Optimal Positioning of Flying Relays for Wireless Networks Junting Chen 1 and David Gesbert 2 1 Ming Hsieh Department of Electrical Engineering, University of Southern California, USA 2 Department of Communication Systems, EURECOM, Sophia-Antipolis, France Acknowledgement This research was supported by the ERC under the European Union’s Horizon 2020 research and innovation program (Agreement no. 670896) 1 9 July 2017
Relaying from the Air Ground relays: Unmanned aerial vehicle (UAV) • Constrained / fixed positions relays: • Shadowing • Flexible positions • Non-adaptive to user • Shadowing avoidance mobility / ad-hoc loading • User mobility adaptive Feasibility / opportunity: • Decreasing fabrication cost • mmWave applications 2 9 July 2017
Microscopic Viewpoint of UAV Relaying Traditional application scenario: Application to cellular networks: • Establish connectivity from tens • Fill the coverage / capacity hole to hundreds kilometers away within 1 kilometers • Path loss dominant • Shadowing dominant • Service to an area • Avoid propagation blockage • Service to a selected group of users 3 9 July 2017
Key Challenge: How to model the air-to-ground propagation? Traditional relay problem UAV positioning problem § Relay positions are to be optimized § Relay positions are fixed § Communication channels are § Comm channels are unknown, known or can be estimated before the UAV is in position § UAV-user, UAV-BS channels are functions of the UAV position, and the environment (e.g., blockage) etc. 4 9 July 2017
Macroscopic Propagation Models versus Fine-grained Structure Exploitation Existing works usually based on macroscopic propagation models § Line-of-sight (LOS) propagation assumption § Probability model for LOS propagation [Hourani14] A. Al-Hourani, S. Kandeepan, and S. Lardner, “Optimal LAP Altitude for Maximum Coverage”, IEEE Comm. Lett. , 2014. [Mozaffari16] M. Mozaffari, W. Saad, M. Bennis, and M. Debbah, “Optimal Transport Theory for Power-Efficient Deployment of Unmanned Aerial Vehicles”, IEEE ICC , 2016. Limitations § Not performance guaranteed for individual users! E.g., a QoS-demanding user in the “shadow of a building” (say, in low mobility case) § The local fine-grained terrestrial structure has not been exploited! 5 9 July 2017
UAV Positioning in Dense Urban Areas To place a UAV to relay the signal to a QoS-demanding user on the ground 6 9 July 2017
Where to Place the UAV Relay? Simplest scenario: To increase the end-to-end transmission rate to one target user on the ground, by placing the UAV relay to the best position. A possibly good UAV relay position View the dense urban area Received power of UAV-user link End-to-end capacity of from the top BS-UAV-user link 7 9 July 2017
Problem Formulation End-to-end rate maximization for a simple single user case maximize min { r B ( x D ) , r D ( x D ) } x D where ⇣ ⌘ r B ( x D ) = log 2 1 + P B · g B ( x D ) ⇣ ⌘ r D ( x D ) = log 2 1 + P D · g D ( x D ) More generally, minimize F ( g U ( x ) , g B ( x )) x ∈ R 3 § Challenge 1: Simple mathematical description on the channels g B and g D in terms of the drone position, such that the fine-grained environment structure is preserved (i.e., LOS/NLOS). § Challenge 2: Efficient algorithm to find the optimal UAV position x D . 8 9 July 2017
Ray-tracing Propagation Model with Segmented Approximation Shadowing Classical log-distance model (LOS/NLOS, etc), reflection, � � � � 10 log 10 g U ( x ) = 10 log 10 ( β ) � 10 α log 10 k x � x U k + ξ diffraction, etc. Recent UAV literature: LOS model, or probabilistic LOS model Conventional relay literature, obtained by online estimation 9 9 July 2017
Ray-tracing Propagation Model with Segmented Approximation Shadowing Classical log-distance model (LOS/NLOS, etc), reflection, � � � � 10 log 10 g U ( x ) = 10 log 10 ( β ) � 10 α log 10 k x � x U k + ξ diffraction, etc. Segmented model ξ k + ˜ ξ k § Partition the space of ( x , x U ) into K disjoint segments, each corresponding to a type of propagation (LOS, NLOS, etc.) ignored X g U ( x ) = g k ( x ) I { ( x , x U ) ∈ D k } Propagation segment, where k e.g., LOS/NLOS � � � � 10 log 10 g k ( x ) = 10 log 10 ( β k ) � 10 α k log 10 k x � x U k Q. Feng, J. McGeehan, E. K. Tameh, and A. R. Nix, “Path loss models for air-to-ground radio channels in urban environments,” in Proc. IEEE Semiannual Veh. Technol. Conf. , vol. 6, 2006, pp. 2901–2905. 10 9 July 2017
Geometry Property Assumption / restriction § Assume LOS propagation for the BS-UAV link. § For the UAV-user link, propagation parameters and the segments known perfectly § Propagation segments arranged in order § UAV flies at a fixed height ρ Intuition: § the key is to search for the LOS propagation segment ( D 1 ) § it will be convenience to work in the polar-coordinate system 11 9 July 2017
Algorithm Special case for two segments: k = 1 for LOS and k = 2 for NLOS § When UAV is in NLOS, search along the contour of F ( g 1 ( x ) , g 1 ( x )) = C § When UAV is in LOS, increases (moving away from the user) ρ § Repeat until some stopping criterion is met Theorem: The continuous trajectory constructed by the above algorithm finds the global optimal UAV position 12 9 July 2017
UAV Search Trajectory L • The search trajectory scales only linearly with L (user-BS distance) • Significant improvement over exhaustive search L 2 13 9 July 2017
Numerical Results 10,000 random user locations, buildings 5 - 45 meters, UAV 50 meter height Simple UAV positioning : Only search over the BS-user line segment Offline UAV positioning: First, learn the empirical LOS probability function ⇤ − 1 ⇥ P (LOS , θ ) = 1 + a exp( − b [ θ − a ]) Then, compute the optimal UAV position based on channel gain Direct BS-user link: Directly BS à user transmission without UAV relaying Significant gains for cell edge users 14 9 July 2017
Conclusions Problem: UAV positioning for relaying between a BS to a ground user § Dense urban scenario § Key challenge to avoid obstacle blockage § UAV fixed height (2D optimization) Applications: § Quality-demanding service, first aid (road side assistant), surveillance, etc. § Communications in very high frequencies Segmented propagation model § Simple; able to exploit the structure for blockage avoidance Positioning algorithm § Online algorithm § Exploit the segmented propagation model § Global optimal convergence 15 9 July 2017
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