Massive MIMO As Enabler for Communications with Drone Swarms

Transcription

1 Massive MIMO As Enabler for Communications with Drone Swarms Prabhu Chandhar, Danyo Danev, and Erik G. Larsson Division of Communication Systems Dept. of Electrical Engineering Linköping University, Sweden June 8, Drone Swarms June 8, / 17

2 Motivation Civilian and military applications of micro UAVs keep growing Challenges in communication between ground station (GS) and UAV: High throughput, low latency, and low power consumption High mobility Mismatch of polarization and radiation pattern Existing wireless technologies: WiFi, ZigBee Limited to short range, low throughput, and low mobility Not suitable for applications involving large number of UAVs Can Massive MIMO be an enabler for UAV communications? - Drone Swarms June 8, / 17

3 Massive MIMO Single antenna UAV Base station Single antenna terminal (a) Cellular system Ground station antenna array (b) UAV network Figure: Massive MIMO enabled UAV networks An emerging multi-user MIMO technology for 5G cellular communication Hundreds of antennas at the BS, single antenna at the terminal Energy efficient transmission through beamforming - Drone Swarms June 8, / 17

4 The Questions We Ask and Answer What is the achievable uplink data rate by an UAV when there is a swarm of UAVs that simultaneously communicate with the GS equipped with a large number of antennas? How much power reduction is possible at the UAV? How does the antenna configuration (i.e. antenna orientation and polarization) affects the link budget? - Drone Swarms June 8, / 17

5 System Model - Geometric Model Moving direction y z ψ k θ k z ˆψ k ˆrk x δ θ k ψ k ˆθk Mδ φ k y x l-th antenna position: (x l, y l, z l ) = ((l 1)δ, 0, 0), l {1, 2,..., M}. k-th UAV s position: (x k, y k, z k ) = (d k cos φ k sin θ k, d k sin φ k sin θ k, d k cos θ k ). - Drone Swarms June 8, / 17

6 System Model - Channel Model The channel between the l-th GS antenna and the k-th UAV s antenna is characterized by Distance dependent pathloss Antenna gain Polarization mismatch loss Phase The distance between the l-th GS antenna and the k-th UAV s antenna: ( d kl = d k dk 2 (l 1) 2 δ ) 1 2 (l 1)δ cos φ k sin θ k. d k When the UAV is far away from the array (i.e. Mδ d k << 1), d kl d k + (l 1)δ cos φ k sin θ k. - Drone Swarms June 8, / 17

7 UAV Rotation Model - Rotation Matrix Roll (α x): rotation along x-axis Pitch (α y ): rotation along y-axis Yaw (α z): rotation along z-axis calc,3d,arrows tdplotscreencoords/.style = x = (1cm, 0cm), y = (0cm, 1cm), z = ( 1cm, 1cm) z Yaw Pitch y Roll calc,3d,arrows x tdplotscreencoords/.style = x = (1cm, z 0cm), z y = (0cm, 1cm), z = ( 1cm, 1cm) z Yaw αx y Pitch y y Roll (αx) Roll x x x z z Figure: UAV rotation model αx y y Roll (αx) x x Transformed coordinate system due to roll: x y = cos α x sin α x x y. z 0 sin α x cos α x z The general rotation matrix that rotates around the sequence x-axis, y-axis, and z-axis: R zyx(α z, α y, α x) = R x(α x)r y (α y )R z(α z). - Drone Swarms June 8, / 17

8 Power Loss due to Polarization Mismatch Let the 2 2 matrix that represents the polarization mismatch be [ ] cos a1 cos a T 2 = 2. cos b 1 cos b 2 The elements of T 2 are functions of the rotation matrix R zyx (α z, α y, α x ). For details, see paper. The effective gain (including polarization mismatch factors): E kl = E GS (θ kl, ψ kl ) T T 2 E UAV (θ kl, ψ kl). Polarization loss factor (PLF): PLF kl = E kl 2 E GS (θ kl, ψ kl ) 2 E UAV (θ kl, ψ kl ) 2. - Drone Swarms June 8, / 17

9 Channel Gain The M 1 channel vector from the k-th terminal to the GS: where g k = [g k1 g k2... g km ] T, k = 1, 2,..., K, g kl = β kl E kl e i2πd kl λ = β kl E kl e i2π λ (d k +(l 1)δ cos φ k sin θ k ), where β kl = η d 2 kl represents pathloss component and η is a constant. The M K channel matrix between the GS and the K UAVs g 11 g 21.. g K1 g 12 g 22.. g K2 G = g 1M g 2M.. g KM - Drone Swarms June 8, / 17

10 Uplink Data Transmission The M 1 received signal vector at the BS: where p u - transmit power of UAVs y = p u Gq + n, q = [q 1, q 2,..., q K ] T (normalized such that E{ q k 2 } = 1, k) n CN (0, N 0 I M ). By using the maximum-ratio combining (MRC) receiver, the estimated signal vector r: r =G H y = p u G H Gq + G H n. - Drone Swarms June 8, / 17

11 Achievable Rate with Perfect CSI With perfect channel state information (CSI), the received signal of k-th UAV: The post-processing SINR: r k = p u g H k g k q k + p u K j=1,j k gh k g j q j + g H k n. γ k = p u g k 4 p u K j=1,j k gh k g j 2 + g k 2 N 0. The ergodic rate achieved by the k-th terminal: ( ) ( ) R k Rk lb log E { p } u βk 2 1 = log 2 1+ χ2 k M2 K γ k p u j=1,j k E{ g H k g j 2}, + β k χ k MN 0 where χ k = E k 2. - Drone Swarms June 8, / 17

12 Ergodic Rate g H k g j 2 = β k β j χ k χ j M 1 n=0 2 2π ei λ nδ(cos φ j sin θ j cos φ k sin θ k ) E{ g H k g j 2 } = β k β j χ k χ j (M + Ω), For spherically uniformly distributed UAVs positions: f θk (θ) = sin θ 2, 0 θ π, f φ k (φ) = 1 2π, 0 φ 2π where Ω = M 1 M 1 m=0 n=0,n m sinc2( 2(m n) λ) δ. Ergodic Rate R lb k = log 2 ( 1 + ) β k χ k M (1 + Ω M ) K j=1,j k β jχ j + N. 0 p u - Drone Swarms June 8, / 17

13 Achievable Rate vs Number of GS Antennas Ergodic Capacity (bits/s/hz) K = 5 K = 20 K = Number of anntennas at the GS (M) Figure: Lower bound on ergodic capacity for different numbers of GS antennas for MRC with perfect CSI for pu N 0 = 30 db, R = 500 m, and R min = 50 m. - Drone Swarms June 8, / 17

14 Observations Target capacity: 1 b/s/hz With 10 MHz bandwidth: 10 Mbps per UAV Reduction of the UAV transmit power With single antenna at the GS: p u = W With Massive MIMO, for M = 60 and K = 20: p u = W Nearly 20 db reduction of the UAV s transmit power Number of UAVs that can be supported By increasing M from 40 to 80 K is increased from 5 to 50 - Drone Swarms June 8, / 17

15 Polarization Loss due to UAV Rotation (when θ k = π 2, φ k = π) Polarization mismatch loss (db) X axis rotation Y axis rotation Z axis rotation X and Y axis rotation Polarization mismatch loss (db) X axis rotation Y axis rotation Z axis rotation Rotation angle (degrees) Rotation angle (degrees) Polarization mismatch loss (db) Y and Z axis rotation X axis rotation Y axis rotation Z axis rotation Polarization mismatch loss (db) X axis rotation Y axis rotation Z axis rotation Y and Z axis rotation Rotation angle (degrees) Rotation angle (degrees) Figure: 1: GS antenna: vertical polarized, UAV antenna: vertical polarized 2: GS antenna: Dually polarized, UAV antenna: vertical polarized 3: GS antenna: Dually polarized, UAV antenna: Dually polarized 4: GS antenna: Circular polarized, UAV antenna: Dual polarized - Drone Swarms June 8, / 17

16 Conclusions Massive MIMO is a potential enabler for high capacity UAV networks Uplink capacity of UAVs can be increased several folds More antennas at the GS reduced transmit power Using circular polarized antennas reliable link conditions - Drone Swarms June 8, / 17

17 Questions?