast is able to keep alternating channels seamlessly as the vehicles go through each channel region, achieving consistent high rewards in both modes compared to Agnostic. One complication in this case is that a vehicle can receive more than one schedules from dierent channels. AutoCast breaks ties by randomly selecting for such vehicles one cluster to join (Figure 4.23). AutoCast chooses not to use the channel region center as the sharing region center, but uses the leader cluster head location instead, to enable dynamic sharing regions. One complication from having a vehicle picking one cluster over the other is that any partial views of this vehicle cannot be shared in the current sharing phase with nearby vehicles which belong to a neighboring sharing region. One approach to address this would be to have vehicles in the 112 boundary between neighboring clusters to alternate between clusters. We leave as future work to further investigate this. PHY Implications When a schedule is broadcasted, the cooperative execution of that schedule among all participating vehicles have dierent PHY layer implications with respect to which V2V technology is used. If DSRC or LTE-V is used, the default mode is to use carrier sensing to count the transmissions and wait for its turn in the schedule to transmit. When LTE-V is used, a second mode is possible which is to use SC-FDMA where RSU or cluster head can assign frequency-time slots to vehicles based on the schedule. In LTE-V Mode 3, the network takes charge of performing the allocation and sharing the scheduling to the vehicles via the control plane. In LTE-V Mode 4, vehicles autonomously select and manage their radio resources depending on a sensing-based distributed scheduling protocol. The synchronization resolution can be as precise as 1 ms per time slot [11]. 4.9 Conclusion In this paper we designAutoCast, an ecient system to share visual information among nearby vehicles with the goal of maximizing the amount of useful information which is shared within a given time-frame. We also implement all supporting vehicle cooperation protocols of AutoCast in a state of the art autonomous vehicle simulator. AutoCast partitions views into partial views, uses a novel data assessment methodology to prioritize among partial views, and applies a novel near-optimal scheduling scheme to share useful views among nearby vehicles. This way, it can deliver up to 200% more useful information to participating vehicles compared to a baseline algorithm which shares full views of vehicles in a round robin fashion. 113 Chapter 5 Conclusion In this thesis, we have discussed several essential problems for enabling VR/AR over dense wireless networks. Between the core network and base stations, we have proposed the optimal mmWave wireless backhauling, mmHAUL, for dense base station deployments to have high-data-rate access networks. Based on the network architecture, we have studied how to deliver VR/AR applications over wireless networks eciently. Between base stations and VR/AR users, we have improved the quality of experience of VR users by two approximate user-cell association algorithms, ELVA and EVA, in wireless access networks. Finally, among VR/AR users, we have demonstrated that AutoCast is eective in sharing visual and sensing information in autonomous-driving systems. Some future directions are as follows: MmHaul backhauling with antenna grouping In mmHAUL, we assume that the access networks and the backhaul systems use dierent carrier frequencies. However, the access networks might also need to use the mmWave band to support VR/AR users, leading to the interference between the access networks and the backhaul systems. A new technique is required in this spectrum sharing system to avoid the performance downgrading due to the interference. User-cell association for VR/AR users In Chapter 3, we assume the reward as a linear function mapping the number of received enhanced views to the quality of experience. 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Huang, Po-Han
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Enabling virtual and augmented reality over dense wireless networks
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Viterbi School of Engineering
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Computer Engineering
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06/22/2020
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360-degree video,approximation algorithm,autonomous driving,dense small-cell deployments,hybrid beamforming,hybrid multicast and unicast,Markov decision process,mmWave communication,multicasting scheduling,OAI-PMH Harvest,resource allocation,V2V communications,wireless backhaul networks,wireless virtual/augmented reality
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Tags
360-degree video
approximation algorithm
autonomous driving
dense small-cell deployments
hybrid beamforming
hybrid multicast and unicast
Markov decision process
mmWave communication
multicasting scheduling
resource allocation
V2V communications
wireless backhaul networks
wireless virtual/augmented reality