Emmanouel T. Michailidis Athanasios G. Kanatas

Transcription

1 Emmanouel T. Michailidis George Efthymoglou gr) Athanasios G. Kanatas University of Piraeus Department of Digital Systems Wireless Communications Laboratory

2 Introduction The 3-D Land Mobile HAP-MIMO Channel Model Space-Time Correlation Functions Numerical Results Conclusions 2

3 High Altitude Platforms (HAPs) are an alternative or complement to terrestrial and satellite infrastructure for providing narrowband and broadband wireless access. The ITU has licensed 48/47 GHz for the world wide 4G communications systems, 31/28 GHz for Asians countries and 2 GHz for 3G communications systems through h HAPs. HAPs typically operate in lower stratosphere (approximately 20 km above ground). 3

4 Even though HAPs can provide quasi- stationary communication platforms, winds or pressure variations have to be compensated. In practice, HAPs may move in any direction at a varying speed (6 degrees of freedom). The ITU has specified that a HAP should be kept within a circle of 400m radius, with height variations of ±700m, in order for the services to be available. 4

5 High elevation angles imply the presence of a predominant radio wave path of line-of-sight i (LOS), but also multipath propagation (NLOS) should be considered in urban and indoor areas (2 GHz band) Rain attenuation effects are negligible at this frequency range. 5

6 Traditional Multiple Input-Multiple Output (MIMO) techniques for terrestrial systems exploit effectively the propagation environments with rich scattering. An uncorrelated MIMO channel matrix can enhance the performance of communication systems, provide increased data rates and maximize channel capacity. 6

7 We consider a Stratospheric Base Station (SBS) and a Terrestrial Mobile Station (TMS) that constitute a 2 2 HAP-MIMO system with ULA antennas. Both SBS and TMS are in motion. Previous studies indicated that vertical stratospheric winds are almost insignificant, therefore SBS is considered to move within a circle, instead of a cylinder. 7

8 Definition of Parameters (a) 8

9 Definition of Parameters (b) 9

10 z p R HAP O T q The LOS paths of the 3-D cylinder model for 2 2 HAP-MIMO channels l ψ O R q% y θ T p% γ T u T β HAP O O m% m LOS α Rl θ l% R R γ R ur x 10

11 z p R HAP O T q The NLOS paths of the 3-D cylinder model for 2x2 HAP-MIMO channels ( n) S l ( n) β S ψ O R q% y θ T p% u T γ T ( n) a T ( n) S % m ( n) O O m% a R θ l% R R γ R ur x 11

12 Since the number of local scatterers is infinite, the impulse response of the NLOS component can be modeled as a low pass zero mean complex Gaussian process and therefore its envelope is Rayleigh distributed (due to the central limit theorem) The impulse response of the sub-channel p-l is a superposition of the LOS and NLOS rays: ( ) = ( ) + ( ) h t h t h t pl pl, LOS pl, NLOS 12

13 The impulse responses of the LOS and NLOS components are, respectively: 2πH π LOS K j j δt cosθt+ δr cos( αrl θr) cosψ LOS LOS sin cos j2 tft,max cos( Rl T ) j2 tfr,max cos( Rl ) pl λ β λ π π α γ + π α γ HAP βhap hpl, LOS ( t) e e e K + 1 pl N 1 1 jϕ ( ) h () t lim a b e e + pl, NLOS p, S S, l K 1 N pl n = 1 N where: a ps, ( n) ( n) j2πt f,max ( Δ sinγ sinαr + cosγ ) + f,max cos αr γ ( ) n T T T R R ( n ) 2π H πδ T cosθ T πδ T Δsin θ T sin αr j j j λ sin β λcosβ λcos β = e e e HAP HAP HAP 2πR π ( n) π ( n) ( n) π ( n) ( n) j j δrsinψ sin βs j δrcosψcosβs cosθrcosαr j δrcosψcosβs sinθrsinαr λ λ λ λ b = e e e e Sl,, 13

14 The Space-Time Correlation function between two sub-channels p-l and q-m is defined as: LoS NLOS ( δ, δ, τ) = ( δ, δ, τ) + ( δ, δ, τ) R R R pl, qm T R pl, qm T R pl, qm T R { }, Using the far-field assumption: δ δ D T R O O the Space-Time Correlation function of the LOS component can be written as: j2π λcosβ max,, K ( T cos T R cos R cos ) pl K δ θ δ θ ψ LOS qm j2πτ ft,max cos T fr,max cos HAP γ γr Rpl, qm ( δt, δr, τ) e e. K + 1 K + 1 pl qm 14

15 Random scatterer s discrete angle of arrival and elevation angle can be replaced with continuous random variables with probability density functions: f 1 α exp[ kcos ( α μ) ], - π α π, R R R 2π I ( ) 0 ( k) Von Mises p.d.f. for non-isotropic environments and: f π π β βs = cos, βs βs π / 2. 4 β S,max 2 β S,max S ( ),max Parson s p.d.f. for scatterer s elevation angle 15

16 The Space-Time Correlation function of the NLOS component can be written as: a + β 4 S,max ( ) ( ) ( ) NLOS 1 1 ae 3 a5 sin βs 2 2 pl, qm δt δr τ = 3βS βs K K I k pl + 1 qm R,, cos a e I a a d, K K I k β where ( ) S,max 2πδ Δ sinθ 2π T T a = j 2 πτ f sin γ j 2 πτ f Δ sin γ + j + j δ cos ψ cos β sin θ + k sin μ, 1 R,max R T,max T R S R λcos β λ 2 a = j2πτ f cos γ + j π δ cosψ cos β cosθ + kcos μ, 2 R,max R R S R λ a = π /2 β, 3 S,max HAP 2πδ cosθ T T a = j j 2 πτ f cos γ, 4 T,max T λcos βhap 2π a = j sin. 5 δ R ψ λ 16

17 In HAP-MISO channels, assuming isotropic scattering, the Spatial Correlation Function is the following: 1 1 R e K K I a { ( )} a4 ( δ ) = + ( Δ θ ) tan. MISO pl, qm T pl qm 0 4 T Kpl + 1 Kqm + 1 In HAP-SIMO channels, assuming isotropic scattering, the Spatial Correlation Function is the following: a5 cosθr + βs,max 1 1 SIMO tanψ cos β a HAP 3 a5 sin β a S 5 Rpl, pm ( δr ) = Kpl Kqme + cos( a3βs ) e I0 cos βs dβs. Kpl + 1 Kqm tanψ β S,max 17

18 60 Kψ0 μo o T θ90 kβ60 β45 R D MAX o R S HAP OO OT, Spatially Correlated 3-D HAP-MIMO Fading Channels Examined Scenario 18

19 Spatial Correlation of a HAP-MISO channel versus normalized antenna element spacing for different amount of local scattering at the TMS k=2 Corre elation k=1 k= k= δ /λ T 19

20 Spatial Correlation of a HAP-SIMO channel for different scatterers' maximum elevation angle values 1 Co orrelation ψ=0 β S,max =π/4 ψ=π/2 β S,max =π/4 ψ=π/2 β S,max =π/9 ψ=π/2 β S,max =π/ δ /λ R 20

21 Spatial Correlation of a 2x2 HAP-MIMO channel with horizontally placed TMS antennas Cor rrelation δ R /λ R δ /λ Τ

22 Spatial Correlation of a 2x2 HAP-MIMO channel with vertically placed TMS antennas Corr rrelation δ R /λ δ T /λ

23 The geometrical model can be used to estimate the required HAP inter-element distance to achieve an uncorrelated HAP-MIMO channel matrix. At 2 GHz, considering an isotropic scattering environment, the SBS antennas require a separation of around 12 meters. MIMO techniques are applicable in a single HAP in a single HAP 23

24 Spatial correlation increases as the scattering becomes more non-isotropic. For a HAP-SIMO channel When TMS antennas are vertically placed, as scatterer s maximum elevation angle increases, the correlations between the two sub-channels reduce dramatically. When TMS antennas are horizontally placed, their correlation is always significantly small. Low correlations can be obtained in a 2 2 system, if we arrange the SBS and TMS antenna element spacing, such that their correlation falls in the valleys of the plots. 24

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